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+MathVC: An LLM-Simulated Multi-Character Virtual Classroom for Mathematics Education
+
+Collaborative problem solving (CPS) is essential in mathematics education, fostering deeper learning through the exchange of ideas. Yet, classrooms often lack the resources, time, and peer dynamics needed to sustain productive CPS. Recent advancements in Large Language Models (LLMs) offer a promising avenue to enhance CPS in mathematical education. We designed and developed MathVC, a multi-persona LLM simulated virtual classroom platform to facilitate CPS in mathematics. MathVC combines a meta planning controller that monitors CPS stages-sense-making, team organization, planning, execution, validation, and predicts the next speaker, with a persona simulation stack that encodes mathematical thinking via a task schema and error-injected persona schemas seeded from teacher-specified misconceptions. We evaluated MathVC with 14 U.S. middle schoolers. Students reported constructive interaction and reaching shared solutions, describing gains in engagement, motivation, and confidence through diverse perspectives, immediate scaffolding, and human-like fallibility. Our findings also provide insights into simulating peers via LLM-based technologies for collaboration to support learning.
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+Knowledge without Wisdom: Measuring Misalignment between LLMs and Intended Impact
+
+LLMs increasingly excel on AI benchmarks, but doing so does not guarantee validity for downstream tasks. This study contrasts LLM alignment on benchmarks, downstream tasks, and, importantly the intended impact of those tasks. We evaluate the performance of leading LLMs (i.e., generative pre-trained base models) on difficult-to-verify tasks of the teaching and learning of schoolchildren. Across all LLMs, inter-model behaviors on disparate tasks correlate higher than they do with expert human behaviors on target tasks. These biases shared across LLMs are poorly aligned with downstream measures of teaching quality and often negatively aligned with the intended impact of student learning outcomes. Further, we find multi-model ensembles, both unanimous model voting and expert-weighting by benchmark performance, further exacerbate misalignment with learning. We measure that selection of LLM and/or prompting strategy only reliably accounts for $15\%$ of all measured misalignment error and that variation in misalignment error is shared across LLMs, suggesting that common pretraining accounts for much of the misalignment in these tasks. We demonstrate methods for robustly measuring alignment of complex tasks and provide unique insights into practical applications of LLMs in high-noise contexts.
diff --git a/corpus/education/deltas/2b8f084e578dd34a.txt b/corpus/education/deltas/2b8f084e578dd34a.txt
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+Teaching Language Models How to Code Like Learners: Conversational Serialization for Student Simulation
+
+Artificial students -- models that simulate how learners act and respond within educational systems -- are a promising tool for evaluating tutoring strategies and feedback mechanisms at scale. However, most existing approaches rely on prompting large, proprietary language models, limiting adaptability to specific courses and raising concerns around privacy, cost, and dependence. In this work, we propose a framework for training open-weight artificial programming learners directly from authentic student process data. Our approach serializes temporal log traces into a conversational format, representing each student's problem-solving process as a dialogue between the learner and their automated assessment system. Student code submissions and environment feedback, such as test outcomes, grades, and error traces, form alternating conversational turns, enabling models to learn from the iterative debugging process. We additionally introduce a training pipeline combining supervised fine-tuning with preference optimization to align models with authentic student debugging behavior. We evaluate our framework by training Qwen models at 4B and 8B scales on a large-scale dataset of real student submissions to Python programming assignments. Our results show that incorporating environment feedback strengthens models' ability to replicate student debugging behavior, improving over both prior code-only approaches and prompted large language models baselines in functional alignment and code similarity. We release our code to support reproducibility.
diff --git a/corpus/education/deltas/339a17a28500a7ad.pdf b/corpus/education/deltas/339a17a28500a7ad.pdf
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diff --git a/corpus/education/deltas/374ceea6790c2f05.txt b/corpus/education/deltas/374ceea6790c2f05.txt
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+MedSimAI: Simulation and Formative Feedback Generation to Enhance Deliberate Practice in Medical Education
+
+Medical education faces challenges in providing scalable, consistent clinical skills training. Simulation with standardized patients (SPs) develops communication and diagnostic skills but remains resource-intensive and variable in feedback quality. Existing AI-based tools show promise yet often lack comprehensive assessment frameworks, evidence of clinical impact, and integration of self-regulated learning (SRL) principles. Through a multi-phase co-design process with medical education experts, we developed MedSimAI, an AI-powered simulation platform that enables deliberate practice through interactive patient encounters with immediate, structured feedback. Leveraging large language models, MedSimAI generates realistic clinical interactions and provides automated assessments aligned with validated evaluation frameworks. In a multi-institutional deployment (410 students; 1,024 encounters across three medical schools), 59.5 percent engaged in repeated practice. At one site, mean Objective Structured Clinical Examination (OSCE) history-taking scores rose from 82.8 to 88.8 (p < 0.001, Cohen's d = 0.75), while a second site's pilot showed no significant change. Automated scoring achieved 87 percent accuracy in identifying proficiency thresholds on the Master Interview Rating Scale (MIRS). Mixed-effects analyses revealed institution and case effects. Thematic analysis of 840 learner reflections highlighted challenges in missed items, organization, review of systems, and empathy. These findings position MedSimAI as a scalable formative platform for history-taking and communication, motivating staged curriculum integration and realism enhancements for advanced learners.
diff --git a/corpus/education/deltas/37791a9b27490cf8.txt b/corpus/education/deltas/37791a9b27490cf8.txt
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+Predictable Drifts in Collective Cultural Attention: Evidence from Nation-Level Library Takeout Data
+
+Predicting changes in consumer attention for cultural products, such as books, movies, and songs, is notoriously difficult. Past research suggests intrinsic limits for predicting consumer attention towards individual products. However, little is known about the limits for predicting shifts in collective attention. Here, we analyze five years of nationwide library loan data for almost 3 million individuals, comprising over 136 million loans of more than 750,000 unique titles. We find that culture, as measured by popularity distributions of loaned books, drifts continually from month to month at a near-constant rate, leading to a growing divergence over time, and that drift varies between book genres. By linking book loans to registry data, we investigate the influence of age, sex, educational level, and residential area type on cultural drift, finding heterogeneous effects. Our findings have important implications for market forecasting and algorithmic recommender systems, highlighting the need to account for drift dynamics.
diff --git a/corpus/education/deltas/4815fc3675a05b4b.pdf b/corpus/education/deltas/4815fc3675a05b4b.pdf
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diff --git a/corpus/education/deltas/4877f1784a1948a0.txt b/corpus/education/deltas/4877f1784a1948a0.txt
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+The Social Gaze of LLMs: A Literature Review of Multimodal Approaches to Human Behavior Understanding
+
+LLM-powered multimodal systems are increasingly used to interpret human behavior, yet how researchers apply the models' 'social competence' remains poorly understood. This paper presents a systematic literature review of 176 publications across different application domains (e.g., healthcare, education, and entertainment). Using a four-dimensional coding framework (application, technical, evaluative, and ethical), we find (1) frequent use of pattern recognition and information extraction from multimodal sources, but limited support for adaptive, interactive reasoning; (2) a dominant 'modality-to-text' pipeline that privileges language over rich audiovisual cues, striping away nuanced social cues; (3) evaluation practices reliant on static benchmarks, with socially grounded, human-centered assessments rare; and (4) Ethical discussions focused mainly on legal and rights-related risks (e.g., privacy), leaving societal risks (e.g., deception) overlooked--or at best acknowledged but left unaddressed. We outline a research agenda for evaluating socially competent, ethically informed, and interaction-aware multi-modal systems.
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diff --git a/corpus/education/deltas/6887eff768e7bbaf.txt b/corpus/education/deltas/6887eff768e7bbaf.txt
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+Fundamental Mechanisms of Human Learning: Implications for Research and Practice in Education
+
+Learning underlies nearly all human behavior and is central to education and education reform. Although recent advances in neuroscience have revealed the fundamental structure of learning processes, these insights have yet to be integrated into research and practice. Specifically, neuroscience has found that decision-making is governed by a structured process of perception, action-selection, and execution, supported by multiple neural systems with distinct memory stores and learning mechanisms. These systems extract different types of information (categorical, predictive, structural, and sequential) challenging canonical models of memory used in learning and behavioral science research by providing a mechanistic account of how humans acquire and use knowledge. Because each system learns differently, effective teaching requires alignment with system-specific processes. We propose a unified model that integrates these neuroscientific insights, bridging basic mechanisms with outcomes in education, identity, belonging, and wellbeing. By translating first principles of neural information processing into a generalizable framework, this work advances theories of skill acquisition and transfer while establishing a foundation for interdisciplinary research to refine how learning is understood and supported across domains of human behavior.
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diff --git a/corpus/education/deltas/72ea55b4a9117f92.pdf b/corpus/education/deltas/72ea55b4a9117f92.pdf
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diff --git a/corpus/education/deltas/79d6a6fa7b98bae3.txt b/corpus/education/deltas/79d6a6fa7b98bae3.txt
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+Thinking Less, Trusting More: GenAI's Impacts on Students' Cognitive Habits
+
+Objectives: When students use generative AI in coursework, what are its persistent effects on their intellectual development? We investigate (RQ1-How) how students' trust in and routine use of genAI affect their cognitive engagement habits in STEM coursework, and (RQ2-Who) which students are particularly vulnerable to cognitive disengagement. Method: Drawing on dual-process, cognitive offloading, and automation bias theories, we developed a statistical model explaining how and to what extent students' trust-driven routine genAI use affected their cognitive engagement -- specifically, reflection, the need for understanding, and critical thinking in coursework, and how these effects differed across students' cognitive styles. We empirically evaluated this model using Partial Least Squares Structural Equation Modeling on survey data from 299 STEM students across five North American universities. Results: Students who trusted and routinely used genAI reported significantly lower cognitive engagement. Unexpectedly, students with higher technophilic motivations, risk tolerance, and computer self-efficacy -- traits often celebrated in STEM -- were more prone to these effects. Interestingly, students' prior experience with genAI or academia did not protect them from cognitively disengaging. Implications: Our findings suggest a potential cognitive debt cycle where routine genAI use weakens students' intellectual habits, potentially driving and escalating over-reliance. This poses challenges for curricula and genAI system design, requiring interventions that actively support cognitive engagement.
diff --git a/corpus/education/deltas/809504e2705e4531.txt b/corpus/education/deltas/809504e2705e4531.txt
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+Designing Human-AI Collaboration to Support Learning in Counterspeech Writing
+
+Online hate speech has become increasingly prevalent on social media, causing harm to individuals and society. While automated content moderation has received considerable attention, user-driven counterspeech remains a less explored yet promising approach. However, many people face difficulties in crafting effective responses. We introduce CounterQuill, a human-AI collaborative system that helps everyday users with writing empathetic counterspeech - not by generating automatic replies, but by educating them through reflection and response. CounterQuill follows a three-stage workflow grounded in computational thinking: (1) a learning session to build understanding of hate speech and counterspeech, (2) a brainstorming session to identify harmful patterns and ideate counterspeech ideas, and (3) a co-writing session that helps users refine their counter responses while preserving personal voice. Through a user study (N = 20), we found that CounterQuill helped participants develop the skills to brainstorm and draft counterspeech with confidence and control throughout the process. Our findings highlight how AI systems can scaffold complex communication tasks through structured, human-centered workflows that educate users on how to recognize, reflect on, and respond to online hate speech.
diff --git a/corpus/education/deltas/8854c4d54ed37f1c.pdf b/corpus/education/deltas/8854c4d54ed37f1c.pdf
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diff --git a/corpus/education/deltas/8e8ed55b1d4fc17f.txt b/corpus/education/deltas/8e8ed55b1d4fc17f.txt
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+Global Automation Atlas
+
+Automation can displace or complement labour, but this need not be constant across economies. Existing exposure measures typically assign fixed scores to tasks or occupations and capture cross-country variation through employment structure. Here we show that feasible automation depends jointly on task content and country-level conditions. We use a large language model to classify 18,797 work tasks in 124 economies by exposure, labour margin, technology channel and artificial-intelligence materiality. Construct-matched components of the measure correlate strongly with established exposure indices, observed work-related ChatGPT use, AI preparedness and firm-reported adoption. The exposed share of tasks ranges from 3.3% to 61.6%, rises with income yet remains heterogeneous within income groups. Lower-income economies are more concentrated in rule-based and labour-substituting forms of automation, whereas physical execution, planning and inference channels, together with labour-augmenting uses of artificial intelligence, become more prominent with development. Country conditioning changes occupation exposure rankings, especially in lower-income economies. Combined with employment data, we find that women are disproportionately employed in occupations with substitution-facing exposure. Machine-learning hypothesis generation identifies digital records, capital equipment, local judgement, trust-based markets and data integration as conditions associated with exposure differences.
diff --git a/corpus/education/deltas/99ecdbe2e09cf45a.txt b/corpus/education/deltas/99ecdbe2e09cf45a.txt
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+Quantifying Perception-Based Student Success with Generative AI: An Exploratory Monte Carlo Simulation
+
+Generative artificial intelligence (GenAI) tools such as ChatGPT have attracted growing attention in higher education, particularly in relation to how students perceive their usefulness, usability, and educational value. This study develops an exploratory Monte Carlo simulation framework for quantifying perception-based student success in the context of GenAI use. A PRISMA-informed structured literature search in Scopus identified nineteen empirical studies published between 2023 and 2025, of which six reported item-level means and standard deviations suitable for probabilistic modelling. One coherent 10-item, 5-point Likert-scale usability-oriented instrument was selected as a canonical proof-of-concept dataset and used to parameterise an inverse-variance-weighted Monte Carlo simulation generating 10,000 synthetic observations. The results show that the weighting structure substantially influences the simulated outcome, with System Efficiency and Learning Burden receiving the largest inverse-variance weight and therefore the strongest influence on the composite score. The study offers a transparent, reproducible, and privacy-preserving proof-of-concept framework linking structured literature search, item-level summary statistics, and probabilistic modelling.
diff --git a/corpus/education/deltas/9af2af83ac0b3c00.pdf b/corpus/education/deltas/9af2af83ac0b3c00.pdf
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diff --git a/corpus/education/deltas/a71986260ec905b7.txt b/corpus/education/deltas/a71986260ec905b7.txt
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+Artificial Intelligence in Sports: Insights from a Quantitative Survey among Sports Students in Germany about their Perceptions, Expectations, and Concerns regarding the Use of AI Tools
+
+Generative Artificial Intelligence (AI) tools such as ChatGPT, Copilot, or Gemini have a crucial impact on academic research and teaching. Empirical data on how students perceive the increasing influence of AI, which different types of tools they use, what they expect from them in their daily academic tasks, and their concerns regarding the use of AI in their studies are still limited. The manuscript presents findings from a quantitative survey conducted among sports students of all semesters in Germany using an online questionnaire. It explores aspects such as students' usage behavior, motivational factors, and uncertainties regarding the impact of AI tools on academia in the future. Furthermore, the social climate in sports studies is being investigated to provide a general overview of the current situation of the students in Germany. Data collection took place between August and November 2023, addressing all sports departments at German universities, with a total of 262 students participating. Our Findings indicate that students have a strong interest in using AI tools in their studies, expecting them to improve their overall academic performance, understand the complexity of scientific approaches, and save time. They express confidence that the proliferation of AI will not compromise their critical thinking skills. Moreover, students are positive about integrating more AI-related topics into the curriculum and about lecturers adopting more AI-based teaching methods. However, our findings also show that students have concerns about plagiarism, lecturer preparedness and their own skills and future skill development.
diff --git a/corpus/education/deltas/b42910926555f069.pdf b/corpus/education/deltas/b42910926555f069.pdf
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diff --git a/corpus/education/deltas/b69fe17dcadca304.txt b/corpus/education/deltas/b69fe17dcadca304.txt
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+Web Privacy based on Contextual Integrity: Measuring the Collapse of Online Contexts
+
+The collapse of social contexts has been amplified by digital infrastructures but surprisingly received insufficient attention from Web privacy scholars. Users are persistently identified within and across distinct Web contexts, in varying degrees, through and by different websites and trackers, losing the ability to maintain a fragmented identity. To systematically evaluate this structural privacy harm, we operationalize the theory of Privacy as Contextual Integrity and measure persistent user identification within and between distinct Web contexts. We crawl the top-700 popular websites across the contexts of health, finance, news \& media, LGBTQ, eCommerce, adult, and education websites, for 27 days, and created network graphs to learn how persistent browser identification via third-party cookies and JavaScript fingerprinting is diffused within and between Web contexts. Past work measured Web tracking in bulk, highlighting the volume of trackers and tracking techniques. These measurements miss a crucial privacy implication of Web tracking - the collapse of online contexts. Our findings reveal how persistent browser identification varies between and within contexts, diffusing user IDs to different distances, contrasting known tracking distributions across websites, and conducted as a joint or separate effort via cookie IDs and JS fingerprinting. Our network analysis informs the construction of browsers' storage containers to protect users against real-time context collapse. This is a first modest step in measuring Web privacy as Contextual Integrity, opening new avenues for contextual Web privacy research.
diff --git a/corpus/education/deltas/b8781b02fc3b27ba.pdf b/corpus/education/deltas/b8781b02fc3b27ba.pdf
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diff --git a/corpus/education/deltas/beb1c8828f676fa5.txt b/corpus/education/deltas/beb1c8828f676fa5.txt
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+PACEE: Parent-Centered AI Scaffolding for Emotion Education in Early Childhood Conversations
+
+Emotion education is critical for children aged 3 to 6. However, existing technologies largely focus on children's direct interaction with AI, overlooking the central role of parents in guiding early emotional development at home. To address this gap, we conducted co-design sessions with five kindergarten teachers and five parents to identify key parental challenges and opportunities for AI support in family emotion education. Based on these insights, we developed PACEE, an LLM-based assistant designed to support parents in guiding children's emotional development through conversations, rather than directly interacting with children. PACEE provides parent-centered AI scaffolding that supports parents in real-time conversation through personalized guidance, post-hoc reflection through trackable feedback, and understanding children's emotional states through modeling. We evaluated PACEE with 16 families. Results show that PACEE enhances parent-child engagement, fosters deeper emotional communication, and improves parents' expertise and overall experience in guiding their children. Our findings extend emotion coaching practices to the context of generative AI and offer design insights for building AI systems that support parent-centered family education.
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diff --git a/corpus/education/deltas/c6ffe5c910ecd3bc.txt b/corpus/education/deltas/c6ffe5c910ecd3bc.txt
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+Physical partisan proximity outweighs online ties in predicting US voting outcomes
+
+Affective polarization and increasing social divisions affect social mixing and the spread of information across online and physical spaces, reinforcing social and electoral cleavages and influencing political outcomes. Here, using individual survey data and aggregated and de-identified co-location and online network data, we investigate the relationship between partisan exposure and vote choice in the US by comparing offline and online dimensions of partisan exposure. By leveraging various statistical modeling approaches, we consistently find that partisan exposure in the physical space, as captured by co-location patterns, more accurately predicts electoral outcomes in US counties, outperforming online and residential exposures. Similarly, offline ties at the individual level better predict vote choice compared to online connections. We also estimate county-level experienced partisan segregation and examine its relationship with individuals' demographic and socioeconomic characteristics. Focusing on metropolitan areas, our results confirm the presence of extensive partisan segregation in the US and show that offline partisan isolation, both considering physical encounters or residential sorting, is higher than online segregation and is primarily associated with educational attainment. Our findings emphasize the importance of physical space in understanding the relationship between social networks and political behavior, in contrast to the intense scrutiny focused on online social networks and elections.
diff --git a/corpus/education/deltas/d63d2ad7348e3986.pdf b/corpus/education/deltas/d63d2ad7348e3986.pdf
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diff --git a/corpus/education/deltas/d9ce5bde7e7c0050.txt b/corpus/education/deltas/d9ce5bde7e7c0050.txt
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+Toward LLM-Supported Automated Assessment of Critical Thinking Subskills
+
+As the world becomes increasingly saturated with AI-generated content, disinformation, and algorithmic persuasion, critical thinking - the capacity to evaluate evidence, detect unreliable claims, and exercise independent judgment - is becoming a defining human skill. Developing critical thinking skills through timely assessment and feedback is crucial; however, there has not been extensive work in educational data mining on defining, measuring, and supporting critical thinking. In this paper, we investigate the feasibility of measuring "subskills" that underlie critical thinking. We ground our work in an authentic task where students operationalize critical thinking by writing argumentative essays. We developed a coding rubric based on an established skills progression and completed human coding for a corpus of student essays. We then evaluated three distinct approaches to automated scoring: zero-shot prompting, few-shot prompting, and supervised fine-tuning, implemented across three large language models (GPT-5, Llama 3.1 8B, and ModernBERT). Fine-tuning Llama 3.1 8B achieved the best results and demonstrated particular strength on subskills with highly separable proficiency levels with balanced labels across levels, while lower performance was observed for subskills that required detection of subtle distinctions between proficiency levels or imbalanced labels. Our exploratory work represents an initial step toward scalable assessment of critical thinking skills across authentic educational contexts. Future research should continue to combine automated critical thinking assessment with human validation to more accurately detect and measure dynamic, higher-order thinking skills.
diff --git a/corpus/education/deltas/e66720898f395955.pdf b/corpus/education/deltas/e66720898f395955.pdf
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diff --git a/corpus/education/deltas/ec38bdba2c82be73.txt b/corpus/education/deltas/ec38bdba2c82be73.txt
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+Bridging LMS and generative AI: dynamic course content integration (DCCI) for enhancing student satisfaction and engagement via the ask ME assistant
+
+Integration of Large Language Models (LLMs) with Learning Management Systems (LMSs) can enhance task automation and accessibility in education. However, hallucination where LLMs generate inaccurate or misleading information remains a challenge. This study introduces the Dynamic Course Content Integration (DCCI) mechanism, which dynamically retrieves course content from Canvas LMS and structures it within an LLM's context window via prompt engineering, enabling the LLM-powered assistant, Ask ME, to deliver context-aware, curriculum-aligned responses while mitigating hallucinations. A mixed-methods pilot study grounded in Self-Determination Theory (autonomy, competence) and the Technology Acceptance Model (perceived usefulness, ease of use) evaluated DCCI's effectiveness with 120 first-year programming students at E\"otv\"os Lor\'and University. The course focused on foundational programming patterns in C#, including writing program specifications. We analyzed 14,746 logged interactions and a post-course survey completed by 101 students. User satisfaction was measured via a 5-point Likert scale (turn-level ratings), while the survey assessed usability, engagement, and ethical concerns. Results indicated high satisfaction (mean 4.65/5) and strong recognition of Ask ME's ability to provide timely, contextually relevant answers to administrative and course-related queries. 78.06% agreed that Ask ME's Canvas integration reduced platform switching, improving usability, engagement, comprehension, and topic exploration. Many students reported reduced hesitation to ask questions and increased motivation for self-directed learning, though concerns about over-reliance on AI and reduced student-teacher interaction emerged. This study demonstrates that DCCI enhances LLM reliability, student satisfaction, and engagement in AI-driven educational automation, while highlighting the importance of balancing
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diff --git a/corpus/education/deltas/fce5355ddc7bc2f5.txt b/corpus/education/deltas/fce5355ddc7bc2f5.txt
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+Facial-Expression-Aware Prompting for Empathetic LLM Tutoring
+
+Large language models (LLMs) enable increasingly capable tutoring-style conversational agents, yet effective tutoring requires sensitivity to learners' affective and cognitive states beyond text alone. Facial expressions provide immediate and practical cues of confusion, frustration, or engagement, but remain underexplored in LLM-driven tutoring. We investigate whether facial-expression-aware signals can improve empathetic tutoring responses through prompt-level integration, without end-to-end retraining. We build a scalable simulated tutoring environment where a student agent exhibits diverse facial behaviors from a large unlabeled human facial expression video dataset, and compare four tutor variants: a text-only LLM baseline, a multimodal baseline using a random facial frame, and two Action Unit estimation model (AUM)-based methods that either inject textual AU descriptions or select a peak-expression frame for visual grounding. Across 960 multi-turn conversations spanning three tutor backbones (GPT-5.1, Claude Opus 4.5, and Gemini 2.5 Pro), we evaluate targeted pairwise comparisons with five human raters and an exhaustive AI evaluator. AU-based conditioning consistently improves empathetic responsiveness to facial expressions across all tutor backbones, while AUM-guided peak-frame selection outperforms random-frame visual input. Textual AU abstraction and peak-frame visual injection show model-dependent advantages. Control analyses show that this improvement does not come at the expense of worse pedagogical clarity or responsiveness to textual cues. Overall, our results show that lightweight, structured facial expression representations can meaningfully enhance empathy in LLM-based tutoring systems with minimal overhead. Future work should evaluate these methods using real student facial data collected during authentic learning interactions.
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+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Sci Rep
+Journal ID: Sci Rep
+NLM Journal ID: 101563288
+
+Scientific Reports
+
+EISSN: 2045-2322
+Publisher: Nature Publishing Group
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC13379370
+PMID: 42469335
+DOI: 10.1038/s41598-026-62136-8
+Article ID: 62136
+Article version: 1
+Subjects: Article
+
+Casting process optimization of stainless-steel pump impellers using finite element simulation
+
+https://orcid.org/0000-0003-2485-2681 Essam Mahmoud A. mahmoud.elsefy@hti.edu.eg
+1 2
+Abdeltawab Noha M. 3
+Shash Ahmed Y. 3 4
+El-Sayed Mostafa M. 5
+1 https://ror.org/051q8jk17 grid.462266.2 0000 0004 0377 3877 Mechanical Engineering Department, Higher Technological Institute (HTI), 10th of Ramadan City, Egypt
+2 https://ror.org/03q21mh05 grid.7776.1 0000 0004 0639 9286 Faculty of Engineering, City University of Cairo (CUC), New Heliopolis City, Egypt
+3 https://ror.org/03rjt0z37 grid.187323.c 0000 0004 0625 8088 Faculty of Engineering and Materials Science, German University in Cairo, Cairo, Egypt
+4 https://ror.org/03q21mh05 grid.7776.1 0000 0004 0639 9286 Mechanical Design and Production Engineering Department, Faculty of Engineering, Cairo University, Giza, 12316 Egypt
+5 https://ror.org/02dmj8v04 Manufacturing and Production Engineering Department, Modern Academy for Engineering and Technology, Cairo, Egypt
+Electronic publication date: 2026 Jul 17
+Publication date: 2026
+Volume: 16
+Electronic Location ID: 22514
+Received 2026 Feb 6; Accepted 2026 Jul 9
+Copyright: © The Author(s) 2026
+Copyright year: 2026
+License: Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Keywords: Centrifugal pump impeller, Casting simulation, Shrinkage porosity, Directional solidification, Gating and feeding optimization
+Keywords: Engineering, Materials science
+
+Funding: Higher Technological Institute 10th of Ramadan Open access funding provided by The Science, Technology & Innovation Funding Authority (STDF) in cooperation with The Egyptian Knowledge Bank (EKB).
+
+issue-copyright-statement: © Springer Nature Limited 2026
+
+Ÿ==============================Ÿ
+This study employed ProCAST numerical simulation to assess and enhance the casting design of a stainless-steel CF8M pump impeller by analyzing six gating and feeding configurations. The simulations were executed at a pouring temperature of 1650 °C, an initial mould temperature of 25 °C, and an estimated filling duration of 20 s. The examined configurations comprised a baseline horizontal design and modified designs featuring enhanced riser and gate arrangements, mould tilt angles ranging from 5° to 20°, and supplementary ventilation in the final design. The findings indicated that the original design resulted in detrimental temperature distribution and localized final solidification within the impeller body, especially around the hub and blade-hub connections, hence heightening the propensity for shrinkage porosity. The progressive alteration of the riser, sprue, gate configuration, mould angle, and ventilation system optimized the temperature gradient, augmented feeding efficiency, and relocated the final solidification zone towards the riser/feeder. Design 6, optimized with a 20° mould tilt and ventilators, had the most advantageous solidification characteristics and reduced anticipated shrinkage porosity within the functioning impeller body. The findings indicate that numerical simulation can significantly diminish dependence on conventional trial-and-error casting experiments by facilitating virtual evaluation of several design options before to production. This study presents a simulation-based approach for regulating solidification behavior, enhancing feeding efficiency, and reducing shrinkage porosity in the casting of stainless-steel pump impellers.
+
+Introduction and Literature Review
+
+In a variety of industrial industries, such as water treatment, power generation, chemical processing, oil and gas, and marine applications, centrifugal pump impellers are essential rotating parts that transform mechanical energy into fluid kinetic energy1. Impellers must meet strict standards for structural integrity, dimensional precision, and fatigue resistance because of their continuous operation under high rotational speeds, pressure fluctuations, and corrosive environments2. Even minute manufacturing flaws might cause premature failure, raise vibration levels, and drastically shorten service life. Therefore, one of the main concerns in foundry engineering is making sure that impellers are produced without defects2.
+
+For metallic impellers, casting is still the most popular manufacturing method because it can create intricate geometries at a lower cost than significant machining or additive manufacturing. For stainless steel impellers, sand casting and investment casting are the most often used casting methods. Investment casting is preferable when great dimensional accuracy and thin-walled features are needed, but sand casting is preferred for its flexibility and economic feasibility for making medium-to-large components. However, both procedures are intrinsically vulnerable to flaws brought on by non-uniform cooling, complex molten metal flow behavior, and solidification shrinkage, particularly in parts like impellers that have complex blade geometries and wide variations in wall thickness2,3.
+
+According to recent academic and industrial research, casting-related flaws account for between 30 and 70% of rejected components in some production lines, making them a major contributor to foundry trash rates. It has been demonstrated that inadequate gating and feeding design in the case of stainless-steel pump impellers can restrict casting yield to values as low as 41–45%, leading to significant material waste and higher production costs. As a result, increasing casting yield and quality through scientific process design has emerged as a key goal for both industry and research4.
+
+Consistently producing impellers without defects is still a difficult undertaking, even with extensive industrial experience in impeller casting. The main challenge is that the casting process is highly linked, with nonlinear interactions between molten metal flow, heat transfer, solidification kinetics, and thermomechanical stresses3. The empirical design guidelines and trial-and-error modifications of gating systems, riser diameters, and pouring parameters are still widely used in traditional foundry practice. Even though these methods work well for simple geometries, they frequently fall short for intricate parts like impellers1.
+
+Impeller castings that passed visual inspection but had interior shrinkage voids and porosity that were only discovered through machining or numerical analysis are documented in a number of studies. Despite the lack of obvious surface flaws, Jurković et al.‘s investigation of sand-cast AISI 316 L pump impellers revealed shrinkage porosity only after internal machining. Subsequent numerical simulations verified that the likelihood of shrinkage faults in crucial areas above 60%, signifying a basic shortcoming of the conventional inspection and design approach. Furthermore, impeller designs have been pushed toward thinner blades, lower mass, and tighter dimensional tolerances due to growing industrial needs for higher efficiency pumps2.
+
+These developments make trial-and-error methods more expensive, time-consuming, and unreliable by further reducing the processing window and increasing sensitivity to heat gradients and feeding circumstances5. Among the most frequent quality problems in impeller manufacturing are casting defects such shrinkage porosity, gas porosity, non-metallic inclusions, misruns, and hot tears. Because of their substantial volumetric contraction during solidification and very broad solidification range, shrinkage porosity is especially important in stainless steel impellers. When feeding is inadequate, this defect usually develops in dense areas, blade–hub junctions, and areas that harden last6.
+
+Kim et al. investigated the investment casting of centrifugal pump impellers and showed that low casting yield and persistent shrinkage problems were caused by incorrect riser sizing and positioning. Oversized risers and ineffective feeding routes in their original form limited the casting yield to 41.5%. They achieved a far higher yield of 65.2% by utilizing numerical simulation to optimize the runner–riser system, reducing the riser diameter from 133 mm to 66 mm while totally removing shrinkage flaws7.
+
+This finding emphasizes the close connection between material waste and defect generation in traditional casting methods. Air entrainment, oxide film formation during mold filling, and turbulent molten metal flow are the main causes of gas porosity and inclusion defects7.
+
+Because of the quick variations in cross-sectional area along the blade channels, these flaws are especially troublesome in impeller castings. Kim et al. also demonstrated how irregular flow rates during filling caused gas and inclusion flaws to concentrate on the impeller’s front and rear covers, endangering fatigue resistance and operational dependability. Because trial-and-error approaches don’t provide anything about internal flow patterns, solidification sequences, or defect creation mechanisms, they are essentially insufficient to address these problems7,8.
+
+Because each physical trial necessitates mold preparation, melting, pouring, cooling, and inspection, development cycles are lengthy and expenses are expensive. Additionally, empirical changes frequently target symptoms rather than underlying causes, producing less-than-ideal and non-reproducible results. Despite the widespread use of casting simulation in recent years, a rigorous analysis of the literature identifies several unanswered questions. Much of the research that is now available concentrates on the behavior of mold filling or solidification separately, failing to completely integrate flow, thermal, and mechanical phenomena. For example, some studies forecast shrinkage porosity using thermal criteria, ignoring flow-induced turbulence and gas entrapment, which are equally important in impeller castings9.
+
+Furthermore, optimization attempts are frequently restricted to a small number of parameters, including gating cross-section or riser size, while ignoring tilt angle, mold orientation, or the relationship between feeding efficiency and flow stability. Although Kim et al. showed that mold tilting significantly reduced gas and inclusion flaws, many impeller-focused studies have not thoroughly examined such solutions. Additionally, many efforts still need quantitative confirmation of simulation results. Fewer studies describe numerical probabilities of defect development or offer systematic comparisons between simulated and experimental yields, even though defect locations are often predicted qualitatively7.
+
+This emphasizes the necessity of comprehensive, quantitatively verified frameworks that incorporate finite element analysis, casting simulation, and process optimization, especially designed for intricate impeller geometries. Fundamental physical processes pertaining to fluid flow, heat transfer, phase transition, and stress development control the development of casting defects. When liquid supply is insufficient during solidification, the volumetric contraction of molten metal causes shrinkage porosity. Areas with poor cooling rates and minimal temperature gradients are especially vulnerable. Several studies use Niyama criteria, which connect the local temperature gradient to the cooling rate as a measure of shrinkage susceptibility, to quantify this behavior. Kim et al. used the Niyama criterion in ProCAST simulations to assess the likelihood of shrinkage in impeller castings, and they showed that areas with low Niyama values had a strong correlation with shrinkage problems that were discovered in experiments1,6.
+
+Their findings demonstrated that, even when the riser size is greatly reduced, appropriate directional solidification toward the riser is necessary to remove shrinkage porosity. During mold filling, air entrainment and turbulent flow are the main causes of gas porosity and inclusion flaws. According to Jurkovicé et al., local velocity spikes brought on by abrupt changes in cross-sectional areas at the impeller inlet encouraged turbulence and oxide film entrainment4. It was demonstrated that these factors considerably raise the likelihood of defects in areas close to thick hubs and thin blades. Thermal stresses produced during restricted solidification are the cause of thermomechanical flaws such hot tearing and distortion. Wide solidification intervals, harsh mold conditions, and uneven cooling all contribute to stress accumulation, which is why thermomechanical analysis is crucial to defect prediction10.
+
+Tools for casting simulation have been extremely useful for comprehending and improving intricate casting procedures. Numerical modeling of mold filling, heat transfer, solidification, and defect generation within a single framework is made possible by commercial software programs like ProCAST, MAGMASOFT, and Any Casting. Because of its finite element-based formulation and integration with thermodynamic databases, ProCAST is one of these that is frequently utilized in both academic and industrial research5.
+
+To model mold filling, solidification behavior, and defect generation in investment-cast impellers, Kim et al. used ProCAST. The runner-riser system and mold tilt angle were redesigned with the help of their simulations, which accurately anticipated shrinkage, gas, and inclusion flaws. Ultrasonic testing was used to experimentally evaluate the numerical results, demonstrating the dependability of simulation-based process optimization11.
+
+The location and degree of shrinkage porosity seen in actual castings were also faithfully replicated by numerical simulations when Jurković et al. used ProCAST to investigate sand-cast stainless-steel impellers. According to their study, simulation enables the assessment of several design options without the necessity for expensive physical testing, which significantly cuts down on development time and scrap rate12.
+
+Modern casting modeling relies heavily on finite element analysis because it makes it possible to solve coupled governing equations for mass, energy, and momentum conservation accurately predicts hot spots and areas that are prone to shrinkage in solidification modeling by capturing feeding behavior, phase fraction evolution, and transient temperature fields. Typical simulations for stainless steel impellers include latent heat values of around 273 kJ/kg and temperature-dependent thermal conductivity values that range from about 26 W/m·K at pouring temperature to 14 W/m·K at room temperature12.
+
+FEA is being used more in thermomechanical modeling in addition to thermal analysis to forecast residual stresses, deformation, and crack susceptibility offers crucial insight into defect mechanisms that thermal analysis alone is unable to capture by combining solidification shrinkage with mechanical constraints imposed by the mold. A significant step toward predictive, optimization-driven impeller casting is the integration of flow simulation, solidification modeling, and thermomechanical analysis inside a single FEA framework12.
+
+This study specifically examines filling behavior, temperature distribution, cooling rate, solidification sequence, and shrinkage porosity prediction in impeller casting, despite previous research identifying hot tearing, deformation, thermal stress, and strain as significant casting-related defects. Consequently, the existing simulation framework was restricted to thermal-flow and solidification analysis, rather than encompassing a fully linked thermo-mechanical study. The discourse on stress-related flaws is presented solely as a general context to underscore the wider significance of casting simulation. A comprehensive assessment of thermal stress, strain, hot tearing propensity, and deformation will be conducted in further research utilizing integrated thermo-mechanical models and experimental verification.
+
+The study aims to accomplish a series of cohesive objectives. A conservative baseline casting design (Design 1) is produced and subjected to numerical analysis to identify crucial sections susceptible to defects and inefficiencies in feeding and filling behavior. Secondly, a sequence of optimal designs (Designs 2–6) is methodically created by altering riser dimensions, gating geometry, mold tilting angle, and ventilation approach. The impact of these adjustments on temperature distribution, cooling rate, solidification sequence, and defect likelihood is quantitatively assessed by ProCAST simulations and defect prediction criteria. The assessment of casting yield and internal soundness across all designs aims to discover the ideal configuration that guarantees directional solidification, stable filling, and low material waste. The project seeks to establish that simulation-guided design iteration can supplant conventional trial-and-error methods for intricate impeller castings.
+
+Methodology and numerical method
+
+Overall computational workflow
+
+To reduce casting flaws and increase material efficiency during the sand casting of a stainless-steel impeller, a systematic, simulation-driven workflow was used in this study. The process starts with creating a three-dimensional computer-aided design (CAD) model of the impeller and its related casting system, which includes the sprue, runner, gates, and risers. This first setup, known as Design 1, is a cautious baseline design that prioritizes fault prevention over material efficiency.
+
+ProCAST was then used to predict mold filling, heat transfer, solidification behavior, and defect generation in finite element-based casting simulations. Quantitative defect indicators, including shrinkage porosity %, temperature distribution, cooling rate, and void location, were used to assess the outcomes of each simulation. A series of optimized designs, from Design 2 to Design 6, were produced as a result of specific changes made to the casting system geometry and process parameters in response to these findings. Until a casting with no flaws and increased material efficiency was attained, this iterative cycle of simulation, assessment, and redesign was maintained.
+
+Geometry and casting system description
+
+The investigated component is a centrifugal pump impeller characterized by complex internal flow passages, variable wall thickness, and a central hub, which collectively pose challenges for uniform mold filling and directional solidification. The casting system was designed for gravity sand casting and comprised a pouring basin, vertical sprue, horizontal runner network, multiple ingates, and a feeding riser positioned above the hub region.
+
+In the baseline configuration (Design 1), the casting system incorporated oversized gating elements and a large riser to ensure sufficient feeding during solidification. While this approach effectively eliminated shrinkage defects, it resulted in excessive material usage and prolonged solidification time. Across subsequent designs, geometric modifications were applied progressively to the riser dimensions, sprue geometry, runner layout, and gate positioning to improve flow stability and feeding efficiency while reducing non-functional metal volume. In later design stages, the central hole of the impeller was removed from the casting geometry and planned for post-casting machining, simplifying flow paths and enhancing solidification uniformity.
+
+Material models
+
+The component under investigation is a centrifugal pump impeller, which presents difficulties for consistent mold filling and directed solidification due to its intricate internal flow passageways, variable wall thickness, and central hub. A pouring basin, vertical sprue, horizontal runner network, several ingates, and a feeding riser above the hub area made up the casting system, which was made for gravity sand casting.
+
+To guarantee enough feeding during solidification, the casting system in the baseline configuration (Design 1) included a big riser and enlarged gating elements. Although this method successfully removed shrinkage problems, it used too much material and took a long time to solidify. To increase flow stability and feeding efficiency while lowering the volume of non-functional metal, geometric changes were gradually made to the riser size, sprue geometry, runner arrangement, and gate positioning in later iterations. Later design stages simplified flow routes and improved solidification uniformity by removing the impeller’s central hole from the casting geometry and planning for post-casting machining.
+
+The casting material used in the numerical simulations was stainless steel CF8M, which is commonly used for corrosion-resistant pump and valve components. Since the prediction of solidification behavior and shrinkage porosity is strongly affected by the thermophysical properties of the alloy, the material model was defined using temperature-dependent properties where available in the ProCAST material database. The most relevant properties used in the simulation are summarized in Table 1.
+
+The selected properties directly influence the calculated temperature field, cooling rate, solidification time, liquid feeding behavior, and shrinkage porosity tendency. In particular, the liquidus and solidus temperatures define the solidification interval, while the latent heat of fusion controls heat release during phase transformation. Thermal conductivity and specific heat affect the rate of heat extraction through the mold, whereas density and solidification shrinkage influence the feeding requirement during solidification.
+
+The values in Table 1 denote the material input utilized to characterize the thermal and solidification behavior of the casting alloy. Temperature-dependent values were utilized where accessible in the simulation database, and indicative ranges are documented to enhance transparency. The same properties were systematically applied throughout all six examined gating and feeding designs, ensuring that the observed variations in shrinkage porosity, cooling rate, and solidification behavior could be ascribed to design alterations rather than fluctuations in material input.
+
+In the simulation, the molten alloy was set at the designated pouring temperature, whilst the mould was set at ambient temperature. The alloy was regarded as an incompressible Newtonian fluid throughout the filling process and as a temperature-sensitive solidifying substance during cooling. The latent heat emitted between the liquidus and solidus temperatures was incorporated using the enthalpy-based solidification model, enabling the simulation to accurately represent the mushy zone and delineate final solidifying areas prone to shrinkage porosity.
+
+Table 1 Thermophysical and solidification properties of stainless steel CF8M used in the ProCAST simulation.
+
+Property	Symbol	Value used in simulation	Unit	
+Alloy	—	Stainless steel CF8M	—	
+Density	ρ	7700–7800	kg/m³	
+Liquidus temperature	TL	1450–1480	°C	
+Solidus temperature	TS	1370–1400	°C	
+Pouring temperature	Tp	1650	°C	
+Initial mold temperature	Tm	25	°C	
+Thermal conductivity	k	Temperature-dependent, approximately 15–30	W/m·K	
+Specific heat capacity	Cp	Temperature-dependent, approximately 500–750	J/kg·K	
+Latent heat of fusion	L	approximately 270	kJ/kg	
+Dynamic viscosity	µ	Temperature-dependent	Pa·s	
+Solidification shrinkage	βs	Material-database value	%	
+Mold material	—	Silica sand	—	
+
+Simulation environment, mesh strategy, solver settings, and boundary conditions
+
+All numerical simulations were conducted using ProCAST, which utilizes the finite element approach to address coupled temperature, fluid flow, and mechanical issues. The computational domain encompassed the impeller, gating and riser systems, as well as the adjacent mold. A three-dimensional adaptable mesh was created, with refinement focused on crucial areas such as the blade-hub junctions, gating channels, and riser, where significant temperature gradients and intricate flow patterns were anticipated.
+
+The numerical setup was organized into two parts: boundary and initial conditions, and solver-control settings. This separation was adopted to avoid confusion between physical boundary conditions and numerical time-stepping parameters.
+
+Initial and boundary conditions
+
+The computational domain consisted of the impeller casting cavity, sprue, runner, gates, riser/feeder, and surrounding silica sand mold. The molten stainless steel CF8M was initialized at the pouring temperature of 1650 °C, while the silica sand mold was initialized at 25 °C. Mold filling was modeled under gravity-driven conditions. A prescribed inlet velocity was applied at the sprue entrance to control the metal flow into the mold cavity. Heat transfer between the molten metal and the mold was represented using a casting–mold interfacial heat-transfer condition, while heat loss from the external mold surfaces was modeled using convective air-cooling boundary conditions.
+
+Time-stepping and solver-control settings
+
+The transient filling and solidification calculations were performed using automatic time integration in ProCAST as shown in Table 2. In this context, the maximum number of time steps refers to the maximum number of calculation increments allowed during the simulation, while the time-step size refers to the time increment advanced by the solver at each calculation step13.
+
+The maximum number of time steps was set to 50,000 to provide sufficient numerical allowance for the filling, solidification, and cooling stages. The initial time-step size was set to 1 s, which defines the first-time increment used at the start of the calculation. The maximum time-step size was also limited to 1 s to prevent excessively large increments during the transient thermal calculation. Therefore, the value of 1 s refers to the time increment size, not to the number of time steps. The simulation was terminated according to the selected thermal stopping criterion after the casting reached the specified final temperature condition.
+
+Table 2 Numerical time-stepping and solver-control settings used in the ProCAST simulation.
+
+Parameter	Meaning	Value used	
+Maximum number of time steps	Maximum number of calculation increments allowed by the solver	50,000	
+Initial time-step size	First time increment used at the start of the transient calculation	1 s	
+Maximum time-step size	Upper limit imposed on the time increment during the calculation	1 s	
+Filling mode	Physical filling condition applied during mold filling	Gravity filling	
+Stopping criterion	Condition used to terminate the thermal calculation	Final temperature criterion	
+Evaluated stages	Simulation stages covered by the transient calculation	Filling, solidification, and cooling	
+
+The mold was set at 25 °C, Table 3 shows simulation parameters used in gravity filling analysis.Boundary conditions comprised a specified inflow velocity at the sprue entry, determined to attain a total filling duration of roughly 20 s, and convective heat dissipation from the external mold surfaces via film-coefficient-based air cooling. The alloy was characterized as linearly elastic to facilitate thermal stress assessment, but the mold was regarded as mechanically rigid.
+
+The numerical simulation was conducted under gravity filling conditions using predefined time-stepping and stopping criteria to ensure numerical stability and accurate capture of the filling and solidification stages. Appropriate limits for the initial, filling, and maximum time steps were selected, while consistent units for temperature, heat flux, velocity, and pressure were defined to allow reliable post-processing and comparison of thermal–fluid results14.
+
+Table 3 Simulation parameters used in gravity filling analysis.
+
+Parameter	Description	Type	Value	Unit	
+NSTEP	Stop criterion: Maximum number of steps	Constant	50,000	—	
+TSTOP	Stop criterion: Final temperature	Constant	1.3090 × 10³	°C	
+DTI	Initial time step	Constant	1.0000 × 10⁻³	s	
+DTMAXFIL	Maximum time step during filling	Constant	1.0000 × 10⁻¹	s	
+DTMAX	Maximum global time step	Constant	1.0000 × 10⁰	s	
+
+The mold and casting volumes were specified together with their corresponding materials and beginning heat conditions to accurately simulate the investment casting environment as shown in Table 4. Boundary conditions were implemented to simulate air-cooling heat transfer at the exterior mold surfaces, a specified pouring temperature, and an inlet velocity condition to precisely predict heat dissipation, molten metal inflow, and thermo-mechanical behavior during the filling phase.
+
+Table 4 Volume definition and boundary conditions used in the numerical simulation.
+
+Category	Name	Type	Material/Entity	Fill %	Initial Temperature (°C)	Boundary Condition	Area (mm²)	Stress/Notes	
+Volume	Mold	Mold	Silica Sand	100.00	25.00	—	—	Rigid	
+Volume	Model	Alloy	Stainless Steel CF8M	0.00	1650.00	—	—	Linear Elastic	
+Boundary	Heat_1	Heat	EXT_Mold	—	—	Air cooling (film condition)	59,794.40	Heat loss to ambient	
+Boundary	Temperature_1	Temperature	USER_Temperature_1	—	1650.00	Prescribed temperature	530.99	Pouring temperature	
+Boundary	Velocity_1	Velocity	USER_Temperature_1	—	—	BC_Velocity_15	530.99	Inlet velocity condition	
+
+The inlet velocity was determined using the integrated velocity calculator, which relied on the designated filling time, inlet cross-sectional area, and the assumption of gravity-driven flow. This method guarantees a regulated and realistic filling rate of the molten metal, reducing excessive turbulence while ensuring complete mold filling within the designated timeframe. Pouring and filling parameters used in the numerical simulation were shown in Table 5.
+
+Table 5 Pouring and filling parameters used in the numerical simulation.
+
+Parameter	Description	Value	Unit	
+Computer Mode	Selected calculation mode	Fill Time	—	
+Velocity	Inlet molten metal velocity	8.77	mm/s	
+Area	Inlet cross-sectional area	530.99	mm²	
+Fill Limit	Target filling percentage	100	%	
+Flow Direction	Pouring direction	Gravity	—	
+Fill Time	Total mold filling time	20.0	s	
+Governing Relation	Filling time equation	Fill Time (s) = \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\frac{Volume\:X\:Fill\:Limit\:\%}{100\:X\:Area\:X\:Velocity}$$\end{document}	s	
+
+Because shrinkage porosity prediction is sensitive to the resolution of the computational mesh, a mesh sensitivity analysis was performed to ensure that the numerical results were not strongly dependent on the selected element size. Three mesh densities were evaluated, namely coarse, medium, and fine meshes. The comparison focused on the predicted shrinkage porosity distribution, maximum shrinkage porosity percentage, temperature field, cooling-rate distribution, and location of the final solidifying regions.
+
+The coarse mesh was used only for preliminary evaluation because it captured the general filling and solidification trends but provided less detailed resolution near the blade–hub junctions and feeder connection as explained in Table 6. The medium mesh improved the resolution in critical regions such as the hub, blade–hub junctions, gates, and riser neck. The fine mesh provided additional refinement in these regions but required a substantially higher computational cost.
+
+The mesh sensitivity results showed that the predicted locations of shrinkage porosity and final solidification remained almost unchanged when the mesh was refined from the medium to the fine level. Only minor variations were observed in the maximum shrinkage porosity value and local cooling-rate magnitude. Therefore, the medium mesh was adopted for the full set of simulations because it provided a good compromise between accuracy and computational efficiency.
+
+Based on this comparison, the medium mesh was considered sufficiently accurate for comparing the six gating and feeding configurations. Since the defect locations, final solidifying regions, and overall thermal trends did not change significantly between the medium and fine meshes, the conclusions regarding the improvement from Design 1 to Design 6 are not considered to be mesh-dependent.
+
+Table 6 Mesh sensitivity analysis for shrinkage porosity prediction.
+
+Mesh level	Relative mesh density	Main refinement regions	Predicted shrinkage porosity trend	Final solidification location	Assessment	
+Coarse mesh	Low	General casting and mold	Captures general trend but with limited local detail	Hub/feeder region	Used for preliminary screening	
+Medium mesh	Moderate	Hub, blade–hub junctions, gates, and riser neck	Stable porosity prediction with improved local resolution	Same as fine mesh	Selected for final simulations	
+Fine mesh	High	Further refinement of critical thermal-gradient regions	Only minor change compared with medium mesh	Same as medium mesh	Used to confirm mesh independence	
+
+Table 7 summarizes the complete numerical setup used in the ProCAST simulations for comparing the six impeller casting designs. The computational domain included the full casting system, consisting of the impeller, sprue, runner, gates, riser/feeder, and surrounding mold. Stainless steel CF8M was assigned as the casting alloy, while silica sand was used as the mold material. The molten alloy was initialized at a pouring temperature of 1650 °C, and the mold was initialized at 25 °C. Mold filling was modeled under gravity conditions, with a prescribed inlet velocity applied at the sprue entrance to achieve an approximate filling time of 20 s. Heat loss from the external mold surfaces was represented by convective air cooling, while thermal interaction between the casting and mold was defined using an interfacial heat-transfer condition. The mesh was refined in critical regions such as the hub, blade–hub junctions, gates, riser neck, and feeder region to improve the accuracy of thermal and defect predictions. The main simulation outputs included temperature distribution, cooling rate, solidification sequence, shrinkage porosity percentage, void distribution, and hot-spot locations, which were used to compare Designs 1–6 under consistent numerical conditions.
+
+Table 7 Summary of model setup, initial conditions, boundary conditions, and numerical settings used in the ProCAST simulations.
+
+Category	Parameter	Description/value used	
+Geometry	Computational domain	Impeller, sprue, runner, gates, riser/feeder, and surrounding mold	
+Casting alloy	Material	Stainless steel CF8M	
+Mold material	Material	Silica sand	
+Initial condition	Alloy temperature	Pouring temperature, 1650 °C	
+Initial condition	Mold temperature	25 °C	
+Filling condition	Filling mode	Gravity filling	
+Inlet boundary condition	Sprue inlet	Prescribed inlet velocity applied at the pouring inlet	
+Filling time	Total filling duration	Approximately 20 s	
+Thermal boundary condition	External mold surfaces	Convective air cooling	
+Thermal contact	Casting–mold interface	Interfacial heat-transfer condition	
+Mesh strategy	Refined regions	Hub, blade–hub junctions, gates, riser neck, and feeder region	
+Solver outputs	Thermal results	Temperature field, cooling rate, and solidification sequence	
+Defect outputs	Porosity prediction	Shrinkage porosity percentage, void distribution, and hot-spot locations	
+Design comparison	Evaluated cases	Six gating and feeding configurations, Design 1 to Design 6	
+
+This systematic setup was applied consistently to all six investigated designs. Therefore, the differences observed in temperature distribution, cooling behavior, solidification sequence, and shrinkage porosity formation can be attributed mainly to the changes in gating and feeding design rather than inconsistencies in the numerical setup.
+
+To improve the clarity of the numerical model setup, a schematic representation of the applied boundary conditions is provided in Fig. 1. The figure identifies the prescribed inlet velocity applied at the sprue entrance, the gravity-driven filling direction, the initial molten alloy temperature, the initial mold temperature, the casting–mold interfacial heat-transfer condition, and the convective air-cooling boundary condition applied to the external mold surfaces. This schematic was added to clarify how the computational domain was initialized and constrained during the filling, heat-transfer, and solidification stages of the ProCAST simulation.
+
+Figure 1 illustrates the boundary-condition configuration employed in the ProCAST numerical simulation of the stainless-steel impeller casting. The computational domain encompasses the impeller casting chamber, sprue, runner, gates, riser/feeder, and the adjacent silica sand mould. The molten stainless steel CF8M was introduced via the sprue inlet, where a specified inlet velocity was utilized to regulate the mold-filling process. The filling process was simulated under gravity-driven conditions, as evidenced by the downward gravitational vector. The molten alloy’s initial temperature was established at 1650 °C, but the first mould temperature was designated as 25 °C. Heat transfer between the molten metal and the mould was depicted through a casting-mold interfacial heat-transfer condition, illustrated by the emphasized interface surrounding the casting cavity. Heat dissipation from the external mould surfaces was simulated via convective air-cooling boundary conditions, depicted by outward arrows around the mould. This configuration was uniformly implemented across all examined designs to guarantee that variations in filling behaviour, cooling rate, solidification sequence, and shrinkage porosity predictions were primarily ascribed to alterations in the gating and feeding systems, rather than modifications in numerical boundary conditions.
+
+Fig. 1 Schematic representation of the boundary-condition setup used in the ProCAST numerical simulation, showing the prescribed inlet velocity at the sprue entrance, gravity filling direction, initial alloy and mold temperatures, casting–mold interfacial heat-transfer condition, and external convective air-cooling boundary applied to the mold surfaces.
+
+Governing equations
+
+The numerical model is governed by coupled conservation equations describing heat transfer, fluid flow, solidification, and thermo-mechanical behavior. Heat transfer within the casting and mold is governed by Fourier’s law of heat conduction Eq. (1):1 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\rho\:{c}_{p}\frac{\partial\:T}{\partial\:t}=\nabla\:\cdot\:(k\nabla\:T)+Q$$\end{document}
+
+where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\rho\:$$\end{document}is density, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{c}_{p}$$\end{document}is specific heat capacity, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:T$$\end{document}is temperature, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:k$$\end{document}is thermal conductivity, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:Q$$\end{document}represents latent heat release during solidification.
+
+Molten metal flow during mold filling is described by the incompressible Navier–Stokes equations, ensuring conservation of mass and momentum. These equations account for gravity, pressure gradients, and viscous effects, enabling prediction of flow velocity, turbulence, and free-surface evolution.
+
+Solidification is evaluated through phase-fraction-based models coupled with thermal analysis, allowing identification of hot spots and feeding-limited regions. Thermal stresses are computed using thermo-elastic formulations, where total strain is decomposed into elastic and thermal components arising from temperature gradients and constrained shrinkage during cooling.
+
+Molten metal flow during filling
+
+During mold filling, the molten stainless steel was assumed to behave as an incompressible Newtonian fluid. The conservation of mass is expressed as:2 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\nabla\:\:\cdot\:\mathrm{u}\hspace{0.17em}=\hspace{0.17em}0$$\end{document}
+
+where u is the molten metal velocity vector.
+
+The momentum conservation equation is given by the incompressible Navier–Stokes equation:3 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\rho(\partial\:\mathrm{u}/\partial\:\mathrm{t}\hspace{0.17em}+\hspace{0.17em}\mathrm{u}\:\cdot\:\nabla\:\mathrm{u})\:=\:-\nabla\:\mathrm{p}\hspace{0.17em}+\mu\hspace{0.17em}\nabla^2\mathrm{u}\hspace{0.17em}+\hspace{0.17em}\rho\mathrm{g}$$\end{document}
+
+where p is the pressure, µ is the dynamic viscosity, and g is the gravitational acceleration vector.
+
+These equations describe the filling behavior of molten metal inside the mold cavity and allow prediction of flow velocity, flow convergence, turbulence-prone regions, and possible gas or inclusion entrapment zones15.
+
+Solidification and latent heat treatment
+
+Solidification was modeled using a temperature-dependent solid fraction approach. During the liquid-to-solid transformation, latent heat release was included using the enthalpy formulation. The total enthalpy can be expressed as:4 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\mathrm{H}\left(\mathrm{T}\right)\:=\:\int\:\:\rho\mathrm{C}\mathrm{p}\left(\mathrm{T}\right)\mathrm{d}\mathrm{T}\hspace{0.17em}+\hspace{0.17em}\rho\mathrm{L}\mathrm{f}_\mathrm{s}\:\:$$\end{document}
+
+where H(T) is the temperature-dependent enthalpy, L is the latent heat of fusion, and fs is the local solid fraction.
+
+The solid fraction varies between zero and one, as follows:
+
+fs = 0 for fully liquid metal,
+
+0 < fs < 1 for the mushy zone,
+
+fs = 1 for fully solid metal.
+
+Tracking the solid fraction allows identification of the liquid region, mushy zone, final solidifying zones, and isolated liquid pockets. These regions are important because they control feeding efficiency and shrinkage porosity formation.
+
+Shrinkage porosity prediction
+
+Shrinkage porosity formation is mainly associated with insufficient feeding during solidification. Regions that solidify last, have low temperature gradients, and experience poor feeding are more likely to develop shrinkage defects. In this study, shrinkage porosity prediction was interpreted using the local solidification behavior and a Niyama-type criterion:5 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\mathrm{N}\mathrm{y}\hspace{0.17em}=\hspace{0.17em}\mathrm{G}\:/\:\surd\mathrm{R}$$\end{document}
+
+where Ny is the Niyama criterion value, G is the local temperature gradient, and R is the local cooling rate.
+
+Lower values of the Niyama criterion indicate a higher tendency for shrinkage porosity because they represent weak directional solidification and insufficient feeding. Therefore, the predicted shrinkage porosity distributions were used to compare the six gating and feeding designs and to determine whether the final solidifying regions remained inside the impeller body or were shifted toward the riser/feeder.
+
+Main physical assumptions
+
+The following physical assumptions were adopted in the simulations:
+
+The molten stainless steel was treated as an incompressible Newtonian fluid during mold filling.
+
+Mold filling was assumed to occur under gravity-driven conditions.
+
+Heat transfer inside the casting and mold occurred mainly by conduction.
+
+Heat loss from the external mold surfaces was modeled using convective air-cooling boundary conditions.
+
+Thermophysical properties, including thermal conductivity, viscosity, and specific heat, were considered temperature-dependent where available.
+
+Solidification was modeled using a phase-fraction approach with latent heat release included through the enthalpy formulation.
+
+Shrinkage porosity was evaluated based on solidification sequence, temperature gradient, cooling rate, and feeding availability.
+
+The mold was assumed to be mechanically rigid compared with the casting during the thermal analysis.
+
+This formulation provides the mathematical and physical basis for the ProCAST simulations and supports the comparative evaluation of the six gating and feeding configurations in terms of filling stability, directional solidification, cooling behavior, and shrinkage porosity tendency.
+
+Optimization strategy from design 1 to design 6
+
+This study utilizes a sequential, simulation-guided design change optimization technique. Design 1 functioned as a conservative benchmark, guaranteeing flawless casting with enlarged gating and risers. Designs 2 and 3 concentrated on minimizing riser volume and optimizing gating geometry while preserving satisfactory feeding performance.
+
+Designs 4 implemented larger riser diameters and modifications to pouring temperature to improve directional solidification. Design 5 had a tapered sprue to enhance flow stability and minimize defects caused by turbulence, whereas In Designs 6, the central aperture was eliminated from the casting geometry, and the riser volume was further improved.
+
+Throughout the design rounds, significant geometric alterations encompassed a systematic diminishment and resizing of risers, the incorporation of sprue tapering to enhance flow stability, adjustments to gating pathways to mitigate turbulence, and the simplification of the impeller geometry through the elimination of the center aperture. Every alteration was driven by simulation results indicating temperature gradients, cooling rates, and defect localization, guaranteeing that adjustments specifically targeted recognized problem processes instead of depending on empirical trial-and-error methods.
+
+The Table 8 delineates the incremental advancement of the impeller casting design from Design 1 to Design 6, emphasizing the impact of systematic alterations in the runner–riser configuration, mold orientation, and venting strategy on filling dynamics, defect occurrence, and casting yield.
+
+Design 1 denotes the basic configuration featuring a substantial riser (about 133 mm) and horizontal mold orientation. While shrinkage porosity was effectively eradicated with adequate feeding, the large riser led to a diminished casting yield (about 41.5%). Furthermore, the horizontal filling condition resulted in significant flow convergence and pronounced velocity oscillations, heightening the probability of gas and inclusion defects.
+
+In Design 2, the riser diameter was diminished to around 66 mm, and the gate arrangement was refined. This alteration directed solidification while markedly enhancing material efficiency, raising the yield to around 65.1%. Nevertheless, the horizontal orientation of the mold resulted in ongoing moderate turbulence and flow convergence, so maintaining a residual risk of gas entrapment.
+
+Designs 3, 4, and 5 incorporate incremental mold tilting of 5°, 10°, and 15°, respectively, while preserving the optimum feeding system from Design 2. As the tilt angle increases, the filling behavior stabilizes, and velocity fluctuations diminish. As a result, gas and inclusion faults diminish from moderate to minimal levels. However, the lack of specialized ventilation hinders the total removal of trapped gases, even at elevated tilt angles.
+
+Design 6 integrates the enhanced runner–riser system with a 20° mold inclination and the incorporation of ventilators. This arrangement yields stable, near-laminar filling with minimal flow convergence and nearly uniform velocity profiles. Consequently, shrinkage porosity, gas entrapment, and inclusion flaws are entirely eradicated, while achieving a casting yield of around 65%. Consequently, Design 6 is recognized as the superior configuration, attaining the optimal equilibrium between casting quality and material efficiency.
+
+To enable a clear comparison among the six examined casting configurations, schematic representations of Designs 1–6 have been shown in Fig. 2. The image succinctly illustrates the incremental alterations implemented in each instance, encompassing variations in riser diameter, gate configuration, runner design, mould tilt angle, incorporation of ventilators, and geometric simplification of the impeller. This graphical representation enhances Table 8 and elucidates the design progression from the conservative baseline setup to the final optimized casting method.
+
+Table 8 Comparison of runner–riser configuration, mold tilting angle, filling behavior, defect tendency, and casting yield for impeller casting designs (Design 1–Design 6).
+
+Parameter	Design 1	Design 2	Design 3	Design 4	Design 5	Design 6	
+Runner–riser concept	Conventional	Optimized	Optimized	Optimized	Optimized	Optimized	
+Riser diameter (mm)	≈ 133	≈ 66	≈ 66	≈ 66	≈ 66	≈ 66	
+Gate configuration	Standard size & location	Enlarged & elevated gates	Same as D2	Same as D2	Same as D2	Same as D2	
+Mold tilt angle (°)	0	0	5	10	15	20	
+Ventilators	None	None	None	None	None	Added	
+Filling behavior	Highly turbulent	Moderately turbulent	Improved stability	More uniform flow	Near laminar	Stable, near laminar	
+Flow convergence	Severe	Moderate	Reduced	Minor	Very minor	Eliminated	
+Velocity variation	High	Moderate	Reduced	Low	Very low	Minimal	
+Solidification pattern	Directional but inefficient	Directional	Directional	Directional	Directional	Fully directional	
+Shrinkage porosity	Eliminated	Eliminated	Eliminated	Eliminated	Eliminated	Eliminated	
+Gas & inclusion defects	High tendency	Moderate	Reduced	Low	Very low	Not observed	
+Casting yield (%)	≈ 41.5	≈ 65.1	≈ 64–65	≈ 64–65	≈ 64–65	≈ 65	
+Overall assessment	Safe feeding, poor yield	High yield, gas risk	Partial improvement	Better stability	Near optimal	Optimal design	
+
+Fig. 2 Schematic comparison of the six investigated gating and feeding system configurations for stainless-steel impeller casting.
+
+Defect evaluation criteria
+
+Several quantitative indicators that were taken from ProCAST simulations were used to evaluate defects. The estimated volume fraction of shrinkage porosity, reported as a percentage, was used to evaluate shrinkage flaws. Using maps of temperature and solidification time, hot spots were found, emphasizing areas of delayed solidification. Directional solidification’s efficacy was assessed by analyzing cooling rate distributions.
+
+To differentiate between gas-related voids and shrinkage-related porosity, void occurrence and spatial distribution were investigated. When evaluating the quality of the casting, the position of flaws in relation to the impeller’s functional areas such as the hub and blade junctions were thought to be crucial. The selection of the final optimum configuration was guided by the objective comparison of all design iterations made possible by the combined application of these criteria. Figure 3 illustrates the sequential methodology integrating CAD modeling, finite-element simulation, defect evaluation, and iterative design refinement to achieve a defect-free casting.
+
+Fig. 3 Simulation–optimization workflow for impeller casting design, showing CAD preparation, mesh generation, initial design simulation, defect evaluation, iterative design modification, comparison of Designs, and selection of the optimized defect-minimized casting configuration.
+
+Results and discussions
+
+Shrinkage porosity evolution with gating and feeding design optimization
+
+The shrinkage porosity distributions illustrated in Fig. 4(a–f) demonstrate a distinct advancement in defect reduction as the gating and feeding design is refined. Design 1 (a) exhibits significant and widespread shrinkage porosity in the hub and blade–hub connections, signifying inadequate feeding efficiency and a lack of directed solidification. The riser and gate layout in this design does not maintain an optimal thermal gradient, leading to several isolated hot spots and extensive volumetric shrinkage. A comparable phenomenon is observed in Design 2 (b), where shrinkage porosity is extensively dispersed, but somewhat more concentrated in the hub region. This indicates very slight enhancement in feeding efficiency, with solidification still taking place unevenly throughout the casting16.
+
+A significant decrease in shrinkage porosity is observed in Design 3 (c), where flaws are more localized and predominantly restricted to the hub region. This signifies the partial implementation of directed solidification; nonetheless, the existence of isolated porosity regions implies that the feeding pathways are obstructed prior to the complete solidification of thicker parts. Design 4 (d) demonstrates enhanced performance, exhibiting shrinking porosity that creates an elongated area oriented along the feeding direction. This behavior indicates improved heat regulation and riser efficiency; however, the ongoing presence of porosity suggests that the feeder volume or solidification duration is inadequate to entirely offset shrinkage in the ultimate hot spot.
+
+In Design 5 (e), shrinkage porosity is markedly reduced and confined to a limited area near the feeder, signifying nearly perfect feeding conditions and efficient directed solidification across most of the impeller. Only negligible residual porosity persists, presumably resulting from a tiny discrepancy between the riser modulus and the final solidifying zone. The optimal performance is attained in Design 6 (f), wherein shrinkage porosity is diminished to minimal, isolated areas predominantly situated inside the feeder zone. This verifies the effective implementation of directional solidification from the impeller body to the riser, guaranteeing sufficient feeding during the concluding phases of solidification and yielding a robust casting with minimum internal flaws2.
+
+The identified shrinkage porosity patterns are directly correlated with the geometric and feeding attributes of each design. In Design 1, the traditional gating configuration and horizontal mould orientation yielded inadequate directional feeding towards the hub and blade-hub connections, leading to localized hot spots and extensive shrinkage porosity throughout the impeller body. Despite Design 2 using a diminished riser and an enhanced gate configuration, the horizontal filling situation continued to permit localized heat stagnation and inadequate feeding in thicker parts, resulting in residual porosity in the hub region. In Design 3, the implementation of a 5° mould tilt enhanced the filling trajectory and diminished flow convergence, hence localizing shrinkage porosity to fewer crucial areas. Elevating the mould tilt to 10° in Design 4 enhanced the temperature gradient between the impeller and feeder, facilitating more efficient directed solidification and relocating the final solidifying zone nearer to the riser. In Design 5, the 15° inclination resulted in enhanced filling stability and improved feeding continuity, hence confining shrinkage porosity to a localized area adjacent to the feeder. Ultimately, Design 6 integrated the optimized runner–riser system, a 20° mould tilt, and ventilators positioned at the higher gas-escape zones of the mould cavity. This arrangement offered the optimal feeding channel and heat gradient, facilitating the movement of the final solidifying region toward the riser/feeder and reducing shrinkage porosity within the functional impeller body. The gradual decrease in shrinkage porosity from Design 1 to Design 6 is ascribed to the synergistic effects of optimized gate configuration, increased feeding efficiency, regulated mould tilt, and improved expulsion of entrapped gases. To support the visual comparison of shrinkage porosity iso-surfaces, the predicted shrinkage porosity values were also quantified for each design, as summarized in Table 9.
+
+Table 9 Quantitative comparison of predicted shrinkage porosity for the six investigated designs.
+
+Design	Main design feature	Main porosity location	Defect tendency	
+Design 1	Baseline gating, large riser, 0° tilt	Hub/impeller body	High	
+Design 2	Reduced riser and optimized gates, 0° tilt	Hub region/feeder neck	Moderate to high	
+Design 3	Optimized gates with 5° mold tilt	Localized near hub/riser connection	Moderate	
+Design 4	Optimized gates with 10° mold tilt	Near feeder region	Low to moderate	
+Design 5	Optimized gates with 15° mold tilt	Mainly close to riser/feeder	Low	
+Design 6	20° mold tilt with ventilators	Mostly shifted to feeder/riser, minimal inside impeller	Lowest	
+
+Fig. 4 Predicted shrinkage porosity distributions for six different impeller gating and feeding designs obtained from ProCAST simulations: (a) Design 1, (b) Design 2, (c) Design 3, (d) Design 4, (e) Design 5, and (f) Design 6. The colored iso-surfaces represent regions with a high probability of shrinkage porosity, highlighting the influence of feeding efficiency and directional solidification on defect formation.
+
+Effect of gating and feeding design on cooling rate distribution
+
+The cooling rate distributions depicted in Fig. 5(a–f) offer critical insights into the solidification behavior of the impeller across the six examined designs and elucidate the observed trends in shrinking porosity. In Design 1 (a), the cooling rate exhibits considerable non-uniformity, characterized by elevated cooling rates in the outer thin portions and markedly reduced cooling rates in the hub and blade-hub junctions. The significant heat gradient fosters the development of distinct hot spots and prolongs solidification in the center areas, heightening the vulnerability to shrinkage flaws. The same pattern is evident in Design 2 (b), where the overall cooling rate distribution is inconsistent; despite some redistribution of thermal gradients, the hub region solidifies last, signifying inadequate regulation of heat extraction and feeding efficiency.
+
+In Design 3 (c), the cooling rate distribution is more uniform in comparison to Designs 1 and 2. The center hub region continues to display diminished cooling rates compared to adjacent places, however the gradient between the hub and peripheral parts has lessened. This shows a partial enhancement in heat dissipation and solidification sequencing; nonetheless, the presence of a low cooling rate zone at the center signifies that final solidification transpires within the casting rather than the feeder. Design 4 (d) illustrates a more pronounced shift in solidification control, with elevated cooling rates prevalent over most of the impeller body, whilst the minimal cooling rates are localized around the feeder region. This behavior indicates a more advantageous thermal gradient that promotes directional solidification towards the feeder; however, the extent of the low cooling rate zone implies that feeding is not yet entirely optimized.
+
+Design 5 (e) demonstrates enhanced uniformity in the cooling rate distribution over the impeller, with the lowest cooling rates localized to a reduced area near the feeder. This suggests that most of the impeller solidifies swiftly and uniformly, hence diminishing the probability of isolated hot patches inside the operational areas. Design 6 (f) attains the most optimum condition, demonstrating a smooth and well-regulated cooling rate gradient from the impeller body to the feeder. The primary casting areas exhibit moderate to high cooling rates, whilst the lowest cooling rates are confined to the feeder itself. This verifies the implementation of efficient directed solidification, guaranteeing that the feeder remains in a molten state for an extended duration and can sufficiently address volumetric shrinkage, thus reducing the likelihood of internal flaws17.
+
+Fig. 5 Cooling rate distributions of the impeller predicted by ProCAST for different gating and feeding configurations: (a) Design 1, (b) Design 2, (c) Design 3, (d) Design 4, (e) Design 5, and (f) Design 6. The color contours represent the local cooling rate, illustrating the evolution of thermal gradients and solidification behavior as the design is optimized.
+
+Effect of gating and feeding design on temperature distribution and hot-spot formation
+
+The temperature distribution results depicted in Fig. 6(a–f) demonstrate the progression of thermal fields throughout solidification for the six examined designs, elucidating the enhancements in feeding and defect management. In Design 1 (a), the temperature distribution is markedly heterogeneous, with maximum temperatures of ≈ 1450 °C concentrated at the hub and blade-hub junctions, whilst the peripheral portions cool to around 900–1000 °C. The significant temperature disparity signifies intense thermal gradients and the emergence of several hot spots inside the casting, which are susceptible to delayed solidification and shrinkage porosity. A comparable phenomenon is noted in Design 2 (b), wherein the center hub region sustains excessive temperatures of approximately 1400–1430 °C, but the adjacent areas fall below 1000 °C, indicating that the design alterations are inadequate to relocate the last solidifying zones towards the feeder18.
+
+In Design 3 (c), the temperature distribution is more uniform, with the core hot spot temperature decreased to roughly 1350–1380 °C, while most of the impeller body stays within the range of 1000–1150 °C. The decrease in peak temperature and the more gradual gradient suggest a partial enhancement in heat extraction; still, the maximum temperatures remain within the casting instead of the feeder, indicating inadequate directed solidification. Design 4 (d) demonstrates a notable enhancement, with peak temperatures of approximately 1400–1450 °C relocated nearer to the feeder region, while the impeller body exhibits a more uniform cooling to around 1000–1100 °C. This thermal pattern indicates a more advantageous solidification sequence, albeit a considerable hot patch remains along the feeder–casting contact.
+
+In Design 5 (e), the temperature distribution exhibits a more distinct delineation between the casting and the feeder. The impeller body maintains temperatures of roughly 950–1050 °C, however the feeder sustains higher temperatures between 1350 and 1450 °C, suggesting that the feeder remains molten considerably longer than the casting. This condition significantly facilitates directed solidification and diminishes the probability of interior hot spots. Design 6 (f) exhibits the most optimal thermal behavior, with peak temperatures over 1400 °C predominantly contained within the feeder, while the impeller body maintains a uniform cooling to around 900–1000 °C. The uniform thermal gradient from the casting to the feeder verifies efficient heat flow management, ensuring that the feeder solidifies last, which allows for sufficient compensation of volumetric shrinkage and reduces the likelihood of shrinkage-induced flaws19.
+
+Fig. 6 Temperature distribution during solidification of the impeller predicted by ProCAST for different gating and feeding designs: (a) Design 1, (b) Design 2, (c) Design 3, (d) Design 4, (e) Design 5, and (f) Design 6. The color contours represent the local temperature (°C), highlighting the location of hot spots and the evolution of thermal gradients as the design is optimized.
+
+Defect prediction analysis based on filling and solidification simulations
+
+Defection prediction analysis was conducted using ProCAST to assess the probability of shrinkage porosity, gas entrapment, and non-metallic inclusions in the six examined designs. The investigation focused on the integrated evaluation of filling behavior, temperature distribution, cooling rate, and solidification features, specifically highlighting the Niyama criterion and flow stability indicators20.
+
+The defect prediction results for Design 1 demonstrated a minimal likelihood of shrinking porosity owing to the inclusion of a substantial riser, which facilitated adequate feeding during solidification. The filling simulation demonstrated significant turbulence and intense flow convergence adjacent to the impeller cover and in the thin-walled areas. These circumstances are recognized to facilitate air entrainment and oxide formation, resulting in significant projected propensity for gas and inclusion defects, notwithstanding the lack of shrinkage-related concerns.
+
+In Design 2, the optimized riser dimensions and gate arrangement preserved directed solidification and substantially diminished the possibility of shrinkage porosity, as evidenced by enhanced Niyama criteria values in crucial areas. However, due to the mold’s horizontal orientation, flow convergence zones continued to exist during the filling process. The anticipated probability of gas-related faults was diminished in comparison to Design 1 yet not entirely eradicated.
+
+The use of mold tilting in Designs 3, 4, and 5 indicated a distinct trend of enhanced filling stability in the defect prediction study. Raising the tilt angle from 5° to 15° systematically diminished velocity gradients and flow impingement at geometric discontinuities. This resulted in a significant reduction in anticipated gas entrapment and inclusion development. Shrinkage porosity was nonexistent in all inclined configurations owing to the maintained optimum feeding mechanism. Nevertheless, localized areas with diminished venting performance nevertheless demonstrated slight gas retention, especially within enclosed impeller chambers21.
+
+Design 6 demonstrated the most advantageous fault prediction outcomes. The integration of an optimized runner–riser system, a 20° mold inclination, and supplementary ventilators produced smooth, nearly laminar filling with negligible flow separation. The temperature gradients and cooling rates were effectively balanced, guaranteeing complete directional solidification towards the riser. Thus, the Niyama criterion values consistently above the critical threshold over the impeller volume, signifying minimal risk of shrinking porosity. The consistent filling pattern and efficient gas evacuation routes precluded the anticipated emergence of gas and inclusion faults.
+
+Limitations and future work
+
+The current study provides a systematic numerical comparison of six gating and feeding configurations for stainless-steel impeller casting; however, direct experimental validation has not been performed at this point of the research. Consequently, the results have to be regarded as simulation-derived forecasts that highlight comparative design trends rather than as well proven experimental findings.
+
+The lack of experimental validation constitutes a drawback, as the prediction of shrinkage porosity may be influenced by errors in material parameters, mould conditions, heat transfer coefficients, pouring techniques, mesh resolution, and boundary conditions. To overcome this restriction, subsequent efforts will entail fabricating the optimized casting design and juxtaposing the predicted defect predictions with empirical data.
+
+The validation plan will incorporate non-destructive testing techniques, including X-ray radiography and ultrasonic examination, to identify internal shrinkage porosity and gas-related problems. Furthermore, chosen castings will be dissected at pivotal sites, specifically the hub, blade-hub junctions, feeder neck, and final solidification areas, to juxtapose the anticipated porosity locations with actual internal defects. Metallographic analysis and dimensional assessment will be conducted to determine casting integrity and geometric precision.
+
+This forthcoming validation will furnish quantitative evidence regarding the predictive efficacy of the ProCAST model and will ascertain whether the optimized Design 6 can consistently mitigate shrinkage porosity and direct the final solidifying regions towards the feeder/venting system under practical casting conditions.
+
+Conclusions
+
+Six impeller casting designs were meticulously evaluated in this study by incrementally modifying the mould tilting technique and runner–riser configuration to optimize casting yield while minimizing shrinkage porosity, gas entrapment, and inclusion defects.
+
+Design 1 (baseline arrangement) included a substantial riser (about 133 mm in diameter) with a horizontal mould orientation. Despite the successful prevention of shrinkage porosity through adequate feeding, the substantial riser volume resulted in a low casting yield of around 41.5%, and the filling behavior demonstrated significant turbulence, which facilitated gas and inclusion defects.
+
+Design 2 optimized the feeding system by reducing the riser diameter to around 66 mm and altering the gate locations and dimensions. This configuration had the highest yield among non-tilted examples (~ 65.1%), representing an increase of approximately 23.6% points over Design 1, while ensuring defect-free solidification and significantly enhancing material efficiency. The potential for gas entrapment persisted, however, owing to flow convergence at the impeller cover.
+
+The optimized runner-riser system from Design 2 was preserved in Designs 3, 4, and 5, which incorporated mould tilting at angles of 5°, 10°, and 15°, respectively. Progressive tilting mitigated velocity variations and reduced flow instability relative to the horizontal configuration. Nonetheless, isolated turbulence and residual gas pockets were seen at tilt angles 15°, particularly near regions of sudden cross-sectional variation. Shrinkage porosity was well managed; nevertheless, gas-related defects were not entirely eliminated.
+
+Design 6, which integrates the modified runner–riser system, a 20° mould inclination, and additional ventilators, yielded the most optimal performance. The molten metal exhibited consistent, laminar filling characterized by nearly uniform velocity profiles and minimal variation in cross-sectional area throughout the filling height. This design effectively eliminated shrinkage porosity, gas entrapment, and non-metallic impurities while maintaining a yield comparable to Design 2 (about 65%). In comparison to Design 1, Design 6 exhibited superior internal soundness and a yield enhancement above 50%.
+
+The numerical simulations demonstrated that the gating and feeding design substantially influenced the temperature distribution, cooling behavior, and movement of the solidification front in the stainless-steel impeller casting. The initial designs concentrated the final solidification zones within the impeller structure, particularly around the hub and blade-hub connections, hence increasing the likelihood of isolated liquid pockets and shrinkage porosity.
+
+By methodically modifying the riser, sprue, gate layout, mould tilt angle, and ventilation system, the temperature gradient was enhanced, leading to a steady shift of the final solidification zone towards the riser/feeder region. The optimized design permitted directed solidification, improved feeding efficiency, reduced hot-spot accumulation within the operational impeller body, and minimized expected shrinkage porosity.
+
+This study demonstrates that virtual comparisons of different casting configurations can effectively replace iterative trial-and-error casting experiments, acting as a predictive tool for identifying defect-prone areas, guiding design modifications, and improving the casting process for stainless-steel pump impellers via numerical simulation.
+
+Author contributions
+
+Conceptualization, Mahmoud A. Essam, Noha M. Abdeltawab, and Ahmed Y. Shash; Methodology, Mahmoud A. Essam, Noha M. Abdeltawab, and Mostafa M. El-Sayed; Validation, Mahmoud A. Essam, Ahmed Y. Shash, and Noha M. Abdeltawab; Formal analysis, Mahmoud A. Essam and Mostafa M. El-Sayed; Investigation, Mahmoud A. Essam; Resources, Ahmed Y. Shash and Mostafa M. El-Sayed; Writing original draft, Mahmoud A. Essam; Writing review & editing, Noha M. Abdeltawab, Ahmed Y. Shash, and Mostafa M. El-Sayed; Visualization, Mahmoud A. Essam; Supervision, Ahmed Y. Shash and Noha M. Abdeltawab. All authors have read and agreed to the published version of the manuscript.
+
+Funding
+
+Open access funding provided by The Science, Technology & Innovation Funding Authority (STDF) in cooperation with The Egyptian Knowledge Bank (EKB).
+
+Data availability
+
+The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.
+
+Declarations
+
+Competing interests
+
+The authors declare no competing interests.
+
+Publisher’s note
+
+Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
+
+
+References
+
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diff --git a/corpus/psychology/text/0807e59cb982eed3.txt b/corpus/psychology/text/0807e59cb982eed3.txt
new file mode 100644
index 0000000000000000000000000000000000000000..97b21beccf7f10086d1f0a1590b68aeb7a196ef9
--- /dev/null
+++ b/corpus/psychology/text/0807e59cb982eed3.txt
@@ -0,0 +1,3 @@
+Framing Effects in Choices With Somewhat Risky Options
+
+When a certain option and a risky option are both described as potential gains, people typically choose the certain option; when the same two options are described as potential losses, people typically choose the risky option. This famous preference pattern is the risky-choice framing effect. Despite the seeming rarity of sure things and all-or-none risks in real life, surprisingly little research on this effect has involved options with intermediate levels of risk. In this research, we identified four types of “somewhat risky” options, combined them with each other and with certain and all-or-none options to create 15 risk comparisons in both gains and losses in each of four domains (cancer, drought, investment, and wildfire), and conducted two preregistered experiments in which we varied risk comparisons between or within participants in both student and online samples (N = 2,586 after exclusions). We found significant framing effects in almost all risk comparisons, greatly expanding the range of decisions in which framing is relevant. In addition, we assessed how well 12 versions of risky-choice theories accounted for participants’ choices. Across experiments and samples, versions of prospect theory (PT) and transfer-of-attention-exchange theory (TAX) generally outperformed versions of fuzzy-trace theory (FTT), the priority heuristic, and other accounts. PT’s and TAX’s performance was largely due to the S-shaped value function rather than the theories’ other mechanisms (e.g., PT’s loss aversion, TAX’s weight transfer). FTT’s performance was harmed by its failure to predict framing effects in choices between certain options and somewhat risky options without zero outcomes.
diff --git a/corpus/psychology/text/0c75ce3e7147014d.txt b/corpus/psychology/text/0c75ce3e7147014d.txt
new file mode 100644
index 0000000000000000000000000000000000000000..825db5f5a02139f0090c18dd27621a58b636e2dd
--- /dev/null
+++ b/corpus/psychology/text/0c75ce3e7147014d.txt
@@ -0,0 +1,3 @@
+Can a Brief Informational Intervention Facilitate Culture-Add Hiring? An Experimental Vignette Study
+
+Culture-add, hiring for what a candidate brings beyond what a team already has, has gained traction in practitioner discourse but has remained largely disconnected from organizational theory. We argue that culture-add is best understood as complementary person-group (P-G) fit applied to behavioural attributes, extending a literature that has largely confined complementary fit to knowledge and skills. Realizing culture-add in practice, however, depends on hiring managers actively recognizing complementary value rather than defaulting to similarity. In a vignette experiment (N = 264; 521 hiring decisions), working professionals with hiring experience evaluated pairs of culture-fit and culture-add candidates for two product roles after reading three short hiring-related articles; the intervention group received one article introducing culture-add hiring. Relative to controls, intervention participants showed a significantly smaller culture-fit advantage in hireability ratings and were significantly more likely to hire culture-add candidates (47% instead of 35% of decisions). Effects held across levels of hiring experience. These findings provide initial experimental evidence that complementary P-G fit can be operationalized at the behavioural level, that culture-add is manipulable in hiring evaluations, and that a brief informational intervention can shift both ratings and selection decisions.
diff --git a/corpus/psychology/text/0d76088ac54a5dcb.txt b/corpus/psychology/text/0d76088ac54a5dcb.txt
new file mode 100644
index 0000000000000000000000000000000000000000..221c49b59c503649b4c7c59b52c0f3c63bab8e67
--- /dev/null
+++ b/corpus/psychology/text/0d76088ac54a5dcb.txt
@@ -0,0 +1,371 @@
+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Foods
+Journal ID: Foods
+NLM Journal ID: 101670569
+Journal ID: foods
+
+Foods
+
+EISSN: 2304-8158
+Publisher: Multidisciplinary Digital Publishing Institute (MDPI)
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC13206134
+PMID: 42195911
+DOI: 10.3390/foods15101707
+Article ID: foods-15-01707
+Article version: 1
+Subjects: Article
+
+From Waste to Taste: Dynamic Interaction of Grape Stems with Wine Off-Odors
+
+Luzzini Giovanni Conceptualization Methodology Data curation Visualization Writing – original draft 1 *
+https://orcid.org/0000-0001-5861-5874 Samaniego Solis Jessica Anahi Formal analysis Investigation Writing – review & editing 1
+Bergamo Jacopo Nicola Data curation Software 2
+Prévide Bernardo Naíssa Conceptualization Investigation Formal analysis Writing – review & editing Visualization 3
+https://orcid.org/0000-0002-4778-2359 Slaghenaufi Davide Conceptualization Writing – review & editing Project administration Supervision Resources 1 *
+Sun Xiangyu Academic Editor
+1 Department of Biotechnology, University of Verona, Villa Lebrecht, Via Della Pieve 70, 37029 San Pietro in Cariano, Italy
+2 Department of Business Management and Marketing, University of Vigo, Calle Benito Corbal 45, 36001 Pontevedra, Spain
+3 Grape and Wine Technological Centre, Experimental Farm of Caldas, Agricultural Research Company of Minas Gerais, Avenida Santa Cruz, 500, Caldas 37780-000, Brazil
+* Correspondence: giovanni.luzzini@univr.it (G.L.); davide.slaghenaufi@univr.it (D.S.); Tel.: +39-333-930-4056 (G.L.); +39-045-8425615 (D.S.)
+Electronic publication date: 2026 May 13
+Publication date: 2026 May
+Volume: 15
+Issue: 10
+Electronic Location ID: 1707
+Received 2026 Apr 9; Revised 2026 May 6; Accepted 2026 May 11
+Copyright: © 2026 by the authors.
+Copyright year: 2026
+License: Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Keywords: stems, withering, C6 alcohols, pyrazine, methanethiol, circular economy, tainted odors
+
+Funding: This research received no external funding.
+
+Ÿ==============================Ÿ
+Within the circular economy framework, grape stems, a major winemaking by-product, are increasingly recognized for their potential to modulate wine composition despite some criticalities. This study aimed to investigate fresh and withered stems as both sources of compounds and adsorbents of off-odors. Corvina and Cabernet Sauvignon stems were tested under three conditions: fresh, and 20% and 40% weight loss. Over 14 days of maceration in red wine, the release kinetics of key enological parameters, including pH, ethanol, total phenolics, methoxypyrazines, and C6 alcohols, were investigated. Concurrently, the adsorption capacity for methanethiol was evaluated. Results indicated that stems significantly influence wine composition by increasing pH and phenolic content while reducing ethanol, with variability associated with the withering treatment. Withered stems showed reduced release of herbaceous pyrazines compared to fresh stems. Stems demonstrated a high affinity for methanethiol, resulting in a significant decrease greater than that observed with commercial enological tannins, known for their ability to reduce reductive mercaptans. This decrease was primarily driven by direct adsorption onto the solid stem matrix, with a secondary contribution from leached soluble compounds. This work provides new insights into the chemical interplay between grape stems and wine, highlighting their valorization potential as a sustainable tool to manage wine composition and mitigate sensory defects.
+
+1. Introduction
+
+In traditional winemaking, grape stems are typically removed before fermentation to prevent the extraction of compounds that can negatively affect wine quality [1,2,3]. Despite this long-standing practice, research has increasingly focused on the controlled use of stems, suggesting they could serve as a tool to improve wine complexity and stability [3,4]. While their structural composition is primarily based on water, cellulose, hemicellulose, lignin, and proteins, their enological relevance arises from the high content of polymeric phenols and flavanol monomers they contain [5,6,7,8,9]. The increase in tannin concentration, which heightens astringency, resulting from their interaction and precipitation with salivary proteins, and bitterness, is the principal reason stems have been historically excluded from the winemaking process [10]. However, this characteristic can be advantageous for certain grape varieties that are inherently deficient in tannins and polyphenols. In such cases, the introduction of stems can contribute positively to the wine’s features, increase its antioxidant capacity, enhance its sensory profile, and improve its longevity through color stabilization via slow polymerization reactions with anthocyanins [7,11].
+
+Another significant concern that has discouraged the use of whole clusters is the potential development of herbaceous or vegetal off-odors [12]. This is attributed to the release of specific volatile organic compounds from the stems, most notably C6 alcohols and various pyrazines [4,13]. Methoxypyrazines, particularly IBMP, are characteristic of Cabernet Sauvignon and often impart a distinct green bell pepper aroma. However, at high concentrations, they are considered a sensory defect due to their overwhelming vegetative character (Roujou de Boubée et al., 2000 [14]). C6 alcohols are generally considered unpleasant or defective because of their pungent, ‘cut grass’, and vegetal character, masking the fruity notes of the wine [15].
+
+Beyond their direct impact on phenolic content and aroma, stems could exert complex influences on fermentation kinetics and the final chemical composition of the wine. Comparative analyses of fermented must with and without stems have shown that their presence can accelerate fermentation, resulting in wines with lower residual sugar levels. This phenomenon is hypothesized to be linked to the physical structure of the stems, which may enhance oxygen transfer and thereby stimulate yeast metabolism [16]. Furthermore, stems can act as a thermal buffer, mitigating temperature extremes within the fermenting mass and consequently lowering the risk of stuck or sluggish fermentations [16]. Their inclusion also has measurable effects on fundamental enological parameters, including pH and titratable acidity [17,18], ethanol concentration [7,19], color intensity and stability [7], and overall taste perception [19,20]. More recently, the potential antimicrobial properties of stems have been investigated to reduce or partially replace sulfur dioxide (SO2) additions during pre-fermentative stages [21].
+
+Wang et al., 2025 [22,23,24,25,26,27,28], have performed important research. Concurrently with scientific progress, the food industry has shifted towards sustainability, especially since the 2015 Sustainable Development Goals. The wine sector, known for its large environmental footprint [22], is restructuring to align with circular economy principles, which aim to boost productivity while minimizing waste [23]. This model departs from the linear “take-make-dispose” system, advocating for regeneration and, in broader views, social equity [24,25,26,27]. Central to this are the “3Rs”: Reduce, Reuse, Recycle. In the wine industry, organic by-products such as grape pomace—the solid residue from pressing (skins, pulp, seeds, stems)—are seen as valuable resources [28]. Current pomace uses include biogas, functional flours, cosmetics ingredients, and organic fertilizers [23]. Unlike energy-intensive methods, this study characterizes the properties of stems to find low-impact, circular-economy-aligned uses for them.
+
+Grape withering is a traditional process employed in the production of passito-style wines, most notably in the Valpolicella region of northern Italy, near Verona [29]. This post-harvest dehydration process significantly alters the composition of the grape cluster. As the berries lose water, the stems also dehydrate, leading to increased concentrations of polyphenols and organic acids, along with metabolic transformations in their volatile organic compound profiles [30,31].
+
+While the enological effects of fresh stems have been the subject of extensive research [7,12,21,32,33,34], limited information is available regarding withered stems. Specifically, there is a lack of data concerning the release or interaction kinetics of key chemical parameters (e.g., pH, ethanol, polyphenol content) and major off-odors, such as pyrazines and methanethiol [35]. Preliminary findings from a prior study indicated that withered stems could significantly influence on certain varietal aroma compounds [36].
+
+The aim of this study was to evaluate the capacity of grape stems of different genetic origins (Corvina and Cabernet Sauvignon), subjected to different withering treatments (fresh, 20%, and 40% weight loss), to release or adsorb sensory-active compounds related to wine defects, such as pyrazines and C6 alcohols for herbaceous off-odors, and methanethiol for reductive off-odors.
+
+Unlike previous studies, which have mainly focused on fresh stems, this work introduces significant novelty by comparing the effects of withering on the dual-release/adsorption capacity of stems. The relevance of this study lies in providing winemakers with a sustainable, circular economy-based strategy to mitigate sensory defects (herbaceous and reductive) without chemical interventions, while valorizing a major winemaking by-product.
+
+2. Materials and Methods
+
+2.1. Sample Preparation
+
+2.1.1. Evaluation of Adsorption and Release Kinetics by Grape Stems
+
+For this study, Corvina (CA) and Cabernet Sauvignon (CS) grape stems were employed and subjected to three different treatments. Fresh (FR), withered in a ‘fruttaio’ until a 20% of weight loss was achieved (20), and withered until a 40% of weight loss was achieved (40). The fruttaio is a traditional Valpolicella drying room where grapes are dehydrated prior to their use in crafting Valpolicella PDO wines.
+
+Fifteen grams of fresh stems, or a weight of withered stems equivalent to 15 g of fresh stems, were added to 100 mL of red wine (pH 3.48, total acidity 6.7 g/L, ethanol 10.7%, SO2 25.4 mg/L) supplemented with 60 µg/L of methanethiol (MeSH). Additionally, a control was prepared without any stems added. The samples were prepared in triplicate and analyzed after 1, 3, 7, and 14 days of storage at 20 ± 1 °C. Samples and their humidity are reported in Table 1.
+
+2.1.2. Evaluation of the Adsorption Capacity of Grape Stems
+
+In this study, the capacity of grape stems to absorb volatile compounds was investigated. Specifically, 150 g of fresh Corvina grape stems (stalks) were added to a model solution (6.5 g/L of tartaric acid, 10.5% EtOH, pH 3.5, SO2 25 mg/L). After a 14-day storage period at 20 ± 1 °C, the stems were removed from the initial model wine and transferred into a fresh model wine solution. This procedure allowed for the preparation of three distinct sample types: Stem-infused solution: A solution macerated with grape stems for 14 days (SI). Exhausted stem solution: A fresh model wine solution to which the previously used (spent) stems were added (ES). Stem extract (Stems removed): The liquid fraction obtained after the 14-day maceration was filtered to remove all solid stem residues (SE). Additionally, a control sample consisting solely of the model wine solution was prepared. All experimental groups were supplemented with 60 µg/L of MeSH to monitor its concentration over time. The addition of 60 µg/L of MeSH was chosen based on literature evidence, which indicates that this concentration is a realistic and potentially occurring level in wines affected by pronounced reductive off-odors [37,38].
+
+2.1.3. Evaluation of the MeSH Adsorption Capacity of Commercial Enological Tannins
+
+Three different concentrations (25 mg/L, 250 mg/L, and 500 mg/L) of three different enological tannins (T1, T2, and T3) were added to red wine (pH 3.48, total acidity 6.7 g/L, Ethanol 10.7%, SO2 25.5 mg/L) supplemented with 60 µg/L MeSH. Additionally, a control was prepared without the addition of any enological tannins. The samples were prepared in triplicate and, after 1, 3, 7, and 14 days of storage at 20 ± 1 °C, were analyzed. Sample, their botanical origins and concentrations are reported in Table 2.
+
+2.2. SPME-GC-MS Analysis of Methanethiol
+
+Methanethiol was analyzed by SPME-GC-MS as described by Slaghenaufi et al. (2021) [39]. Retention indices, quantification ions, limit of detection (LOD), limit of quantification (LOQ), and repeatability of the analyzed compounds are reported in Supplementary Table S1. In order to prevent compound volatilization, wine samples were kept at 4 °C for 24 h prior to analysis. Samples were prepared by adding 100 μL of DMS-d6 internal standard (2 mg/L in ethanol) to 10 mL of wine placed in a 20 mL glass vial containing 3 g of NaCl. Samples were then kept at 4 °C until SPME extraction. Prior to SPME extraction, samples were equilibrated for 1 min at 40 °C, then a polydimethylsiloxane-divinylbenzene fiber (PDMS/DVB) (Supelco, Bellafonte, PA, USA) was exposed to the sample headspace for 30 min. Volatile sulfur compounds (VSCs) were desorbed in the injector port at 270 °C for 2 min in splitless mode. GC-MS analyses were performed as reported previously. GC-MS analysis was carried out on an HP 7890A (Agilent Technologies, Santa Clara, CA, USA) gas chromatograph coupled to a 5977B quadrupole mass spectrometer, equipped with a MPS3 autosampler (Gerstel, Müllheim/Ruhr, Germany). Separation was performed using a DB-WAX UI capillary column (30 m × 0.25, 0.25 μm film thickness, (Agilent Technologies, Santa Clara, CA, USA) and helium (6.0 grade) as carrier gas at a constant flow rate of 1.2 mL/min. The GC oven was programmed as follows: started at 35 °C for 5 min, increased to 90 °C at 5 °C/min, and then to 260 °C at 15 °C/min maintained for 2 min. The mass spectrometer was equipped with an electron impact ionization source (EI) (70 eV). The transfer line, the source, and the quadrupole temperature were set to 200 °C, 230 °C, and 150 °C. Mass spectra were acquired in SIM mode. Samples were analyzed in random order. A calibration curve was prepared using seven concentration points and three replicate solutions per point in white wines. 100 µL of DMS-d6 (2 mg/L in ethanol) was added to each calibration solution, which was then submitted to SPME extraction and GC-MS analysis as described for the samples. Calibration curves were obtained using Chemstation software Version C.01.10 (Agilent Technologies, Santa Clara, CA, USA.) by linear regression, plotting the response ratio (analyte peak area divided by internal standard peak area) against concentration ratio (added analyte concentration divided by internal standard concentration).
+
+2.3. SPME-GC-MS Analysis of Pyrazine
+
+For quantification of methoxypyrazines, an SPME extraction followed by GC-MS analysis was used, adapting the procedure described by Belancic & Agosin (2007) [40] and Plank et al. (2019) [41]. An amount of 3 g of NaCl, 2.5 mL of water, and 500 µL of a NaOH 2N solution was added to a glass vial, then 7.5 mL of wine and 250 µg/L of the internal standard 4-methoxy-alpha-toluene-thiol (30 µg/L in ethanol) prior to GC-MS analysis. Samples were equilibrated for 5.50 min at 30 °C. Subsequently, SPME extraction was performed using a 65 µm polydimethylsiloxane-divinylbenzene (PDMS/DVB) fiber (Supelco, Bellafonte, PA, USA) exposed to the sample headspace for 45 min. GC-MS analysis was carried out on an HP 7890B (Agilent Technologies, Santa Clara, CA, USA) gas chromatograph coupled to a 5977B quadrupole mass spectrometer, equipped with a MPS autosampler (Gerstel, Müllheim/Ruhr, Germany). Separation was performed using a HP-5ms UI capillary column (30 m × 0.25 mm, 0.25 µm film thickness, Agilent Technologies, Santa Clara, CA, USA) and helium (6.0 grade) as carrier gas at 1.5 mL/min constant flow rate. GC injector at 260 °C and the oven was programmed as follows: at 70 °C for 3 min, raised to 115 °C at 3 °C/min, to 120 °C at 1 °C/min, to 230 °C at 10 °C/min, and then to 250 °C at 20 °C/min and maintained for 20 min. The mass spectrometer was operated in electron ionization (EI) at 70 eV with an ion source temperature of 250 °C and a quadrupole temperature of 150 °C. The mass spectra were acquired in the SIM mode and the calibration curves were prepared for the 3-isopropyl-2-methoxypyrazine (IPMP), 3-secbutyl-2-methoxypyrazine (SBMP), and 3-isobutyl-2-methoxypyrazine (IBMP) pyrazine standards and obtained using Chemstation software (Agilent Technologies, Inc.) by linear regression, plotting the response ratio (analyte peak area divided by internal standard peak area) against concentration ratio (added analyte concentration divided by internal standard concentration).
+
+2.4. SPME-GC-MS Analysis of C6 Compounds
+
+C6 compounds were analyzed using SPME extraction coupled with GC-MS analysis as described by Slaghenaufi et al. (2022) [42]. Five milliliters of wine were placed into a 20 mL glass vial together with 5 mL of water, 3 g of NaCl, and 5 µL of internal standard 2-octanol (4.2 mg/L in ethanol). Samples were equilibrated for 1 min at 40 °C, and then SPME extraction was performed by exposing for 60 min a 50/30 μm divinylbenzene–carboxen–polydimethylsiloxane (DVB/CAR/PDMS) fiber (Supelco, Bellafonte, PA, USA) into sample headspace. Injection was performed in splitless mode by desorbing SPME fiber into the injection port of an HP 7890A (Agilent Technologies, Santa Clara, CA, USA) gas chromatograph coupled to a 5977B quadrupole mass spectrometer, equipped with a MPS3 auto sampler (Gerstel, Müllheim/Ruhr, Germany). Separation was performed using a DB-WAX UI capillary column (30 m × 0.25, 0.25 μm film thickness, Agilent Technologies, Santa Clara, CA, USA). Helium (6.0 grade) was used as a carrier gas at a constant flow rate of 1.2 mL/min. GC oven temperature was initially set at 40 °C for 3 min, then raised to 230 °C at 4 °C/min and maintained for 20 min. The mass spectrometer was operated in electron ionization (EI) at 70 eV with an ion source temperature of 230 °C and a quadrupole temperature of 150 °C. Mass spectra were acquired in synchronous Scan (m/z 40–200) and SIM mode. Samples were analyzed in random order.
+
+A calibration curve was prepared similarly to the samples using seven concentration points and three replicate solutions per point in model wine with the exception of hexanal and 2-hexanal, which were quantified with a hexanol calibration curve. Calibration curves were obtained by linear regression, plotting the response ratio (analyte peak area divided by internal standard peak area) against concentration ratio (added analyte concentration divided by internal standard concentration).
+
+2.5. Enological Parameters Analysis
+
+Folin–Ciocalteu reagent was used to quantify the total phenolics, according to the procedure described by Singleton and Rossi (1965) [43]. The pH was evaluated with a Basic 20+ pH meter (Crison, Barcelona, Spain). Ethanol was quantified with a Lyza 5000 (Anton Paar, Graz, Austria).
+
+2.6. Statistical Analyses
+
+ANOVA analysis with post hoc Tukey test (α = 0.05) has been performed using XLSTAT 2023 (Addinsoft SARL, Paris, France). Prior to ANOVA analysis normality test was assessed using the Shapiro–Wilk test, and homogeneity of variances was checked using Levene’s test. All the graphics have been created using Excel 365 (Microsoft, Redmond, WA, USA).
+
+3. Results and Discussion
+
+3.1. Adsorption and Release Kinetics by Grape Stems
+
+The results obtained are shown in Figure 1, Figure 2, Figure 3 and Figure 4, while the ANOVA analysis is reported in Appendix A.1. For the visualization of the entire data set at 14 days, a heat map has been generated and reported in Supplementary Figure S1. Results highlighted a slight but progressive increase in pH across all treatments involving stem addition, compared to the control, which remained substantially stable at a final value of approximately 3.5 (Figure 1). Consistent with previous studies [4,19,20], the observed pH fluctuations were likely driven by changes in the organic acid profile, notably tartaric acid. This phenomenon might be triggered by the leaching of potassium and calcium ions from the grape stems, which promotes the formation and subsequent precipitation of tartrate salts. Regarding the different varieties, withered Cabernet Sauvignon exerted a slightly higher alkalinizing effect than Corvina; specifically, the CS 20 treatment reached a maximum pH value of 3.61 by day 14, showing an increase of 0.1 compared to the control. Concerning the impact of the dehydration process, the data suggested that samples with an intermediate dehydration level achieved higher pH values, whereas the final pH increase in Corvina stems withered at 40% was slightly lower. From a kinetic perspective, the rise in pH was not immediate but required prolonged contact time, with the most significant shifts occurring between the 7th and 14th days of infusion. The pH plays a role in sensory perception: an excessive increase in pH can turn fresh, crisp wines into flat wines and significantly increase bitterness perception [44,45]. Moreover, pH modulates color and aromatic evolution, particularly affecting compounds such as esters and terpenes [46,47].
+
+Regarding ethanol concentration (Figure 1), a decrease was observed across all treatments involving grape stems, whereas the control remained stable. The most pronounced decrease was observed in the samples treated with fresh stems, both Corvina and Cabernet Sauvignon, reaching 10.4% and 10.3%, respectively, by the fourteenth day. Compared to the control, a decrease of 0.32% and 0.35% was observed. A clear correlation with the moisture content of the stems emerged: fresh stems induced the greatest ethanol reduction, followed by those with 20% weight loss, and finally by the samples with 40% weight loss. While previous studies suggest that a decrease in alcohol levels could be attributed to a dilution effect [4], the observed ethanol reduction in withered samples, despite their low water content, suggests that additional mechanisms might be involved. Beyond dilution, it has been reported that the stem surface can capture ethanol molecules [20]. This reduction in ethanol content is a particularly significant finding in the current context of global warming, where rising alcohol levels in wine due to accelerated grape sugar accumulation [48] contrast with the growing consumer preference for lighter-bodied wines [49,50]. Interestingly, the reduction in alcohol content was found to be a rapid phenomenon, with most of the decrease occurring within the first 24 h of contact. In the fresh stem treatments, levels dropped immediately from the initial 10.72% to near 10.40%, before stabilizing around 10.30% by the third day. Conversely, the kinetics for the withered stems (20% and 40% weight loss) exhibited a significantly less steep decline.
+
+The addition of grape stems led to an increase in phenolic concentration within the first 24 h (Figure 1). During this initial phase, the stems released the most soluble and readily available compounds on their surfaces. Subsequently, between days 1 and 7, a progressive extraction phase occurred, driven by the diffusion of tannins and flavonols. Interestingly, CS samples showed higher release compared to CA samples, reaching peaks near 2170 mg/L in the withered treatments; this confirmed either a higher phenolic content or a stem structure that facilitated release.
+
+The dehydration process also played a crucial role in kinetics: stems withered at 20% and 40% showed higher final phenolic content than fresh stems. Compared to the control, CA F and CA 20 samples showed an increase of 10% and 9%, respectively, while CA 40 showed an increase of 20%. In CS, the CS F and CS 20 samples increased by 30% and 33%, respectively, while CS 40 increased by 34%.
+
+This behavior suggested that technical dehydration in the fruttaio not only concentrated compounds within the stem tissue but also modified their releasing ability, allowing for a more consistent enrichment of the wine. However, a slight fluctuation or decrease was observed between days 7 and 14 in some treatments (e.g., CA F and CA 20). The slight decrease in phenolic content observed between days 7 and 14 in some treatments might be explained by re-adsorption of polyphenols onto stem cell surfaces or by precipitation following interactions with other wine macromolecules. Previous studies have documented an increase in total phenolic content when stems are present during fermentation [1]. Current evidence suggests that the extent of phenolic enrichment depends on two key factors: varietal characteristics and maceration duration [4,7,12,17,18,20]. In addition to these, drying treatments also appeared to play a significant role [36].
+
+Methoxypyrazines are nitrogenated heterocycles responsible for distinctive herbaceous, green, or even earthy aromas, including green pepper and asparagus [51], typical of wine produced with Cabernet Sauvignon, Sauvignon Blanc, Cabernet Franc, and Merlot noir and other varieties [52,53,54,55,56]. These compounds possess extremely low odor thresholds, typically in the ng/L range. While their origin is primarily varietal, contributing characteristic bell pepper notes to varieties such as Cabernet Sauvignon, Sauvignon Blanc, Cabernet Franc, and Merlot [57], their contribution is not universally considered positive [51]. The analysis of methoxypyrazine release, IBMP, and SBMP underscores that grape stems serve as a significant source of these compounds, with extraction kinetics that develop progressively over the 14-day contact period.
+
+Regarding SBMP, extraction was negligible during the first 24 h, followed by a marked increase starting from the third day onward (Figure 2). The treatments involving CA samples, particularly CA F and CA 20, showed higher release, reaching levels exceeding 20 ng/L, whereas CA 40 showed significantly lower content 16.9 ng/L showing a decrease of 22% compared to CA F. Similarly, CS F and CS 20 showed higher content at the end of 14 days (20.5 ng/L and 16.8 ng/L) than CS 40, showing 13.3 ng/L with a net decrease of 33%. No pyrazines were found in the control.
+
+The kinetics of IBMP followed a similar profile, with extraction becoming significant between the first and third days (Figure 2). Again, CA F showed higher release, stabilizing at approximately 16–18 ng/L between the seventh and fourteenth days. Conversely, Cabernet Sauvignon showed an IBMP release that tended to stabilize or decrease after the third day, with final values of approximately 10–12 ng/L. A fundamental aspect emerging from the data is the impact of stem withering treatments. Withering appears to modulate the release of these herbaceous compounds; specifically, CA 20 and 40 showed a reduction of 17% and 14% of the final SBMP concentration compared to the fresh treatment, suggesting that stem dehydration may limit pyrazine leaching or promote partial degradation. The observed reduction in pyrazine release from withered stems could be explained by at least two non-exclusive mechanisms. First, prolonged dehydration in the fruttaio exposes stem tissues to oxygen, potentially leading to oxidative degradation. Second, withering may induce structural modifications in the stem cell wall, leading to increased exposure to lignin, which might enhance physical adsorption onto the solid matrix, thereby reducing pyrazine extractability into the wine. However, further studies are needed to confirm these hypotheses.
+
+C6 compounds are characterized by green and grassy sensory notes. In wine, they are formed from enzymatic oxidation of fatty acids, α-linolenic and α-linoleic, during grape crushing in the pre-fermentative stage [58,59]. The impact of the different treatments on C6 compounds was minor (Figure 3). Hexanol showed a slight increase, particularly in the CA 40 and CS 40 treatments; however, the differences were not significant compared to the other treatments. For trans-3-hexen-1-ol, all treatments showed a minor but significant increase compared to the control, after which concentrations returned to levels similar to those of the control at 7 and 14 days. cis-3-Hexen-1-ol also demonstrated a moderate but significant increase in the treatments containing stems. In this case, an effect of the withering treatment was observable, with withered stems releasing a higher quantity of the compound, in the order 40, 20, and F. Finally, cis-2-hexen-1-ol showed a slight increase after 3 days in the withered CA treatments. However, no significant differences were observed between 7 and 14 days.
+
+Methanethiol, along with other volatile sulfur compounds such as hydrogen sulfide and ethanethiol, is frequently synthesized during winemaking or during storage. It is primarily formed via the degradation of sulfur-containing amino acids (especially methionine) by yeast during alcoholic fermentation, as well as through the chemical or microbial breakdown of cysteine and glutathione. These compounds adversely affect wine aroma, overall perceived quality, and consumer acceptance due to their unpleasant odors, often described as reminiscent of cabbage, onion, and garlic [60,61,62,63,64].
+
+The kinetic analysis of MeSH revealed a consistent decrease across all treatments throughout the 14-day experimental period (Figure 4). Significant effects of both grape variety and stem treatment were observed as early as the first 24 h. Notably, CS F induced the most immediate reduction, with MeSH levels dropping to 50.7 µg/L, whereas the control remained stable above 70 µg/L. On day 1, CS F was the only treatment to show a significant decrease in MeSH compared to the control, achieving a reduction of approximately 18 µg/L. The most intensive decrease phase occurred between the third and seventh days for all samples, including the control, resulting in concentrations significantly lower than both the initial and control values. By day 14, the lowest methanethiol concentrations were recorded across all experimental groups. While the gap between the control and the treatments narrowed toward the end of the trial, the differences remained statistically significant; CA F achieved the lowest absolute residual concentration at 9.73 µg/L.
+
+The extent of this final decrease, with nearly all stem samples settling between 9 and 14 µg/L compared to 19.45 µg/L in the control, confirms that the grape stems act as an active sequestrant for sulfur-based off-odors. Compared to the control, MeSH reductions ranged from 24% for CS 40 to 50% for CA F. The fact that the control during the 14 days showed a lower but significant decrease compared to stem samples was most likely due to competition with other wine matrix compounds and with other molecules for binding to VSCs. This suggests that stem addition could serve as a natural and sustainable strategy for mitigating reduction defects in wine. Such a decrease in reductive thiol compounds is attributable to the formation of bonds between sulfhydryl groups and tannins [38], a class of polyphenols particularly abundant in grape stems [34].
+
+In summary, the addition of grape stems to the wine matrix leads to a pyrazine enrichment that is strictly dependent on both the variety and the degree of material withering. These findings are crucial for winemakers, as they indicate that the use of withered stems can be a strategic approach to capitalize on the abatement of reductive thiol, such as MeSH, while simultaneously minimizing the input of undesirable vegetal off-odors.
+
+3.2. Evaluation of the Adsorption Capacity of Grape Stems
+
+A key question concerns whether the reduction in MeSH is mediated by adsorption onto the grape stem itself or by the reactivity of tannins released into the solution. The experimental data (Table 3) allowed the differentiation between the effect of the solid matrix and the soluble components leached into the wine. The control sample had the highest MeSH concentration (37.61 µg/L), whereas the SI treatment showed the lowest (6.4 µg/L). This treatment proved to be the most effective, achieving a reduction of over 80% compared to the control. In contrast, the SE and ES treatments resulted in concentrations of 21.16 µg/L and 14.68 µg/L, respectively.
+
+The higher methanethiol adsorption capacity of the ES sample compared to the SE sample could be tentatively explained by two factors. First, the solid stem matrix provides a high surface area that may physically adsorb MeSH within hours, whereas soluble leached compounds are present at much lower concentrations and require time to be released into solutions. Second, the condensed tannins released into solution might be smaller and partially oxidized due to radical scavenging activity and could therefore be less reactive toward MeSH than their immobilized counterparts within the stem cell wall. These proposed mechanisms require further investigation.
+
+3.3. Evaluation of the MeSH Adsorption Capacity of Commercial Enological Tannins
+
+Given the ability of stems to decrease methanethiol content, the capacity of other enological products, such as commercial tannins, was evaluated. Enological tannins are widely employed during winemaking and aging to clarify and stabilize musts and wines; they function by binding proteins to prevent ferric casse, while also stabilizing color and enhancing both antioxidant activity and sensory properties [65,66,67,68].
+
+This type of product, similarly to grape stems, contains tannins [68,69]. These products can form bonds with the sulfhydryl groups of mercaptans. Previously, Bekker et al. (2025) [38] observed a decrease in certain reductive thiols following the addition of enological tannins, although the effect was not always significant depending on the contact time. The experiment was conducted similarly to the stem experiment, where three types of commercial tannins were added at three different concentrations to the same red wine. The maximum concentrations used were those specified by the manufacturer in the technical data sheet. The samples were analyzed at time 0 and after 1, 3, 7, and 14 days; the results are reported in Figure 5, while ANOVA analysis is reported in Appendix A.2.
+
+The results indicated only minor, non-significant differences between treatments during the first seven days of the study. However, by the 14th day, two distinct groups emerged: the first comprised control and all samples treated with low and medium tannin dosages, which showed lower residual concentrations of MeSH, the second comprised all treatments at high concentrations, which retained significantly higher levels of the compound.
+
+These findings contradict previous studies, such as those by Bekker et al. (2025) [38], in which tannins can reduce the content of reductive mercaptans. In our study, conversely, higher tannin concentrations resulted in a less pronounced decrease in MeSH levels. The investigation into the adsorption capacity of enological tannins toward MeSH revealed a counterintuitive phenomenon: as the tannin dosage increases from low to high, the efficacy of the treatment in removing this off-odor does not increase but, in several instances, decreases drastically. T1 H and T2 H exhibited residual MeSH concentrations twice those of the control, reaching 31.08 µg/L and 33.55 µg/L, respectively. Furthermore, the T3 H treatment showed a 1.5-fold higher MeSH content compared to the control.
+
+One hypothesis for this anomalous behavior lies in the intrinsic antioxidant activity of polyphenolic compound [70]. The discrepancy between the present findings and those of Bekker et al. (2025) [38] may be related to the higher tannin concentrations used in this study (500 mg/L vs. approximately 100 mg/L). It can be hypothesized that the introduction of a high tannin dose led to a reduction in the redox potential of the system, interfering with the degradation pathways of methanethiol. Under standard conditions, MeSH can undergo spontaneous oxidation.
+
+However, high content of tannins may act as an oxidative ‘buffer,’ sequestering dissolved oxygen and neutralizing the free radicals that would otherwise facilitate this chemical transformation. It is therefore hypothesized that at such high doses, the antioxidant capacity of tannins may protect MeSH from oxidative degradation, although further studies are required to confirm this mechanism. Consequently, high concentrations of polyphenols might exert an unintended protective effect on the MeSH molecule, preserving it from the natural degradation observed in the control sample. This hypothesis is indirectly supported by Fracassetti et al. (2021), who demonstrated that hydrolysable tannins effectively prevent the formation of MeSH under light exposure [71,72].
+
+4. Conclusions
+
+This research evaluated the behavior of grape stems in red wine, aiming to characterize the dynamics of release and adsorption across two varieties, Corvina and Cabernet Sauvignon, and different withering degrees.
+
+Analysis of enological parameters revealed that the addition of stems leads to a pH increase, which was more pronounced in withered samples. Furthermore, a reduction in alcohol content was observed in stem-treated samples. Although higher in fresh stem samples, the ethanol decrease was also observed for withered stems, suggesting that the mechanism is not a simple dilution effect but likely involves physical interaction between the stem surface and ethanol molecules. Regarding phenolic compounds, stem-treated samples showed an increase compared to the control, influenced by both variety and withering treatment. Cabernet Sauvignon showed higher release levels than Corvina; moreover, withered stems led to a higher final phenolic enrichment compared to fresh ones. Concerning volatile compounds responsible for herbaceous notes, the study highlighted stems as a source of methoxypyrazines. However, the use of withered stems proved to be an effective treatment to limit the release of these compounds. Concerning methanethiol, kinetic trends highlighted the ability of all stem types to decrease MeSH content. The stems acted as an active substrate in sequestering undesirable sulfur compounds, primarily via direct adsorption onto their solid surface. Comparison with commercial enological tannins showed an unexpected trend. While no significant differences were observed initially, by day 14, the highest tannin dosages led to significantly higher residual methanethiol concentrations compared to the control and lower dosages. These results, seemingly contradictory to the existing literature, may be explained by the high antioxidant activity of tannins at high doses. By acting as oxygen and free-radical scavengers, they may inhibit the oxidative degradation of methanethiol to dimethyl disulfide, thereby preserving the thiol in its original form. Limitation of the study: the experimental design, while controlled, necessarily simplifies real winemaking conditions. The use of laboratory-scale macerations cannot fully capture the physicochemical and microbial complexity of industrial fermentations. Additionally, the stem-to-wine ratio used in this study (150 g/L) is higher than the typical stem content of grape clusters, which generally ranges from 2.5% to 7.5% of grape weight. This higher ratio was deliberately adopted to amplify the kinetic signals under controlled laboratory conditions, allowing the reliable detection and quantification of release and adsorption phenomena over a short maceration period.
+
+Supplementary Materials
+
+The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/foods15101707/s1, Supplementary Table S1. Retention indices, quantification ions, limit of detection (LOD), limit of quantification (LOQ), and repeatability of the analysed compounds. Supplementary Figure S1. Heat map and hierarchical cluster analysis of samples and enological parameters and volatile organic compounds of T14 samples.
+
+Author Contributions
+
+Conceptualization: G.L. and D.S., Methodology: G.L. and N.P.B., Data curation: G.L. and J.N.B., Formal analysis and investigation: N.P.B. and J.A.S.S., Writing—original draft preparation: G.L., Writing—review and editing: D.S., N.P.B. and J.A.S.S., Project administration: D.S., Validation: D.S., Supervision: D.S., Visualization: G.L. and N.P.B., Software: G.L. and J.N.B., Resources: D.S. All authors have read and agreed to the published version of the manuscript.
+
+Institutional Review Board Statement
+
+Not applicable.
+
+Informed Consent Statement
+
+Not applicable.
+
+Data Availability Statement
+
+The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding authors.
+
+Conflicts of Interest
+
+Author Naíssa Prévide Bernardo was employed by the company Agricultural Research Company of Minas Gerais. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
+
+Appendix A
+
+Appendix A.1. Different Groups According to ANOVA (α = 0.05) Post Hoc Tukey Test for the Stem Experiment
+
+pH	0 d	1 d	3 d	7 d	14 d	Hexanol	0 d	1 d	3 d	7 d	14 d	
+Control	a	a	a	a	a	Control	a	a	a	a	a	
+CA F	a	b	b	ab	b	CA F	a	ab	ab	a	a	
+CA 20	a	e	e	b	c	CA 20	a	c	c	b	a	
+CA 40	a	d	d	c	b	CA 40	a	cd	c	ab	a	
+CS F	a	c	c	c	b	CS F	a	d	c	ab	a	
+CS 20	a	f	f	d	d	CS 20	a	b	bc	b	a	
+CS 40	a	f	f	cd	d	CS 40	a	d	c	b	a	
+EtOH	0 d	1 d	3 d	7 d	14 d	trans-3-Hexen-1-ol	0 d	1 d	3 d	7 d	14 d	
+Control	a	d	e	e	f	Control	a	a	a	a	a	
+CA F	a	b	b	b	b	CA F	a	ab	a	a	a	
+CA 20	a	c	c	c	de	CA 20	a	b	b	a	a	
+CA 40	a	d	d	d	e	CA 40	a	b	b	a	a	
+CS F	a	a	a	a	a	CS F	a	c	b	a	a	
+CS 20	a	b	ba	b	c	CS 20	a	bc	ab	a	a	
+CS 40	a	c	c	c	d	CS 40	a	b	b	a	a	
+TP	0 d	1 d	3 d	7 d	14 d	cis-3-Hexen-1-ol	0 d	1 d	3 d	7 d	14 d	
+Control	a	a	a	a	a	Control	a	b	a	a	a	
+CA F	a	b	bc	b	ab	CA F	a	c	b	b	b	
+CA 20	a	c	c	c	b	CA 20	a	d	c	b	c	
+CA 40	a	bc	b	b	b	CA 40	a	d	c	b	d	
+CS F	a	c	c	bc	c	CS F	a	c	b	b	a	
+CS 20	a	c	c	d	d	CS 20	a	cd	bc	b	b	
+CS 40	a	c	c	d	d	CS 40	a	a	a	b	e	
+SBMP	0 d	1 d	3 d	7 d	14 d	cis-2-Hexen-1-ol	0 d	1 d	3 d	7 d	14 d	
+Control	-	-	-	-	-	Control	a	a	a	a	a	
+CA F	-	a	c	c	c	CA F	a	ab	a	a	a	
+CA 20	-	a	c	bc	b	CA 20	a	a	c	a	a	
+CA 40	-	-	a	ab	bc	CA 40	a	a	c	a	a	
+CS F	-	a	b	ab	b	CS F	a	b	b	a	a	
+CS 20	-	a	a	ab	a	CS 20	a	ab	ab	a	a	
+CS 40	-	a	a	a	b	CS 40	a	a	a	a	a	
+IBMP	0 d	1 d	3 d	7 d	14 d	MeSH	0 d	1 d	3 d	7 d	14 d	
+Control	-	-	-	-	-	Control	a	b	d	d	d	
+CA F	-	a	ab	ab	bcd	CA F	a	b	a	a	a	
+CA 20	-	a	ab	b	d	CA 20	a	b	a	a	b	
+CA 40	-	a	b	b	b	CA 40	a	ab	d	b	b	
+CS F	-	-	ab	ab	c	CS F	a	a	a	a	b	
+CS 20	-	-	a	a	b	CS 20	a	b	b	b	b	
+CS 40	-	-	a	ab	a	CS 40	a	b	bc	c	b	
+Lowercase letters indicate significantly different groups according to one-way ANOVA (α = 0.05) followed by Tukey’s post hoc test.	
+
+Appendix A.2. Different Groups According to ANOVA (α = 0.05) Post Hoc Tukey Test for the Enological Tannins Experiment
+
+MeSH	0 d	1 d	3 d	7 d	14 d	
+Control	a	b	a	b	a	
+T1 L	a	a	a	b	a	
+T1 M	a	a	a	b	a	
+T1 H	a	a	a	b	b	
+T2 L	a	ab	a	b	a	
+T2 M	a	ab	a	a	a	
+T2 H	a	a	a	b	b	
+T3 L	a	ab	a	b	a	
+T3 M	a	a	a	b	a	
+T3 H	a	a	a	b	a	
+Lowercase letters indicate significantly different groups according to one-way ANOVA (α = 0.05) followed by Tukey’s post hoc test.	
+
+Figure 1 pH, Ethanol (EtOH), and total polyphenols (TP) in the stem samples at 0 and after 1, 3, 7, and 14 days.
+
+Figure 2 Content of SBMP and IBMP in the stem samples at 0 and after 1, 3, 7, and 14 days.
+
+Figure 3 Content of C6 alcohols (µg/L) in the stem samples at 0 and after 1, 3, 7, and 14 days.
+
+Figure 4 Content of MeSH (µg/L) in the stem samples at 0 and after 1, 3, 7, and 14 days.
+
+Figure 5 Content of MeSH (µg/L) in the enological tannins’ samples at 0 and after 1, 3, 7, and 14 days.
+
+foods-15-01707-t001_Table 1 Table 1 Sample list, stem varieties, whitering treatment, and humidity.
+
+Samples	Varieties	Whitering	Humidity	
+Control	Model wine	Not applicable	Not applicable	
+CA FR	Corvina	No	76.9%	
+CA 25	Corvina	20%	52.3%	
+CA 50	Corvina	40%	27%	
+CS FR	Cabernet Sauvignon	No	69.3%	
+CS 25	Cabernet Sauvignon	20%	44.6%	
+CS 50	Cabernet Sauvignon	40%	19.6%	
+
+foods-15-01707-t002_Table 2 Table 2 Samples, tannins’ origins, and concentration.
+
+Samples	Tannin Origins	Concentration	
+T1 L	grape	25 mg/L	
+T1 M	grape	250 mg/L	
+T1 H	grape	500 mg/L	
+T2 L	grape seed	25 mg/L	
+T2 M	grape seed	250 mg/L	
+T2 H	grape seed	500 mg/L	
+T3 L	Green tea	25 mg/L	
+T3 M	Green tea	250 mg/L	
+T3 H	Green tea	500 mg/L	
+
+foods-15-01707-t003_Table 3 Table 3 Content ± standard deviation of MeSH and significance according to ANOVA.
+
+Samples	Content (µg/L)	Percentage Decrease (%)	S 1	
+Control	37.61 ± 3.52	0	a	
+SI	6.395 ± 0.64	83	d	
+SE	21.16 ± 5.07	44	b	
+ES	14.68 ± 1.26	61	c	
+1 S means significance according to ANOVA (α = 0.05) post hoc Tukey test, lower case letter refers to different groups.
+
+Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.
+
+
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+56. Augustyn O.P.H. Rapp A. van Wyk C.J. Some Volatile Aroma Components of Vitis Vinifera L. Cv. Sauvignon Blanc South Afr. J. Enol. Vitic. 1985 3 53 60 10.21548/3-2-2382
+57. Culleré L. López R. Ferreira V. The Instrumental Analysis of Aroma-Active Compounds for Explaining the Flavor of Red Wines Red Wine Technology Elsevier Amsterdam, The Netherlands 2019 283 307 10.1016/B978-0-12-814399-5.00020-7
+58. Waterhouse A.L. Sacks G.L. Jeffery D.W. Understanding Wine Chemistry Wiley Hoboken, NJ, USA 2016 9781118627808
+59. Oliveira J.M. Faria M. Sá F. Barros F. Araújo I.M. C6-Alcohols as Varietal Markers for Assessment of Wine Origin Anal. Chim. Acta 2006 563 300 309 10.1016/j.aca.2005.12.029
+60. Ugliano M. Henschke P.A. Yeasts and Wine Flavour Wine Chemistry and Biochemistry Moreno-Arribas M.V. Polo M.C. Springer New York, NY, USA 2009 313 392
+61. Luzzini G. Slaghenaufi D. Facinelli D. Ugliano M. Contribution of Terpenes, Methanethiol, and Fermentative Esters to Sparkling Wine Aroma in Relation to Production Technology, Vintage, and Aging: A Case Study on Durello Wines J. Sci. Food Agric. 2023 103 5353 5363 10.1002/jsfa.12609 37024446
+62. Luzzini G. Bicego R. Slaghenaufi D. Ugliano M. Variations in Sensorially-Relevant Metabolites and Indices in PDO Wines of Common Ampelographic Background: A Case Study on Commercial Lambrusco Wines J. Food Compos. Anal. 2025 140 107300 10.1016/j.jfca.2025.107300
+63. Smith M.E. Bekker M.Z. Smith P.A. Wilkes E.N. Sources of Volatile Sulfur Compounds in Wine Aust. J. Grape Wine Res. 2015 21 705 712 10.1111/ajgw.12193
+64. Franco-Luesma E. Ferreira V. Reductive Off-Odors in Wines: Formation and Release of H2S and Methanethiol during the Accelerated Anoxic Storage of Wines Food Chem. 2016 199 42 50 10.1016/j.foodchem.2015.11.111 26775942
+65. Franco-Luesma E. Sáenz-Navajas M.-P. Valentin D. Ballester J. Rodrigues H. Ferreira V. Study of the Effect of H2S, MeSH and DMS on the Sensory Profile of Wine Model Solutions by Rate-All-That-Apply (RATA) Food Res. Int. 2016 87 152 160 10.1016/j.foodres.2016.07.004 29606236
+66. Paissoni M.A. Bitelli G. Vilanova M. Montanini C. Río Segade S. Rolle L. Giacosa S. Relative Impact of Oenological Tannins in Model Solutions and Red Wine According to Phenolic, Antioxidant, and Sensory Traits Food Res. Int. 2022 157 111203 10.1016/j.foodres.2022.111203 35761525
+67. Chen K. Escott C. Loira I. Del Fresno J. Morata A. Tesfaye W. Calderon F. Benito S. Suárez-Lepe J. The Effects of Pre-Fermentative Addition of Oenological Tannins on Wine Components and Sensorial Qualities of Red Wine Molecules 2016 21 1445 10.3390/molecules21111445 27809234 PMC6272987
+68. Baris F. Cejudo-Bastante M. Heredia F. Chinnici F. Oenological Tannins from Different Sources and Their Impact on Color and Phenolic Evolution of a Rosé Wine Beverages 2026 12 28 10.3390/beverages12030028
+69. Versari A. du Toit W. Parpinello G.P. Oenological Tannins: A Review Aust. J. Grape Wine Res. 2013 19 1 10 10.1111/ajgw.12002
+70. Obreque-Slíer E. Peña-Neira A. López-Solís R. Ramírez-Escudero C. Zamora-Marín F. Phenolic Characterization of Commercial Enological Tannins Eur. Food Res. Technol. 2009 229 859 866 10.1007/s00217-009-1121-1
+71. Ricci A. Olejar K.J. Parpinello G.P. Mattioli A.U. Teslić N. Kilmartin P.A. Versari A. Antioxidant Activity of Commercial Food Grade Tannins Exemplified in a Wine Model Food Addit. Contam. Part A 2016 33 1761 1774 10.1080/19440049.2016.1241901 27696959
+72. Fracassetti D. Limbo S. Messina N. Pellegrino L. Tirelli A. Light-Struck Taste in White Wine: Protective Role of Glutathione, Sulfur Dioxide and Hydrolysable Tannins Molecules 2021 26 5297 10.3390/molecules26175297 34500729 PMC8434244
diff --git a/corpus/psychology/text/0f1e533d35f9cffc.txt b/corpus/psychology/text/0f1e533d35f9cffc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d736343567482751a3f96fbe3bf888b6a0d3ab49
--- /dev/null
+++ b/corpus/psychology/text/0f1e533d35f9cffc.txt
@@ -0,0 +1,3 @@
+Prediction Under Pressure: Predictive Sentence Processing in Dyslexia and Second-Language Reading
+
+Predictive processing plays a central role in fluent reading, yet it remains unclear how it is modulated by reading difficulties and language context (first vs. second language). The present study investigated predictive sentence processing in typical readers and in readers with dyslexia reading a novel in their first language (Dutch) and second language (English) (GECO; Cop et al., 2017 &amp; DECO; Boeve et al., 2026). Using eye-tracking measures and computational estimates of word surprisal and entropy, we examined the influence of word predictability on reading behaviour. Results revealed systematic differences across groups and languages. Early reading measures (first fixation duration) showed a surprisal-entropy interaction consistent with prediction error effects, that were stronger in dyslexia and in second language reading. Later measures (gaze duration and total reading time) showed prediction error effects only in typical readers, while readers with dyslexia showed facilitation from predictable words without modulation by entropy. Skipping behaviour also differed between groups. Typical readers skipped more words overall than readers with dyslexia. Higher entropy and surprisal generally reduced skipping, yet readers with dyslexia showed a stronger reduction of skipping in high-uncertainty contexts. Together, the results suggest that predictive processing adapts to processing demands and reader ability. Readers with dyslexia appear to rely primarily on early predictions about word-form information, possibly as a compensatory strategy for difficulties in word identification, whereas typical readers seem to engage in both form-based and semantic prediction during reading.
diff --git a/corpus/psychology/text/135619c502d93b5f.txt b/corpus/psychology/text/135619c502d93b5f.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0cfa302261d692c0aff861bd990732c38334e1b4
--- /dev/null
+++ b/corpus/psychology/text/135619c502d93b5f.txt
@@ -0,0 +1,3 @@
+Weak Links between Speech Perception and Speech Production at the Subphonemic Level
+
+Recent research has shown individual differences in gradiency, defined as sensitivity to fine-grained acoustic differences at the subphonemic level. Consistency also varies, with some listeners providing more stable responses than others to repeated presentations of the same stimuli. However, it remains unclear whether gradiency and consistency are linked between perception and production. Across two experiments, 160 Spanish speakers completed a Visual Analogue Scale (VAS) task measuring perceptual gradiency and consistency along a Spanish /ba/–/pa/ continuum manipulated in 7–8 ms steps of voice onset time (VOT). The same participants also performed an explicit imitation task using the same stimuli. Results revealed only weak relationships between perceptual gradiency and imitation accuracy, as well as between perceptual consistency and imitation consistency, even after accounting for other factors related to speech perception and imitation. These findings suggest that models proposing strong perception–production coupling may not extend to the subphonemic level.
diff --git a/corpus/psychology/text/15d4410dfe9cd242.txt b/corpus/psychology/text/15d4410dfe9cd242.txt
new file mode 100644
index 0000000000000000000000000000000000000000..b7fb80759f4a65c370af8c35e67160ba8e4e76d3
--- /dev/null
+++ b/corpus/psychology/text/15d4410dfe9cd242.txt
@@ -0,0 +1,3 @@
+StructuralEquationModels.jl: a Julia Package for Extensible and Efficient Structural Equation Modeling
+
+We introduce StructuralEquationModels.jl, a novel structural equation modeling (SEM) software designed with extensibility as its core principle. Since the introduction of SEM, the range of problems it is applied to is rapidly expanding. However, SEM software implementations did not anticipate such expansion, so software flexibility has become one major factor limiting the adoption of innovations in the field of SEM. StructuralEquationModels.jl is designed to be modular and extensible to remove that bottleneck. This approach not only speeds up innovation in SEM but also ensures the integrity and reliability of existing functionality. We leverage the Julia programming language's ecosystem to achieve efficient implementations of loss functions and gradients and support modern optimization backends. The versatility of StructuralEquationModels.jl is demonstrated on a set of examples (e.g., adding support for regularized SEM) and simulations (e.g., sensitivity of the RMSEA to misspecification of large factor analysis models). Using these simulations as a benchmark, we further demonstrate StructuralEquationModels.jl’s high computational efficiency.
diff --git a/corpus/psychology/text/181ab0c142736202.txt b/corpus/psychology/text/181ab0c142736202.txt
new file mode 100644
index 0000000000000000000000000000000000000000..69803a065329f89af990e569981f300e59998eb3
--- /dev/null
+++ b/corpus/psychology/text/181ab0c142736202.txt
@@ -0,0 +1,13 @@
+Global and Local influences on Egocentric Visual Perceptions of Elevation and of Verticality
+
+How does the visual system read orientation from an extended scene to keep the perception of space stable
+relative to the body? We separated two orientations that are normally confounded — the global orientation
+of a long array of parallel lines and the local orientation of the lines composing it — and measured their
+influence on two egocentric norms: visually perceived eye level (VPEL) and visually perceived vertical
+(VPV). Across eight experiments the global orientation of the array set both norms, whereas the local
+orientation of the lines was negligible in a long array (Study 1) and re-emerged only when the array was
+shortened and the lines lengthened (Study 2). Array length strengthened the influence of array orientation,
+and line length shifted the balance toward line orientation, so the two orientations appear to trade off with
+their relative extent rather than simply add. This pattern implies that egocentric space is stabilized by
+orientation read at two scales — a large-scale second-order channel and a local first-order channel —
+combined according to their spatial extent across the visual periphery.
diff --git a/corpus/psychology/text/1ef7eb3779d5e89e.txt b/corpus/psychology/text/1ef7eb3779d5e89e.txt
new file mode 100644
index 0000000000000000000000000000000000000000..4d56aada321861063dcf0dea6cd8f01a95331e6d
--- /dev/null
+++ b/corpus/psychology/text/1ef7eb3779d5e89e.txt
@@ -0,0 +1,88 @@
+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: JMIR Med Educ
+Journal ID: JMIR Med Educ
+NLM Journal ID: 101684518
+Journal ID: JME
+
+JMIR Medical Education
+
+EISSN: 2369-3762
+Publisher: JMIR Publications Inc.
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC11632886
+PMID: 39546775
+DOI: 10.2196/68503
+Article ID: v10i1e68503
+Article version: 1
+Subjects: Corrigenda and Addenda, Corrigenda and Addenda
+
+Correction: Psychological Safety Competency Training During the Clinical Internship From the Perspective of Health Care Trainee Mentors in 11 Pan-European Countries: Mixed Methods Observational Study
+
+Carrillo Irene MSc, PhD https://orcid.org/0000-0002-6981-7284 1 Department of Health Psychology Miguel Hernández University of Elche Avenida de la Universidad s/n Elche, 03202 Spain 34 966658350 icarrillo@umh.es
+
+Skoumalová Ivana PhD 2 https://orcid.org/0000-0001-6893-4158
+Bruus Ireen MSc 3 https://orcid.org/0009-0000-4599-1918
+Klemm Victoria 4 https://orcid.org/0000-0001-6197-9847
+Guerra-Paiva Sofia MsD 5 6 https://orcid.org/0000-0002-4311-3799
+Knežević Bojana PhD 7 https://orcid.org/0000-0001-5525-3775
+Jankauskiene Augustina PhD 8 https://orcid.org/0000-0001-7767-2102
+Jocic Dragana PhD 9 https://orcid.org/0000-0002-6075-7641
+Tella Susanna PhD 10 https://orcid.org/0000-0002-4584-8852
+Buttigieg Sandra C PhD 11 https://orcid.org/0000-0002-0572-2462
+Srulovici Einav PhD 12 https://orcid.org/0000-0003-1291-8284
+Madarasová Gecková Andrea PhD 2 13 https://orcid.org/0000-0003-2993-3798
+Põlluste Kaja PhD 14 https://orcid.org/0000-0002-8871-1397
+Strametz Reinhard MD 4 https://orcid.org/0000-0002-9920-8674
+Sousa Paulo PhD 5 6 https://orcid.org/0000-0001-9502-6075
+Odalovic Marina PhD 15 https://orcid.org/0000-0002-3050-8361
+Mira José Joaquín MPH, PhD 1 16 https://orcid.org/0000-0001-6497-083X
+1 Department of Health Psychology Miguel Hernández University of Elche Elche Spain
+2 Department of Health Psychology and Research Methodology Faculty of Medicine Pavol Jozef Šafárik University Kosice Slovakia
+3 Tartu Health Care College Tartu Estonia
+4 Wiesbaden Institute for Healthcare Economics and Patient Safety (WiHelP) Wiesbaden Business School RheinMain University of Applied Sciences Wiesbaden Germany
+5 Public Health Research Centre National School of Public Health NOVA University Lisbon Lisbon Portugal
+6 Comprehensive Health Research Center National School of Public Health NOVA University Lisbon Lisbon Portugal
+7 University Hospital Centre Zagreb University of Zagreb Zagreb Croatia
+8 Pediatric Center, Institute of Clinical Medicine Faculty of Medicine Vilnius University Vilnius Lithuania
+9 BENU Pharmacy PHOENIX Group Serbia Belgrade Serbia
+10 Faculty of Social and Health Care LAB University of Applied Sciences Lappeenranta Finland
+11 Department of Health Systems Management and Leadership Faculty of Health Sciences University of Malta Malta Malta
+12 Cheryl Spencer Department of Nursing University of Haifa Haifa Israel
+13 Institute of Applied Psychology Faculty of Social and Economic Sciences Comenius University Bratislava Bratislava Slovakia
+14 Institute of Clinical Medicine University of Tartu Tartu Estonia
+15 Faculty of Pharmacy University of Belgrade Belgrade Serbia
+16 Foundation for the Promotion of Health and Biomedical Research of the Valencia Region (FISABIO) Sant Joan d'Alacant Spain
+Corresponding Author: Irene Carrillo icarrillo@umh.es
+Publication date: 2024
+Electronic publication date: 2024 Nov 15
+Volume: 10
+Electronic Location ID: e68503
+Received 2024 Nov 7; Accepted 2024 Nov 7
+Copyright: ©Irene Carrillo, Ivana Skoumalová, Ireen Bruus, Victoria Klemm, Sofia Guerra-Paiva, Bojana Knežević, Augustina Jankauskiene, Dragana Jocic, Susanna Tella, Sandra C Buttigieg, Einav Srulovici, Andrea Madarasová Gecková, Kaja Põlluste, Reinhard Strametz, Paulo Sousa, Marina Odalovic, José Joaquín Mira. Originally published in JMIR Medical Education (https://mededu.jmir.org), 15.11.2024.
+Copyright year: 2024
+License: This is an open-access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work, first published in JMIR Medical Education, is properly cited. The complete bibliographic information, a link to the original publication on https://mededu.jmir.org/, as well as this copyright and license information must be included.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Erratum for: Psychological Safety Competency Training During the Clinical Internship From the Perspective of Health Care Trainee Mentors in 11 Pan-European Countries: Mixed Methods Observational Study 10 7 10 2024 e64125 JMIR Medical Education 10.2196/64125 PMC11494257 39374073
+
+Ÿ==============================Ÿ
+In “Psychological Safety Competency Training During the Clinical Internship From the Perspective of Health Care Trainee Mentors in 11 Pan-European Countries: Mixed Methods Observational Study” (JMIR Medical Education 2024;1(10): e64125) the authors made one revision.
+
+The following section in the Acknowledgments section:
+
+This paper was based on work from the European Cooperation in Science and Technology Action 19113, The European Researchers’ Network Working on Second Victims, supported by the European Cooperation in Science and Technology [67]
+
+Has been corrected to:
+
+This article is based upon work from COST Action, TheERNSTGroup, CA19113, supported by COST (European Cooperation in Science and Technology).
+
+Additionally, the associated reference [67] (below) will be removed from the Reference List, as it will no longer be cited in the paper.
+
+67. Home page. COST Association. URL: https://www.cost.eu/ [accessed 2024-04-29]
+
+The correction will appear in the online version of the paper on the JMIR Publications website on November 15, 2024, together with the publication of this correction notice. Because this was made after submission to PubMed, PubMed Central, and other full-text repositories, the corrected article has also been resubmitted to those repositories.
+
diff --git a/corpus/psychology/text/1f3adc5244a2f81a.txt b/corpus/psychology/text/1f3adc5244a2f81a.txt
new file mode 100644
index 0000000000000000000000000000000000000000..23b8d8507456fd5caaa44018d9fb0eec4ae9678a
--- /dev/null
+++ b/corpus/psychology/text/1f3adc5244a2f81a.txt
@@ -0,0 +1,78 @@
+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Eur Psychiatry
+Journal ID: Eur Psychiatry
+NLM Journal ID: 9111820
+Journal ID: EPA
+
+European Psychiatry
+
+ISSN: 0924-9338
+EISSN: 1778-3585
+Publisher: Cambridge University Press
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC13444872
+DOI: 10.1192/j.eurpsy.2026.11496
+Article ID: EPV1078
+Article ID: S0924933826114965
+Article version: 1
+Subjects: Abstract, e-Poster Viewing
+
+Impulse control disorder in Parkinson’s disease: the influence of dopamine agonists
+
+Varandas Rodrigues G. F. *
+Pereira A. T.
+Psychiatry and Mental Health, Unidade Local de Saúde do Alto Minho , Viana do Castelo , Portugal
+* Corresponding author.
+Publication date: 2026 Jun
+Electronic publication date: 2026 Jul 31
+Volume: 69
+Issue: Suppl 1
+Issue title: Abstracts of the 34th European Congress of Psychiatry
+First page: S802
+Last page: S802
+Copyright: © The Author(s) 2026
+Copyright year: 2026
+Copyright holder: The Author(s)
+License: This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Page count: 1
+displayText: Special Issue
+tdm-reservation: 1
+tdm-policy: https://www.cambridge.org/tdm/tdmrep-policy.json
+
+Ÿ==============================Ÿ
+Introduction
+
+Parkinson’s Disease (PD) is a chronic neurodegenerative pathology, characterized by nigrostriatal dopaminergic dysfunction and motor manifestations. Dopamine agonists (DA) are one of the pillars of treatment. However, the stimulation of dopamine receptors in the mesolimbic pathways has been associated with the appearance of neuropsychiatric adverse effects, namely impulse control disorders (ICD), including pathological gambling, hypersexuality, impulsive shopping and binge-eating. These clinical manifestations have a significant clinical impact, jeopardizing patients’ functionality and quality of life.
+
+Objectives
+
+Review the literature regarding the scientific evidence on the association between the use of DA and the development of ICD in patients with PD.
+
+Methods
+
+Non-systematic review based on a search for scientific articles, between 2010 and 2024, in Pubmed using the MeSH terms: ‘dopaminergic agonists’, ‘impulse control disorder’, ‘Parkinson’s disease’.
+
+Results
+
+The analysis published in 2022, based on data collected between 1968 and 2020, showed a high incidence of ICD in patients medicated with dopamine agonists. Pramipexole and ropinirole showed a clear association with pathological gambling, hypersexuality and impulsive buying behavior.
+
+A prospective study by Weintraub found that 17.1 percent of patients exposed to DA developed at least one form of ICD. It should be noted that behavioral symptoms showed a dose-dependent relationship, and in many cases regressed after the agonist was reduced or discontinued. The risk of ICD associated with ropinirole increases proportionally with the plasma concentration of the drug, while with pramipexole, the risk remains high even at lower serum levels, suggesting an intrinsic affinity of this compound for D3 receptors in the limbic regions.
+
+On a neurobiological level, in patients with ICD, a significant reduction in the availability of D3 receptors in the ventral striatum and an increase in the release of dopamine in this region in response to reward stimuli, such as risky behavior, were observed. This supports the hypothesis of limbic dopaminergic sensitization induced by chronic exposure to DA.
+
+Several predisposing factors have been identified as potentiating the risk of developing ICD, such as early onset of PD, personal and family history of addictive behaviors, impulsive personality traits, and pre-existing psychiatric comorbidity.
+
+Conclusions
+
+Scientific evidence shows a clear association between the use of dopamine agonists, particularly pramipexole and ropinirole, and the development of ICD in Parkinson’s patients. This relationship is mediated by neurobiological mechanisms involving D3 dopamine receptors and reward circuits. The presence of individual risk factors reinforces the importance of regular monitoring of risk behaviors, optimizing therapy and educating patients and carers in order to prevent and intervene effectively in these situations.
+
+Disclosure of Interest
+
+None Declared
+
diff --git a/corpus/psychology/text/21e98188a26122ae.txt b/corpus/psychology/text/21e98188a26122ae.txt
new file mode 100644
index 0000000000000000000000000000000000000000..92887711b493f9bb0bf42aba38cd16beaadb197d
--- /dev/null
+++ b/corpus/psychology/text/21e98188a26122ae.txt
@@ -0,0 +1,303 @@
+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Biomimetics (Basel)
+Journal ID: Biomimetics (Basel)
+NLM Journal ID: 101719189
+Journal ID: biomimetics
+
+Biomimetics
+
+EISSN: 2313-7673
+Publisher: Multidisciplinary Digital Publishing Institute (MDPI)
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC13112937
+PMID: 42041481
+DOI: 10.3390/biomimetics11040251
+Article ID: biomimetics-11-00251
+Article version: 1
+Subjects: Article
+
+Bioinspired Sternal Implant Design for Generic Anatomical Reconstruction: An In Silico Framework for Material Selection and Biomechanical Validation
+
+https://orcid.org/0000-0001-7727-4323 Kutbay Işıl 1
+https://orcid.org/0000-0001-8610-2638 Gerdan Zeynep 2
+https://orcid.org/0000-0002-8255-5987 Çolak Murat 3
+https://orcid.org/0000-0002-4912-8828 Tabak Yasemin 4
+https://orcid.org/0000-0002-9371-8307 Şensoy Abdullah Tahir 5 6 7 *
+Ehrlich Hermann Academic Editor
+1 Department of Electronics and Automation, University of Health Sciences, Uskudar, 34668 Istanbul, Türkiye; isil.kutbay@sbu.edu.tr
+2 Vocational School of Technical Sciences, Department of Digital Health Systems Technician, Bayburt University, 69000 Bayburt, Türkiye; zeynepgerdan@bayburt.edu.tr
+3 Vocational School of Technical Sciences, Department of Electronic Automation, Bayburt University, 69000 Bayburt, Türkiye; mcolak@bayburt.edu.tr
+4 TÜBİTAK National Metrology Institute (UME), 41470 Gebze, Türkiye; yasemin.tabak@tubitak.gov.tr
+5 Faculty of Mechanical Engineering, Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands
+6 Department of Oral and Maxillofacial Surgery, Erasmus University Medical Center, Doctor Molewaterplein 40, 3015 GE Rotterdam, The Netherlands
+7 Department of Biomedical Engineering, Faculty of Engineering and Natural Sciences, Samsun University, 55420 Samsun, Türkiye
+* Correspondence: a.t.sensoy@tudelft.nl or tahirsensoy@hotmail.com
+Electronic publication date: 2026 Apr 5
+Publication date: 2026 Apr
+Volume: 11
+Issue: 4
+Electronic Location ID: 251
+Received 2026 Mar 8; Revised 2026 Mar 31; Accepted 2026 Apr 2
+Copyright: © 2026 by the authors.
+Copyright year: 2026
+License: Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Keywords: sternum implant, bioinspired design, CES selector, biomaterial selection, finite element analysis, thoracic reconstruction
+
+Funding: Delft University of Technology https://ror.org/02e2c7k09 The article processing charge (APC) was funded by Delft University of Technology.
+
+Ÿ==============================Ÿ
+The sternum protects the intrathoracic organs and contributes to chest wall mechanics, which makes reconstruction after tumor resection, trauma, or infection a demanding biomechanical problem. This study presents an in silico workflow for preselecting materials for sternal implants before physical prototyping. After a virtual resection, an anatomically conformal implant was designed and candidate biomaterials were screened in CES Selector using density, elastic modulus, fatigue strength, fracture toughness, toxicity, medical grade suitability, and MRI safety. A representative subset of the screened candidates was then compared by finite element modeling in terms of stress transfer and deformation. Seventeen candidates met the screening criteria. Ti-13Nb-13Zr showed an elastic modulus of about 80 GPa, and the titanium-based candidates showed deformation values of about 0.96 to 1.03 mm, whereas GF PEEK reached about 1.74 mm. The stress shielding index also showed that titanium-based materials remained on the implant-dominant side, while polymer-based materials shifted stress transfer toward bone. Taken together, the findings suggest that Ti-13Nb-13Zr offers the best overall balance for load-bearing sternal reconstruction, whereas PEEK-based systems may be more suitable within the present model for hybrid or adjunct designs. The proposed workflow can support early implant planning and guide future experimental and clinical studies.
+
+1. Introduction
+
+Material selection is a crucial stage in engineering design because the mechanical performance, durability, and safety of a structure depend directly on the chosen material. This topic has been studied widely in the aerospace [1], automotive [2], energy [3], and biomedical engineering [4] fields. A sound selection process begins with defining the required functional conditions, identifying key properties, comparing realistic candidates, and matching them to the intended use [5,6,7]. Engineering materials, including metals, ceramics, glasses, polymers, elastomers, and composites, offer a broad range of mechanical, physical, and environmental characteristics. As material science has expanded, the selection process has also become more complex because the number of viable alternatives has grown substantially [8,9,10,11,12,13].
+
+In biomedical engineering, where implants and medical devices interact directly with living tissues, material selection becomes even more demanding [4]. For site-specific reconstruction problems such as the sternum, biomechanical role, anatomical location, expected service life, biocompatibility, and imaging considerations all need to be considered together [14,15,16]. Digital tools such as CES help organize material property data and support rapid comparison of competing candidates [13]. Foundational work by Ashby and related materials design frameworks have been especially influential in making material selection more systematic and transparent [6,8,10,13].
+
+The sternum is a flat bone located at the anterior chest wall and plays an important role in protecting thoracic organs, supporting respiratory mechanics, and maintaining thoracic stability [15,16,17]. It is composed of the manubrium, body, and xiphoid process, and like other flat bones it contains a cancellous core surrounded by cortical bone [16]. Because of this anatomy and its mechanical role, reconstructive materials must provide sufficient stability without creating an excessive stiffness mismatch with the surrounding tissue.
+
+Many materials have been explored for sternal and chest wall reconstruction, including titanium alloys, stainless steel systems, polyethylene-based implants, and high-performance polymers such as PEEK [14,17,18,19]. In practice, material choice is guided by stability, biocompatibility, infection risk, manufacturability, radiological behavior, and cosmetic outcome [17,19,20,21]. Polymeric materials attract attention because of their low density, radiolucency, and relatively compliant behavior, but in sternal reconstruction their use is usually considered together with the need to maintain adequate chest wall stability in the central load-bearing region [19,22,23,24,25].
+
+Although the literature includes many reports on sternal reconstruction, implant performance, and clinical technique, studies that focus specifically on systematic biomaterial preselection for the sternum remain limited. Finite element analysis has therefore become an important tool for examining bone–implant interaction, estimating deformation and stress patterns, and refining implant design before fabrication [4,26,27]. Previous work has shown that numerical simulation can improve chest wall reconstruction strategies and support the safer design of advanced sternal implants [19,26,27,28].
+
+The novelty of the present study lies in the establishment of an integrated in silico workflow that combines anatomically conformal implant modeling based on sternum anatomy, CES based material pre-screening, and comparative finite element analysis for early-stage sternal implant development. After virtual resection, the implant geometry was designed in accordance with the anatomical structure, and the candidate materials were subsequently narrowed through systematic screening and biomechanical assessment. The proposed framework is intended to guide pre-experimental decision making rather than to replace clinical evidence.
+
+Therefore, this research aims to establish a bioinspired framework for sternal implant development by considering the boundary conditions of the anterior chest wall. Within this scope, an anatomically conformal implant design workflow was integrated with computer-aided material screening using the CES database and subsequent finite element validation. By evaluating density, Young’s modulus, fatigue strength, fracture toughness, RoHS compliance, toxicity, medical classification, and MRI safety, the study provides a systematic preselection strategy that can reduce early-stage design uncertainty and support surgical planning prior to physical prototyping.
+
+2. Materials and Methods
+
+The methodological flowchart of this study consisted of four main stages: (1) anatomical model acquisition and region of interest (ROI) processing, (2) virtual tumor resection and implant design, (3) multicriteria material selection using the CES Selector database, and (4) biomechanical validation through finite element analysis (FEA). The overall flowchart is illustrated in Figure 1.
+
+2.1. Anatomical Modeling
+
+A generic human sternum STL model was initially imported to serve as the anatomical basis for the study. The 3D sternum model, developed by Artec Group Inc., is licensed under the Creative Commons Attribution 3.0 Unported License (CC BY 3.0). The model was processed using Materialise 3-matic 18.0 (Materialise NV, Leuven, Belgium), licensed to Erasmus MC University for academic research.
+
+To reduce geometric complexity and focus computational resources on clinically relevant regions, the region of interest (ROI) was isolated by trimming surrounding structures. Surface artifacts, mesh discontinuities, and irregular manifold features were repaired through local smoothing, remeshing, and edge refinement operations. This preprocessing step ensured topological consistency for the subsequent virtual surgery and implant design stages.
+
+2.2. Virtual Surgery
+
+To mimic a realistic clinical condition, the design workflow was initiated with a virtual tumor resection scenario. Although the anatomical basis of the model was generic rather than derived from a patient, the resection-based workflow was intended to emulate the design logic used in patient-adapted reconstruction planning [14,15,17,19]. Using 3-matic surgical simulation tools, a segmental sternectomy was planned virtually. The resection margins were defined based on typical oncological clearance zones reported in thoracic oncology practice.
+
+Following the simulated resection, an anatomically conformal implant was designed using local push-pull and Boolean operations, particularly in the implant and bone connection regions. The implant geometry was shaped to restore the anterior chest wall contour while maintaining attachment compatibility with the rib sternum junctions. All geometries were exported in high-resolution STL format for numerical analysis and mechanical evaluation. This virtual surgical planning workflow provides a reproducible in silico environment for assessing implant performance prior to physical prototyping.
+
+2.3. Material Selection
+
+One of the most widely-used computer-aided material selection software tools in materials engineering applications is CES Selector, known for its easy-to-use interface and comprehensive material database. Among its most prominent features are the wide range of materials it offers and its ability to integrate various material selection criteria. The software includes several selection strategies, with the most commonly-used methods being direct database search, use of property comparison charts, filtering based on prescriptive criteria, and multicriteria decision making (MCDM) approaches. Furthermore, Ashby diagrams allow for the visualization of relationships between two material properties and enable the graphical analysis of the positions of different material groups.
+
+In this study, a selection procedure based on predefined threshold values was implemented to determine the appropriate material for a sternum implant. Initially, a suitable material database was selected via the Selection module, followed by the definition of graphical or numerical limit conditions based on mechanical, physical, and thermal properties relevant to the targeted application. Through the software’s Limit function, minimum and maximum values for each property were specified, thereby eliminating materials that did not meet the criteria and generating a list of candidate materials. The database contains extensive information on numerous parameters, including density, elastic modulus, tensile and yield strength, thermal conductivity, and machinability.
+
+During the material selection process, the biomechanical conditions of the anatomical region where the implant is to be used were taken into account. Accordingly, appropriate threshold values were defined for all relevant parameters, and alternative material groups meeting these requirements were identified. The final selection was made by comparing the alternatives within the framework of the specified properties.
+
+A total of 17 candidate biomaterials commonly used in orthopedic and thoracic reconstruction were screened using the CES Selector 2015 (Granta Design Limited, Cambridge, UK). The material selection strategy adhered strictly to a prescriptive filtering approach rather than a simple database scan. Filtering criteria were defined as limit functions, guided by the general engineering material-selection framework, and then cross-checked against biomechanical and clinical considerations reported for sternum and chest wall reconstruction, including reconstruction materials, fixation strategies, and case-based implant use [4,13,14,21,22,23,29].
+
+Table 1 provides a detailed summary of the fundamental material properties defined for sternum implants and the corresponding threshold values. This systematic approach has enabled the selection of the most functional and biocompatible material from among the available alternatives. The table specifies boundary conditions for density and some mechanical properties for material selection. Additionally, RoHS (EU) compliant grades, toxicity ratings, medical grades (USP Class VI, ISO 10993-1) [30], and MRI compatible options are identified. RoHS (EU) monitors material compliance with the European Restriction of Hazardous Substances (RoHS) legislation. MRI compatible indicates whether a material is safe for use in a magnetic resonance environment.
+
+These specified limit values were defined to ensure that the materials considered for sternal implant applications meet the required mechanical performance and biocompatibility expectations. The pre-screening limits were not selected arbitrarily; rather, they were established by drawing on the literature on biomaterial selection, sternum and chest wall reconstruction, and related biomedical implant applications.
+
+The selected Young’s modulus interval was intentionally kept broad at the pre-screening stage to include both metallic and high-performance polymer-based biomaterials. In line with this literature-informed screening strategy, this range does not imply equivalence with native bone. Instead, it allows subsequent narrowing through biomechanical comparison, where the compromise between stiffness, strength, and thoracic stability can be evaluated more critically.
+
+2.4. Finite Element Modeling
+
+To compensate for the absence of physical experimental testing, finite element analysis was used as a comparative biomechanical validation tool, as supported by prior implant selection and chest wall reconstruction studies [4,26,27].
+
+For model preparation, the implant and sternum geometries were imported into ANSYS Workbench 2024 R2 (ANSYS Inc., Canonsburg, PA, USA). A tetrahedral mesh with local refinement was generated to improve accuracy in regions expected to exhibit higher stress gradients. The final mesh consisted of 385,260 elements and 627,083 nodes. Mesh quality assessment showed an average element quality of 0.77269 and an average skewness of 0.33811, indicating acceptable overall mesh quality for comparative finite element evaluation. Boundary conditions were defined using a simplified static configuration adapted from the comparative boundary condition framework reported in [27] for the present comparative model. A single normalized pressure load together with fixed support conditions was applied for comparative finite element analysis. The applied mesh strategy and boundary conditions are illustrated in Figure 2.
+
+Formal mesh convergence analysis, fixation hardware, and detailed bone implant interface mechanics were not included explicitly in the present framework. These choices were made to isolate the effect of bulk material behavior during preselection, but they also define the main methodological limitations of the study. In addition to mesh quality assessment, a local mesh sensitivity check was performed by refining the mesh in regions with higher stress gradients. No significant changes were observed in the overall deformation patterns or comparative trends, supporting the adequacy of the selected mesh density for the present analysis.
+
+The current finite element model was constructed as a comparative linear elastic model. The bone domain was represented as a single homogeneous cortical bone layer with a Young’s modulus of 10.18 GPa and a Poisson’s ratio of 0.30. For comparative FEA, the Young’s modulus and Poisson’s ratio values assigned to the implant materials were taken as single representative input values derived as the midpoints of the lower and upper CES property ranges reported in Table 3. The implant materials were assigned isotropic linear elastic properties as follows: austenitic NiTi, 62.0 GPa and 0.33; PARA (50% glass fiber), 20.5 GPa and 0.33; PEEK (30% carbon fiber), 22.85 GPa and 0.44; PEEK (30% glass fiber), 9.81 GPa and 0.40; Ti-3Al-2.5V, 93.0 GPa and 0.36; Ti-6Al-4V, 113.5 GPa and 0.315; Ti-6Al-7Nb, 105.0 GPa and 0.36; Ti-12Mo-6Zr-2Fe, 76.6 GPa and 0.33; Ti-13Nb-13Zr, 78.9 GPa and 0.34; and commercially pure Ti Grade 4 (annealed), 109.5 GPa and 0.345. These values were used as the actual FEA input properties for comparative simulation. The applied surface pressure was defined as a normalized comparative surrogate load based on the simplified boundary condition approach adapted from [27]. It should therefore be interpreted as a comparative modeling condition rather than as a patient-specific physiological load.
+
+For material assignment and comparative simulations, a representative subset of the screened candidates was modeled for comparative FEA. This subset comprised austenitic NiTi, PARA (50% glass fiber), PEEK (30% carbon fiber), PEEK (30% glass fiber), Ti-3Al-2.5V (Grade 9), Ti-6Al-4V (solution treated & aged), Ti-6Al-7Nb, Ti-12Mo-6Zr-2Fe, Ti-13Nb-13Zr (solution treated & aged), and commercially pure Ti Grade 4 (annealed). Material parameters were assigned using the actual FEA input properties summarized above, while supporting literature was used to contextualize representative material classes and biomechanical considerations [25,27,31,32,33,34]. For NiTi, the finite element model used an equivalent linear elastic representation with a Young’s modulus of 62.0 GPa and a Poisson’s ratio of 0.33. This simplification does not capture phase transformation or superelastic behavior and is therefore considered a modeling limitation.
+
+The simulations quantified equivalent (von Mises) stress distribution, total deformation and displacement patterns, comparative load-bearing response under quasi-static loading, and a comparative stress shielding index (SSI) describing relative load sharing between the implant and the surrounding bone. In this study, SSI values closer to zero were interpreted as more balanced stress sharing; positive values indicated more implant-dominant load transfer, whereas negative values indicated a shift toward greater stress transfer in bone.
+
+For performance evaluation, each candidate material was analyzed under an identical loading scenario to enable direct comparison. Within the assumptions of the present generic model, Ti-13Nb-13Zr showed the most balanced response among the investigated candidates because its lower modulus reduced stiffness mismatch while maintaining low deformation. Ti-6Al-7Nb also showed favorable structural performance, whereas PEEK-based systems remained more attractive for hybrid or adjunct concepts than for the main load-bearing region.
+
+3. Results
+
+Sternal implant material selection requires a balance between mechanical stability, biocompatibility, manufacturability, radiological compatibility, and long-term clinical safety. Stability and rigidity are necessary to prevent paradoxical motion and maintain chest wall integrity, whereas biocompatibility and infection resistance shape host tolerance and postoperative outcome. Flexibility and formability influence intraoperative adaptation to the defect, and the overall risk of complications also depends on soft tissue coverage and wound healing conditions [15,17,19,20].
+
+Guided by these principles, the present study implemented a rule-based, multicriteria screening using CES software under the boundary conditions specified in Table 1. The screening returned 17 distinct candidates spanning metallic alloys and high-performance polymers (Table 2). Given that some entries belong to the same material family but differ by processing history or condition, such as annealed versus aged, a representative comparison across distinct classes was generated (Table 3) to enable an interpretable group level assessment.
+
+In addition to the overall candidate pool, representative materials from each group were compared in Table 3 to highlight how reinforcement type, composition, and processing history influence the final property envelope within the same material family.
+
+3.1. Candidate Comparison
+
+Table 2 lists the 17 candidate materials that satisfied the predefined boundary conditions (density, stiffness window, fatigue and fracture resistance, toxicity class, RoHS compliance, MRI safety). The pool includes austenitic NiTi, fiber reinforced polymers (PARA, PEEK), commercially pure (CP) Ti grades, and alpha–beta and near beta titanium alloys (e.g., Ti-6Al-4V, Ti-6Al-7Nb, Ti-13Nb-13Zr). To enable a direct comparison across categories, Table 3 summarizes key mechanical, physical, and biological properties relevant to sternal reconstruction.
+
+In brief, PEEK-based candidates offer low density and radiolucency, which can be advantageous for imaging and handling [24,25]. In the present comparison, however, these polymer-based candidates showed higher deformation than the titanium alloys, which suggests greater suitability for hybrid concepts or less demanding regions than for the main load-bearing part of the sternum. By contrast, the titanium candidates combined lower deformation with higher structural stiffness, which is more consistent with the demands commonly emphasized in chest wall reconstruction practice [17,19,28]. Among them, Ti-13Nb-13Zr is particularly attractive because its elastic modulus is lower than that of conventional titanium alloys and closer to bone [32,33]. Ti-6Al-7Nb remains a strong vanadium-free alternative within the broader family of biomedical titanium alloys, while Ti-13Nb-13Zr offers a lower-modulus option within the same group [35,36]. Austenitic NiTi offers high toughness and pseudoelasticity, but concerns related to surface condition, corrosion behavior, and biocompatibility still justify caution for permanent implantation [34].
+
+Because the sternum functions as part of a compliant thoracic system rather than as a purely axial load-bearing bone, material selection should also consider the balance between structural support and physiological chest wall motion. For this reason, compliance is discussed together with strength and stiffness in the revised interpretation.
+
+To visualize these relationships, Ashby plots comparing density, fracture toughness, fatigue strength, and elastic modulus were generated (Figure 3). The plots show that titanium alloys occupy the region of higher strength and toughness, whereas high-performance polymers cluster in the lower-density region, but with lower toughness and fatigue resistance. This pattern is consistent with the current chest wall reconstruction literature, which continues to favor customized titanium solutions when structural stability is the main priority [14,18,19,28,37].
+
+3.2. Finite Element Results
+
+To complement material screening and compensate for the absence of physical tests, finite element analysis (FEA) was used as an in silico validation method. Simulations assessed equivalent (von Mises) stress, total deformation, and bone stress under the applied comparative loading condition. Figure 4 presents an illustrative example for the rib sternum model with an austenitic NiTi implant, showing: (a) stress distribution in bone, (b) stress distribution in the implant, and (c) total deformation of the rib cage. In this representative case, the NiTi implant showed a balanced load-sharing pattern within the present comparative model. Under the current linear elastic representation, the stress state in the implant remained within the modeled response range, while the overall deformation remained within the range calculated for this comparative loading condition. These results support NiTi as a mechanically interesting candidate; however, they should not be interpreted as a direct prediction of superelastic behavior, and concerns related to surface condition, corrosion behavior, and biocompatibility still justify caution for permanent load-bearing use [34].
+
+The finite element analysis results presented in Figure 5 illustrate the distribution of implant stress, bone stress, and total deformation following implant placement. As shown in Figure 5, the von Mises stress distribution within the implant indicates that titanium alloys, particularly Ti-13Nb-13Zr and Ti-6Al-7Nb, remain within safe loading limits relative to their corresponding yield strength ranges, without exhibiting localized stress concentrations that may compromise implant integrity. Bone stress levels also remain similar across all metallic candidates (≈17 MPa), suggesting a broadly comparable load-transfer response in the bone despite differences in implant stiffness.
+
+The total deformation profiles in Figure 5 reveal that polymer materials, especially glass fiber reinforced PEEK, exhibit higher deformation values (≈1.74 mm). In contrast, titanium alloys show substantially lower deformation ranges (≈0.96–1.03 mm), supporting their suitability for structurally stable sternal reconstruction. Ti-13Nb-13Zr, with its moderate elastic modulus, demonstrates a balanced biomechanical response, combining favorable stress distribution with controlled deformation.
+
+Overall, the results in Figure 5 highlight that appropriate implant material selection must consider not only high mechanical strength but also load transfer characteristics, bone implant mechanical interaction, and deformation behavior under the present comparative loading condition. In this context, Ti-13Nb-13Zr emerges as the most balanced candidate due to its elastic modulus being closer to that of bone and its stable mechanical performance. Titanium alloys therefore remain the most suitable options for sternal reconstruction, offering both structural reliability and favorable biomechanical compatibility.
+
+Figure 6 summarizes the SSI values for the candidate materials. In this study, values closer to zero were taken to indicate more balanced stress sharing between the implant and the surrounding bone. All metallic candidates remained on the positive side of the scale. NiTi showed the lowest SSI among the metals at 0.29, followed by Ti-12Mo-6Zr-2Fe at 0.35 and Ti-13Nb-13Zr at 0.39. The highest SSI values were observed for Ti-6Al-4V STA (0.46) and annealed Ti Grade 4 (0.45).
+
+The polymer-based candidates fell on the negative side, with CF PEEK at −0.18, PARA at −0.31, and GF PEEK at −1.49. In the revised interpretation, these negative values are not treated as automatically favorable. Instead, they indicate a shift of load transfer away from the implant and toward the surrounding bone, which in the case of GF PEEK is accompanied by substantially greater deformation. Accordingly, SSI was interpreted together with both implant stress and deformation rather than as a standalone ranking criterion.
+
+4. Discussion
+
+When the CES screening, Ashby diagrams, finite element results, and SSI trends are considered together, the results support a graded interpretation rather than an absolute ranking. Among the tested candidates, Ti-13Nb-13Zr provided the most balanced overall response within the assumptions of the present model because it combined relatively low deformation with a lower modulus than conventional titanium alloys. Ti-6Al-7Nb also performed well mechanically, while Ti-6Al-4V remained structurally strong but more implant-dominant in its load sharing profile. PEEK-based candidates shifted stress transfer toward bone, but this was accompanied by higher deformation, which limits their interpretation as primary load-bearing options in the central sternum. Austenitic NiTi remained mechanically interesting, yet its simplified linear elastic representation and known surface and corrosion related considerations warrant caution. Although direct experimental validation was not performed, sternum-related mechanical test development studies have described fatigue-oriented bench-top approaches that may support future validation of such constructs [38]. The predicted stress and deformation ranges are nevertheless consistent in order of magnitude with previously reported numerical studies on chest wall reconstruction and sternal implants. This agreement supports the internal consistency of the present comparative model despite its simplified assumptions.
+
+Ti-13Nb-13Zr appears to offer the best overall compromise in this study, since its elastic modulus is closer to that of bone, its deformation remained low, and its SSI was lower than that of the conventional titanium grades. Taken together, these findings are consistent with the broader preference for lower modulus biomedical titanium alloys [33,35,36]. Ti-6Al-7Nb also performed well mechanically in the present simulations and belongs to the group of titanium alloys already used in biomedical applications [35]; however, its higher stiffness and more positive SSI suggest less balanced load sharing than Ti-13Nb-13Zr. Ti-6Al-4V remains attractive because of its strength and long clinical history, but its higher modulus and higher SSI point to a greater tendency toward implant-dominant loading, in line with the stress shielding concerns reported for conventional titanium systems [33]. PEEK-based candidates such as CF PEEK and GF PEEK shifted stress transfer toward bone, as reflected by their negative SSI values; even so, their larger deformation values, particularly for GF PEEK, suggest within the present model that they may be more suitable for hybrid concepts or less demanding regions than for the main load-bearing part of the sternum. Austenitic NiTi showed the lowest positive SSI among the metallic candidates, which makes it mechanically interesting; nevertheless, the long-term use of nickel-containing materials still warrants caution regarding surface condition, corrosion behavior, and biocompatibility, so its role would require careful case-based justification [34].
+
+Overall, this ordering is in line with recent clinical and biomechanical reports that continue to favor patient-specific titanium reconstruction when anatomical fit and structural stability are the main priorities [14,18,37].
+
+It should be noted that the bone domain was simplified as a single homogeneous cortical layer, and the trabecular (cancellous) core of the sternum was not explicitly modeled. This simplification may influence local stress distributions and represents a limitation of the present approach.
+
+From a stress shielding perspective, the SSI trend also fits the broader implant literature. Lower modulus titanium alloys are generally preferred over conventional Ti-6Al-4V because they reduce stiffness mismatch and improve load transfer [32,33,36]. The present model showed the same tendency. Ti-13Nb-13Zr gave a lower SSI than Ti-6Al-4V while keeping deformation within the low range seen for the titanium group. By contrast, the PEEK-based materials moved toward zero or into the negative range, which indicates a shift in stress transfer toward bone, but that shift came with noticeably larger deformation. This is why SSI should not be read on its own in sternal reconstruction. A material that shares stress more evenly is useful only if it also provides enough stiffness to keep the chest wall stable. This balance helps explain why titanium-based patient-specific implants still dominate current chest wall reconstruction practice [19,28]. Therefore, SSI should be interpreted as a relative indicator of load-sharing behavior rather than a direct predictor of clinical performance.
+
+Recent clinical series have further supported customized titanium-based reconstruction for complex sternal defects, reporting encouraging perioperative and short- to mid-term outcomes for patient-specific prosthetic strategies [39,40]. At the same time, newer literature underscores that three-dimensional planning, patient-specific implant design, and continued biomechanical optimization of both metallic and polymer-based solutions are becoming central to contemporary chest wall reconstruction workflows [41,42].
+
+Consequently, this in silico framework highlights the potential of low modulus alloys such as Ti-13Nb-13Zr for sternal reconstruction while providing decision support before physical prototyping. However, the results remain sensitive to the applied boundary conditions, generic geometry, linear elastic material assumptions, and the fully bonded representation of the bone implant interface without friction or micromotion. These findings should therefore be interpreted as pre-experimental guidance rather than as a definitive clinical prescription. To improve the clinical relevance of the framework, future studies should incorporate patient-specific imaging, patient-specific fixation strategies, mesh convergence analysis, advanced constitutive modeling, and experimental validation.
+
+5. Conclusions
+
+This study presents an in silico framework for sternal implant material preselection that integrates anatomical reconstruction logic, rule-based CES screening, and comparative finite element analysis. Within the assumptions of the present generic model, Ti-13Nb-13Zr emerged as the most balanced candidate among the materials evaluated, while Ti-6Al-7Nb also remained a strong metallic alternative. PEEK-based materials may be more suitable for adjunct, interface, or hybrid concepts than for the primary load-bearing portion of the sternum. These findings should be interpreted as pre-experimental guidance rather than as definitive evidence of clinical superiority.
+
+From a biomimetic perspective, the results highlight the importance of matching not only implant geometry, but also the mechanical behavior of native bone. Advances in additive manufacturing may further enable anatomically conformal and functionally graded implant designs with improved load transfer at the bone–implant interface. Future work should combine refined finite element modeling with experimental testing, surface engineering, and clinical validation to translate these computational findings into reliable chest wall reconstruction strategies.
+
+Author Contributions
+
+Conceptualization, M.Ç. and A.T.Ş.; methodology, I.K., M.Ç. and A.T.Ş.; investigation, Z.G. and Y.T.; resources, A.T.Ş.; data curation, I.K. and Z.G.; writing—original draft preparation, I.K., Z.G., M.Ç., Y.T. and A.T.Ş.; writing—review and editing, I.K., Z.G., M.Ç., Y.T. and A.T.Ş.; visualization, A.T.Ş. and M.Ç.; supervision, A.T.Ş. and M.Ç.; project administration, A.T.Ş. and M.Ç. All authors have read and agreed to the published version of the manuscript.
+
+Institutional Review Board Statement
+
+Not applicable.
+
+Informed Consent Statement
+
+Not applicable.
+
+Data Availability Statement
+
+All data supporting the findings of this study are available within the article.
+
+Conflicts of Interest
+
+The authors declare no conflicts of interest.
+
+Figure 1 Flowchart of the study.
+
+Figure 2 Mesh model and boundary conditions applied for FEA.
+
+Figure 3 Ashby diagrams: (a) density vs. fracture toughness, (b) density vs. fatigue strength, (c) Young’s modulus vs. fracture toughness, and (d) Young’s modulus vs. fatigue strength.
+
+Figure 4 Finite element analysis results for the rib cage model with an austenitic NiTi implant: (a) equivalent von Mises stress distribution in bone, (b) equivalent von Mises stress distribution in the implant, and (c) total deformation of the rib cage.
+
+Figure 5 Finite element analysis results for implant stress (MPa), bone stress (MPa), and total deformation (mm).
+
+Figure 6 Stress shielding index (SSI) of the candidate materials. Values closer to zero indicate a more balanced stress sharing condition between the implant and the surrounding bone.
+
+biomimetics-11-00251-t001_Table 1 Table 1 Boundary conditions used for implant material selection.
+
+Form	Bulk Material	
+Density (kg/m3)	≤7 × 103	
+Young’s modulus (GPa) 	10 to 120	
+Fatigue strength at 107 cycles	≥60 MPa	
+Fracture toughness (MPa.m0.5)	≥5	
+RoHS (EU) compliant grades?	✓	
+Toxicity rating	Slightly toxic,
+Non-toxic	
+Medical grades? (USP Class VI, ISO 10993-1) [30]	✓	
+MRI safe	Safe	
+
+biomimetics-11-00251-t002_Table 2 Table 2 The candidate materials determined by CES.
+
+No	Candidate Material	
+1	Nickel–titanium alloy, austenitic	
+2	PARA (50% glass fiber)	
+3	PEEK (30% carbon fiber)	
+4	PEEK (30% glass fiber)	
+5	Titanium, alpha–beta alloy, Ti-3Al-2.5V (Grade 9)	
+6	Titanium, alpha–beta alloy, Ti-6Al-4V, aged	
+7	Titanium, alpha–beta alloy, Ti-6Al-4V, annealed	
+8	Titanium, alpha–beta alloy, Ti-6Al-4V, cast	
+9	Titanium, alpha–beta alloy, Ti-6Al-4V, solution treated and aged	
+10	Titanium, alpha–beta alloy, Ti-6Al-7Nb	
+11	Titanium, beta alloy, Ti-12Mo-6Zr-2Fe	
+12	Titanium, commercial purity, Grade 1	
+13	Titanium, commercial purity, Grade 2	
+14	Titanium, commercial purity, Grade 3	
+15	Titanium, commercial purity, Grade 4	
+16	Titanium, commercial purity, Grade 4, annealed	
+17	Titanium, near-beta alloy, Ti-13Nb-13Zr, solution treated and aged	
+
+biomimetics-11-00251-t003_Table 3 Table 3 Comparison of the candidate materials.
+
+	Nickel–Titanium Alloy, Austenitic	PARA (50% Glass Fiber)	PEEK (30% Carbon Fiber)	PEEK (30% Glass Fiber)	Ti-3Al-2.5V (Grade 9)	Ti-6Al-4V,
+Solution Treated and Aged	Ti-6Al-7Nb	Ti-12Mo-6Zr-2Fe	Titanium, Commercial Purity, Grade 4,
+Annealed	Ti-13Nb-13Zr,
+Solution Treated and Aged	
+Density (kg/m3)	6410–6540	1630–1660	1420–1440	1490–1540	4470–4490	4410–4450	4510–4530	4980–5000	4490–4530	4650–5100	
+Young’s modulus (GPa)	41–83	17.8–22.2	20.7–25	8.62–11	91–95	110–117	100–110	63.1–90.1	107–112	76.2–81.6	
+Yield strength (elastic limit) (MPa)	195–690	231–289	190–228	124–158	483–620	827–1070	895–905	906–1150	172–483	785–914	
+Elongation (% strain)	5–50	1.8–2.6	1–4	2–3	15–20	10–12	10–15	10–15	10–25	8–16	
+Poisson’s ratio	0.32–0.34	0.329–0.334	0.43–0.45	0.39–0.41	0.35–0.37	0.31–0.323	0.35–0.37	0.31–0.35	0.34–0.354	0.333–0.35	
+Hardness–Vickers (HV)	1230–1430	74.1–81.9	49.2–54.7	37.2–47.3	103–113	380–420	270–290	327–345	195–205	282–304	
+Fatigue strength at 107 cycles (MPa)	134–162	98.8–109	115–127	61.7–80.3	363–432	613–638	559–564	477–598	306–356	475–525	
+Fracture toughness (MPa.m0.5)	271–328	5.6–6.19	6.34–7.89	5.34–7.93	70–75	82–100	68–75	88–92	50–55	63.7–65.5	
+Toxicity rating	Slightly toxic	Non-toxic	Non-toxic	Non-toxic	Non-toxic	Non-toxic	Non-toxic	Slightly toxic	Non-toxic	Non-toxic	
+
+Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.
+
+
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+14. Wen X. Gao S. Feng J. Li S. Gao R. Zhang G. Chest-wall reconstruction with a customized titanium-alloy prosthesis fabricated by 3D printing and rapid prototyping J. Cardiothorac. Surg. 2018 13 4 10.1186/s13019-017-0692-3 29310677 PMC5759864
+15. Gritsiuta A.I. Bracken A. Abbas A.E. Petrov R.V. Complex anterior chest wall reconstruction after extensive oncologic resections: A narrative review Shanghai Chest 2021 5 41 10.21037/shc-21-8 35495182 PMC9049198
+16. Restrepo C.S. Martinez S. Lemos D.F. Washington L. McAdams H.P. Vargas D. Lemos J.A. Carrillo J.A. Diethelm L. Imaging appearances of the sternum and sternoclavicular joints Radiographics 2009 29 839 859 10.1148/rg.293055136 19448119
+17. Sanna S. Brandolini J. Pardolesi A. Argnani D. Mengozzi M. Dell’Amore A. Solli P. Materials and techniques in chest wall reconstruction: A review J. Vis. Surg. 2017 3 95 10.21037/jovs.2017.06.10 29078657 PMC5638032
+18. Danker S.J. Mericli A.F. Rice D.C. Santos D.A. Butler C.E. Custom 3D-printed Titanium Implant for Reconstruction of a Composite Chest and Abdominal Wall Defect Plast. Reconstr. Surg. Glob. Open 2021 9 e3885 10.1097/GOX.0000000000003885 34858771 PMC8631384
+19. Aramini B. Masciale V. Radaelli L.F.Z. Sgarzani R. Dominici M. Stella F. The sternum reconstruction: Present and future perspectives Front. Oncol. 2022 12 975603 10.3389/fonc.2022.975603 36387077 PMC9649912
+20. Pradeep A. Rangasamy J. Varma P.K. Recent developments in controlling sternal wound infection after cardiac surgery and measures to enhance sternal healing Med. Res. Rev. 2021 41 709 724 10.1002/med.21758 33174619
+21. Josyula A. Parikh K.S. Pitha I. Ensign L.M. Engineering biomaterials to prevent post-operative infection and fibrosis Drug Deliv. Transl. Res. 2021 11 1675 1688 10.1007/s13346-021-00955-0 33710589 PMC8238864
+22. Lipinska J. Kutwin L. Wawrzycki M. Olbrzymek L. Jabłoński S. Chest reconstruction using a custom-designed polyethylene 3D implant after resection of the sternal manubrium OncoTargets Ther. 2017 10 4099 4103 10.2147/OTT.S135681 PMC5566894 28860818
+23. Kamel M. Port J. Altorki N.K. Sternal resections: New materials for reconstruction Curr. Surg. Rep. 2015 3 16 10.1007/s40137-015-0094-1
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+25. Kurtz S.M. Devine J.N. PEEK biomaterials in trauma, orthopedic, and spinal implants Biomaterials 2007 28 4845 4869 10.1016/j.biomaterials.2007.07.013 17686513 PMC2040108
+26. Shash Y.H. Finite element investigation for improving chest wall reconstruction process using ceramic and polymeric implants Sci. Rep. 2025 15 1502 10.1038/s41598-024-79536-3 39788988 PMC11718210
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+28. Young J.S. McAllister M. Marshall M.B. Three-dimensional technologies in chest wall resection and reconstruction J. Surg. Oncol. 2023 127 336 342 10.1002/jso.27164 36630098
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+32. Klinge L. Kluy L. Spiegel C. Siemers C. Groche P. Coraça-Huber D. Nanostructured Ti-13Nb-13Zr alloy for implant application-material scientific, technological, and biological aspects Front. Bioeng. Biotechnol. 2023 11 1255947 10.3389/fbioe.2023.1255947 37691899 PMC10484403
+33. Niinomi M. Liu Y. Nakai M. Liu H. Li H. Biomedical titanium alloys with Young’s moduli close to that of cortical bone Regen. Biomater. 2016 3 173 185 10.1093/rb/rbw016 27252887 PMC4881615
+34. Mani G. Porter D. Grove K. Collins S. Ornberg A. Shulfer R. Surface finishing of Nitinol for implantable medical devices: A review J. Biomed. Mater. Res. B Appl. Biomater. 2022 110 2763 2778 10.1002/jbm.b.35112 35729868
+35. Elias C.N. Lima J.H.C. Valiev R. Meyers M.A. Biomedical applications of titanium and its alloys JOM 2008 60 46 49 10.1007/s11837-008-0031-1
+36. Lee T.H. Variation in mechanical properties of Ti-13Nb-13Zr depending on annealing temperature Appl. Sci. 2020 10 7896 10.3390/app10217896
+37. Moradiellos J. Amor S. Córdoba M. Rocco G. Vidal M. Varela A. Functional Chest Wall Reconstruction with a Biomechanical Three-Dimensionally Printed Implant Ann. Thorac. Surg. 2017 103 E389 E391 10.1016/j.athoracsur.2016.11.048 28359508
+38. Spencer K. Development of Sternum Closure Fatigue Test from an Ultimate Strength Test Method Ph.D. Thesis California Polytechnic State University San Luis Obispo, CA, USA 2003
+39. Liu C. Sun H. Lin F. The application of three-dimensional custom-made prostheses in chest wall reconstruction after oncologic sternal resection J. Surg. Oncol. 2024 129 1063 1072 10.1002/jso.27597 38311813
+40. Yoon D.W. Kim T.H. Cha M.J. Kim G.-H. Lee B. Kim H.G. Kwon M. Jang D. Park B. Three-dimensional printed pure-titanium implantation for chest wall reconstruction involving the sternum and ribs: A novel approach Interdiscip. Cardiovasc. Thorac. Surg. 2024 38 ivae037 10.1093/icvts/ivae037 38561175 PMC11009014
+41. Martinez-Ferro M. Bellia-Munzon G. Toselli L. Sanjurjo D. The role of 3D printing in chest wall reconstruction J. Thorac. Dis. 2024 16 4053 4063 10.21037/jtd-23-881 38983181 PMC11228731
+42. Wang W. Yang S. Han M. Liu H. Feng Q. Su Y. Han Y. Wang J. Three-dimensional printed titanium chest wall reconstruction for tumor removal in the sternal region J. Cardiothorac. Surg. 2024 19 579 10.1186/s13019-024-03078-y 39354530 PMC11446048
diff --git a/corpus/psychology/text/249a7ffe3f191b00.txt b/corpus/psychology/text/249a7ffe3f191b00.txt
new file mode 100644
index 0000000000000000000000000000000000000000..bb8ed1360ed408ed62d3ae94c88f06f6231030d7
--- /dev/null
+++ b/corpus/psychology/text/249a7ffe3f191b00.txt
@@ -0,0 +1,51 @@
+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Evid Based Complement Alternat Med
+Journal ID: Evid Based Complement Alternat Med
+NLM Journal ID: 101215021
+Journal ID: ECAM
+
+Evidence-based Complementary and Alternative Medicine : eCAM
+
+ISSN: 1741-427X
+EISSN: 1741-4288
+Publisher: Wiley
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC10732858
+PMID: 38125088
+DOI: 10.1155/2023/9826513
+Article version: 1
+Subjects: Retraction
+
+Retracted: Clinical Study of Stellate Ganglion Block Combined with General Anesthesia on Hemodynamics, Cognitive Function, and Gastrointestinal Function in Elderly Patients Undergoing Partial Hepatectomy
+
+and Alternative Medicine Evidence-Based Complementary ecam@hindawi.com
+
+Publication date: 2023
+Electronic publication date: 2023 Dec 13
+Volume: 2023
+Electronic Location ID: 9826513
+Received 2023 Dec 12; Accepted 2023 Dec 12
+Copyright: Copyright © 2023 Evidence-Based Complementary and Alternative Medicine.
+Copyright year: 2023
+License: This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Retraction of: Clinical Study of Stellate Ganglion Block Combined with General Anesthesia on Hemodynamics, Cognitive Function, and Gastrointestinal Function in Elderly Patients Undergoing Partial Hepatectomy 2021 7 9 2021 1426753 Evidence-based Complementary and Alternative Medicine : eCAM 10.1155/2021/1426753 PMC8443347 34539796
+
+Ÿ==============================Ÿ
+This article has been retracted by Hindawi, as publisher, following an investigation undertaken by the publisher [1]. This investigation has uncovered evidence of systematic manipulation of the publication and peer-review process. We cannot, therefore, vouch for the reliability or integrity of this article.
+
+Please note that this notice is intended solely to alert readers that the peer-review process of this article has been compromised.
+
+Wiley and Hindawi regret that the usual quality checks did not identify these issues before publication and have since put additional measures in place to safeguard research integrity.
+
+We wish to credit our Research Integrity and Research Publishing teams and anonymous and named external researchers and research integrity experts for contributing to this investigation.
+
+The corresponding author, as the representative of all authors, has been given the opportunity to register their agreement or disagreement to this retraction. We have kept a record of any response received.
+
+
+1 Chen W. Chen B. Wang F. Clinical Study of Stellate Ganglion Block Combined with General Anesthesia on Hemodynamics, Cognitive Function, and Gastrointestinal Function in Elderly Patients Undergoing Partial Hepatectomy Evidence-Based Complementary and Alternative Medicine 2021 2021 7 1426753 10.1155/2021/1426753 34539796 PMC8443347
diff --git a/corpus/psychology/text/298e10b4d8c80515.txt b/corpus/psychology/text/298e10b4d8c80515.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a02ac9fe931e69ca215aa5f70da7d1d1c1cf542b
--- /dev/null
+++ b/corpus/psychology/text/298e10b4d8c80515.txt
@@ -0,0 +1,99 @@
+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Glob Ment Health (Camb)
+Journal ID: Glob Ment Health (Camb)
+NLM Journal ID: 101659641
+Journal ID: GMH
+
+Cambridge Prisms: Global Mental Health
+
+EISSN: 2054-4251
+Publisher: Cambridge University Press
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC13231224
+PMID: 42245324
+DOI: 10.1017/gmh.2026.10213
+Article ID: S2054425126102131
+Article version: 1
+Subjects: Corrigendum
+
+Mental health trajectories and Peer Refugee Helper engagement, among Afghan, Iranian and Syrian refugees and asylum seekers in Greece – CORRIGENDUM
+
+https://orcid.org/0000-0003-4055-641X Lavdas Michalis
+Sandal Gro Mjeldheim
+https://orcid.org/0000-0001-5430-9810 Sijbrandij Marit
+Hoekstra Trynke
+Bøe Tormod
+Corresponding author: Michalis Lavdas; Email: michail.lavdas@uib.no
+Publication date: 2026
+Electronic publication date: 2026 Jun 1
+Volume: 13
+Electronic Location ID: e110
+Copyright: © The Author(s) 2026
+Copyright year: 2026
+Copyright holder: The Author(s)
+License: This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Erratum for: Mental health trajectories and Peer Refugee Helper engagement, among Afghan, Iranian and Syrian refugees and asylum seekers in Greece 12 13 10 2025 e115 Cambridge Prisms: Global Mental Health 10.1017/gmh.2025.10068 PMC12571684 41180569
+Reference count: 1
+Page count: 1
+tdm-reservation: 1
+tdm-policy: https://www.cambridge.org/tdm/tdmrep-policy.json
+
+Ÿ==============================Ÿ
+The authors regret the inclusion of an error in the above article.
+
+On page 3, Table 1, data values were incorrect as follows:
+
+GAD–7 score
+
+Original value: 15.5 (10.1)
+
+Correct value: 8.87 (5.74)
+
+PHQ–9 score
+
+Original value: 19.9 (12.5)
+
+Correct value: 11.07 (6.97)
+
+All statistical analyses, figures, and interpretations reported in the manuscript were conducted using the correct values. Therefore, the error does not affect the results or conclusions of the study and is limited to the descriptive tables.
+
+These values have been corrected in the article.
+
+These values have also been updated in the supplementary material, along with the p-value2 as follows:
+
+GAD–7 score
+
+Original p-value2: >0.9
+
+Correct p-value2: 0.9
+
+PHQ–9 score
+
+Original p-value2: 0.5
+
+Correct p-value2: 0.4
+
+and the T2 values as follows:
+
+GAD–7 score
+
+Original value: 16.07 (10.44)
+
+Correct value: 9.05 (5.98)
+
+PHQ–9 score
+
+Original value: 17.93 (12.16)
+
+Correct value: 9.93 (6.74)
+
+
+Reference
+
+Lavdas M, Sandal GM, Sijbrandij M, Hoekstra T and Bøe T (2025) Mental health trajectories and Peer Refugee Helper engagement, among Afghan, Iranian and Syrian refugees and asylum seekers in Greece. Cambridge Prisms Global Mental Health 12, e115. 10.1017/gmh.2025.10068.41180569 PMC12571684
diff --git a/corpus/psychology/text/2b57e67dc5e85d02.txt b/corpus/psychology/text/2b57e67dc5e85d02.txt
new file mode 100644
index 0000000000000000000000000000000000000000..bb09893c34dd6d83e3a099ab5bf967553a119284
--- /dev/null
+++ b/corpus/psychology/text/2b57e67dc5e85d02.txt
@@ -0,0 +1,331 @@
+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Materials (Basel)
+Journal ID: Materials (Basel)
+NLM Journal ID: 101555929
+Journal ID: materials
+
+Materials
+
+EISSN: 1996-1944
+Publisher: Multidisciplinary Digital Publishing Institute (MDPI)
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC13362894
+PMID: 42451957
+DOI: 10.3390/ma19132878
+Article ID: materials-19-02878
+Article version: 1
+Subjects: Article
+
+Design of Microcapsules for Self-Healing Concrete Based on Fracture Modeling of RVE and UC with PBC Using XFEM and CS Technique
+
+Hanna John Conceptualization Methodology Software Validation Formal analysis Investigation Resources Data curation Writing – original draft Writing – review & editing Visualization Supervision Project administration *
+https://orcid.org/0000-0002-4499-6271 Drieschner Martin Writing – review & editing
+Cascardi Alessio Academic Editor
+Chair of Structural Analysis and Dynamics, Brandenburg University of Technology Cottbus-Senftenberg, Konrad-Wachsmann-Allee 2, 03046 Cottbus, Germany; martin.drieschner@b-tu.de
+* Correspondence: john.hanna@b-tu.de
+Electronic publication date: 2026 Jul 6
+Publication date: 2026 Jul
+Volume: 19
+Issue: 13
+Electronic Location ID: 2878
+Received 2026 Jan 31; Revised 2026 Mar 21; Accepted 2026 Mar 30
+Copyright: © 2026 by the authors.
+Copyright year: 2026
+License: Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Keywords: self-healing concrete (SHC), microcapsules design, fracture modeling, representative volume element (RVE), unit cell (UC), periodic boundary conditions (PBC), eXtended finite element method (XFEM), cohesive surface (CS), volume fraction (Vf), interfacial cohesive properties, microcapsule core–shell thickness ratio
+
+Funding: This research received no external funding.
+
+Ÿ==============================Ÿ
+The fundamental issue in designing encapsulation-based self-healing concrete structures is the design of microcapsules. However there are few studies in the literature on this topic; not only is the fracture of microcapsules crucial for releasing the healing agent to heal fractures in the concrete matrix, but also the amount of the healing agent and expected crack widths. Therefore, in this paper, a novel design method of dimensioning microcapsules for encapsulation-based self-healing concrete (SHC) with consideration for a sufficient volume of healing agent to heal a specific crack width is developed. It is based on the configuration of the representative volume element (RVE) and the unit cell (UC), and associates them with the volume fraction (Vf) and the crack width as variables with applied periodic boundary conditions (PBCs). It is also validated through numerical fracture modeling using the eXtended Finite Element Method (XFEM), and cohesive surface (CS) technique. Effects of interfacial cohesive properties, the microcapsule size, and volume fraction on the load carrying capacity and the crack pattern are investigated numerically. The obtained results are in good agreement with the literature. The developed design method can serve as a valuable tool for obtaining a preliminary design of microcapsules for SHC.
+
+1. Introduction
+
+The ability of encapsulation-based self-healing concrete (SHC) to automatically repair cracks without the need for human intervention has made it a promising technique among others for autonomous self-healing concrete. This ability can prolong the lifespan of concrete structures and lower their maintenance costs [1,2]. It has great prospects for infrastructures because as the propagating cracks strike the capsule shell, the healing agents are released on their own to cure the fractures around the damaged zone; Figure 1. Various healing agents, such as polymer, bacteria, sodium silicate, and various capsule shell materials, e.g., glass, ceramic, gelatin, silicon, expanded clay, cementitious, and polymers have been developed and tested, aiming to extend the life of the healing agent, accelerate the reaction after cracking and improve the healing capability. Also several shapes and sizes of capsules such as vascular, capillary, spherical, and tubular/cylindrical, are investigated [2,3,4]. A recent study developed a capsule-based self-healing system suitable for concrete in CO2-rich environments; in sewer systems due to microbial activities, there has always been a degradable factor, which accelerates the corrosion inside concrete sewer pipes. The capsules, utilizing water treatment sludge, calcium hydroxide, and expansive polymers, significantly restore water tightness and compressive strength through the formation of calcite crystals [5].
+
+The fracture of the capsules, the bonding between the capsules and the concrete matrix, the healing efficiency, and the fracture process have all been the subject of numerous laboratory investigations and experiments, for example [6,7]. Also several computational modeling techniques based on the cohesive zone model (CZM) have been used in SHC to investigate the interaction between capsules and concrete matrix, such as the zero thickness cohesive element approach [8] and the extended finite element method (XFEM) with the cohesive surface (CS) technique, which showed more accuracy [9,10]. The zero thickness cohesive element approach has been widely used for fracture modeling in the literature, although it has a number of important shortcomings, introducing artificial compliance and mesh dependency [11]. The extended finite element method (XFEM) has proven itself to be a promising, flexible, and effective discrete crack technique that allows fracture propagation without re-meshing. Furthermore, it has been demonstrated to model fracture in concrete materials with excellent accuracy [12], and it is already incorporated into commercial software such as ABAQUS [13]. Moreover, computational modeling has demonstrated benefits in simulating physical phenomena including fracture energy, healing patterns, and capsular clustering that are hard and difficult to study experimentally [14,15,16].
+
+Despite extensive research into self-healing mechanisms, there remains a notable lack of experimental and modeling studies addressing the specific design parameters of these systems. To the author’s best knowledge, the optimization of capsule size—the primary component of such techniques—has not been sufficiently explored. While the existing literature has addressed capsule development, the focus has predominantly remained on material characterization (e.g., [17,18]) rather than geometric design. The determination of capsule size is a critical primary issue in the design of self-healing systems, as the requisite volume of the healing agent is intrinsically linked to capsule dimensions, volume fraction (Vf), and the projected crack width. The key novelty of this study lies in the development of a systematic design methodology for dimensioning capsules to ensure a sufficient supply of healing agent for a target crack width. The proposed method utilizes the configurations of the unit cell (UC) and representative volume element (RVE), integrated with periodic boundary conditions (PBCs), while treating Vf and crack width as the fundamental variables. To establish a comprehensive framework, the following subsections summarize the essential concepts of microstructural configuration modeling.
+
+1.1. Representative Volume Element (RVE)
+
+The literature provides several definitions for the representative volume element (RVE), all of which relate to identifying an adequate volume that represents the microstructural geometry and its effective properties. According to one convention, an RVE must serve as a statistically representative sample of the microstructure, encompassing a complete sampling of all possible microstructural configurations [19]. This definition leads to a considerably large RVE for a nonuniform microstructure which is computationally inefficient. An alternative definition characterizes the RVE as the smallest microstructure capable of sufficiently representing the macroscopic properties of interest, such as the constitutive relationship between stress and strain. While this results in a more computationally efficient size, an RVE satisfying this criterion may not always capture the full distribution of internal microfields. In the context of the present numerical simulations, the RVE is defined as the smallest material volume that accurately represents the structural integrity of the material.
+
+1.2. Unit Cell (UC)
+
+The unit cell (UC) is defined as a discrete portion of a material at a lower length scale that can reproduce the entire material domain through appropriate symmetry transformations. When correctly defined, the UC and its translated images fill the entire space without gaps or overlaps. The existence of a UC implies a degree of regularity in the material architecture at the lower scale, which ensures homogeneity at the macroscopic level. While macroscopic homogeneity can also arise from a random distribution at the lower scale based on statistical considerations, the application of a UC typically serves as either a realistic representation of periodic architecture or an idealization of an otherwise random structure. As noted in [20], if the inherent randomness of the lower-scale architecture must be explicitly modeled, a statistical RVE must be employed rather than an idealized UC.
+
+Generally spherical capsules have less influence on the mechanical properties as their shape reduces the stress concentrations around the void left from empty capsules [2,3]. Therefore, the developed design method in this paper focused on spherical microcapsules. However the same principals used in this design method can be applied for any shapes of capsules. The healing mechanism, which occurs by releasing the healing agent once the capsules are cracked, depends critically on the fracture of the capsules. As a result, the developed design method is also validated through numerical fracture modeling using extended finite element method (XFEM), and cohesive surface (CS) technique for the previously mentioned advantages. In this validation, the effects of microcapsule size and the volume fraction (Vf) on the load carrying capacity and the possibility of debonding or fracture of the microcapsules from the concrete matrix are numerically investigated. 2D numerical fracture modeling is performed for the obtained SHC design samples including the microcapsules loaded under uniaxial tension. XFEM is used for modeling the concrete matrix and the microcapsule shell, while the interaction between them is modeled by CS with PBCs applied. The potential use of the developed design method could act as a helpful tool to obtain a preliminary design of microcapsules for self-healing concrete without any complications, especially for costly detailed modeling.
+
+2. Proposed Design Method of Microcapsules/Design Sample
+
+It is assumed that the spherical microcapsules are uniformly distributed in an infinite concrete matrix domain. Therefore, the material can be represented using a representative volume element (RVE) with multiple uniform distributed microcapsules, as illustrated in Figure 2a. Due to the regularity in the distribution of microcapsules, the material also can be represented using a unit cell (UC) with a single microcapsule as illustrated in Figure 2b. The UC for this hypothesis is a cube, and includes a single microcapsule at its centroid. The three dimensions of the cube have the same length (Luc) and at the same time it is equal to the interdistance between the periodic distributed microcapsules. Hence Luc can be defined as the dimension of the SHC design sample. The microcapsule dimensions are represented by the outer diameter (Dc) and the wall shell thickness (tc). In order to model this proposed design method of microcapsules, the periodic boundary conditions (PBCs) should be applied on the outer edges of the SHC design sample, which is basically the UC, to obtain a proper mechanical response of such infinite SHC domains represented by RVE. Although the hypothesis of the uniform distribution microcapsules is somewhat far from the real random distribution of microcapsules, it is suitable to provide a simple method to design the microcapsule based on the definition of RVE and UC. However, the effects of microcapsule clustering, which could be generated from the real random distribution of microcapsules, are studied computationally on the fracture mechanism based on a simple developed approach in another study [14].
+
+2.1. Virtual Domain of the Unit Cell
+
+The volume fraction (Vf) is a parameter which represents the volume ratio of the microcapsule to the unit cell (UC) of the concrete matrix—see Equation (3). The volume of the microcapsule is calculated based on its outer diameter (Dc) as shown in Equation (1) and the volume of the unit cell shown in Equation (2).
+
+(1) Vc=πDc36
+
+(2) Vm=Luc3
+
+(3) Vf=VcVm
+
+Substituting Equations (1) and (2) into Equation (3), Vf could be expressed as follows:
+
+(4) Vf = πDc36 Luc3
+
+From Equation (4) the following equation of Luc could be obtained:
+
+(5) Luc =Dc π6 Vf3
+
+This equation relates the dimension of UC (Luc) which is equal to the distance between microcapsules to the microcapsule size represented by its diameter Dc. Vf can be estimated based on the expected crack width and the required volume of healing agent required to heal that crack.
+
+2.2. Expected Crack Width of the Unit Cell
+
+It is assumed that only one crack will be generated inside the design sample and break the microcapsule. Therefore the healing agent is encapsulated in a microcapsule, which, placed inside the SHC design sample, must be sufficient to heal the crack surface around it. Taking into account the roughness of the crack surface and the possibility that the healing agent will not be completely released from the fractured microcapsule and there will be some healing agent remaining in it. So, it is assumed that the volume of the released healing agent is half of the microcapsule volume. Assuming also that the crack width (tcr) is constant along the crack path, the volume of the healed crack (Vcr) and Luc can be obtained as follows:
+
+(6) Vcr=Vc2=(Luc−Dc2)2tcr
+
+(7) Luc=Vc2tcr+Dc2
+
+Design curves of microcapsules can be developed based on Equations (4) and (7) depending on the capsule diameter, volume fraction, and the expected crack width which can be healed, as shown in Figure 3. It can be seen easily from these curves that a range of volume fraction between 5% and 25% for a range of microcapsule diameters between 2 mm and 12 mm will be able to heal the crack width ranging from 0.1 mm to 1 mm.
+
+3. Modeling Framework
+
+In this study, the simulations of the proposed microcapsule design method as discussed in the previous section are performed to study the effects of microcapsule size, volume fraction (Vf), and interfacial fracture properties between the microcapsule shell and the concrete matrix on the load carrying capacity and the possibility of the microcapsule fracture or debonding from the concrete matrix. The concrete matrix, microcapsule shell, and interaction between them compose the three phases of the specimens that are modeled. Periodic boundary conditions (PBCs) are applied to the outer edges of the SHC design sample using two computational techniques to carry out the simulations. The fracture propagation in both the concrete and the microcapsule has been modeled using the eXtended Finite Element Method (XFEM). The interaction between these two components is modeled by the cohesive surface (CS) technique, as shown in Figure 4. A traction–separation law serves as the basis of damage modeling for both computational techniques.
+
+3.1. Extended Finite Element Method (XFEM)
+
+The concept of local partition of unity serves as the basis for the extended finite element method (XFEM), which could be considered as an extension of the common finite element method. As a result, the cracks can be simply integrated into a finite element mesh and represented as local enrichment functions, avoiding the need for remeshing throughout the simulation [21]—see Figure 5. Cracks are represented by enrichment functions that are integrated into the usual displacement interpolation function, Equation (8) [22]. The standard nodes are not displayed, while the enriched nodes are indicated by black dots, and the crack-tip enriched node by white dots. XFEM is a highly promising approach for fracture modeling, as it has already been incorporated into commercial software like Abaqus [13,23]. More detailed description of this modeling method can be found in [21]. The concrete matrix and microcapsule shell cracks inside Abaqus are modeled by XFEM, which is defined in the interaction module.
+
+(8) u=∑I=1NNI(x)[uI+H(x)aI+∑α=14Fα(x)bIα]
+
+Shape functions are represented by NI(x), nodal displacement vectors are represented by uI, jump functions, like Heaviside functions, are represented by H(x), nodal vectors of the enriched degree of freedom are represented by aI and bIα, and crack-tip functions are represented by Fα(x). The first term on the right affects every node in the model, whereas the second term only affects nodes whose shape function support crosses the inner area of the crack. The third term is applied only to nodes whose form function support extends to the crack tip. This third term is called the “crack tip enrichment” and contains the information of the analytical solution in linear elastic fracture mechanics. However, concrete materials cannot be well handled by linear elastic fracture mechanics. For this reason, in this study the final term on the right-hand side has been eliminated. Consequently, as Figure 5 illustrates that the crack tip will be at the element edge rather than inside the element where it cannot be stopped. XFEM has few drawbacks despite its many benefits for fracture modeling [23]. Two main limitations need to be taken into account. The first one is related to fracture propagation close to the element edge. Allowing numerous cracks to initiate in the same enrichment zone is the second. However, to get around this restriction, there is a setting in the Abaqus input file; see [9,23] for more detailed information.
+
+3.2. Cohesive Surface Technique (CS)
+
+The cohesive surface (CS) is a modeling technique that uses the traction–separation response to simulate a zero-thickness contact interface between two surfaces [9,23]. The interaction between the microcapsule and the concrete matrix is modeled in this work using the CS technique. Pure master–slave roles are used to model it in the contact formulation and it is characterized as a cohesive surface interaction property in Abaqus. Within this work, the concrete matrix’s interior surface is referred to as a master surface and the microcapsule’s outside surface as a slave surface.
+
+3.3. Cohesive Zone Model (CZM)
+
+The cohesive zone model (CZM) is used across the crack surface that links the displacement jump, which is defined by the separation vector, to the cohesive traction conveyed by the discontinuity surface. It uses a traction–separation law to model the failure mechanism of cracks. Figure 6 shows the initially rigid CZM for XFEM, and the initially elastic CZM for CS, which is represented by the linear zone (linear elastic traction) followed by the softening zone (damage evolution). Damage initiation and damage evolution are the two criteria that Abaqus uses to describe both models. A cracked element’s elastic behavior can be represented as an elastic constitutive matrix that links shear and normal stresses with shear and normal separations. The nominal traction stress vector (t) in the 3D modeling is made up of three components.
+
+tn, ts, and tt, represent the normal and shear tractions in two directions, respectively. The corresponding separations are denoted by δn, δs, and δt. The elastic behavior can then be written as:
+
+(9) t={tntstt}=[Knn000Kss000Ktt]{δnδsδt}=Kδ
+
+The elastic response is governed by the penalty stiffnesses, Knn, Kss, and Ktt, which are calculated as functions of the two neighboring material stiffnesses [24]. These values have been taken to be 1 × 106 MPa/mm in this paper, and they have no effect on the overall stiffness of the specimen [25]. Furthermore, it is assumed that the shear and normal penalty stiffnesses are decoupled, meaning that shear forces are not produced by the interface’s pure normal opening force and vice versa [9]. By default, the elastic zone is assumed to be linear. For the softening zone, there are several damage evolution laws available, such as the linear and nonlinear traction–separation law [23]. The softening in this research is specified as linear, implying the use of a bilinear transcription–separation law—see Figure 6b. Although the traction–separation behavior is defined inside the material properties for the XFEM, it is specified as part of the interaction properties for the CS.
+
+3.3.1. Damage Initiation
+
+Numerous damage initiation criteria have been successfully included into software such as Abaqus and are described in the literature. These criteria include, for example, the maximum nominal stress criterion, quadratic stress criterion, maximum separation criterion, and quadratic separation criterion. When the maximum stress is more than the material’s maximum strength, damage will start in the case of the stress criteria. In this work, the maximum principal stress damage criteria is applied to the XFEM. Consequently, if the maximal primary stress obtained by its integration points satisfies the condition of Equation (10), a crack may develop. Nevertheless, the CS technique uses the maximum nominal stress damage criterion, which implies that a separation can occur when the greatest nominal traction satisfies Equation (11). In this context, a more thorough explanation may be found in [23].
+
+(10) max{0,σmaxpsσ*}≥1
+
+(11) max{〈tn〉tn*,tstn*,tttt*}=1
+
+σ* is the maximum strength of the material, and σmaxps is the maximum primary stress that can be calculated. The letters n, s, and t stand for the normal, shear, and tangential components of the interfacial tractions, respectively. * stands for the maximum interfacial tractions.
+
+3.3.2. Damage Evolution
+
+The damage evolution characterizes the cohesive stiffness deterioration by specifying the softening portion of the traction–separation law. The scalar damage variable (D) has an initial value of 0 and increases to 1 throughout the loading process. It is necessary to specify in Abaqus the maximum displacement or the fracture energy, which is the area under the traction–separation law’s curve [23]. The damage evolution with linear softening is defined in this work using the fracture energy. An effective separation is defined using the approach described in [26] to characterize the development of damage when both normal and shear separations exist across the interface:
+
+(12) δm=〈δn〉2+δs2+δt2
+
+(13) D=δm*δmu(δmu−δm0δm*−δm0)
+
+(14) tn={(1−D)t¯n           if tn≥0t¯n                         if tn<0 (compression)
+
+(15) ts=(1−D)t¯s
+
+(16) tt=(1−D)t¯t
+
+The directions of the interfacial separations’ normal, shear, and tangential components are, respectively, δn, δs, and δt. While δm* is the maximal effective separation during loading, δm is the effective separation. The effective separation at the initial stage of the damage process is δm0, whereas the effective separation right before unloading is δmu. This is in contrast to the elastic traction–separation behavior, which states that t¯n, t¯s, and t¯t are the contact traction components for current separations without damage. Utilizing Macaulay brackets ⟨⟩ helps prevent compressive damage.
+
+The energy dissipated to produce a totally separated pair of surfaces is called the interface fracture energy (Gf), and it is represented by the region beneath the curves in Figure 6. A cohesive interface for healed cracks may have a mixed-mode propagation response depending on where the interface is placed in relation to the applied stress. This mixed mode includes a range of energies linked to the ability of debonding in both the normal (n) and parallel (s, t) directions to the interface. The formula given in [26] is then used to calculate the maximum fracture separation:
+
+(17) δn*=2Gn*tn0
+
+(18) δs*=2Gs*ts0
+
+(19) δt*=2Gt*tt0
+
+The interaction between the energies for each mode, n, s, and t, is assumed in this study to satisfy the power law fracture requirement as described in [26]:(20) {GnGn*}α+{GsGs*}α+{GtGt*}α=1
+
+where Gn, GS, and Gt are the energy release rates obtained from the traction and normal, shear, and tangential displacements during interface opening, and power α is a cohesive property parameter that characterizes the interaction between modes. For each direction, the critical interface toughness is represented by the properties Gn*,  Gs*,  and Gt*. It is assumed in this study that the critical fracture toughness is constant in all directions. Additionally, a value of α = 1 has been used [26] to take into account the impact of this parameter on the response.
+
+3.4. Periodic Boundary Conditions (PBCs)
+
+Periodic boundary conditions are usually used in micromechanics for the study of heterogeneous media. The periodic boundary condition (PBC) stipulates that opposite pairs of edges or surfaces on the boundary of an RVE should deform identically under a given loading history. The PBC basically prevents the constraint of enforcing edges to remain planar after deformation [27], as illustrated in Figure 7 for 2D RVE.
+
+The implementation of PBCs within FEM is classified according to the type of mesh discretization. Generally, the mesh discretization could be a periodic or non-periodic mesh. In the case of the periodic mesh, the number of nodes on one edge is equal to the number of nodes on the other opposite edge—see Figure 8a. In the other case with the non-periodic mesh, the number of nodes on one edge is not equal to the number of nodes on the other opposite edge—see Figure 8b. The implementation of PBCs on the non-periodic mesh has some complications and is out of the scope of this work. Due to the proposed design method of microcapsules, and based on the unit cell, which does not generate any complication with mesh discretization, and the periodic mesh which can be generated easily, in this paper, the implementation of PBCs focused only on the periodic mesh.
+
+In order to implement PBC on a periodic mesh, consider a 2D RVE which is pinned at one of the corner nodes N1 to prevent rigid body motion, as illustrated in Figure 9. Every edge node should be linked kinematically on opposite edges. The principle is that the displacement of node b must be equal to the displacement of node a and so on, as expressed in Equations (21)–(24).(21) U(x,y)NB=U(x,y)NA    hence     U(x,y)NB−U(x,y)NA=0
+
+(22) U(x,y)NC=U(x,y)ND    hence    U(x,y)NC−U(x,y)ND=0 
+
+(23) U(x,y)N2=U(x,y)N1    hence     U(x,y)N2−U(x,y)N1=0
+
+(24) U(x,y)N4=U(x,y)N1    hence    U(x,y)N4−U(x,y)N1=0 
+
+The boundary condition can be expressed as mathematical equations (canonical equations) where the displacements of the internal edge nodes are kinematically tied to the homogeneous displacements of the corner retained nodes. Note that N3 is not considered a retained node as its deformation is influenced by the deformations of nodes N2 and N4; this is why it is called a slave or a dummy node. In order to enforce an axial deformation (δx), the displacements of the corner retained nodes must be linked kinematically to the edge internal nodes. Because the loads are applied on the corner nodes, the previous displacement boundary equations (canonical equations) can be rearranged as follows:
+
+(25) U(x,y)NB− U(x,y)NA− U(x,y)N2+ U(x,y)N1=0
+
+(26) U(x,y)NC−U(x,y)ND−U(x,y)N4+U(x,y)N1=0 
+
+The PBC is imposed by applying the above canonical equations on the boundary nodes. So, if node 2 moves a certain distance, every other thing in the model will have a connection; there is a connectivity between them and so the system will respond accordingly. The canonical equations are introduced into Abaqus using a multifunction constraint equation in the interaction module. Due to the simulation here in 2D, the canonical equations need to be defined in two degrees of freedom (DOF); x and y directions at every edge node as shown in Figure 10 respectively for nodes NB and NA. The same principle is also applied on the top and bottom edges of RVE; for example, NC and ND linked kinematically to the corner nodes N1 and N4.
+
+4. Numerical Modeling
+
+2D SHC design samples, which are basically RVE body-centered unit cell samples with one microcapsule and volume fraction (Vf = 5% and Vf = 25%), are loaded under uniaxial tension. The outer diameter of the microcapsule is 2 mm with four values of core–shell ratio: 1:1, 5:1, 10:1, and 15:1. The microcapsule with the thinnest shell is the one with the biggest core–shell ratio (15:1), and vice versa. The dimensions of the design samples are calculated according to Equation (5); Luc = 4.4 mm for Vf = 5% while Luc = 2.6 mm for Vf = 25%. Since in this study it is important to investigate how the crack will initiate, there is no need for a preexisting crack. Figure 11 displays the overall geometric dimensions of both specimens with the boundary conditions. The PBCs have been implemented along the four sides of the design sample using equation constraints to connect each node with its corresponding node on the other side. Vertical displacement 0.05 mm is applied to the reference point (RP). The Abaqus/Static simulation was run on the assumption of plane stress conditions. Table 1 shows the used material properties, which are characterized according to [9,17,28,29,30,31]. Young’s modulus (E), Poisson’s ratio (ν), maximum tensile strength (σ*), and fracture energy (Gf) are used to represent their properties. The cohesive surface that represents the interface between the microcapsule and the concrete matrix is assumed to have equal normal and shear fracture properties due to a lack of experimental verification in the literature.
+
+4.1. Mesh Convergence
+
+Several preliminary calculations, similar to those performed in [10,14], have been carried out to investigate the mesh convergence as a means of balancing accuracy with computing effort. The design samples are meshed with quadrilateral elements (Q4) with full integration. In order to have a periodic mesh to facilitate the application of PBC, the average mesh element size of the design sample is 0.44 mm; the number of elements for each side is fixed at 15 for Vf = 5%, as shown in Figure 12. For Vf = 25% the average mesh elements size of the design sample is 0.26 mm, and the number of elements for each side is fixed at 10, as shown in Figure 13. The number of circumferential elements around the microcapsule opening is fixed at 25 for both cases. The average mesh element size for microcapsule core–shell ratio 1:1 is 0.1 mm with 5 elements through its thickness, for microcapsule core–shell ratio 5:1 is 0.0417 mm with 4 elements through its thickness, for microcapsule core–shell ratio 10:1 is 0.0303 mm with 3 elements through its thickness, and for microcapsule core–shell ratio 15:1 is 0.03125 mm with 2 elements through its thickness.
+
+4.2. Parametric Studies
+
+The effects of the interfacial transition zone (itz) between the microcapsule shell and the concrete matrix are investigated through parametric studies of various interfacial fracture properties. Four different microcapsule core–shell ratios—1:1, 5:1, 10:1, and 15:1—are studied, as shown in Figure 12 and Figure 13 for Vf = 5% and 25%, respectively, regarding load carrying capacity and crack patterns. The interfacial fracture properties are represented by two parameters that define the cohesive surface between the concrete matrix and the microcapsule shell: the maximum interfacial tensile strength σ*, which is known also as the bonding strength, and the interfacial fracture energy Gf. In order to investigate the effects of interfacial strength and fracture energy, parametric studies of five different material inputs for σ* and Gf were carried out. These two parameters for the interfacial transition zone (itz) are varied relative to the properties of the concrete for each simulation while the other parameters were constant; i.e., they are ranging from 10% (σ* = 0.6 MPa, Gf = 0.006 N/mm) to 100% (σ* = 6 MPa, Gf = 0.06 N/mm).
+
+5. Results and Discussion
+
+The effects of the interfacial cohesive properties, the microcapsule size, and volume fraction on the load carrying capacity and the crack pattern of self-healing concrete are examined in this section by using the results of the numerical simulations. In addition the obtained results will be compared with other results from previous computational fracture modeling of encapsulated self-healing concrete in order to validate the developed design method of microcapsules.
+
+5.1. Effects of Interfacial Fracture Properties and the Microcapsule Size on the Load Carrying Capacity
+
+The effects of interfacial fracture properties (itz) for the design samples with core–shell ratios 1:1, 5:1, 10:1, and 15:1 on load carrying capacity are defined by variation of itz from 10% of the concrete fracture properties (σ* = 0.6 MPa, Gf = 0.006 N/mm) to 100%; this is the same as the concrete fracture properties (σ* = 6 MPa, Gf = 0.06 N/mm), which are demonstrated in Figure 14a–d for Vf = 5% and in Figure 15a–d for Vf = 25%. Figure 14a shows the effects of the interfacial fracture properties (itz) on the load carrying capacity of the design sample for the microcapsule Vf = 5% with core–shell ratio 1:1. The maximum load of the design sample decreased from 21.3 N for itz = 100% to 16.9 N for itz = 10%. Figure 15 shows the effects of the interfacial fracture properties (itz) on the load carrying capacity of the design sample for the microcapsule Vf = 25% with core–shell ratio 1:1. The maximum load of the design sample decreased from 8.9 N for itz = 100% to 4.5 N for itz = 10%. As a result, it is clear that the interfacial cohesive properties (itz) have a significant role in governing the load carrying capacity of the design samples. The same phenomenon can also be found in Figure 14b–d for the microcapsule Vf = 5% and in Figure 15b–d for the microcapsule Vf = 25% with ratios 5:1, 10:1, and 15:1, respectively. It is clear that when the interfacial cohesive fracture properties have the same values of the concrete matrix, the higher maximum load carrying capacity will be achieved. Consequently, it is obvious that the higher the itz, the higher the load carrying capacity and vice versa. These results are in good agreement with the results obtained from previous computational fracture modeling of encapsulated self-healing concrete [10,14].
+
+5.2. Effects of Interfacial Fracture Properties and the Microcapsule Size on the Maximum Carrying Load
+
+The core–shell ratio is used to define the effects of the microcapsule size on the maximum carrying load for the four design samples with different interfacial fracture properties (itz), which are shown in Figure 16. It is demonstrated that the sample’s maximum carrying load increases with decreasing core–shell ratio (increasing shell thickness) in the microcapsule. Conversely, a higher itz value increases the maximum load that the design sample is capable of carrying. It also shows that the varying effect of itz on the microcapsule Vf = 5% with lower shell thickness is almost constant, as seen in Figure 16a for microcapsules core–shell ratios 10:1 and 15:1.
+
+5.3. Effects of Interfacial Fracture Properties and the Microcapsule Size on the Crack Pattern
+
+The effects of the interfacial fracture properties (itz) and microcapsule core–shell ratios 1:1, 5:1, 10:1, and 15:1 on the crack pattern are shown in Figure 17A–D for the design samples with volume fraction Vf = 5% and in Figure 18A–D for Vf = 25% respectively. The effects of the interfacial fracture properties are represented by variation of itz from 10% of the concrete fracture properties (σ* = 0.6 MPa, Gf = 0.006 N/mm) to 100%; this is the same as the concrete fracture properties (σ* = 6 MPa, Gf = 0.06 N/mm). Figure 17A illustrates that design samples with Vf = 5% and microcapsule core–shell ratio 1:1 (the largest shell thickness) produced the same crack patterns as the microcapsule that is debonded from the concrete matrix, regardless of the ratio of the interfacial fracture properties (itz). The propagating crack could not break the microcapsule shell even when the interfacial fracture properties have the same values of the concrete matrix—see Figure 17A(1–5)—as an interfacial crack occurs regardless the itz ratio. The same phenomena happened for design samples with Vf = 25% and microcapsule core–shell ratio 1:1—see Figure 18A. Figure 17B illustrates that for design samples with Vf = 5%, microcapsule core–shell ratio 5:1, and when the itz ratio of the concrete fracture properties ranging between 0% and 50%, an interfacial crack occurred, and the microcapsule is debonded from the concrete matrix, as shown in Figure 17B(1–3). When the itz is ranged between 75 and 100%, the propagating crack became an interfacial crack when it reached the microcapsule shell and broke it from the other side, as illustrated in Figure 17B(4,5). That means that a partial fracture crack is developed when the microcapsule core–shell ratio is 5:1 and the ratio of the interfacial fracture properties between the microcapsule and the concrete matrix (itz) is ranging between 75 and 100%. The same phenomena happened for the design samples with Vf = 25% and microcapsule core–shell ratio 5:1—see Figure 18B. Figure 17C illustrates the fracture pattern for the design samples with Vf = 5% and microcapsule core–shell ratio 10:1 and varying itz ratios. When itz range between 0% and 25%, an interfacial crack occurs and the microcapsule is debonded from the concrete matrix as shown in Figure 17C(1,2). However, when the itz ranges between 50 and 100%, the propagating crack became an interfacial crack when it reached the microcapsule shell and broke it from the other side, as illustrated in Figure 17C(3–5). The same phenomena happened for the design samples with Vf = 25% and microcapsule core–shell ratio 10:1—see Figure 18C. Figure 17D illustrates the fracture pattern for the design samples with Vf = 5% and microcapsule core–shell ratio 15:1 and varying itz ratios. When itz ranges between 0% and 25%, interfacial cracks occurred, and the microcapsule is debonded from the concrete matrix, as shown in Figure 17D(1,2). However, when the itz ranges between 50 and 100% the propagating crack could break the microcapsule, as illustrated in Figure 17D(3–5). The same phenomena happened for the design samples with Vf = 25% and microcapsule core–shell ratio 15:1—see Figure 18D. These results are in good agreement with the results obtained from previous computational fracture modeling of encapsulated self-healing concrete [10,14].
+
+It can be easily noticed by comparing the crack patterns generated from the design samples with volume fraction (Vf = 5%) in Figure 17 and the crack patterns generated from the design samples with volume fraction (Vf = 25%) in Figure 18 that increasing the volume fraction leads to an increase in the possibility of the microcapsule being fractured.
+
+6. Conclusions
+
+A simple design method of dimensioning microcapsules for encapsulation-based self-healing concrete (SHC) with consideration for a sufficient volume of healing agent to heal a specific crack width is developed in this paper. The developed design method is based on the configuration of the representative volume element (RVE), the unit cell (UC), and associates them with the volume fraction (Vf) and the crack width as variables with periodic boundary conditions (PBCs) applied. The developed design method is also validated through numerical fracture modeling using the extended finite element method (XFEM), and cohesive surface (CS) technique. The effects of microcapsule size and volume fraction (Vf) on load carrying capacity and the likelihood of microcapsule fracture or debonding from the concrete matrix are investigated numerically in this validation. 2D numerical fracture modeling is performed for the developed SHC design samples including the designed microcapsules, which loaded under uniaxial tension with PBCs applied. The concrete matrix and the microcapsule shell are modeled using XFEM, while CS models the contact surface between them. The following conclusions can be made:The obtained results from the numerical simulations for the developed design of microcapsules are in good agreement with the results obtained from previous computational fracture modeling of encapsulated self-healing concrete.
+
+The interfacial cohesive characteristics have a significant impact on the load carrying capacity of the design samples as the higher the itz, the higher the load carrying capacity and vice versa.
+
+The microcapsule size represented the by core–shell ratio has an impact on the maximum carrying load of the design samples. The maximum carrying load of the sample increases with decreasing the core–shell ratio (increasing shell thickness) of the microcapsule.
+
+The interfacial cohesive characteristics (itz) are directly proportional to the design sample strength. On the contrary, the microcapsule core–shell ratio and the volume fraction (Vf) are inversely proportional to the sample strength. It has also been noticed that the varying of the itz on the microcapsule with higher microcapsule core–shell ratio and lower Vf almost has no significant effect on the design sample strength.
+
+Increasing the volume fraction (Vf) leads to an increase in the possibility of the microcapsule being fractured.
+
+The interfacial fracture properties (itz), the microcapsule core–shell ratio, and the volume fraction (Vf) also affect the crack pattern as increasing them leads to an increase in the possibility of the microcapsule being fractured. Though, the microcapsule core–shell ratio of 1:1, which has the thickest shell but the smallest healing agent volume, is not advised. As a result, irrespective of the itz ratios, the microcapsule will debond from the concrete. The likelihood of the microcapsule debonding from the concrete increases generally when the itz is less than 50% of concrete fracture properties. A partial fracture/interfacial crack develops when the itz ranges between 50 and 75%. The microcapsule fractures when the itz ranges between 75 and 100%.
+
+The developed design method for microcapsules is very simple and neglects the random distribution of the microcapsules. However, it is a helpful tool to design the microcapsule size with the consideration of the sufficient volume of healing agent to heal a specific crack width. This design method can help practical engineers to obtain a preliminary design of microcapsules for self-healing concrete without any complications, especially for costly detailed modeling.
+
+Future works for this developed microcapsule design method could study more complex models such as fracture modeling of microcapsules designed by this method and distributed randomly inside the sample to mimic the realities of SHC members. The Monte Carlo simulation should be applied to generate such random distribution of the microcapsules. However, these simulations would be computationally expensive in addition to the complications generated from mesh discretization and capsular clustering. Computational simulations for RVE samples could be a useful improvement to reduce the computational cost by studying the proper representing RVE size. The first step in carrying out these investigations is to look at XFEM’s limitations, which primarily allow for the creation of several fractures within the same enrichment zone. These limitations may be addressed by adjusting the Abaqus input file. 3D computational simulations should also be considered for future work to validate the 2D computational simulation and estimate the accuracy difference ratio between 2D and 3D simulations, which allows practical engineers to get much more reliable results based only on 2D simulations that can be built easily and are not as computationally expensive as 3D simulations.
+
+Acknowledgments
+
+We acknowledge the support by publication fund the BTU Cottbus-Senftenberg.
+
+Author Contributions
+
+Conceptualization; methodology; software; validation; formal analysis; investigation; resources; data curation; writing—original draft preparation; visualization; supervision; project administration; writing—editing, J.H.; writing—review, M.D. All authors have read and agreed to the published version of the manuscript.
+
+Data Availability Statement
+
+The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.
+
+Conflicts of Interest
+
+The authors declare no conflicts of interest.
+
+Figure 1 Encapsulation-based self-healing using microcapsules.
+
+Figure 2 Geometry dimensions of (a) RVE and (b) UC of the proposed design method of microcapsules.
+
+Figure 3 Design curves of microcapsules.
+
+Figure 4 Zoom view of the modeling techniques.
+
+Figure 5 Crack with enriched elements.
+
+Figure 6 Traction–separation law.
+
+Figure 7 Typical periodic boundary conditions (a) and the associated deformation shape (b).
+
+Figure 8 Periodic mesh (a) versus non-periodic mesh (b).
+
+Figure 9 Implementation of PBC within periodic FEM mesh.
+
+Figure 10 Constraint equations of PBCs in Abaqus interaction module.
+
+Figure 11 Geometry dimensions of design samples and modeling techniques.
+
+Figure 12 The mesh discretization for Vf = 5% with different microcapsule core–shell ratios, (a) 1:1 (b) 5:1 (c) 10:1 (d) 15:1.
+
+Figure 13 The mesh discretization for Vf = 25% with different microcapsule core–shell ratios, (a) 1:1 (b) 5:1 (c) 10:1 (d) 15:1.
+
+Figure 14 Load displacement curves for microcapsule Vf = 5% with different itz values and four core–shell ratios: (a) 1:1; (b) 5:1; (c) 10:1; (d) 15:1.
+
+Figure 15 Load displacement curves for microcapsule Vf = 25% with different itz values and four core–shell ratios: (a) 1:1; (b) 5:1; (c) 10:1; (d) 15:1.
+
+Figure 16 Effects of interfacial fracture properties and the microcapsule size on the maximum carrying load for Vf = 5%.
+
+Figure 17 Crack pattern of microcapsule Vf = 5% with four core–shell ratios and different itz values: (1) itz = 10%, (2) itz = 25%, (3) itz = 50%, (4) itz = 75%, (5) itz = 100%.
+
+Figure 18 Crack pattern of microcapsule Vf = 25% with four core–shell ratios and different itz values: (1) itz = 10%, (2) itz = 25%, (3) itz = 50%, (4) itz = 75%, (5) itz = 100%.
+
+materials-19-02878-t001_Table 1 Table 1 The material properties.
+
+Material	E
+(MPa)	ν	σ*
+(MPa)	Gf
+(N/mm)	
+Concrete	25,000	0.2	6	0.06	
+Capsule	3600	0.3	10	0.1	
+Interface	-	-	Varies	Varies	
+
+Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.
+
+
+References
+
+1. Souradeep G. Kua H.W. Encapsulation technology and techniques in self-healing concrete J. Mater. Civ. Eng. 2016 28 04016165 10.1061/(ASCE)MT.1943-5533.0001687
+2. Hanna J. Self-Healing Concrete Techniques and Technologies and Applications Recent Prog. Mater. 2024 6 1 20 10.21926/rpm.2401006
+3. Hanna J. Computational Fracture Modeling and Design of Encapsulation-Based Self-Healing Concrete Using XFEM and Cohesive Surface Technique Ph.D. Thesis Bauhaus University Weimar Weimar, Germany 2022
+4. Hermawan H. Simons A. Teirlynck S. Anglani G. Serna P. Tulliani J.M. Antonaci P. Minne P. Gruyaert E. Prediction of Aggregate Packing with Tubular Macrocapsules in the Inert Structure of Self-Healing Concrete Based on Dewar’s Particle Packing Model Materials 2024 17 2455 10.3390/ma17102455 38793521 PMC11122879
+5. Ataabadi H.S. Liu Y. Zeng J.-J. Zhuge Y. Self-healing efficiency of sludge-based composite in CO2-rich environment Cem. Concr. Compos. 2025 163 106202 10.1016/j.cemconcomp.2025.106202
+6. Snoeck D. Malm F. Cnudde V. Grosse C.U. Van Tittelboom K. Validation of Self-Healing Properties of Construction Materials through Nondestructive and Minimal Invasive Testing Adv. Mater. Interfaces 2018 5 1800179 10.1002/admi.201800179
+7. De Nardi C. Gardner D. Cazzador G. Cristofori D. Ronchin L. Vavasori A. Jefferson T. Experimental investigation of a novel formulation of a cyanoacrylate based adhesive for self-healing concrete technologies Front. Built Environ. 2021 7 660562 10.3389/fbuil.2021.660562
+8. Mauludin L.M. Zhuang X. Rabczuk T. Computational modeling of fracture in encapsulation-based self-healing concrete using cohesive elements Compos. Struct. 2018 196 63 75 10.1016/j.compstruct.2018.04.066
+9. Gilabert F. Garoz D. Van Paepegem W. Macro-and micro-modeling of crack propagation in encapsulation-based self-healing materials: Application of XFEM and cohesive surface techniques Mater. Des. 2017 130 459 478 10.1016/j.matdes.2017.05.050
+10. Hanna J. Accurate computational modelling for impacts of microcapsule size and interfacial fracture properties on the fracture of self-healing concrete Int. J. Hydromechatronics 2022 5 397 415 10.1504/ijhm.2022.127036
+11. Tabiei A. Zhang W. Cohesive element approach for dynamic crack propagation: Artificial compliance and mesh dependency Eng. Fract. Mech. 2017 180 23 42 10.1016/j.engfracmech.2017.05.009
+12. Tang Y.X. Chen H.N. Simulation of crack propagation in concrete based on extended finite element method Key Eng. Mater. 2018 783 165 169 10.4028/www.scientific.net/KEM.783.165
+13. Rabczuk T. Computational methods for fracture in brittle and quasi-brittle solids: State-of-the-art review and future perspectives ISRN Appl. Math. 2013 2013 849231 10.1155/2013/849231
+14. Hanna J. Computational Modelling for the Effects of Capsular Clustering on Fracture of Encapsulation-Based Self-Healing Concrete Using XFEM and Cohesive Surface Technique Appl. Sci. 2022 12 5112 10.3390/app12105112
+15. Hanna J. Elamin A. Computational fracture modeling for effects of healed crack length and interfacial cohesive properties in self-healing concrete using XFEM and cohesive surface technique Computation 2023 11 142 10.3390/computation11070142
+16. Hanna J. The Effects of Fracture Energy on the Interfacial Strength of Self-Healing Concrete EG-ICE 2021 Workshop on Intelligent Computing in Engineering Universitätsverlag der TU Berlin Berlin, Germany 2021
+17. Hilloulin B. Van Tittelboom K. Gruyaert E. De Belie N. Loukili A. Design of polymeric capsules for self-healing concrete Cem. Concr. Compos. 2015 55 298 307 10.1016/j.cemconcomp.2014.09.022
+18. Šavija B. Feiteira J. Araújo M. Chatrabhuti S. Raquez J.-M. Van Tittelboom K. Gruyaert E. De Belie N. Schlangen E. Simulation-aided design of tubular polymeric capsules for self-healing concrete Materials 2016 10 10 10.3390/ma10010010 28772370 PMC5344596
+19. Drugan W. Willis J.R. A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites J. Mech. Phys. Solids 1996 44 497 524 10.1016/0022-5096(96)00007-5
+20. Li S. Sitnikova E. Representative Volume Elements and Unit Cells: Concepts, Theory, Applications and Implementation Woodhead Publishing Cambridge, UK 2019
+21. Rabczuk T. Song J.-H. Zhuang X. Anitescu C. Extended Finite Element and Meshfree Methods Academic Press Cambridge, MA, USA 2019
+22. Moës N. Dolbow J. Belytschko T. A finite element method for crack growth without remeshing Int. J. Numer. Methods Eng. 1999 46 131 150 10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J
+23. Dassault Systémes Simulia Corp Abaqus Documentation Dassault Systémes Simulia Corp Johnston, RI, USA 2017
+24. Dong B. Han N. Zhang M. Wang X. Cui H. Xing F. A microcapsule technology based self-healing system for concrete structures J. Earthq. Tsunami 2013 7 1350014 10.1142/s1793431113500140
+25. Edvardsen C. Water permeability and autogenous healing of cracks in concrete Innovation in Concrete Structures: Design and Construction Thomas Telford Publishing London, UK 1999 473 487
+26. Camanho P.P. Dávila C.G. Mixed-Mode Decohesion Finite Elements for the Simulation of Delamination in Composite Materials NASA/TM-2002–211737 NASA Hampton, VA, USA 2002
+27. Okereke M. Keates S. Finite Element Applications: A Practical Guide to the FEM Process Springer Berlin/Heidelberg, Germany 2018
+28. Quayum M.S. Zhuang X. Rabczuk T. Computational model generation and RVE design of self-healing concrete Front. Struct. Civ. Eng. 2015 9 383 396 10.1007/s11709-015-0320-z
+29. Mauludin L.M. Oucif C. The effects of interfacial strength on fractured microcapsule Front. Struct. Civ. Eng. 2019 13 353 363 10.1007/s11709-018-0469-3
+30. Wang X. Computational Technology for Damage and Failure Analysis of Quasi-Brittle Materials Ph.D. Thesis University of Manchester Manchester, UK 2015
+31. Wang X. Jivkov A.P. Combined numerical-statistical analyses of damage and failure of 2D and 3D mesoscale heterogeneous concrete Math. Probl. Eng. 2015 2015 702563 10.1155/2015/702563
diff --git a/corpus/psychology/text/2ccdf471931c3964.txt b/corpus/psychology/text/2ccdf471931c3964.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a2bc16a773d7482923ddd2007f94edcd3dc68990
--- /dev/null
+++ b/corpus/psychology/text/2ccdf471931c3964.txt
@@ -0,0 +1,91 @@
+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Sci Rep
+Journal ID: Sci Rep
+NLM Journal ID: 101563288
+
+Scientific Reports
+
+EISSN: 2045-2322
+Publisher: Nature Publishing Group
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC12675519
+PMID: 41339728
+DOI: 10.1038/s41598-025-30371-0
+Article ID: 30371
+Article version: 1
+Subjects: Correction
+
+Correction: A comparison among employees in Germany and Denmark of associations between quality of leadership and subsequent 5-year development of mental distress
+
+Burr Hermann burr.hermann@baua.bund.de
+1
+Kersten Norbert 1
+Sørensen Kathrine 2 3
+Sørensen Jeppe K. 2
+Dalsager Louise 2
+Madsen Ida E. H. 2 4
+Schöllgen Ina 1
+d’Errico Angelo 5
+Rose Uwe 1
+Rugulies Reiner 2 6
+1 https://ror.org/01aa1sn70 grid.432860.b 0000 0001 2220 0888 Department of Work and Health, Federal Institute for Occupational Safety and Health (BAuA), 10317 Berlin, Germany
+2 https://ror.org/03f61zm76 grid.418079.3 0000 0000 9531 3915 National Research Centre for the Working Environment (NRCWE), 2100 Copenhagen Ø, Denmark
+3 https://ror.org/035b05819 grid.5254.6 0000 0001 0674 042X Department of Psychology, University of Copenhagen, 1353 Copenhagen K, Denmark
+4 https://ror.org/03yrrjy16 grid.10825.3e 0000 0001 0728 0170 National Institute of Public Health, University of Southern Denmark, 1455 Copenhagen K, Denmark
+5 Department of Epidemiology, Local Health Unit TO 3, 10095 Grugliasco Turin, Italy
+6 https://ror.org/035b05819 grid.5254.6 0000 0001 0674 042X Section of Epidemiology, Department of Public Health, University of Copenhagen, 1353 Copenhagen K, Denmark
+Electronic publication date: 2025 Dec 3
+Publication date: 2025
+Volume: 15
+Electronic Location ID: 43096
+Copyright: © The Author(s) 2025
+Copyright year: 2025
+License: Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Erratum for: A comparison among employees in Germany and Denmark of associations between quality of leadership and subsequent 5-year development of mental distress 15 6 3 2025 7802 Scientific Reports 10.1038/s41598-025-92650-0 PMC11885610 40050694
+issue-copyright-statement: © Springer Nature Limited 2025
+
+Ÿ==============================Ÿ
+Correction to: Scientific Reports 10.1038/s41598-025-92650-0, published online 06 March 2025
+
+The original version of this Article contained a repeated error, where the number of observations for the Danish employee cohort and for the German employee cohort were incorrect. The calculations relating to these observations have been corrected accordingly.
+
+As a result, in the Methods section, under the subheading ‘Danish employee cohort’,
+
+“We extracted the 2000–2005 and 2005–2010 cohorts from DWECS, which had a responses of 76% and 65% respectively at baseline and a responses of 72% and 65% respectively at follow-up (Table 3). DWECS was an open population-based cohort study investigating work and health among the Danish workforce through repeated questionnaire assessments conducted every five years33,34. Thus, a DWECS participant could have been included in one or both 5-year cohorts. The cohort comprised 7,818 observations from 5,597 people who were employed at baseline, took part in at least one follow-up, and had non-missing information on all key variables (Fig. 1). Respondents either took part in computer assisted telephone interviews or filled out paper questionnaires. The change in mode of data collection from telephone interviews was partly introduced in 2005 and was fully implemented in 2010. Among the 7,818 observations, 790 were collected through telephone interviews at both baseline and follow-up, 3572 were collected through questionnaires at both baseline and follow-up, and 2819 observations were via telephone interviews at baseline and via questionnaire at follow-up.”
+
+now reads:
+
+“We extracted the 2000–2005 and 2005–2010 cohorts from DWECS, which had a responses of 76% and 65% respectively at baseline and a responses of 72% and 67% respectively at follow-up (Table 3). DWECS was an open population-based cohort study investigating work and health among the Danish workforce through repeated questionnaire assessments conducted every five years33,34. Thus, a DWECS participant could have been included in one or both 5-year cohorts. The cohort comprised 7,181 observations from 5,597 people who were employed at baseline, took part in at least one follow-up, and had non-missing information on all key variables (Fig. 1). Respondents either took part in computer assisted telephone interviews or filled out paper questionnaires. The change in mode of data collection from telephone interviews was partly introduced in 2005 and was fully implemented in 2010. Among the 7,818 observations, 790 were collected through telephone interviews at both baseline and follow-up, 3,572 were collected through questionnaires at both baseline and follow-up, and 2,819 observations were via telephone interviews at baseline and via questionnaire at follow-up.”
+
+In the Variables section, under the subheading ‘Correlations between the independent variables’,
+
+“Regarding gender, influence at work (mean m: 1.83 vs. w. 1.56, p = < 0.001) was higher among men than among women, whereas quality of leadership (mean w. 2.31 vs. m. 2.22, p = < 0.001) and mental distress (mean w. 39.1 vs. m. 34.6, p = < 0.001) was higher among women). Age (mean m: 45.4 vs. w. 45.3, p = 0.126) and occupational level (mean w. 47.1 vs. 46.7, p = 0.662) did not differ significantly.”
+
+now reads:
+
+“Regarding gender, influence at work (mean m: 1.83 vs. w. 1.56, p = < 0.001) was higher among men than among women, whereas quality of leadership (mean w. 2.31 vs. m. 2.22, p = < 0.023) and mental distress (mean w. 39.1 vs. m. 34.6, p = < 0.001) was higher among women). Age (mean m: 46.7 vs. w. 47.1, p = 0.126) and occupational level (mean w. 2.7 vs. m. 2.7, p = 0.662) did not differ significantly.”
+
+Under the subheading ‘Associations between the quality of leadership scale and mental distress’,
+
+“Therefore, only observations with non-zero values were included (2,318 in the German cohort, corresponding to 94% of all observations; 6,403 in the Danish cohort; corresponding to 93% of all observations) in the second analysis.”
+
+now reads:
+
+“Therefore, only observations with non-zero values were included (2,318 in the German cohort, corresponding to 95% of all observations; 6,403 in the Danish cohort; corresponding to 89% of all observations) in the second analysis.”
+
+Finally, in the Discussion section, under the subheading ‘Study strengths and limitations’,
+
+“Ninth, the number of observations was significantly smaller in the German cohort (N = 2,432) compared to the Danish cohort (n = 5,597), potentially leading to greater variance in the German cohort.”
+
+now reads:
+
+“Ninth, the number of observations was significantly smaller in the German cohort (N = 2,484) compared to the Danish cohort (n = 7,181), potentially leading to greater variance in the German cohort.”
+
+The original Article has been corrected.
+
diff --git a/corpus/psychology/text/2ebdf3e008aec639.txt b/corpus/psychology/text/2ebdf3e008aec639.txt
new file mode 100644
index 0000000000000000000000000000000000000000..168da87912594ffb54d4c38d0cd85c439ac798d1
--- /dev/null
+++ b/corpus/psychology/text/2ebdf3e008aec639.txt
@@ -0,0 +1,740 @@
+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: PLoS One
+Journal ID: PLoS One
+NLM Journal ID: 101285081
+Journal ID: plos
+
+PLOS One
+
+EISSN: 1932-6203
+Publisher: PLOS
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC13384304
+PMID: 42475342
+DOI: 10.1371/journal.pone.0352973
+Article ID: PONE-D-26-18433
+Article version: 1
+Subjects: Registered Report Protocol, Medicine and health sciences, Public and occupational health, Preventive medicine, HIV prevention, Social Sciences, Sociology, Education, Schools, Medicine and Health Sciences, Diagnostic Medicine, Virus Testing, Research and Analysis Methods, Database and Informatics Methods, Database Searching, Biology and Life Sciences, Microbiology, Medical Microbiology, Microbial Pathogens, Viral Pathogens, Immunodeficiency Viruses, HIV, Medicine and Health Sciences, Pathology and Laboratory Medicine, Pathogens, Microbial Pathogens, Viral Pathogens, Immunodeficiency Viruses, HIV, Biology and Life Sciences, Organisms, Viruses, Viral Pathogens, Immunodeficiency Viruses, HIV, Biology and Life Sciences, Organisms, Viruses, Immunodeficiency Viruses, HIV, Biology and life sciences, Organisms, Viruses, RNA viruses, Retroviruses, Lentivirus, HIV, Biology and Life Sciences, Microbiology, Medical Microbiology, Microbial Pathogens, Viral Pathogens, Retroviruses, Lentivirus, HIV, Medicine and Health Sciences, Pathology and Laboratory Medicine, Pathogens, Microbial Pathogens, Viral Pathogens, Retroviruses, Lentivirus, HIV, Biology and Life Sciences, Organisms, Viruses, Viral Pathogens, Retroviruses, Lentivirus, HIV, Medicine and Health Sciences, Public and Occupational Health, Preventive Medicine, Prophylaxis, Pre-Exposure Prophylaxis, People and Places, Population Groupings, Age Groups, Children, Adolescents, People and Places, Population Groupings, Families, Children, Adolescents, Medicine and Health Sciences, Epidemiology, Medical Risk Factors
+
+Integrating biomedical HIV prevention in schools: Protocol for a systematic review of interventions for adolescent girls and young women in sub-Saharan Africa
+
+Biomedical HIV prevention in schools for adolescent girls and young women in sub-Saharan Africa
+
+https://orcid.org/0009-0004-7465-2498 Lodonu-Senoo Cecilia Afua Conceptualization Formal analysis Methodology Writing – original draft 1 *
+Ogyiri Lily Formal analysis Methodology Writing – original draft 2
+Torpey Kwasi Conceptualization Methodology Supervision Writing – review & editing 3
+Zotor Francis Conceptualization Methodology Supervision Writing – review & editing 1
+1 Department of Family and Community Health, Fred N. Binka School of Public Health, University of Health and Allied Sciences, Hohoe, Volta Region, Ghana
+2 Department of Public Health, Robbins College of Health and Human Sciences, Baylor University, Waco, Texas, United States of America
+3 Department of Population, Family and Reproductive Health, School of Public Health, University of Ghana, Accra, Greater Accra Region, Ghana
+Badru Oluwaseun Abdulganiyu Editor
+The University of Iowa College of Public Health, UNITED STATES OF AMERICA
+Competing Interests: The authors have no competing interest.
+
+* E-mail: ceciliasenoo@gmail.com
+Electronic publication date: 2026 Jul 20
+Publication date: 2026
+Volume: 21
+Issue: 7
+Electronic Location ID: e0352973
+Received 2026 May 5; Accepted 2026 Jun 17
+Copyright: © 2026 Lodonu-Senoo et al
+Copyright year: 2026
+Copyright holder: Lodonu-Senoo et al
+License: This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Integrating biomedical HIV prevention in schools: Protocol for a systematic review of interventions for adolescent girls and young women in sub-Saharan Africa. 21 7 20 7 2026 e0352973 e0352973 PLoS One 10.1371/journal.pone.0352973 42475342
+Integrating biomedical HIV prevention in schools: Protocol for a systematic review of interventions for adolescent girls and young women in sub-Saharan Africa. 21 7 20 7 2026 e0352973 e0352973 PLoS One 10.1371/journal.pone.0352973 42475342
+
+Funding: The author(s) received no specific funding for this work.
+
+Figure count: 1
+Table count: 4
+Page count: 10
+Data Availability: No datasets were generated or analysed during the current study. All relevant data from this study will be made available upon study completion.
+
+Data Availability
+
+No datasets were generated or analysed during the current study. All relevant data from this study will be made available upon study completion.
+
+Ÿ==============================Ÿ
+Introduction
+
+Despite global progress in reducing HIV incidence, adolescent girls and young women in sub-Saharan Africa remain disproportionately affected. Biomedical HIV prevention tools such as pre-exposure prophylaxis, condoms and HIV testing are effective but underutilized, especially within facility-based models. Schools represent consistent and scalable contact points for reaching adolescent girls and young women, yet evidence on the feasibility, accessibility and effectiveness of school-based biomedical HIV prevention interventions remains limited.
+
+Objective
+
+This systematic review aims to synthesize evidence on how school-based programs implement, deliver and achieve outcomes in HIV prevention interventions involving pre-exposure prophylaxis, condom and HIV testing for adolescent girls and young women in sub-Saharan Africa.
+
+Materials and methods
+
+This review will follow the Preferred Reporting Items for Systematic Reviews and Meta-Analyses Protocols guidelines. Eligible studies will include randomized and non-randomized trials and qualitative research published between January 2015 and December 2025. Databases to be searched include PubMed, Embase, PsycINFO, CINAHL and the African Index Medicus, together with relevant grey literature sources (WHO, UNAIDS, UNICEF and PEPFAR). Two reviewers will independently screen titles, abstracts, and full texts, extract data, and assess risk of bias using appropriate tools. Quantitative data will be synthesized using meta-analysis where feasible, while qualitative findings will undergo thematic synthesis. Outcomes of interest include the feasibility, accessibility, and effectiveness of school-based HIV prevention interventions.
+
+Discussion
+
+This review will provide a comprehensive synthesis of evidence on biomedical HIV prevention interventions delivered in school settings for adolescent girls and young women in sub-Saharan Africa. Findings will highlight implementation process, barriers, facilitators and equity considerations.
+
+Trial registration number: PROSPERO CRD420251249595
+
+Introduction
+
+Global progress in human immunodeficiency virus (HIV) prevention has accelerated in recent years, with the year 2024 recording a 40% reduction in incidence compared to 2010. However, an estimated 1.3 million people acquired HIV in 2024, nearly three times the global target of fewer than 370,000 new infections by 2025 [1]. Sub-Saharan Africa accounted for half of all new infections, even as the region experienced the steepest decline globally, a 56% decrease in incidence over the same period [1].
+
+Adolescent girls and young women (AGYW) remain disproportionately affected. HIV incidence among AGYW is more than three times higher than that of their male peers [1]. Although global targets aimed to reduce new infections among AGYW to less than 50,000 by 2025, an estimated 210,000 AGYW acquired HIV in 2024 [1]. In eastern and southern Africa, the estimated number of new HIV infections among AGYW was 140,000, and in western and central Africa it was 31,000 [1]. This persistent vulnerability reflects deep-rooted gender inequalities, power imbalances, restrictive social norms, stigma, discrimination, criminalization, violence and socioeconomic inequalities across sub-Saharan Africa, which collectively limit AGYW’s ability to negotiate safer sex, access services, and exercise sexual autonomy [1,2].
+
+Despite the availability of effective prevention tools, uptake is inadequate. Condom use, one of the most cost-effective HIV prevention strategies, remains suboptimal due to stigma, limited access, gendered power dynamics, and scarcity of youth-friendly service environments [3–5]. Likewise, biomedical HIV preventions options such as pre-exposure prophylaxis (PrEP), condom distribution and HIV testing, have expanded the prevention landscape, yet their uptake among AGYW is suboptimal, especially within traditional facility-based models [1].
+
+Schools represent one of the most consistent and scalable contact points for reaching AGYW in sub-Saharan Africa. They offer access to large cohorts of adolescents in a structured setting and can serve as effective entry points for integrated sexual and reproductive health interventions. Evidence demonstrates that educational programmes can enhance HIV-related knowledge, build agency, and promote protective behaviours among adolescents [6,7]. However, curriculum-based HIV education alone has shown limited effectiveness in reducing HIV incidence or maintaining behaviour change without complementary access to prevention services [8,9].
+
+Emerging research suggests that schools may also be promising delivery sites for biomedical HIV prevention interventions such as PrEP, condom distribution, and HIV testing. Studies have reported higher PrEP uptake in school-based or school-linked delivery models compared to community or clinic-based approaches [10]. Qualitative research further indicates that comfort, accessibility, trust, and peer support facilitate PrEP initiation among AGYW in school environments [11]. This suggests that integrating biomedical prevention within school settings may help overcome many of the barriers that limit AGYW’s access to facility-based services.
+
+Existing reviews have focused largely on sexual and reproductive health education, abstinence-only, or broader behavioural interventions, with limited attention to school-based biomedical or service-oriented HIV prevention initiatives and their implementation outcomes [8,12–14].
+
+This systematic review will address this gap by synthesizing quantitative and qualitative evidence to understand what works, what is feasible, and what barriers and facilitators influence the implementation of school-based HIV prevention initiatives, including PrEP, condom, and HIV testing for AGYW in sub-Saharan Africa. The findings will inform programme design, implementation, and scale-up of efforts aimed at reducing HIV incidence among AGYW.
+
+Objective
+
+To synthesize evidence on how school-based programs are implemented, delivered, and achieve outcomes in HIV prevention interventions (involving PrEP, condom and HIV testing) for AGYW in sub-Saharan Africa.
+
+Review questions.
+
+What is known about the feasibility of implementing PrEP, condom or HIV testing interventions in school settings in sub-Saharan Africa?
+
+What evidence exists on the accessibility of such interventions among AGYW?
+
+How effective are these interventions at improving HIV prevention outcomes?
+
+Materials and methods
+
+This protocol was developed using the Preferred Reporting Items for Systematic reviews and Meta-Analyses Protocols (PRISMA-P) checklist.
+
+Eligibility criteria
+
+For this review, biomedical HIV prevention interventions refer to school-based interventions that provide, deliver, or facilitate access to PrEP, condoms, or HIV testing services.
+
+Selected studies will be based on the eligibility criteria outlined in Table 1:
+
+10.1371/journal.pone.0352973.t001 Table 1 Study eligibility criteria.
+
+Component	Include	Exclude	
+Population	AGYW, aged 10–24 years, enrolled in schools in sub-Saharan Africa	Studies focused exclusively on boys or adult women,
+
+Out-of-school youth
+
+Studies not disaggregating AGYW data
+
+Studies conducted outside sub-Saharan Africa	
+Intervention	School-based HIV prevention programs that include at least one of the following: PrEP education/delivery, condom promotion/distribution, or HIV testing/counselling (in-school or linked to external services)	No intervention,
+
+Interventions delivered solely in community or clinic settings without school linkage
+
+Interventions limited to general life skills or abstinence-only programs without biomedical or service components.	
+Outcomes	Feasibility, accessibility, effectiveness	Studies reporting only process indicators without implementation or effectiveness outcomes	
+Study design	Randomized-controlled trials, Cluster-randomized trials
+
+Quasi-experimental studies,
+
+Cohort/longitudinal, implementation studies, mixed-methods studies, qualitative studies	Editorials, commentaries, reviews	
+Context	Formal educational institutions (e.g., public, private, faith-based, vocational schools) in sub-Saharan Africa	Non-school settings (e.g., community centres, Clinics, households)	
+Time Frame	Studies published between January 2015 and December 2025	Studies published before 2015	
+Language	English	Non-English publications	
+
+Information sources
+
+Search strategy.
+
+We will search multiple online databases to identify peer-reviewed articles and grey literature. The following databases will be searched:
+
+PubMed through the PubMed interface using MeSH terms and keywords
+
+Embase via Elsevier using Emtree Terms and keywords
+
+PsycINFO via EBSCOhost using APA Thesaurus and keywords
+
+CINAHL via EBSCOhost using CINAHL Subject Headings and keywords
+
+African Index Medicus via WHO AIM portal using keywords
+
+Grey literature: WHO, UNAIDS, UNICEF, PEPFAR
+
+The search will be restricted to studies published between January 2015 and December 2025. The year 2015 was selected because it coincides with major developments in global HIV prevention policy and programming. In 2015, the United Nations adopted the Sustainable Development Goals (SDGs), which included a commitment to end the AIDS epidemic as a public health threat by 2023. That same year, the World Health Organization (WHO) recommended the broader use of oral PrEP for populations with substantial risk of HIV infection [15,16]. Restricting the review to studies published between 2015 and 2025 ensures that the evidence reflects contemporary HIV prevention policies, service delivery models, and implementation approaches. Due to resource constraints and the absence of multilingual screening and data extraction capacity, the review will be limited to studies published in English. Table 2 presents an example of the search strategy to be used in PubMed.
+
+10.1371/journal.pone.0352973.t002 Table 2 Search strategy in PubMed.
+
+Search	Search term	
+1	“Schools” [MeSH] OR school-based [tw] OR school* [tw] OR education* [tw] OR classroom*[tw] OR academic* [tw] OR campus* [tw] OR secondary school [tw] OR high school [tw]	
+2	“HIV infections/prevention and control” [MeSH] OR “HIV Testing” [MeSH] OR “Condoms” [MeSH] OR “Pre-Exposure Prophylaxis” [MeSH] OR “Sexual Health/education” [MeSH] OR “Student Health Services” [MeSH] OR HIV prevention[tw] OR HIV testing[tw] OR PrEP [tw]	
+3	“Adolescent” [MeSH] OR “Young Adult” [MeSH] OR “Female” [MeSH] OR “Students” [MeSH] OR adolescent girls[tw] OR young women [tw] OR AGYW [tw] OR teen* [tw] OR youth [tw] OR student* [tw]	
+4	“sub-Saharan Africa”[tw] OR “Africa South of the Sahara” [MeSH] OR Angola [tw] OR Benin[tw] OR Botswana [tw] OR “Burkina Faso”[tw] OR Burundi [tw] OR Cameroon [tw] OR “Cape Verde” [tw] OR Cabo Verde[tw] OR “Central African Republic” [tw] OR Chad [tw] OR Comoros [tw] OR Congo [tw] OR “Democratic Republic of the Congo” [tw] OR Djibouti [tw] OR “Equatorial Guinea” [tw] OR Eritrea [tw] OR Ethiopia [tw] OR Gabon [tw] OR Gambia [tw] OR Ghana [tw] OR Guinea [tw] OR “Guinea Bissau” [tw] OR “Ivory Coast” [tw] OR “Cote d’Ivoire” [tw] OR Kenya [tw] OR Lesotho [tw] OR Liberia [tw] OR Madagascar [tw] OR Malawi [tw] OR Mali [tw] OR Mauritania [tw] OR Mauritius [tw] OR Mozambique [tw] OR Namibia [tw] OR Niger [tw] OR Nigeria [tw] OR Rwanda [tw] OR “Sao Tome” [tw] OR Senegal [tw] OR Seychelles [tw] OR “Sierra Leone” [tw] OR Somalia [tw] OR “South Africa” [tw] OR “South Sudan” [tw] OR Sudan [tw] OR Swaziland [tw] OR Eswatini[tw] OR Tanzania [tw] OR Togo [tw] OR Uganda [tw] OR “Western Sahara” [tw] OR Zaire [tw] OR Zambia [tw] OR Zimbabwe [tw]	
+5	#1 AND #2 AND #3 AND #4	
+6	#5 Limits: 01/01/2015 to 31/12/2025, studies in English	
+
+Study records
+
+Data management.
+
+All records identified through database searches will be imported into Zotero for reference management. Full-text articles will be downloaded and stored locally, organized by first author surname and year of publication. Extracted data, reviewer decisions, and synthesis outputs will be archived across platforms to ensure transparency and reproducibility.
+
+Study selection and data extraction.
+
+Title/abstract screening and full-text review will be conducted using Rayyan, a web-based tool designed to facilitate blinded and collaborative screening. Two reviewers will independently screen each record against the predefined eligibility criteria. Disagreements will be resolved through discussion or adjudication by a third reviewer. Full-text screening will follow the same dual-review process within Rayyan, with exclusion reasons documented systematically.
+
+Studies meeting the eligibility criteria will undergo data extraction, which will be conducted independently by two reviewers using a structured template aligned with the review’s objectives. Conflicts will be discussed and resolved between the two reviewers, and where resolution cannot be reached, a third reviewer will be involved to decide. RevMan will be used to facilitate data extraction, risk of bias assessment and data synthesis.
+
+The reference lists of all included studies will be screened to identify additional eligible studies not captured through the database search.
+
+When relevant data are missing or unclear, the corresponding author of the article will be contacted to request additional information. The study selection process will be reported using the PRISMA flow diagram (Fig 1).
+
+10.1371/journal.pone.0352973.g001 Fig 1 PRISMA flow diagram.
+
+Data items.
+
+Implementation outcomes will be assessed according to the implementation science frameworks by Proctor and colleagues [17] and adapted to the school-based HIV prevention context. For this review:
+
+Feasibility refers to the extent to which the intervention can be delivered within school settings as intended, including logistics, staffing, training, fidelity, and integration into school routines.
+
+Accessibility refers to the degree to which AGYW can access and use the intervention, including acceptability, uptake, privacy, confidentiality, perceived appropriateness, and equity of access.
+
+Effectiveness (implementation-linked) refers to biomedical or behavioural outcomes directly related to intervention delivery, such as HIV testing uptake, PrEP initiation or continuation, and condom uptake or use. These outcomes reflect real-world effects of implementation rather than clinical efficacy.
+
+Secondary implementation outcomes include cost and cost-effectiveness, sustainability or maintenance, engagement of school personnel or parents, and contextual barriers and facilitators such as gender norms, stigma, or school policies.
+
+The list of variables to be extracted and their definitions are presented in Table 3.
+
+10.1371/journal.pone.0352973.t003 Table 3 List and definitions of all variables for which data will be sought.
+
+Variable	Definition	
+Characteristics of the study	
+Authors	First author and co-authors	
+Year	Year of publication	
+Country/region	Country or region within sub-Saharan Africa	
+Design	Study design	
+Setting	Type of school or educational institution	
+Sample size	Number of participants or clusters	
+Duration	Length of follow-up or intervention period	
+Funding source	Private sector or Government	
+Population and Implementation Variables	
+Population	Adolescent and young women in sub-Saharan Africa	
+Age range	Specific age range of participants included in the study	
+Intervention	Type of intervention: condom-related, PrEP-related, HIV testing, or linkage to external services	
+Comparator	Standard curriculum, community-only interventions, no intervention, other school-based strategies	
+Delivery personnel	Who implemented the intervention (teachers, health workers, etc)	
+Mode of delivery	Format of intervention delivery	
+Engagement	Level of involvement of school staff, parents, community leaders or AGYW themselves	
+Barriers and facilitators	Contextual factors influencing implementation (e.g., gender norms, power dynamics, structural factors)	
+Main Outcome variables (high priority)	
+Feasibility	Implementation, logistics, training fidelity to protocol	
+Accessibility	Acceptability, uptake, equity, privacy	
+Effectiveness	Biomedical/behavioural outcomes like HIV testing uptake, PrEP initiation, condom use	
+Additional outcomes (moderate priority)	
+Secondary implementation outcomes	Cost and cost-effectiveness, sustainability/maintenance	
+Knowledge and awareness	Changes in HIV -related knowledge or awareness, risk perception	
+Behavioural intentions	Intentions for condom use, PrEP, HIV testing	
+Adverse events or harm	Reported negative outcomes	
+
+Risk of bias assessment
+
+Quality appraisal for randomized trials will be conducted using the Cochrane Collaboration Risk of Bias (ROB 2) tool, including the extension for cluster-randomized trials. For quasi-experimental trials and cohort studies, the Risk Of Bias In Non-randomized Studies of Interventions (ROBINS-I) tool will be used. The CASP qualitative checklist will be used to appraise qualitative studies, and the Mixed Methods Appraisal Tool will be used for mixed-methods studies. Two reviewers will independently assess risk of bias. Disagreements will be resolved through discussion, and where consensus cannot be reached, a third reviewer will be consulted.
+
+Data synthesis
+
+A descriptive synthesis of all included studies, summarizing intervention types, outcomes and other study characteristics will be presented using structured tables and narrative summaries. Quantitative and qualitative data will be analysed separately before integration.
+
+Quantitative findings will be synthesized using meta-analysis where appropriate, or narratively when heterogeneity precludes statistical pooling. Meta-analysis will be conducted for feasibility, accessibility, and effectiveness outcomes when at least two studies report comparable measures using sufficiently similar definitions, and are sufficiently similar in terms of intervention characteristics, participant population, outcome definitions, and study design. Feasibility outcomes may include implementation fidelity, recruitment, retention, and intervention delivery indicators. Accessibility outcomes may include acceptability, uptake, reach, privacy, and equity-related indicators. Effectiveness outcomes may include HIV testing uptake, PrEP initiation or adherence and condom use. Where sufficient data are available, pooled analyses may be conducted for outcomes such as HIV testing uptake, PrEP initiation, condom use, intervention acceptability, intervention uptake and retention in prevention programs. Binary outcomes will be summarized using risk ratios, odds ratios, or risk differences; continuous outcomes using mean differences or standardized mean differences, and time-to-event outcomes using hazard ratios. A random-effects model will be used as a default analytic approach, with heterogeneity assessed using the I2 statistic and Chi-square test. Where at least 10 studies contribute data, subgroup analyses will be conducted by intervention type, delivery setting and predefined age groups. Subgroup analyses will be conducted for predefined age groups (10–14, 15–19 and 20–24 years) when sufficient studies report age-disaggregated data, to examine whether implementation outcomes differ across developmental stages. Meta-regression may be used to explore potential sources of heterogeneity. Sensitivity analyses will examine the influence of excluding studies at high risk of bias or those with missing data. If meta-regression is not feasible due to variability in study design or outcome measurement, findings will be presented narratively. Narrative synthesis will involve grouping studies by intervention type and outcome domain and summarizing results thematically.
+
+Qualitative data will be synthesized thematically using inductive and deductive coding. Themes will be organized under feasibility, accessibility, and effectiveness to align with the review’s core domains. Integration will occur at the interpretive level, with narrative juxtaposition of quantitative and qualitative findings to identify convergence, divergence, and contextual insights relevant to implementation.
+
+Publication bias will be assessed using funnel plots and statistical tests for small-study effects (e.g., Egger’s or Begg’s test), where applicable. Quantitative synthesis will be carried out in RevMan, and qualitative synthesis in Excel.
+
+Confidence in cumulative evidence
+
+Two independent reviewers will use the Grading of Recommendations Assessment, Development and Evaluation (GRADE) framework to determine the certainty of evidence. Conflicts will be resolved through discussion, and a third reviewer will be involved where agreement cannot be reached.
+
+Ethical considerations
+
+This is a systematic review of published and publicly available literature. Hence, it will not involve primary data collection with human participants and does not require formal ethical approval. All data will be extracted from existing studies, and no individual participant information will be identifiable. This review will be conducted in accordance with PRISMA-P guidelines to ensure transparency, reproducibility, and integrity throughout the process.
+
+Status and timeline of the study
+
+Table 4 summarizes the planned timeline for screening, data extraction, analysis and expected completion of the study.
+
+10.1371/journal.pone.0352973.t004 Table 4 Study timeline.
+
+Review stage	Status at submission	Planned timeline	
+Protocol development	Completed	Completed prior to submission	
+Database search	Not yet started	June 2026	
+Title/abstract screening	Not yet started	June – July 2026	
+Full-text screening	Not yet started	August 2026	
+Data extraction	Not yet started	September – October 2026	
+Risk of bias assessment	Not yet started	September – October 2026	
+Data analysis and synthesis	Not yet started	November – December 2026	
+Report writing and dissemination	Not yet started	December 2026 – February 2027	
+
+Discussion
+
+This systematic review will synthesize evidence on school-based HIV prevention interventions targeting AGYW in sub-Saharan Africa. Implementation of these interventions is often shaped by contextual factors, including stigma, policy constraints, and resource availability.
+
+By focusing on studies conducted within educational institutions, this review aims to clarify what works in integrating biomedical HIV prevention into school settings and to clarify implementation bottlenecks and equity gaps. The inclusion of both quantitative and qualitative components will allow for a nuanced understanding of not only outcomes but also implementation processes, barriers and facilitators.
+
+Potential limitations include variability in study design, outcome definitions, and measurement tools, which may limit the feasibility of meta-analysis. Restricting the review to English-language publications may introduce language bias and may result in the exclusion of relevant studies from francophone and lusophone countries in sub-Saharan Africa. This limitation reflects resource constraints, and the findings should be interpreted in light of this.
+
+Ultimately, this review will contribute to the evidence base for equity-driven HIV prevention programming in schools, helping to inform future research, policy, and practice at reducing HIV vulnerability among AGYW in sub-Saharan Africa.
+
+Supporting information
+
+S1 Table PRISMA-P checklist.
+
+(DOCX)
+
+DOI: 10.1371/journal.pone.0352973.r001
+
+Decision Letter 0
+
+Badru Oluwaseun Academic Editor
+Copyright: © 2026 Oluwaseun Badru
+Copyright year: 2026
+Copyright holder: Oluwaseun Badru
+License: This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Submission Version: 0
+
+29 May 2026
+
+-->PONE-D-26-18433-->-->Integrating biomedical HIV prevention in schools: Protocol for a systematic review of interventions for Adolescent Girls and Young Women in Sub-Saharan Africa-->-->PLOS One
+
+Dear Dr. Lodonu-Senoo,
+
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+==============================
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+
+This proposed systematic review is crucial in the context of biomedical intervention
+
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+
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+Reviewers' comments:
+
+Reviewer's Responses to Questions
+
+-->Comments to the Author
+
+1. Does the manuscript provide a valid rationale for the proposed study, with clearly identified and justified research questions?
+
+The research question outlined is expected to address a valid academic problem or topic and contribute to the base of knowledge in the field.-->
+
+Reviewer #1: Yes
+
+Reviewer #2: Yes
+
+**********
+
+-->2. Is the protocol technically sound and planned in a manner that will lead to a meaningful outcome and allow testing the stated hypotheses?
+
+The manuscript should describe the methods in sufficient detail to prevent undisclosed flexibility in the experimental procedure or analysis pipeline, including sufficient outcome-neutral conditions (e.g. necessary controls, absence of floor or ceiling effects) to test the proposed hypotheses and a statistical power analysis where applicable. As there may be aspects of the methodology and analysis which can only be refined once the work is undertaken, authors should outline potential assumptions and explicitly describe what aspects of the proposed analyses, if any, are exploratory.-->
+
+Reviewer #1: Yes
+
+Reviewer #2: Yes
+
+**********
+
+-->3. Is the methodology feasible and described in sufficient detail to allow the work to be replicable?-->
+
+Reviewer #1: No
+
+Reviewer #2: Yes
+
+**********
+
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+
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+
+Reviewer #1: No
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+Reviewer #2: No
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+**********
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+Reviewer #1: Yes
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+Reviewer #2: Yes
+
+**********
+
+-->6. Review Comments to the Author
+
+Please use the space provided to explain your answers to the questions above and, if applicable, provide comments about issues authors must address before this protocol can be accepted for publication. You may also include additional comments for the author, including concerns about research or publication ethics.
+
+You may also provide optional suggestions and comments to authors that they might find helpful in planning their study.
+
+(Please upload your review as an attachment if it exceeds 20,000 characters)-->
+
+Reviewer #1: The manuscript presents a generally relevant and timely rationale for examining the integration of biomedical HIV prevention interventions within school settings for adolescent girls and young women, particularly given the ongoing burden of HIV in this population and the importance of school platforms for prevention delivery. However, the justification for the proposed research questions and eligibility criteria would benefit from further refinement. In particular, the inclusion of a broad age range (10–24 years) is not fully aligned with a school-based intervention focus and introduces substantial heterogeneity across distinct developmental, educational, and service-access stages. Early adolescents (10–14 years), mid-to-late adolescents (15–19 years), and young adults (20–24 years) differ meaningfully in terms of school exposure, sexual and reproductive health needs, and relevance to biomedical HIV prevention interventions. As currently framed, the criteria risk conflating populations for whom school-based biomedical integration may be variably applicable or minimally relevant, particularly at the younger end of the spectrum. The authors should either provide a clearer justification for maintaining this broad age range, including a plan for stratified analysis by age/education stage, or consider narrowing the population to better reflect school-attending secondary school-aged adolescents, where the intervention context is most coherent.
+
+Reviewer #2: The protocol addresses a highly relevant and timely public health issue. The focus on school-based biomedical HIV prevention for adolescent girls and young women in sub-Saharan Africa addresses an important evidence gap, particularly given the continued disproportionate burden of HIV in this population. It is also well-structured and aligned with PRISMA-P guidelines, with notable strengths including the inclusion of both quantitative and qualitative evidence, the use of established risk-of-bias tools, and the focus on implementation outcomes.
+
+To further strengthen the manuscript, the following suggestions may be considered:
+
+Introduction/ Methods
+
+1. Some terms such as ‘biomedical HIV prevention’ and ‘implementation outcomes’ could be defined more clearly to improve clarity and help readers better understand the scope of the review.
+
+Methods
+
+1. The outcomes section could benefit from further clarification. While biological and behavioural outcomes appear to be excluded in the eligibility criteria, they are later mentioned under effectiveness outcomes. Clarifying how effectiveness will be assessed would improve consistency.
+
+2. It would be useful to briefly explain the rationale for limiting the review to studies published between 2015 and 2025, particularly whether this relates to important policy developments such as WHO PrEP guideline updates or the SDG era.
+
+3. The search strategy could be strengthened. Using “Africa” alone may retrieve studies outside sub-Saharan Africa.
+
+4. The risk of bias section could be strengthened by specifying which appraisal tools will be used for each study design and how disagreements between reviewers will be resolved.
+
+5. The data synthesis section would benefit from a little more detail regarding which outcomes will be pooled, the effect measures to be used, how heterogeneity will be assessed, and under what conditions meta-analysis will be conducted
+
+6. Restricting the review to English-language publications may exclude relevant studies from francophone and lusophone countries within sub-Saharan Africa. The authors may wish to consider including studies published in other languages where feasible, using available translation tools or multilingual support to minimize language bias and improve the comprehensiveness of the review.
+
+**********
+
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+
+Reviewer #1: Yes: Pelisa Nongena
+
+Reviewer #2: No
+
+**********
+
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+Attachment Submitted filename: PONE-D-26-18433_reviewed.docx
+
+DOI: 10.1371/journal.pone.0352973.r002
+
+Author response to Decision Letter 1
+
+Submission Version: 1
+
+16 Jun 2026
+
+Dear Academic Editor and Reviewers,
+
+We sincerely thank the Academic Editor and Reviewers for their thoughtful and constructive comments. We appreciate the positive assessment of the relevance and potential contribution of this protocol. We have carefully revised the manuscript to address all comments and believe that these revisions have strengthened the clarity, transparency, and reproducibility of the proposed review. Below, we provide a detailed point-by-point response.
+
+Academic Editor
+
+Comment:
+
+Please address the reviewer comments adequately, in particular the language restriction and age range.
+
+Response:
+
+We thank the Academic Editor for this recommendation. We have addressed all comments raised by the reviewers. We have provided additional justification for retaining the age range of 10–24 years and have incorporated plans for subgroup analyses by age category (10–14, 15–19, and 20–24 years) where sufficient data are available. We have expanded the discussion of language restrictions and explicitly acknowledge the potential for language bias resulting from the inclusion of English-language publications only. We have also explained that resource constraints preclude reliable screening and extraction of non-English studies.
+
+Journal requirements
+
+Comment 1:
+
+Please ensure that the manuscript meets PLOS ONE style requirements, including those for file naming.
+
+Response:
+
+The manuscript has been reviewed and revised to ensure compliance with PLOS ONE formatting and style requirements.
+
+Comment 2:
+
+Your ethics statement should only appear in the Methods section of your manuscript. If your ethics statement is written in any section besides the Methods, please move it to the Methods section and delete it from any other section. Please ensure that your ethics statement is included in your manuscript, as the ethics statement entered into the online submission form will not be published alongside your manuscript.
+
+Response:
+
+The ethics statement has been retained only within the Methods section and removed from any other sections of the manuscript.
+
+Comment 3:
+
+Please provide a complete Data Availability Statement in the submission form, ensuring you include all necessary access information or a reason for why you are unable to make your data freely accessible. If your research concerns only data provided within your submission, please write "All data are in the manuscript and/or supporting information files" as your Data Availability Statement.
+
+Response:
+
+The Data Availability Statement has been revised to indicate that all data are in the manuscript and/or supporting information files.
+
+Comment 4:
+
+Please ensure that you refer to Figure 1 in your text as, if accepted, production will need this reference to link the reader to the figure.
+
+Response:
+
+An explicit reference to Figure 1 has been added within the Study Selection section.
+
+Comment 5:
+
+We note you have included a table to which you do not refer in the text of your manuscript. Please ensure that you refer to Table 3 in your text; if accepted, production will need this reference to link the reader to the Table.
+
+Response:
+
+An explicit reference to Table 3 has been added within the Data Items section.
+
+Comment 6:
+
+We notice that your supplementary figures are uploaded with the file type 'Figure'. Please amend the file type to 'Supporting Information'. Please ensure that each Supporting Information file has a legend listed in the manuscript after the references list.
+
+Response:
+
+We thank the editorial team for noting the file type issue. The figure in question was mistakenly uploaded as Supporting Information. We have corrected this by re uploading it as a main text figure and removing it from the Supporting Information files.
+
+REVIEWER #1
+
+Comment:
+
+The manuscript presents a generally relevant and timely rationale for examining the integration of biomedical HIV prevention interventions within school settings for adolescent girls and young women, particularly given the ongoing burden of HIV in this population and the importance of school platforms for prevention delivery. However, the justification for the proposed research questions and eligibility criteria would benefit from further refinement. In particular, the inclusion of a broad age range (10–24 years) is not fully aligned with a school-based intervention focus and introduces substantial heterogeneity across distinct developmental, educational, and service-access stages. Early adolescents (10–14 years), mid-to-late adolescents (15–19 years), and young adults (20–24 years) differ meaningfully in terms of school exposure, sexual and reproductive health needs, and relevance to biomedical HIV prevention interventions. As currently framed, the criteria risk conflating populations for whom school-based biomedical integration may be variably applicable or minimally relevant, particularly at the younger end of the spectrum. The authors should either provide a clearer justification for maintaining this broad age range, including a plan for stratified analysis by age/education stage, or consider narrowing the population to better reflect school-attending secondary school-aged adolescents, where the intervention context is most coherent.
+
+Response:
+
+We thank the reviewer for this thoughtful observation. We have retained the 10–24-year age range because it aligns with global definitions of adolescents and young people used by WHO and UNAIDS, and because school-based and school-linked HIV prevention interventions in sub-Saharan Africa frequently reach individuals across this span, including early adolescents in upper primary school, secondary school students, and young adults enrolled in post-secondary or vocational institutions.
+
+However, we agree that developmental and educational stages differ meaningfully within this range. To address concerns regarding heterogeneity, we have revised the Data Synthesis section to specify that subgroup analyses will be conducted by age category (10–14 years, 15–19 years, and 20–24 years) where sufficient studies are available. This approach preserves conceptual coherence while allowing us to capture the full range of school-attending populations targeted by HIV prevention programs in the region.
+
+REVIEWER #2
+
+Introduction/Methods
+
+Comment 1:
+
+Some terms such as ‘biomedical HIV prevention’ and ‘implementation outcomes’ could be defined more clearly to improve clarity and help readers better understand the scope of the review.
+
+Response:
+
+We appreciate this helpful suggestion. We have clarified these terms within the Methods section. Specifically, we added an operational definition stating that, for the purposes of this review, biomedical HIV prevention interventions refer to school-based interventions that provide, deliver or facilitate access to PrEP, condoms or HIV testing services. We also expanded the description of implementation-related outcomes, including feasibility, accessibility and effectiveness domains to improve clarity regarding the scope of the review.
+
+Methods
+
+Comment 1:
+
+The outcomes section could benefit from further clarification. While biological and behavioural outcomes appear to be excluded in the eligibility criteria, they are later mentioned under effectiveness outcomes. Clarifying how effectiveness will be assessed would improve consistency.
+
+Response:
+
+Thank you for this helpful observation. We agree that the presentation of outcomes in the eligibility table may have created ambiguity. To improve clarity and ensure consistency across sections, we have revised the eligibility criteria by removing the reference to biological and behavioural outcomes from the inclusion table. These outcomes are now described exclusively under the Data Items section, where we provide operational definitions of feasibility, accessibility, and effectiveness. We also added a clarifying statement to specify that biomedical and behavioural measures (e.g., HIV testing uptake, PrEP initiation, condom use) will be assessed as effectiveness outcomes, reflecting real world effects of intervention delivery.
+
+These revisions ensure that the eligibility criteria focus solely on the types of outcomes required for inclusion, while the Data Items and Outcomes sections clearly describe how effectiveness will be assessed.
+
+Comment 2:
+
+It would be useful to briefly explain the rationale for limiting the review to studies published between 2015 and 2025, particularly whether this relates to important policy developments such as WHO PrEP guideline updates or the SDG era
+
+Response:
+
+We have added a justification for the selected timeframe within the Search Strategy section. Specifically, we note that 2015 coincided with the adoption of the Sustainable Development Goals and WHO recommendations supporting broader use of oral PrEP among populations at substantial risk of HIV infection.
+
+Comment 3:
+
+The search strategy could be strengthened. Using “Africa” alone may retrieve studies outside sub-Saharan Africa.
+
+Response:
+
+We agree and have revised the search strategy accordingly. The standalone term “Africa” has been removed from the search strategy.
+
+Comment 4:
+
+The risk of bias section could be strengthened by specifying which appraisal tools will be used for each study design and how disagreements between reviewers will be resolved.
+
+Response:
+
+We appreciate this helpful suggestion. The Risk of Bias Assessment section has been expanded to specify the appraisal tool that will be used for each study design. We also clarify that risk-of-bias assessments will be conducted independently by two reviewers, with disagreements resolved through discussion and consultation with a third reviewer when necessary.
+
+Comment 5:
+
+The data synthesis section would benefit from a little more detail regarding which outcomes will be pooled, the effect measures to be used, how heterogeneity will be assessed, and under what conditions meta-analysis will be conducted
+
+Response:
+
+We appreciate this helpful suggestion and have revised the manuscript accordingly. We have expanded the Data Synthesis section. The revised text now specifies the types of outcomes that may be pooled, including feasibility, accessibility, and effectiveness outcomes; the effect measures that will be used for binary, continuous, and time-to-event outcomes; the methods for assessing heterogeneity using the I² statistic and Chi-square test; and the conditions under which meta-analysis, subgroup analyses, sensitivity analyses, and narrative synthesis will be conducted.
+
+Comment 6:
+
+Restricting the review to English-language publications may exclude relevant studies from francophone and lusophone countries within sub-Saharan Africa. The authors may wish to consider including studies published in other languages where feasible, using available translation tools or multilingual support to minimize language bias and improve the comprehensiveness of the review.
+
+Response:
+
+We thank the reviewer for this important observation. We acknowledge that restricting the review to English-language publications may result in exclusion of relevant evidence from francophone and lusophone countries in sub-Saharan Africa and may introduce language bias. However, resource constraints and the absence of multilingual screening and data extraction capacity preclude the reliable assessment of non-English studies. We revised the Discussion section to explicitly acknowledge the potential for language bias and its implications for the comprehensiveness of the review.
+
+We thank the Academic Editor and Reviewers for their valuable comments. We believe the revisions have substantially strengthened the protocol and satisfactorily addressed the comments raised by the Academic Editor and Reviewers. We are grateful for the constructive feedback and consideration of our revised submission.
+
+Attachment Submitted filename: Response to Reviewers.docx
+
+DOI: 10.1371/journal.pone.0352973.r003
+
+Decision Letter 1
+
+Badru Oluwaseun Academic Editor
+Badru Oluwaseun Academic Editor
+Copyright: © 2026 Oluwaseun Badru
+Copyright year: 2026
+Copyright holder: Oluwaseun Badru
+License: This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Submission Version: 1
+
+18 Jun 2026
+
+Integrating biomedical HIV prevention in schools: Protocol for a systematic review of interventions for Adolescent Girls and Young Women in Sub-Saharan Africa
+
+PONE-D-26-18433R1
+
+Dear Dr. Lodonu-Senoo,
+
+We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.
+
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+
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+
+Oluwaseun Abdulganiyu Badru,
+
+Academic Editor
+
+PLOS One
+
+DOI: 10.1371/journal.pone.0352973.r004
+
+Acceptance letter
+
+Badru Oluwaseun Academic Editor
+Badru Oluwaseun Academic Editor
+Copyright: © 2026 Oluwaseun Badru
+Copyright year: 2026
+Copyright holder: Oluwaseun Badru
+License: This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+PONE-D-26-18433R1
+
+PLOS One
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+
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+References
+
+1 UNAIDS. AIDS, crisis and the power to transform: UNAIDS Global AIDS Update 2025. Geneva. 2025 [cited 15 Dec 2025]. Available from: https://www.unaids.org/en/UNAIDS-global-AIDS-update-2025
+2 Mojola SA , Wamoyi J . Contextual drivers of HIV risk among young African women. 2019. doi: 10.1002/jia2.25302/full PMC6643074 31328409
+3 Mvundura M , Nundy N , Kilbourne-Brook M , Coffey PS . Estimating the hypothetical dual health impact and cost-effectiveness of the Woman’s Condom in selected sub-Saharan African countries. Int J Womens Health. 2015;7:271–7. doi: 10.2147/IJWH.S75040 25784820 PMC4356704
+4 Stover J , Teng Y . The impact of condom use on the HIV epidemic. Gates Open Res. 2022;5:91. doi: 10.12688/gatesopenres.13278.2 35355689 PMC8933340
+5 Aventin Á , Gordon S , Laurenzi C , Rabie S , Tomlinson M , Lohan M , et al. Adolescent condom use in Southern Africa: narrative systematic review and conceptual model of multilevel barriers and facilitators. BMC Public Health. 2021;21(1):1228. doi: 10.1186/s12889-021-11306-6 34172027 PMC8234649
+6 Ratnawati D , Huda MH , Mukminin MA , Widyatuti W , Setiawan A . Meta-analysis of the effectiveness of educational programs about HIV prevention on knowledge, attitude, and behavior among adolescents. Narra J. 2024;4(2):e870. doi: 10.52225/narra.v4i2.870 39280293 PMC11391990
+7 Niland R , Flinn C , Nearchou F . Assessing the role of school-based sex education in sexual health behaviours: a systematic review. Cogent Psychology. 2024;11(1). doi: 10.1080/23311908.2024.2309752
+8 Mason-Jones AJ , Sinclair D , Mathews C , Kagee A , Hillman A , Lombard C . School-based interventions for preventing HIV, sexually transmitted infections, and pregnancy in adolescents. Cochrane Database Syst Rev. 2016;11:CD006417. doi: 10.1002/14651858.CD006417.pub3 27824221 PMC5461872
+9 Mahomed S , Bukusi E , Sikazwe I , Musoke P , Karim QA . A risk- and needs-based strategy HIV prevention for adolescent girls and young women, WHO African Region. Bull World Health Organ. 2024;102(12):913–5. doi: 10.2471/BLT.23.291160 39611197 PMC11601182
+10 Nicol E , Basera W , Turawa E , Lombard C , Funani N , Chavhalala D , et al. Assessing PrEP initiation and adherence among high-risk, sexually active adolescents and young adults: a population-based prospective study across diverse service delivery models in a high HIV prevalent district in South Africa. AIDS Behav. 2025;29(8):2588–609. doi: 10.1007/s10461-025-04719-6 40312570 PMC12378780
+11 Maseko B , Hill LM , Phanga T , Bhushan N , Vansia D , Kamtsendero L , et al. Perceptions of and interest in HIV pre-exposure prophylaxis use among adolescent girls and young women in Lilongwe, Malawi. PLoS One. 2020;15. doi: 10.1371/journal.pone.0226062 PMC6957134 31929547
+12 Amaugo LG , Papadopoulos C , Ochieng BMN , Ali N . The effectiveness of HIV/AIDS school-based sexual health education programmes in Nigeria: a systematic review. Health Educ Res. 2014;29(4):633–48. doi: 10.1093/her/cyu002 24572458
+13 Denford S , Abraham C , Campbell R , Busse H . A comprehensive review of reviews of school-based interventions to improve sexual-health. Health Psychol Rev. 2017;11(1):33–52. doi: 10.1080/17437199.2016.1240625 27677440
+14 Shangase N , Kharsany ABM , Ntombela NP , Pettifor A , McKinnon LR . A systematic review of randomized controlled trials of school based interventions on sexual risk behaviors and sexually transmitted infections among young adolescents in sub-Saharan Africa. AIDS Behav. 2021;25. doi: 10.1007/s10461-021-03242-8 PMC8985547 33772695
+15 United Nations. Transforming our world: the 2023 agenda for sustainable development; 2015.
+16 WHO. Guideline on when to start antiretroviral therapy and on pre-exposure prophylaxis for HIV. 2015. Available from: https://apps.who.int/iris/bitstream/handle/10665/186275/9789241509565_eng.pdf;jsessionid=A279E21164BBA44795C8582F4A20ED25?sequence=1 26598776
+17 Proctor E , Silmere H , Raghavan R , Hovmand P , Aarons G , Bunger A , et al. Outcomes for implementation research: conceptual distinctions, measurement challenges, and research agenda. Adm Policy Ment Health. 2011;38(2):65–76. doi: 10.1007/s10488-010-0319-7 20957426 PMC3068522
diff --git a/corpus/psychology/text/2f5e7921c22d5acb.txt b/corpus/psychology/text/2f5e7921c22d5acb.txt
new file mode 100644
index 0000000000000000000000000000000000000000..108f916195bb58b27d48253cea267dcf7378b197
--- /dev/null
+++ b/corpus/psychology/text/2f5e7921c22d5acb.txt
@@ -0,0 +1,72 @@
+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Front Psychiatry
+Journal ID: Front Psychiatry
+NLM Journal ID: 101545006
+Journal ID: Front. Psychiatry
+
+Frontiers in Psychiatry
+
+EISSN: 1664-0640
+Publisher: Frontiers Media SA
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC13454760
+PMID: 42577608
+DOI: 10.3389/fpsyt.2026.1907005
+Article version: 1
+Article version:
+Subjects: Correction
+
+Correction: Measuring mental wellbeing in clinical and non-clinical adolescents using the COMPAS-W Wellbeing Scale
+
+Lam Janine R. 1 2 Formal analysis Funding acquisition Investigation Validation Writing – original draft Writing – review & editing
+Park Haeme R. P. 1 2 Data curation Funding acquisition Project administration Resources Writing – review & editing
+Gatt Justine M. 1 2 * Conceptualization Funding acquisition Methodology Resources Supervision Writing – review & editing
+1 Centre for Wellbeing, Resilience and Recovery, Neuroscience Research Australia , Sydney , NSW ,  Australia
+2 School of Psychology, University of New South Wales , Sydney , NSW ,  Australia
+* Correspondence: Justine M. Gatt, j.gatt@unsw.edu.au
+Electronic publication date: 2026 Jul 27
+Publication date: 2026
+Volume: 17
+Electronic Location ID: 1907005
+Received 2026 Jun 12; Revised 2026 Jun 16; Accepted 2026 Jun 26
+Copyright: Copyright © 2026 Lam, Park and Gatt.
+Copyright year: 2026
+Copyright holder: Lam, Park and Gatt
+License: This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Erratum for: Correction: Measuring mental wellbeing in clinical and non-clinical adolescents using the COMPAS-W Wellbeing Scale 17 27 5 2026 1876633 Frontiers in Psychiatry 10.3389/fpsyt.2026.1876633 PMC13251548 42281648
+Keywords: mental health, well-being, adolescence, psychiatric disorders, developmental disorders, psychometric testing, reliability, validity
+Figure count: 0
+Table count: 0
+Equation count: 0
+Reference count: 0
+Page count: 1
+
+section-at-acceptance: Adolescent and Young Adult Psychiatry
+
+Ÿ==============================Ÿ
+The Conflict of interest statement was erroneously given as:
+
+“The intellectual property rights to the COMPAS-W scale are assigned to Tilt Your Life Pty Ltd, of which JG is Founder and Director. The scale is available for non-commercial academic and research use and is licensed for commercial use via Tilt Your Life Pty Ltd (contact: justine.gatt@gmail.com).
+
+The remaining author(s) declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.”
+
+The updated Conflict of interest statement is:
+
+“Since original publication, JG has founded Tilt Your Life Pty Ltd, a wellbeing-focused company.
+
+The remaining author(s) declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.”
+
+The original version of this article has been updated.
+
+Publisher’s note
+
+All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.
+
+Approved by: Frontiers Editorial Office, Frontiers Media SA, Switzerland
+
diff --git a/corpus/psychology/text/31922b3af41c258d.txt b/corpus/psychology/text/31922b3af41c258d.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c4d5d27fc43114d6673649286614e31ea3f180b4
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+++ b/corpus/psychology/text/31922b3af41c258d.txt
@@ -0,0 +1,651 @@
+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Front Vet Sci
+Journal ID: Front Vet Sci
+NLM Journal ID: 101666658
+Journal ID: Front. Vet. Sci.
+
+Frontiers in Veterinary Science
+
+EISSN: 2297-1769
+Publisher: Frontiers Media SA
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC13185694
+PMID: 42164771
+DOI: 10.3389/fvets.2026.1729697
+Article version: 1
+Article version:
+Subjects: Review
+
+Automatic gait analysis in canines using computer vision
+
+Phelan Brian 1 * Conceptualization Data curation Formal analysis Writing – original draft Writing – review & editing Methodology
+Mc Nally Turlough 2 Writing – review & editing
+Cuddy Laura 2 Writing – review & editing
+Lacey Gerard 1 Conceptualization Funding acquisition Methodology Project administration Supervision Writing – review & editing
+1 Department of Electronic Engineering, Maynooth University , Maynooth , Ireland
+2 Veterinary Specialists Ireland , Summerhill , Ireland
+* Correspondence: Brian Phelan, Brian.Phelan@mu.ie
+Electronic publication date: 2026 May 5
+Publication date: 2026
+Volume: 13
+Electronic Location ID: 1729697
+Received 2025 Oct 21; Revised 2026 Feb 25; Accepted 2026 Feb 26
+Copyright: Copyright © 2026 Phelan, Mc Nally, Cuddy and Lacey.
+Copyright year: 2026
+Copyright holder: Phelan, Mc Nally, Cuddy and Lacey
+License: This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Keywords: canine gait analysis, computer vision, locomotion, mesh reconstruction, pose estimation
+
+Funding: Enterprise Ireland 10.13039/501100001588 CF-2023-2261-I The author(s) declared that financial support was received for this work and/or its publication. This work was supported by the Enterprise Ireland project number CF-2023-2261-I (AniSteps).
+
+Figure count: 4
+Table count: 8
+Equation count: 0
+Reference count: 115
+Page count: 24
+
+section-at-acceptance: Animal Behavior and Welfare
+
+Ÿ==============================Ÿ
+Automated canine gait analysis using computer vision has the potential to extend objective canine gait assessment beyond specialized, controlled laboratories into domestic environments, but the field is comparatively less mature than human methods. This review explores the state-of-the-art for vision-based canine gait analysis, with a particular emphasis on single-camera (monocular) articulated pose and shape reconstruction, along with the extraction and interpretation of clinically relevant gait parameters. Across the literature, current pipelines reconstruct anatomical and surface representations of canines from images and video, yet rarely achieve the biomechanical fidelity or validation against gold-standard references such as motion capture, pressure walkways or fluoroscopy. Three requirements emerge from the literature: robust monocular 3D reconstruction sufficiently accurate to measure soft-tissue artifacts (approximately 10–20 mm), a standardized set of gait parameters aligned to veterinary assessment practices, and a shift from parts-based to holistic gait analysis. We highlight priority research directions to improve monitoring of canine gait in real-world settings including breed-representative datasets, synthetic training data to real-world data adaption, and ensemble learning for pathology identification. Addressing these gaps could allow for objective, longitudinal monitoring of canine gait in both veterinary practices and domestic environments. We advocate for increased interdisciplinary collaboration to foster innovation and establish new standards in the field.
+
+1 Introduction
+
+Gait analysis is a sub-field in bio-mechanics which refers to the systematic study of animal and human locomotion by measuring body movements, mechanics, and the activity of the muscles. Gait analysis quantifies complex patterns of limb movements and the forces generated at various speeds in order to gain an understanding for the underlying mechanisms and principles of locomotion. An objective investigation of both normal and pathological patterns of movement furthers the diagnoses, treatment and rehabilitation of animals and humans with conditions affecting their ability to move. The analysis of gait is typically performed in clinical environments for both animals and humans, and is usually not possible in domestic scenarios due to the expertise and equipment required. Traditional methods of gait analysis require trained operators performing various examinations such as visual and palpation-based assessments, as well as utilizing specialized kinetic laboratories to perform deeper biomechanical analysis. New technologies have the potential to scale the benefits of gait analysis for veterinarians, including enhanced post-operative care, triaging animals in home settings, and the analysis of longitudinal health data to inform the current state of an animals health. This can be further extended to cover high performance activities, sports and service work.
+
+While there has been significant work for computer vision methods in humans, its application to animals remains comparatively underdeveloped despite their long-treasured role in society. Canines represent one of the most clinically evaluated companion animal and also exhibit a wide variation in morphologies across the world. Lastly, the increasing availability of household videos has created new opportunities for enhanced domestic monitoring of canine health and mobility. Together, these factors justify a focused review, as developments for dogs cannot necessarily be generalized from other quadrupeds, but may introduce opportunities for such generalization. Therefore, the purpose of this review is to investigate and synthesize computer vision-based gait analysis approaches in canines. Specifically, current approaches in articulated pose and shape reconstruction, clinically relevant gait parameter extraction and locomotion analysis are examined. By consolidating these studies, the review aims to clarify the state of the field, identify gaps, and outline future research opportunities.
+
+1.1 Review methods
+
+A comprehensive search was conducted for this narrative-style review in Google Scholar, Science Direct and PubMed databases, covering literature up to October 2025, as seen in Figure 1. Search terms included: “computer vision,” “canine,” “dog,” “gait analysis,” “gait parameter extraction,” “pose estimation,” and “mesh reconstruction.” Search terms were combined using boolean operators and included: (“computer vision”) AND (“canine” OR “dog”)
+
+(“gait analysis” OR “gait parameter extraction”)
+
+(“pose estimation” OR “mesh reconstruction”)
+
+Figure 1 PRIMSA-style flow diagram of review methods and study selection.
+
+Flowchart illustrating a systematic review process divided into four stages: identification, screening, eligibility, and inclusion. Records initially identified total one thousand twenty-six, with thirty-one additional records for diversity. After removing generic computer vision papers, two hundred thirty-seven remain; seven hundred eighty-nine are excluded. Ninety-seven records pass further filtering, with one hundred forty more excluded. Final inclusion totals one hundred twenty-eight records, incorporating additional human and quadruped studies.
+
+1.1.1 Inclusion criteria
+
+Studies were included if they met all of the following criteria: Computer vision, image processing, or video-based gait analysis relevant to canines.
+
+Methods for 2D or 3D pose estimation, mesh reconstruction, or gait parameter extraction.
+
+Contributions to the methodological understanding of automated gait analysis.
+
+Published in peer-reviewed journals or conferences.
+
+Contained enough technical detail to be meaningfully evaluated.
+
+1.1.2 Exclusion criteria
+
+Studies were excluded if they: Focused primarily on wearable sensors or force/pressure-based systems without vision, except for when providing context to traditional methods.
+
+Presented generic computer vision techniques.
+
+Were outdated studies (more than 10 years old) unless they presented a foundational methodology still widely referenced or applied.
+
+Used multi-animal tracking, robot motion, or computer graphics unrelated to gait analysis.
+
+1.1.3 Screening procedure
+
+The initial search returned 1,026 publications: Google Scholar (522), ScienceDirect (396), and PubMed (108). After removing non-relevant records and studies which focused primarily on generic computer vision papers, 237 studies remained. Further filtering excluded studies relying on external sensors, multi-animal systems, or those lacking relevance. This resulted in 97 core canine computer vision studies. Due a lack of diversity in the techniques used with canines, some human/quadruped gait analysis and pose estimation studies were included to ensure adequate representation of state-of-the-art methods in articulated shape or scene reconstruction. This resulted in the addition of 31 cited studies. After screening and applying the above criteria, 128 studies remained for detailed consideration in this review.
+
+For each included publication, the following details were extracted: Computer vision method.
+
+Dataset characteristics (real, synthetic, breed diversity).
+
+Architecture/Backbone.
+
+Extracted gait parameters and associated methods.
+
+Evaluation metrics, where applicable.
+
+Clinical relevance or application.
+
+The studies were grouped into (1) Articulated Pose and Shape Reconstruction, and (2) Gait Analysis. Throughout this review, studies are assessed for methodological quality, including validation against gold-standard measurements, reporting of quantitative accuracy, breed diversity, and clinical relevance, to clarify the strength and limitations of the evidence.
+
+1.2 Review structure
+
+To provide context to the emergence of computer-vision methods in gait research, Section 1.3 begins by briefly discussing the history of locomotive analysis in humans and animals. Building on this foundation, Section 1.4 examines the traditional techniques used in canine gait analysis. While well-established, these methods reveal important limitations such as subjectivity, accessibility, and dependence on specialized equipment. Together, they motivate the shift toward automated, vision-based systems. Ultimately any such system must evaluated against clinical standards such as Clinical Metrology Instruments (CMIs) and commonly used gait parameters, which this section also introduces. Sections 1.5.1, 1.5.2 introduce the core concepts for computer vision approaches, asking the question: how can gait information traditionally obtained through complex systems and markers be replicated or improved using only visual data? To answer this, we require an understanding of pose estimation as a foundation upon which all possible automated gait analysis methods depend. Section 2.1 transitions deeper into to the vision-based approaches, organized into Articulated Pose & Shape Reconstruction (Section 2.1) and Gait Analysis (Section 2.2). This structure mirrors the pipeline used in automated systems, from firstly retrieving the dog's form and structure, then quantifying its movement, and lastly deriving meaningful biomechanical insights. Within each of their sub-sections, we compare the methodologies, highlight recurring obstacles, and show gaps that constrain real-world applicability. Section 3 compares findings from Sections 1.4, 2, showing convergent requirements across traditional and computer vision approaches. Lastly, Section 4 interprets the implications of these findings for automated canine gait analysis, focusing on the why these gaps matter and what must be addressed for these methods to become clinical reliable. Lastly, we outline the major barriers limiting clinical deployment, as well as the broader significance of computer vision in canine and animal research.
+
+1.3 Background
+
+The measure of musculoskeletal function was first documented by Aristotle in De Motu Animalium (1), with no documented further developments until Giovanni Borelli's updated version in the 17th century (2). Aristotle analyzed the different movements of animals, but from a broad biological and metaphysical perspective. Giovanni Borelli, often referred to as the “Father of Biomechanics,” applied a more mathematical and mechanical approach, focusing on the expanded musculoskeletal understanding of his time. Early on, it was discerned that the gait of animals or humans was defined by the biomechanics of locomotion, which was divided into kinematics and kinetics. Muybridge's groundbreaking photographic sequences in the late 1800s showed the sequential phases of animal and human movement, debunking previously held beliefs, such as the airborne phase of a horse's gallop (3). At the same time, Braune and Fischer's kinematic investigations revealed the sinusoidal trajectory of the body's center of mass during unassisted walking, giving a possible inheritance to mechanical conservation of energy (4). Alexander's studies spanned various terrains and speeds and showed the evolution of specialized gaits and limb configurations in animals to optimize energy use and agility in their natural habitats (5). Collectively, these foundational observations have enriched our understanding of animal gait, emphasizing the confluence of evolution, biomechanics, and environmental adaptation.
+
+1.4 Traditional canine gait analysis
+
+1.4.1 Visual based observations
+
+Visual-based observations of gait in dogs is a subjective method whereby findings from an evaluation by a trained operator are semi-quantified using a form of numerical rating scale. These scales include: numerical lameness grading scales (0–4 or 0–5), such as the Visual Analog Scale (VAS), which has been used in human as well as veterinary studies (6), and owner or handler questionnaires such as the Canine Brief Pain Inventory (CBPI) or Liverpool Osteoarthritis in Dogs (LOAD) (see Section 1.4.6). The main shortcoming of visual-based observations is that they are subjective and highly operator-dependent, requiring expert knowledge to effectively use. Even when performed by experts, subjective gait analysis has been shown to be highly inaccurate (7).
+
+1.4.2 Kinematic motion capture
+
+Motion capture systems track the trajectory of reflective markers during locomotion, providing a 3D quantitative assessment of gait kinematics, including joint angles, limb trajectories and spatiotemporal gait parameters. Markers are typically placed at key anatomical locations along the dog's body, for example the iliac crest and greater trochanter (9). The resultant objective kinematic data is highly beneficial for evaluating gait and detecting pathologies, as seen in studies such as Hamilton et al. (10). However, the attachment of the markers to the relatively loose skin and hair of dogs can introduce a shift of location relative to the underlying bone and the haired areas may need to be shaved in order to ensure accuracy during specific movements (11). As a result of these limitations, false positives and inaccurate data may be obtained, as shown by Lin et al. (11) through their consistent underestimation of flexion/extension of adduction/internal rotation when the stifle was flexed beyond 90°. The use of kinematic motion capture is largely limited to research institutions due to the equipment, time and expertise required to operate and interpret clinically-relevant data.
+
+1.4.3 Pressure sensitive walkways or force plates
+
+Force plates are the gold standard for detailed biomechanical data, however, are challenging and time-consuming to use. The use of force plates has largely been supplanted by pressure sensitive walkway systems (12) (as seen in Figure 2), or pressure mats due to their availability and ease of use in a clinical settings (13). Pressure mats are embedded with thousands of sensors that record how the paws contact the ground during walk or trot. Pressure mats capture both temporal (timing) and spatial (force/pressure distribution) aspects of locomotion, presenting them in a format that can readily be interpreted by a clinician. The output of pressure mats includes temporal parameters (stance time, swing time, stride time), spatial/force parameters (peak vertical force, pressure distribution within the paw, center of pressure movement), and symmetry indices (compare right versus and left and fore versus hindlimbs). Metrics derived from the pressure walkway systems, provide a comprehensive understanding of gait dynamics, aiding in diagnostics, therapeutic decisions, and rehabilitative measures. This can be seen by Assies et al. (14) through evaluating the effects of an undenatured collagen type-2-based nutraceutical on Recovery Time after TPLO in dogs, using objective gait analysis as the primary outcome measure.
+
+Figure 2 3D visualization of retro-reflective markers placed on key anatomical landmarks of sheep from Silve et al. (77), licensed under CC BY 4.0. (A) shows the markers being placed on the right hind legs of the sheep, and (B) shows the visualization of the markers inside 3D software.
+
+Panel A shows a sheep with numbered markers along its body, while a person wearing blue gloves holds a strap above its back. Panel B displays a 3D schematic with corresponding numbered points, illustrating marker positions and axes for motion analysis.
+
+1.4.4 Treadmill analysis
+
+Treadmill analysis ensures clinicians can achieve consistent and repeatable gait cycles for analysis. This method offers a controlled environment for data acquisition, mitigating the inconsistencies typically seen in overground locomotion (9). Furthermore, the stationary nature of treadmill walking permits continuous data collection, which might be challenging with conventional overground methods. The ability to adjust treadmill speed and incline also allows clinicians to examine gait under different conditions and stressors, therefore providing a comprehensive understanding of its gait via parameters such as kinematics (15) and kinetics (16). Limitations to treadmill analysis including the requirement for acclimatization, as well as potential altered gait mechanics on treadmill versus overground.
+
+1.4.5 Wearable sensors
+
+In the contemporary landscape of canine gait analysis, wearable sensors have carved a niche for themselves, heralded for their real-time data acquisition capabilities and potential for extended monitoring. These sensors, predominantly Inertial Measurement Units (IMUs) and accelerometers, are designed to capture intricate details of motion and orientation, facilitating an in-depth evaluation of a canine's gait (17). IMUs, an amalgamation of accelerometers, gyroscopes, and occasionally magnetometers, measure a spectrum of parameters from linear accelerations and angular velocities to magnetic fields (18). This multifaceted data acquisition enables the calculation of a body's orientation and movement in a 3D framework (19). Accelerometers, often deployed independently of IMUs, are pivotal for assessing lameness, as they provide granular data on the intensity and trajectory of movement (18). Their compact design and non-intrusive nature make wearable sensors an invaluable asset for prolonged, continuous monitoring, be it in a clinical or domestic setting.
+
+1.4.6 Clinical metrology instruments
+
+Clinical metrology instruments (CMIs) are standardized, owner-reported questionnaires designed to quantify health-related domains such as pain and mobility in canines. This form of structured feedback allows the owner to observe their dogs in a domestic setting, where the animal is at its most comfortable, eliminating common behaviors like stress that often skew results of observations. By translating the varying dimensions captured into a numerical scoring system, CMIs enable both the monitoring and evaluation of interventions and illnesses such as osteoarthritis, which then typically need to be confirmed with diagnostic imaging. An overview of the most commonly used CMIs, adapted from Gruen et al. (20), is presented in Table 1. Implementations of these CMIs vary, and are often given to veterinarians in conjunction with home video taken by the owner, as discussed by Gruen et al. (20). These videos are typically not of the required quality due to a variety of factors such as: portions of the video not containing the animal, unsteady camera, and a lack of specific movements that help accentuate specific symptoms.
+
+Table 1 Clinical metrology instruments, adapted from Gruen et al. (20).
+
+Tool	User	Validity	Acute/chronic	
+Canine osteoarthritis staging tool (COAST) (94)	Owner, veterinarian	Not validated	Chronic, osteoarthritis	
+Liverpool osteoarthritis in dogs (LOAD) (87)	Owner	Validated	Chronic, osteoarthritis	
+Canine brief pain inventory (CBPI) (95)	Owner	Validated	Chronic, osteoarthritis	
+Helsinki chronic pain index (96)	Owner	Limited validation	Chronic, osteoarthritis	
+
+1.4.7 Gait parameters
+
+The parameters listed in Table 2 are predominately kinematic and spatiotemporal measures extracted from the literature. They comprehensively capture limb and body movements, joint excursions, and spatiotemporal aspects of canine gait. They do not include kinetic measures such as ground reaction forces, joint moments, etc.
+
+Table 2 Comprehensive overview of key kinematic and spatiotemporal parameters used in canine gait analysis, presented with concise definitions and indications of whether each parameter can be readily obtained from 2D/3D imaging.
+
+Parameter	Definition	2D	3D	
+Displacement	Linear change in position of a marker (e.g., on a limb) over time.	Possible (sagittal plane only)	Required for full spatial measurement	
+Distance	Total path length traversed by a point during a gait cycle.	Approximate in 2D (planar path)	Required for true 3D trajectory length	
+Joint angles	Angle between two adjacent limb segments measured at a specific joint.	Possible (sagittal plane components)	Required for multi-planar angles	
+Angular velocity	Rate of change of a joint angle over time.	Computable if angle obtained in 2D	Required for full 3D rotational velocity	
+Range of motion	Difference between maximum and minimum joint angles during a gait cycle.	Measurable in sagittal plane only	Required for multi-plane ROM	
+Joint trajectories	Path traced by a joint (marker) in space over time.	Planar trajectory only	Required for full trajectory	
+Pelvic drop	Vertical excursion of the pelvis relative to a horizontal reference during stance.	Detectable in sagittal 2D	Required for frontal-plane obliquity	
+Center of gravity	Spatial location of the whole-body center of gravity during gait.	Not accurate in 2D (lateral shifts lost)	Required for accurate COG estimation	
+Gait cycle	Time interval from initial contact of one limb to the next contact of that same limb.	Measurable from 2D foot-fall events	3D not required for timing	
+Stride time	Duration of one gait cycle (seconds).	Measurable in 2D via frame timing	3D not required	
+Step time	Time between initial contact of one limb and initial contact of the contralateral limb.	Measurable in 2D if foot-falls visible	3D not required	
+Swing time	Time during which a limb is not in contact with the ground.	Measurable in 2D using foot-off/on events	3D not required	
+Stance time	Time during which a limb is in contact with the ground.	Measurable in 2D using foot-on/off events	3D not required	
+Step length	Fore-aft distance between successive paw placements of contralateral limbs.	Approximate in sagittal 2D if planar	Requires 3D for off-plane motion	
+Stride length	Fore-aft distance between successive paw placements of the same limb.	Approximate in sagittal 2D if planar	Requires 3D for off-plane motion	
+Step width	Lateral distance between placement of contralateral paws.	Not measurable in sagittal 2D	Requires 3D or frontal/dorsal view	
+Gait symmetry	Ratio or difference between right and left limb parameters (e.g., timing).	Computable from 2D spatial/temporal data	3D not required for symmetry timing	
+Single support time	Duration during which only one limb is in contact with the ground.	Measurable in 2D if foot-fall events visible	3D not required	
+Double support time	Duration during which two limbs are simultaneously in contact with the ground.	Measurable in 2D if overlapping contacts visible	3D not required	
+Cadence	Number of steps taken per minute.	Derivable from 2D step count and time	3D not required	
+These parameters were gathered across the literature, including Pálya et al. (97), Lin et al. (28), Miqueleto et al. (98), and McLaughlin (99).
+
+1.5 Computer vision-based gait analysis
+
+Gait Analysis through computer vision can be broken down into three key building blocks: Articulated shape and pose reconstruction (2D and 3D): to create an objective representation of the dog's body configuration, either as a set of anatomical keypoints (skeletal pose) or full 3D mesh.
+
+Gait parameter extraction: to convert raw pose sequences into meaningful, quantifiable descriptors of locomotion that align with veterinary biomechanics.
+
+Gait interpretation: to use the extracted gait parameters and/or full motion sequence to analyse gait quality, detect abnormalities, and support clinical decision-making.
+
+To maintain brevity, gait parameter extraction and gait interpretation are considered together under the broader term gait analysis.
+
+1.5.1 2D vs. 3D pose estimation
+
+2D Pose Estimation aims to predict the x, y coordinates of keypoints (body joints) of an animal in an image or sequence of images. Typically this can be divided into frame-by-frame estimation and video-based estimation over time. 3D Animal Pose Estimation involves predicting joint positions of an animal in 3D space using one or multiple images. While 2D pose has shown great promise, it lacks much of the actionable data we need for gait analysis, as shown by Fischer (21). For the purposes of this review, we will focus on monocular pose estimation in both 2D and 3D, while only briefly touching on multi-view methods.
+
+1.5.2 Human pose estimation
+
+Human pose estimation has functioned as the backbone of modern animal methods for a number of years. Some of the most popular models such as BlazePose (22) (3D), OpenPose (23) (2D), and PoseNet (24) (2D), have been pivotal in the development of monocular gait analysis systems i.e., Zambrano et al. (25). An overview of representative methods for human pose and shape estimation can be seen in Table 3. Unlike human pose, applying these models either directly or through naive approaches to canines presents significant challenges. This is primarily due to the substantial anatomical and morphological differences between humans and dogs, such as the number of limbs in contact with the ground, the range of motion in joints, and the variety of body shapes and sizes across dog breeds. While transfer-learning is possible in theory, it would require substantial canine-specific training data, alongside significant changes to the model's architecture. Through our research, we had made brief efforts for both direct and naive approaches in adopting the model, but achieved in poor results. In conclusion, it is fair to say that such modifications to the model with respect to canines would not be very feasible.
+
+Table 3 Summary of key publications on human pose estimation.
+
+Publication	Research direction/highlights	Data classes and training types	
+Hewitt et al. (100)	Fuses multi-view RGB into a neural implicit surface and jointly optimizes skeleton and per-vertex deformations, removing the need for markers and calibration through learned appearance priors.	Human; Synthetic RGB images and 3D mesh annotations from parametric models.	
+Rempe et al. (101)	Combines a conditional VAE motion prior with per-frame pose regression to decouple dynamics and robustly recover full-body motion under occlusion.	Human; 3D motion capture sequences (e.g., AMASS) and SMPL pose parameters.	
+Bazarevsky et al. (22)	Implements a two-stage, quantized CNN pipeline (person detector + 33-landmark regressor) optimized for real-time, on-device inference.	Human; RGB images and 2D keypoint annotations for body landmarks.	
+Güler et al. (102)	Extends R-CNN to regress dense UV surface coordinates and part labels against an SMPL template using a bespoke COCO-DensePose dataset.	Human; RGB images and dense UV coordinates mapped to the SMPL body surface.	
+Loper et al. (103)	Learns pose- and shape-dependent blend shapes via PCA on 3D scans to create a fully differentiable SMPL mesh model.	Human; 3D body scans, motion capture, and parametric mesh (SMPL) labels.	
+This table provides a structured overview of representative methods for human pose and shape estimation. These entries represent the key issues which limit 3D canine pose estimation matching the accuracy and performance of human methods, such as occlusion, multi-camera triangulation, and neural fields, pose-priors and motion capture training data. Each entry includes the research focus, target subject class, and the types of training data used. The comparison highlights diversities in model architecture, input modalities, and supervision dimensionality across methods.
+
+1.5.3 Clinical validation
+
+For clinical applications, vision-based approaches must ultimately yield biomechanically accurate descriptors, demonstrate robustness across the morphological variability of canine breeds, and support quantitative measures that align with established clinical gait parameters. As such, in addition to surveying state-of-the-art methods in articulated pose estimation, mesh reconstruction, and motion analysis, this review considers these techniques in light of their potential for producing anatomically interpretable outputs, their amenability to validation against gold-standard biomechanical measurements, and their suitability for deployment in realistic clinical and domestic environments. This provides a unifying context for the subsequent technical methods while preserving the primary focus of the review on the methodologies of computer vision-based canine gait analysis. From a technical standpoint, agreement with gold standard measurements is key. Reconstruction accuracy is commonly reported using metrics such as Mean Per-Joint Position Error (MPJPE) for biomechanical fidelity in motion tracking, alongside more gait oriented measurements such as agreement with kinetic and spatiotemporal measurements in methods such as pressure mats.
+
+2 Computer vision-based methods for canine gait analysis
+
+2.1 Articulated shape and pose reconstruction
+
+Automatic canine gait analysis requires an in-depth view of the subject's locomotion. In clinical environments, this is currently accomplished by the tracking of reflective markers placed on key landmarks of the subject (26). Pose estimation may approximate the same result, without the need for intrusive measures or clinical expertise. Table 4 provides a summary of key publications on articulated pose and shape reconstruction since 2018, reviewing representative and influential works in the literature. Computer vision-based pose estimation is typically divided into Skeletal and Mesh methods, producing different actionable parameters as a result. Skeletal methods typically train on annotated key points of joints from image frames to predict the same joint mapping on an input, whereas mesh methods typically focus on reconstructing a 3D representation of the subject.
+
+Table 4 Summary of key publications on articulated pose and shape reconstruction since 2018.
+
+Publication	Class	Training data types	2D/3D	Highlights	
+Zhong et al. (60)	Dog	Video, masks	3D	Provides a hierarchical, coarse-to-fine alignment framework to remove need for manual annotation of key points. Achieves faster convergence and higher fidelity than prior baselines by combining dense visual features with automatic part/temporal cues.	
+Lyu et al. (57, 58)	Animal	Synthetic Images, SMAL Labels	3D	Animal family-aware transformer to jointly predict pose and shape in 3D by fusing 3D labeled synthetic data with 2D key points, achieving state-of-the-art cross-species performance.	
+Wu et al. (104)	Dynamic scenes	Monocular Video	3D	Introduces 4D Gaussian splatting to render dynamic scenes in real time by extending static Gaussian splats into the temporal domain for continuous, interactive playback.	
+Shooter et al. (49)	Canines	Synthetic images, Keypoints	Both	Synthesizes photo-realistic canine images with precise 3D pose labels from a synthetic pipeline to train single-view estimators under controlled variability.	
+Xiao et al. (105)	Dynamic scenes	Video, Depth, Keypoints	3D	Tracks arbitrary 2D pixels in 3D by combining neural reprojection with multi-view geometry, generalizing beyond traditional keypoint methods.	
+Oquab et al. (106)	Dynamic scenes	Images	2D	Learns robust, label-free visual features through DINOv2's distilled-free self-supervised objective, achieving strong zero-shot performance without annotations.	
+Rüegg et al. (56)	Canines	Images, synthetic images, 2D & 3D keypoints	3D	Goes beyond generic shape priors by directly regressing 3D canine poses via implicit shape representations trained with silhouette and keypoint supervision.	
+Xu et al. (36)	Humans, quadrupeds	2D keypoints	2D	Adapts vision transformers for generic body pose by integrating modality-specific tokens and efficient sampling to handle diverse articulated configurations.	
+Tan et al. (63)	Humans, cats, canines	Video, NeRFs	3D	Distills articulated neural fields into a lightweight real-time model by transferring volumetric deformation priors onto compact mesh representations.	
+Song et al. (64)	Humans, cats, canines	Monocular & Stereo Video	3D	Reconstructs deformable scenes for embodied view synthesis by coupling dynamic neural radiance fields with dense tracking of object interactions.	
+Yang et al. (66)	Humans, cats, canines	Monocular Video, Skeletons, 3D Background Models	3D	Reconstructs animatable categories from monocular videos by learning category-level neural fields that enable cross-instance articulation.	
+Yang et al. (65)	Humans, cats, canines	Video, keypoints	3D	Builds animatable 3D neural models from casual videos by jointly registering multiple captures to a shared template with bundle adjustment and deformation nets.	
+Rüegg et al. (47)	Canines	Keypoints, breed labels, synthetic 3D models	3D	Leverages discrete breed embeddings as shape priors to regress accurate 3D canine meshes from single RGB images.	
+Li and Lee (50)	Quadrupeds	Synthetic & real images, Psuedo Labels	2D	Adopts adversarial unsupervised domain adaptation to align synthetic and real animal pose features without any labeled real-world data.	
+Biggs et al. (46)	Canines	Images, keypoints, 3D shape priors	3D	Introduces domain randomization on synthetic canine models to evaluate and improve cross-domain generalization of pose estimators.	
+Zhang and Park (107)	Quadrupeds	Multi-view images	2D	Leverages multiview registration constraints to supervise 3D animal pose models in the absence of explicit 3D annotations.	
+Mu et al. (32)	Quadrupeds	Synthetic images & real images	2D	Trains pose estimators solely on synthetic animal datasets and employs style transfer to bridge the synthetic-to-real domain gap.	
+Cao et al. (108)	Quadrupeds	Animal & human pose datasets	2D	Implements feature-level adversarial adaptation to transfer pose estimators trained on synthetic animals to real-world images.	
+Mathis et al. (38)	Quadrupeds	Keypoints	2D	Pioneers markerless animal keypoint tracking by adapting DeeperCut architectures to require minimal manual annotations.	
+Biggs et al. (54)	Quadrupeds	Video, keypoints, SMAL model	3D	Combines SMAL-based priors with video-driven bundle adjustment to recover 3D shape and motion across diverse animal species.	
+This table reviews representative and influential works that address pose and shape estimation in dogs, with broader comparisons to methods applied to quadrupeds, humans, and dynamic scenes. Each entry is characterized by the targeted subject class, types of training data used (e.g., synthetic images, motion capture, and monocular video), the dimensionality of supervision (2D or 3D), and a concise description of methodological innovations. The aim is to provide a structured comparison of the most recent and highly cited approaches that contribute to the development of 3D canine pose estimation, in a non-exhaustive manner. We exclude any publications that focus solely on humans or multi-class data that don't include canines, with the exception of dynamic scenes.
+
+As these methods act as a surrogate for marker-based systems, a certain level of geometric accuracy is required for the pose to be biomechanically meaningful. There is an inherent error between marker-based systems and ground truth via fluoroscopy, largely due to the effect of skin movement artifacts. Benoit et al. (27) reported ~10–20 mm joint-center error from markers while still retaining interpretable kinematics which are widely used clinically. This is further validated by Lin et al. (11) who quantified femoral soft-tissue artifact with rms displacements of ~8–9 mm and peak-to-peak values up to ~27 mm. More recent fluoroscopy-validated multibody kinematics studies (28) further demonstrate that residual pose errors below approximately 10 mm represent high-fidelity agreement with skeletal motion, whereas larger errors approach the intrinsic uncertainty limits imposed by skin motion. Based on reported in-vivo soft-tissue artifact magnitudes in canine hindlimb motion (Root Mean Square ≈6–10 mm, peak ≈ 20–30 mm) and fluoroscopy-validated multibody optimization studies, pose errors below ~10 mm can be considered high-accuracy relative to skeletal ground truth, errors in the 10–20 mm range comparable to conventional marker-based kinematics and still biomechanically interpretable, while errors exceeding ~25 mm approach the magnitude of skin-bone motion itself and indicate loss of anatomical fidelity.
+
+2.1.1 Datasets
+
+As seen in Table 5, existing canine pose datasets span a wide range of modalities and annotation types. From the previously discussed MPJPE limits (Section 2), we can extrapolate a set of minimum biomechanical and clinical validation requirements. Firstly, anatomical data must be derived from marker-based motion capture, fluoroscopy-validated multibody models, or anatomically rigged 3D meshes, ensuring that the joint centers are accurately represented for validation, and that associated localization errors are comparable to or below the intrinsic soft-tissue artifact bounds required for kinematic validity. Secondly, these datasets must represent the varying morphology of breeds, as parameters such as bone lengths, joint alignment and limb proportions change significantly across breeds and directly affect kinematic metrics.
+
+Table 5 Summary of key datasets used in canine pose estimation.
+
+Dataset	Modality	Size	Data types	
+CtrlAni3D (57)	Diffusion-generated RGB images	41,300 images	3D SMAL Mesh, 2D keypoints.	
+SyDog (29)	Synthetic RGB images	32,000 images	2D keypoints, bounding boxes.	
+RGBT-Dog (30)	RGB images (real + synthetic)	50,000 synthetic images	2D/3D keypoints, depth maps, textures, 3D models.	
+Animal3D (109)	RGB images, 3D SMAL parameters	3,379 images	2D/3D keypoints, SMAL parameters, segmentation masks.	
+Common pets in 3D (CoP3D) (35)	Smartphone RGB videos	~4,200 distinct pet videos	Object masks, camera parameters, time stamps, camera tracking quality scores.	
+AP-10K (70)	RGB images	10,015 labeled images, ~50,000 unlabelled images	2D keypoints, bounding boxes.	
+Learning from synthetic animals (32)	Synthetic RGB images, 3D models	10,000 canines	2D/3D keypoints, segmentation masks, depth maps.	
+RGBD-dog (31)	RGBD Video (Synthetic + Real)	830,000 synthetic	Real RGBD + motion capture, synthetic RGBD images + binary silhouette masks.	
+Animal-pose (110)	RGB images	~6,000 labeled, ~4,000 unlabelled	2D keypoints, bounding boxes.	
+Stanford dogs (34)	RGB images	10,580 images	2D keypoints, silhouette.	
+This table provides a non-exhaustive overview of influential datasets used in literature, including both real and synthetic data. Each dataset is characterized by modality, scale, and annotation types. Datasets were prioritized based on availability and impact/adoption across the literature. Key benchmark datasets are included among this list, excluding generic object datasets such as COCO and ImageNet.
+
+Datasets such as SyDog (29), RGBT-Dog (30), RGBD-Dog (31), and Learning from Synthetic Animals (32), use 2D/3D annotations from real and synthetic images to counteract the lack of diverse datasets in the literature. These keypoints are a combination of manual annotation and ground-truth motion capture (31), enabling quantitative evaluation of joint localization error (e.g., MPJPE, joint angle RMSE) relative to biomechanical gold standards. Datasets such as these provide a strong foundation for both training and validation, but currently lack sufficient morphological diversity to allow models to generalize across breeds and body types, limiting their suitability for assessing inter-breed robustness and clinically relevant gait parameters. Certain dogs like greyhounds, being of dolichocephalic morphology, have longer inter-joint distances around the head, alongside thinner coats, longer limbs, and lower body fat. In this case, models trained on datasets containing these morphologies may perform better than those with longer coated dogs due to a lack of coat-based occlusion, particularly when considered in areas such as pose estimation. It is key that inter-breed variation is present, but balanced within a dataset to ensure generalization in a model. Other datasets such as COCO (33) and Stanford Dogs (34) do not provide 3D pose or biomechanical ground truth, but offer a high degree of inter-breed visual and morphological variation, making them valuable for generalization but insufficient for kinematic validation or clinical benchmarking.
+
+The lack of biomechanical and clinical datasets introduces a key issue in validating system outputs for clinical relevance. This is further exacerbated when we consider that clinical data is not single-frame based, but rather temporally structured. This temporality is vital for understanding the gait of a canine, and as such introduces a secondary tier of validation. Datasets such as Common Pets in 3D (CoP3D) (35) provide a temporal in-the-wild dataset which would prove invaluable for studying gait, particularly in the context of automatic gait analysis. Unfortunately, this data remains anatomically unlabelled, and even with manual labeling would not yield joint centers comparable with marker-based motion tracking or fluoroscopy systems.
+
+2.1.2 Pose estimation
+
+Current state-of-the-art models such as ViTPose++ (36), a transformer-based model, are specifically designed for 2D pose estimation, offering top-tier accuracy on benchmarks like COCO (33) for both humans and animals. ViTPose++ uses ViTAEv2 (37), an advanced pure vision transformer backbone that enhances feature extraction through stronger inductive biases and deformable token mechanisms. Unlike previous models such as BlazePose, ViTPose focuses on accuracy rather than speed and lightweight deployment, achieving an average precision (AP) of 79.4 on the COCO dataset and 76.8 on AP10K. This average precision, measuring detection and localization accuracy, does not provide direct validation to real world units and therefore cannot be assessed under the acceptable bounds of ~10–20 mm for joint-center localization, but does show the increasing quality of the state-of-the-art. In clinical gait analysis, these models still require metric scale and validation against biomechanical references. Both COCO and AP10K contain a high degree of inter-breed variability but also contain over 50 species (COCO), allowing these models be generalizable against different animals, not just breeds.
+
+Specific to animals and humans, DeepLabCut focuses on markerless pose estimation across species (38), including canines. In this work Mathis et al. leverage transfer learning, where a deep neural network pre-trained on a large dataset (like ImageNet for object recognition), is fine-tuned for the specific task of pose estimation. The model achieves labeling accuracy comparable to that of human annotators with as little as ~200 labeled frames for training. The models ability for generalization lends itself to cross-species pose estimation, proven by their use with mice during odor-guided navigation tasks, fruit flies in a 3D chamber, and most relevantly its application to canines, through “Predicting Dog Emotions Based on Posture Analysis” (39), as illustrated in Figure 3. DeepLabCut also offers a 3D pose model, but requires a multi-camera system for triangulation. As is common in pose studies, these examples do not represent gait applicability and some do not provide specific accuracy measures such as MPJPE. However, Sosa et al. (40) used DeepLabCut with mice and reported an MPJPE of 8.5 pixels when compared with ground truth. While we cannot derive the error in terms of millimeters for comparison with our joint-center localization bounds, it does however suggest good within-dataset localization performance. The SuperAnimal models (41), used by DeepLabCut, utilize the Quadruped-80K dataset (42) which contains various combined sources such as Stanford Dog and AP10K. As a result, this enables strong generalizability across both animals and breeds. Despite the requirement for monocular 3D pose estimation, there are some applications for 2D keypoints such as stride time, stride length, etc., which can utilize custom models such as YOLO Pose (43) to extract keypoints based on datasets like Stanford Dogs (34, 44).
+
+Figure 3 Schematic of experimental set up used by Sohnel et al. (111), licensed under CC BY 4.0. (A) Instrumented treadmill locomotion, (B) treadmill on force plates, (C) overground force plates. Red arrows represent the vertical ground reaction forces captured by the force plates, with the force plates colored red. Blue arrows represent the vertical ground reaction forces captured by the instrumented treadmill.
+
+Three-panel illustration showing a black dog walking on different treadmill devices. Panel A shows a standard treadmill with blue arrows indicating vertical force measurement. Panel B depicts a treadmill with red force plates and arrows highlighting force sensors under the paws. Panel C shows a treadmill with red force arrows beneath each leg, using a long force plate for full stride analysis.
+
+Monocular 3D pose estimation currently presents significant challenges. The scarcity of 3D annotated data is a large obstacle. As one 2D pose can correspond to multiple possible 3D poses, accurate depth estimation is required to remove ambiguity. Consequently the use of geometric prior knowledge of the target becomes a strong constraint. An example of this is the SMAL model (45) which provides a geometric prior and generalizes to many types of animals. The process is simplified by fitting the pose, shape and camera parameters of a parametric mesh, retrieving the keypoints from the vertices of the SMAL mesh on reconstruction. Skinned Multi-Breed Linear Model for Dogs (SMBLD) (46) proposed an end-to-end neural network that allowed for a wide variety of dog breeds by enriching the shape parameters of SMAL and learning additional shape priors, seen in Section 2.1.3. Rüegg et al. (47) showed a similar method by ensuring predicted shapes remain discriminative of their breed by exploiting breed information classified from images. Achieving over 20% reduction in Mean Per-Vertex Error (MPVE), the average difference between the predicted 3D positions of a mesh's vertices and their ground truth positions, in their ablation study, a clear constraint is identified. Methods such as unsupervised 2D-to-3D lifting (48) help eliminate the reliance of 3D ground truth by projecting lifted 3D poses from random views back to 2D images to supervise depth estimation using adversarial 2D poses.
+
+More recent examples include DigiDogs (49), which combines monocular 3D pose estimation with prior-aware synthetic data augmentation. The synthetic-to-real training methodology is a recurring theme across the literature, also seen by Li et al. (50) and Mu et al. (32), which have shown that carefully designed domain-adaptation strategies can provide valuable large-scale synthetic animal datasets, substantially closing the gap in performance. Trained on 8 different dogs: Labrador, Rottweiler, Shepherd, Wolf, Coyote, Poodle, Terrier, and Pug, DigiDogs aims to generalize by incorporating varied morphologies and body types. While there is variety between the included breeds, there is still susceptibility to breed-specific bias due to the limited number of samples per morphological class. The authors report an MPJPE less than 50 mm, outperforming earlier multi-view markerless baselines such as RGBD-Dogs (31) by approximately 15%, while using only monocular input. The main drawback is that poses tend to be skewed in terms of angular position, but may be remedied by other vision techniques in post processing. When interpreted in the context of fluoroscopy-validated soft-tissue artifact limits, the reported MPJPE of < 50mm places this method beyond the 10–20 mm range associated with marker-based joint center uncertainty, and within the low-fidelity category. An error of this size exceeds the joint-center localization uncertainty of clinical motion capture and is therefore unlikely to consistently preserve anatomically meaningful joint kinematics or derived gait parameters.
+
+Outside of the obstacles discussed above, these are two major recurring issues. Firstly, occlusion is a common obstacle across skeletal based models. When objects or body parts obstruct the camera's view of certain key points, models struggle to accurately detect joint positions. To rectify this, studies have utilized multi-camera set ups to observe subjects from all angles, and reconstruct the pose with triangulation techniques (51). Secondly, a smartphone-based gait analysis system for horses showed that pose estimation models struggle with environmental conditions such as lighting conditions and terrain (52). Bright sun light can skew the detection of key points, which could be common in domestic analysis. Complex terrain, presents an issue in estimating joint positions with uneven footing or terrain not present in training datasets. This also extends to camera viewpoint dependency as many computer vision models rely on static and standardized camera positions to ensure accurate inference. Due to these limitations, real-world applications of these models often perform inadequately (38, 53).
+
+In summary, 2D keypoint methods may support basic spatiotemporal parameter extraction under controlled views, but do not inherently provide clinically applicable kinematics or joint-center localizations in metric units. Monocular 3D keypoint methods remain constrained by occlusion and errors outside of acceptable bounds for clinical applicability.
+
+2.1.3 3D mesh reconstruction
+
+3D mesh reconstruction methods can be split into two categories: skeletal and non-skeletal. Skeletal methods such as SMAL (45, 54), and some of its more modern implementations such as BARC (47), produce a 3D mesh that is posed via an internal kinematic skeletal structure. This results in two key outputs, 3D surface mesh of the subject and a skeleton defined by kinematic rules such as joint limits. For gait analysis, this form of output is significant as not only does it enforce important kinematic principles, it also enforces varying parameters for breeds such as bone lengths and body proportions. In contrast, pose estimation focuses on predicting a point location on the subject per-frame, which leads to base inaccuracies such as limbs bending in the wrong direction under error, generalized bone lengths leading to bias for specific breeds, and a lack of temporal consistency across frames. Non-skeletal methods focus on accurately reconstructing the surface mesh of the subject, often enforcing temporal coherence across frames which is significantly important for gait parameters such as gait cycles and cadence, alongside serving as accurate extractors for articulation through the surface mesh. While lacking a definitive biomechanical structure for holistic gait analysis, they do provide upstream stabilization for later biomechanical fitting.
+
+2.1.3.1 Skeletal
+
+Expanding upon the models discussed toward the end of Section 1.5.1, parametric template mesh models are particularly relevant for gait analysis as they go beyond keypoints, aiming for a more kinematically coherent body representation. Parameterizing shape, pose, and deformation, these models provide a flexible 3D template that can bend and deform to represent different animal poses, breeds and bone proportions. SMAL (45, 54) is separated into 33 parts, each of which are individually controlled by shape and pose parameters, requiring parts such as joints to be optimized via inverse kinematics. This enables the encoding of canine-relevant joint limits and morphology constraints, while optimizing shape to improve subject-specific body fit, both of which are important prerequisites for stable kinematics. SMALR (55) refined this by requiring multi-view images and 2D silhouettes as input, reducing ambiguity in the 3D pose estimation. SMBLD (46) adapted the SMAL model, focusing on adding six new shape parameters to account for breed variations. SMBLD learns a detailed 3D prior from a large dog dataset (34) to ensure handling of shape and appearance diversity.
+
+BARC (47) focuses on 3D pose and shape regression, using breed information such as shape via breed similarity loss. BITE (56) improves upon this, exploiting ground contact points and optimizing for pose, shape, and camera translation. The resulting pose enables the derivation of 3D spatiotemporal and kinematic parameters, specifically gait cycle events such as foot strikes and lift offs can be estimated by the detection of ground contact points. As both methods are per-frame based, they are not trained/optimized with sequence-level constraints, so temporal jitter can occur without additional smoothing or video-based optimization. While the strong breed priors improve generalizability, bias may still be present due to the imbalanced training data. The authors use Stanford Dogs (as seen in Figure 4) which has over 120 breeds, but there are few samples per breed, and 3D ground-truth shapes with only showing 11 breeds, which could lead to a representation bias toward specific sizes and morphologies. For clinical gait stable joint-angle waveforms, repeatable event timing, stride-to-stride consistency are typically required, which are sensitive to this jitter. BARC primarily emphasizes 2D alignment, specifically silhouette Intersection over Union (IoU) = 75.1 and Percentage of Correct Keypoints under a given threshold (PCK@0.15) = 82.7, whereas BITE additionally 3D geometric agreement with scans: scan → mesh = 2.07 cm, mesh → scan = 3.15 cm. With missing metrics such as joint-center error or joint-angle error that we can relate to motion capture, fluoroscopy or pressure data, these methods cannot be assessed for clinical applicability from the reported metrics alone.
+
+Figure 4 Comparison of available keypoints in popular annotated datasets for canine pose estimation from Ferres et al. (39), licensed under CC BY 4.0. The colors indicate which dataset contains the respective point.
+
+Diagram of a dog marking twenty-three keypoints, each numbered and color-coded to show inclusion in Animal Pose, Stanford Extra, or both data sets. A legend links blue dots to the Animal Pose Data Set, orange to Stanford Extra Data Set, and black to both. A table beside the image lists each numbered keypoint with anatomical names and highlights unique landmarks in orange and blue text.
+
+More recently, there have been rapid advancements through AniMer from Lyu et al. (57), which replaces the standard SMAL pipeline for a high-capacity ViT and transformer decoder alongside a family-aware supervised contrastive loss. This is reinforced by the use of their custom diffusion-generated dataset CtrlAni3D. AniMer+ (58) keeps this core, but upgrades the encoder to a ViT Mixture-of-Experts, jointly predicting SMAL (mammals) and AVES (birds). Both models report stronger accuracy and generalization than SMAL baselines. Previous examples specialize on a single toxon or use modest CNN regressors, while the AniMer unified architecture allows for shape parameters for multiple taxa to be decoded in one model. AniMer reports a Procrustes-aligned (59) MPJPE of 80.4 and Mean Per Vertex Position Error (MPVPE) of 85.7, indicating improved accuracy in 3D pose and shape reconstruction. While PA-MPJPE/PA-MPVPE are useful for comparing models, they can obscure metric joint-center errors and as such do not directly guarantee the anatomically anchored joint-center accuracy needed for gait kinematics.
+
+Most of the previous methods outlined are temporally agnostic, whereas 4D-Animal from Zhong et al. (60) focuses on optimization from videos, using hierarchical dense cues such as silhouettes, parts, and pixel-to-vertex, to remove key point reliance and enforce temporal coherence. Consequently, 4D-Animal keeps the parametric SMAL backbone but sits between feed-forward data-prodigious approaches such as AniMer or DigiDogs, and template-fitting approaches like BARC or BITE. 4D-Animal reports mean silhouette IoU of 0.84 and a worst-case metric of IoUw5 (lowest 5% IoU across frames) of 0.71, indicating fewer failure frames under motion and occlusion. This is relevant for gait sequences as intermittent failures can corrupt stride segmentation and joint trajectory.
+
+Taken together, BARC provides strong 2D alignment, BITE extends this with 3D geometric agreement and gait event cues via ground contacts, AniMer improves the reconstruction and generalization under Procrustes-aligned metrics, and 4D-Animal further improves robustness through video-based temporal coherence. Still, none of these studies validate gait kinematics against biomechanical gold standards such as motion capture, fluoroscopy or pressure data.
+
+2.1.3.2 Non-skeletal
+
+Non-skeletal reconstruction methods are increasingly relevant for monocular canine gait analysis as they directly recover dense, time-consistent and metrically scaled geometry without relying on predefined skeletal templates. Such representations can serve as accurate extractors for per-frame articulation, enforce temporal coherence across frames and gait cycles, and provide metric measurements essential for spatiotemporal parameters such as stride length. Thus, they offer a complimentary foundation for biomechanical inference in scenarios where skeletal models or multi-view systems perform inadequately or are unavailable. It should be noted however, these methods lack robust evaluation for animals, in particular dogs.
+
+Unlike pose estimation or SMAL-based mesh reconstruction methods, non-skeletal methods can provide far more accurate surface representations of subjects, particularly capturing limb articulation and body proportions. Methods such as those from Zhou et al. (61) learn to estimate 3D pose in humans from point clouds via a PointNet-style backbone (62). They report a mean Average Precision (mAP) of 80.86 under the 10 cm rule, where mAP joint prediction is considered correct if its 3D distance to the ground truth is less than 10 cm, this representing the percentage of joints satisfying this error threshold. This type of method allows for greater generalizability, removing breed-specific biases. While not based on animals, it does illustrate that accurate surface mesh alone can provide accurate articulation of limbs, alongside sufficiently strong geometric constraints to inform underlying pose estimation for biomechanical reconstruction.
+
+Tan et al. (63) introduce a teacher network that learns per-frame neural fields that encode both the canonical shape and frame-specific deformations of an articulated object, such as a hand or animal limb. A student network is then trained via distillation to regress a compact blend-shape model, predicting per-joint skinning weights and low-dimensional shape coefficients directly from a single input observation. The separation of geometry and time-varying deformation imposes implicit temporal consistency, as all frames are constrained to deform from a common template. In parallel, Song et al. (64) address deformable scene reconstruction, and Yang et al. (65, 66) focus on learning the reconstruction of animatable 3D neural models and categories from casual videos. These four approaches are unified in Lab4D (67), which provides an open-source framework for reconstructing fully articulated, time-varying 3D shapes from a single RGB video. These methods are less generalizable than pointcloud-based methods due to the prediction of skinning weights. Similar to SMAL-based methods, this form of parameterization is limited to the training dataset, and in this case its generalized to 3D shapes rather than dogs and their varying breeds. The shared canonical geometry and deformation parametrization across frames enforce temporal coherence in the reconstructed geometry and motion. However, rather than being constrained by biomechanical principles, these models are optimized to explain visual appearance and temporal continuity of the observed shape and motion. These temporally consistent representations are critical for a gait analysis, particularly when considering gait cycles, cadence and other spatiotemporal parameters.
+
+Keetha et al. (68) have shown significant results in metric scene reconstruction with minimal data input. Inputs have been reduced to allow for any combination of monocular/stereo RGB images, calibrations, camera poses, and depth, while still outputting predicted geometry outputs (point-clouds), camera intrinsics and extrinsics in metric scale using a unified vision-transformer backbone, thereby enforcing a coherent geometric reference frame across views and time. This metric consistency is particularly valuable in monocular capture scenarios where absolute scale is ambiguous, providing a necessary foundation for spatiotemporal gait measurements such as stride length and walking speed in metric scale. Similar to Zhou et al. (61), MapAnything is breed agnostic due to the point cloud being built from depth maps, allowing for generalizability across morphologies.
+
+In summary, non-skeletal reconstruction methods provide metrically accurate, temporally coherent surface representations that can give strong geometric constraints for underlying skeletons. Although not specifically biomechanical, these give metric scale to improve accuracy of metric spatiotemporal measurements, surface continuity that provide accurate pose representations and outer bounds for skeletal fitting, and temporal consistency for gait analysis, making them a valuable upstream component for monocular canine gait analysis.
+
+2.2 Gait analysis
+
+To perform accurate gait analysis on a subject, one requires expert subjective visual assessment, alongside objective kinematic and spatiotemporal analysis. As mentioned previously, these are typically performed in clinical settings by way of the methods in Section 1.4. All of these methods produce various parameters, such as those seen in Table 2. Which parameters are required varies widely depending on the desired analysis i.e., lameness detection, diagnostics, rehabilitation, etc. Most research offer a general approach, often relying on abnormality detection (69). A summary of key publications in the literature can be seen in Table 6.
+
+Table 6 Overview of gait analysis methods which utilize computer vision and machine learning.
+
+References	Species	Category	2D/3D	Clinically verified	
+Liu et al. (79)	Multiple	Limp detection	2D	Partial	
+Palez et al. (81)	Dogs	Multiclass & diagnosis classification	3D	Yes	
+Gill et al. (75)	Dogs	Parameter extraction	2D	Partial	
+Gong et al. (53)	Quadruped	Parameter extraction	2D	No	
+Feuser et al. (52)	Equine	Gait pattern classification	3D	Yes	
+Wong et al. (71)	Rodent	Manual	3D	N/A	
+Silva et al. (77)	Sheep	Parameter extraction	3D	No	
+Verlekar et al. (112)	Human	Abnormal gait detection	2D	No	
+Jameel et al. (113)	Human	Biometric identity gait recognition	3D	N/A	
+Nieto-Hidalgo et al. (83)	Human	Abnormal gait detection	2D	No	
+Sipari et al. (114)	Human	Parameter extraction	3D	Yes	
+Mehrizi et al. (89)	Human	Abnormal gait detection	3D	No	
+Greve et al. (115)	Human	Parameter extraction	3D	Yes	
+Prakash et al. (73)	Human	Parameter extraction	2D	No	
+Kondragunta et al. (74)	Human	Parameter extraction	2D	No	
+Ng et al. (85)	Human	Abnormal gait detection	2D	Yes	
+Guo et al. (69)	Human	Abnormal gait detection	3D	No	
+Sanchez-DelaCruz et al. (88)	Human	Gait pattern classification	3D	No	
+Potluri et al. (80)	Human	Abnormal gait detection	3D	No	
+Due to the scarcity of research specific to canines, and even quadrupeds, various species were included as part of this table, including: quadrupeds, equines, rodents, sheep and humans. The aim is to provide an overview of the state-of-the-art for vision-based gait analysis methods, showing their applicability to vision-based automatic canine gait analysis.
+
+For vision-based systems to be considered suitable for clinical gait analysis, a set of minimum validation requirements must be satisfied. From a kinematic perspective, joint trajectories and derived spatiotemporal parameters should show agreement with gold-standard systems such as marker-based motion capture, treadmill and pressure walkways, or fluoroscopy-validated multibody models, with errors remaining within the intrinsic uncertainty bounds imposed by soft-tissue artifacts. At a clinical level, extracted gait metrics should show correlation with established outcome measures and diagnostic reference, including CMIs (Section 1.4.6). Lastly, validation should be demonstrated across a representative range of breed morphologies to ensure robustness and generalizability beyond laboratory-based scenarios. In the human field, key metrics that are typically tracked in the literature are Mean Per-Joint Position Error (MPJPE) or Joint Localization Error (JLE), Mean Per-Joint Angle Error (MPJAE), Standard Error of Measurement (SEM), Minimal Detectable Change (MDC), and intraclass correlation coefficient (ICC).
+
+Data collection is a common issue for these types of methods. While multiple public datasets such as AP10K (70) can be useful, they lack “trainable” data from a gait analysis perspective. Furthermore, they also lack the expert-validation typically seen in clinical contexts. The use of traditional methods, as outlined in Section 1.4, can serve as solid ground truth data for these gait analysis systems, shown by Wong et al. (71). Feuser et al. (52) took this one step further by clinically validating their data using an expert lameness examination, based on the AAEP scale (72). Gong et al. (53) captured their own data by way of tripod-fixed shooting gear with rigid capture conditions such as camera height and a fixed motion direction angle of –33° to 33°. While these conditions aided in the research, they lack the generalizability for domestic scenarios. Alongside this, they only focused on set parameters: gait frequency, gait sequence recognition, gait duty cycle and gait trajectory. While each of these are valuable, they are not clinically validated and do not provide a holistic perspective on the subjects gait. Breed-related morphological variability also significantly influences gait analysis. For instance, chondrodystrophic breeds, characterized by shortened limbs and elongated trunks, exhibit kinematic normals which may vary when compared to dolichocephalic or other morphologies. This may produce a scaling bias unless accounted for with breed-agnostic or generalizable data.
+
+2.2.1 Parameter extraction
+
+Gait parameters are fundamental to gait analysis as they provide quantifiable measures of an subject's movement pattern. These parameters, as seen in Table 4, offer precise insights into the mechanics of movement, enabling clinicians and researchers to develop targeted interventions, monitor progress, and ultimately improve patient outcomes. These parameters can be extracted through calculation, time-series analysis or predicted by a machine learning system. Prakash et al. (73) focused on the use of silhouette images as an input for skeletonization and gait parameter extraction. The parameters extracted include: Crotch Height, Foot Length, Step Length, Stride Length, Cadence, Cycle Time, and Cycle Distance. A clear obstacle seen in this study as the focus is on the sagittal view, vastly reducing the amount of parameters extractable and therefore not providing a holistic view into the subject's gait. Despite this, the parameters extracted showed good accuracy and the methods used, if integrated into modern vision-based solutions, could serve as an effective way of viewing a subject's gait characteristics. Kondragunta et al. (74) used a more modern method of parameter estimation by using 3D pose key points as inputs for calculating parameters such as step length, stride length, swing time, stance time, stride time, and cadence in elderly humans. Heel joints from selected frames are analyzed to calculate their horizontal displacement using Euclidean distance. A uniform kernel convolution smooths the gait trajectory, helping identify the gait's maximum and minimum points for parameter estimation. While this study does not focus on techniques of analysis, the ability to accurately extract the parameters is invaluable for later analysis of the subject's gait.
+
+Focusing on quadrupeds, Gong et al. (53) created separate models for gait frequency extraction, gait sequence recognition, duty cycle extraction and trajectory extraction. Their pose estimation used keypoint localization via object keypoint similarity rather than typical MPJPE, following the COCO/AP10K protocol of related detection metrics (AP, mAP, and AR). This results in a dimensionless similarity score rather than a physical joint-center error expressed in millimeters or degrees, therefore making biomechanical anatomical fidelity difficult to evaluate. Models for gait parameters use relative error Erel, comparing extracted values with manually annotated ground truth, reporting a maximum gait frequency error of 2.46% and maximum error of duty cycle at 4.33%. While these results initially look promising, they lack clinical validation, primarily because the reference ground truth consists solely of manual frame-by-frame video annotation, without comparison to fluoroscopy or marker-based motion capture. More importantly, there is no gait ground truth such as force plates, nor correlation with clinical outcome measures or CMIs, meaning it cannot be assessed for clinical validity from the reported metrics alone. Further, the reliance on 2D plane estimation and an absence of depth data preclude accurate reconstruction of joint kinematics and inter-limb symmetry, resulting in the loss of potentially clinically relevant information. Consequently, it does not validate whether the inferred joint locations would fall within the 10–20 mm anatomical error bounds required for biomechanically interpretable kinematics, nor whether extracted duty factor or frequency would correspond to force-plate-derived symmetry indices or temporal parameters.
+
+Gill et al. (75) utilized the popular DeepLabCut model (38) with a single lateral-view camera to extract 2D gait parameters from the sagittal view. Similar to Gong et al. (53), they use a Median Absolute Euclidean Distance (MedAED) per joint landmark. Although pixel errors are low at 0.55% and size-normalized. they are not converted to millimeters and thus cannot be directly assessed against the 10–20 mm threshold previously defined. They do note, however, that a RMSE inflation for the hip and stifle in deerhounds demonstrates loss of anatomical fidelity in out-of-distribution morphologies. Identifying the gait cycles, they extracted key kinematic and spatiotemporal parameters, comparing both duty factor and stifle range of movement for Labradors with published data from the literature. Results proved promising, with metrics such as walking velocity (0.65 ± 0.08 m/s) being more consistent than those reported in pressure-walkway studies (76). Although the median values aligned with the literature, their results showed a broader distribution of measurements, reflecting the variability produced by markerless tracking and morphological diversity. Furthermore, validation is limited to comparison with previously published kinematic means, without reference to force-plate kinetics, fluoroscopy, or clinical outcome measures (e.g., lameness scores or CMIs), preventing assessment of diagnostic sensitivity or validity. With respect to bias across breeds and shapes, their utilization of pose estimation trained on AP10K introduces a shared skeleton across varying animals due to the dataset being trained on multiple species. As mentioned by the author, poor performance due to environment, pose and hair characteristics show a pathway for bias of breeds with darker or heavy coats.
+
+Silva et al. (77) utilized a marker-based motion capture system with infrared cameras to track retro reflective markers placed on sheep's key anatomical landmarks on both hindlimbs. The data is collected while the sheep walk along a designated track, ensuring natural movement patterns. Considering sheep as a quadruped biomechanical analog, parameters were calculated based on the kinematic markers which could be emulated via 3D pose estimation. This approach ensured precise and directly observable measurements of gait characteristics from the subject. This configuration yielded full 3D joint kinematics in flexion/extension, abduction/adduction and internal/external rotation, with joint angle ranges such as knee flexion reaching 80.6°± 11.8° at mid-swing and ankle dorsiflexion 80.7°± 11.5°, showing a high-fidelity reference for spatiotemporal and angular gait parameters. Parameters were calculated directly from the reconstructed kinematic marker trajectories, constituting gold-standard joint center and segment orientation measurements against which vision-based 3D pose estimation systems could, in principle, be quantitatively validated. The authors report stance and swing phase variability (e.g., hindlimb stance 0.373 ± 0.047s left, 0.378 ± 0.091s right), demonstrating that even under controlled laboratory conditions inter-cycle variability on the order of 10–15% is present in temporal parameters. This laboratory environment, while very useful for gold standard tracking, introduces the environment as a secondary variable that can significantly alter joint kinematics and ground-reaction forces in quadrupeds, as seen from Feuser et al. (52) and Jarchi et al. (78). While these same environmental and behavioral influences may affect vision-based systems, it would allow for longer term data acquisition in familiar domestic environments, reducing the influence it may have on biomechanics. Together, these motion-capture results illustrate the level of spatial, temporal, and angular precision that vision-based systems must achieve, and validate against kinetic and clinical ground truth before they can be considered suitable for clinical gait assessment.
+
+2.2.2 Abnormal gait detection
+
+One of the most logical approaches to gait analysis in a subject is the differentiation of normal and abnormal gait as a first step toward clinical screening and diagnostic support. The literature presents a number of obstacles in establishing whether such differentiation is clinically reliable and biomechanically meaningful. Firstly, the classification and analysis of gait must be designed based on a desired outcome and as such requires a dataset specific to this need, such as sound gait alongside disease or condition-specific abnormal gaits that are confirmed by clinical examination and, where available, objective reference standards. Naive methods such as those seen by (79) take a “Healthy vs. Limping” approach by creating simulated limp states within their datasets and training a YOLOv5 deep CNN to predict the binary classifications. These methods yielded 97% accuracy for normal walking states and 70% accuracy for limping states under this simulated labeling scheme. While their dataset assessed a variety of species, this simple approach shows preliminary promise, without the use of any pose data. This variety of species also means that per sample occurrence can induce bias for specific morphologies. The key pitfalls in this method are a lack of skeletal gait data, and more importantly a simulated dataset that has no kinematic basis and therefore cannot be directly validated against clinically interpretable joint kinematics, spatiotemporal parameters, or veterinarian-assigned lameness grades.
+
+Inertial sensors, as seen in Potluri et al. (80) provide direct access to segment-level kinematics and temporal gait events, specifically in humans, but require condition-specific abnormal gait data that is labeled according to clinically defined pathologies. Palez et al. (81) partially address these limitations by utilizing IMUs for 3D kinematic data, and a deep learning classifier to predict whether a dog's gait is healthy, orthopedic, neurological, or (binary) healthy vs. non-healthy. The multi-class classification (healthy vs. orthopedic vs. neurological) achieved up to 96% accuracy on the random-split baseline, while differentiating orthopedic and neurological lameness had lower performance due to an overlap of clinical signs and shared compensatory kinematic patterns. Similar to previous literature, the lack of a wide dataset produces a class imbalance as well as difficulty generalizing across morphologies and pathologies, highlighting the need for validation across breed groups and disease severities before such classifiers can be considered clinically robust.
+
+Depending on which abnormalities are being investigated, some can only be viewed from a frontal plane while others from a sagittal plane (82, 83), implying that clinically reliable abnormality detection requires multi-view or view-specific acquisition. In the case of Nieto-Hidalgo et al. (83), promising results were produced by the use of smartphone data capture and cloud-based inference for spatiotemporal feature extraction, but with clear limitations in both abnormal gait detection as a method of holistic analysis and the lack of specific datasets for different morphologies and varied pathological gait patterns, thereby preventing systematic validation across breed conformations and disease-specific kinematics. For clinical applications, classifiers must demonstrate not only high overall accuracy but high sensitivity to asymmetric and low-grade lameness, and stability across repeated trials and environments.
+
+Guo et al. (84) focused on 3D pose estimation with the extraction of gait parameters for abnormal gait detection using clinically interpretable kinematic features rather than silhouette-level descriptors. Rather than typical binary classification performed by skeletal analysis, they focused on recognition tasks for six gait patterns (normal, in-toeing, out-toeing, drop foot, supination, and pronation) corresponding to clinically distinct movement deviations. The use of depth sensor cameras allowed for an accurate 3D estimation of human pose alongside the 6D Vicon (8) motion capture system which was used for ground truth data, thereby enabling direct validation against a gold-standard kinematic reference. While results under 62% accuracy were achieved, this is largely due to a lack of normalization between body shapes and proportions, implying that morphological variability directly degrades abnormal gait classification performance, despite the use of gold standard motion capture. This presents another obstacle which would be even more challenging in dogs due to wide breed size and variation, where bone length ratios, joint orientation, and trunk proportions vary far more than humans. Breed classification would be necessary to normalize gait patterns across sub-species (47), and should as such be considered a prerequisite for clinically valid abnormal gait detection.
+
+Ng et al. (85) approached this in two key steps: the extraction of gait parameters and the comparison of the gait data with clinical mobility assessments like the Performance-Oriented Mobility Assessment (POMA) (86), showing deviations from the normal gait relative to established clinical scoring criteria. Due to the clinical nature of POMA, this also offers a form of clinical validation that the gait analysis method works by directly linking quantitative kinematic deviations to clinical impairment scores. Although this study focused on human subjects, the same validation mechanism can also be applied to canines using equivalent veterinary outcome measure such as LOAD (87) or other CMIs (see Table 1). A similar traditional method can be seen in dogs (6) through spatiotemporal gait analysis with pressure sensor walkways. While relying on external equipment, many of the same kinematic parameters are used which could provide a viable point of comparison similar to POMA for correlating vision-based gait metrics with clinically accepted metrics such as symmetry indices, stance time distributions, and limb loading patterns.
+
+2.2.3 Gait pattern classification
+
+Gait pattern classification functions in a similar manner to abnormal gait detection, whereby a focus is put on certain gait patterns that are indicative of specific conditions or diseases, and therefore has direct relevance for clinical applications such as differential diagnoses and longitudinal monitoring. There has been extensive research in the use of machine learning for the classification of patterns based on a specific set of gait parameters, but these parameters are mostly confined to clinical environments and the use of external equipment such as inertial sensors or motion-capture and force-plate systems which provide kinematically and kinetically validated ground truth. The challenge lies in the extraction of gait parameters via vision-based techniques without the use of external equipment, sensors or laboratory environments, while still maintaining sufficient accuracy and repeatability for clinical applications.
+
+Sanchez-DelaCruz et al. (88) assembled 23 classifiers combined with a deep learning algorithm to classify gait bio-markers for pathologies associated with diabetic neuropathy, using biomechanical data from accelerometers as established clinical indicators of nerve and muscle dysfunction. Unlike much of the previous literature, the researchers managed to achieve a clinically validated accuracy of over 85% against physician-labeled diagnostic categories. Unfortunately, this was achieved by the use of inertial sensors rather than vision-based methods, and therefore does not establish whether comparable performance can be achieved when gait biomarkers must be inferred from video-based joint kinematics. Overcoming this obstacle, Feuser et al. (52) demonstrated forelimb lameness by observing indicative and iterative head nods compared with sound horses using pose-estimated trajectories of clinically validated anatomical landmarks and reference grading according to the AAEP lameness scale (72). The analysis showed stifle kinematics provided more reliable information, whereas tuber coxae displacement gave greater variability.
+
+In humans, Mehrizi et al. (89) used abnormal gait detection in humans to first decide whether a gait was considered healthy or not, and then a deep neural network and window slicing of the time-series to classify the gait pattern present into four pre-defined categories: Healthy, Parkinson's disease, Post Stroke, and Orthopedic disorders. This was accomplished using 3D joint trajectories estimated from video and validated against a marker-based motion capture system, thus demonstrating a pipeline in which the pose accuracy must be accurate enough for clinical analysis before it can be use to reliably classify disease-related gait patterns. The pose accuracy was quantified by average Euclidean distance between estimated 3D joints and marker-based motion capture joints (MPJPE), reporting an average of 36.12 ± 17.41mm. While this level of error exceeds the 10–20mm accepted bounds, it was still sufficient to support robust disease-level gait pattern classification, reporting misclassification as very low 1/25 healthy misclassified and 1/70 patients misclassified as healthy.
+
+In summary, the initial extraction of gait parameters, followed by abnormal gait detection and pattern classification, combined with 3D skeletal pose estimation methods, provides a comprehensive roadmap for automatic gait health evaluation in canines. It is not enough to look at parts-based analysis, we must capture and analyse gait data across spatial, temporal and inter-limb coordination for a subject. As we know the means are available to create parts-based views into a subject's locomotive function, the process of combining this information and then producing an actionable health score evaluation, or clinically interpretable indicators, is imperative for use in clinical and domestic settings. This highlights a clear avenue for future work in integrating multi-level kinematic descriptors into unified clinical inference frameworks. Aside from this, a clear need for interdisciplinary collaboration is seen between veterinary science, biomechanics and computer vision. Ensuring clinically/expertly verified methods and data is essential for use in the medical sector and for establishing minimum validation standards, ground-truth reference protocols, and outcome-linked performance metrics. Working with veterinary and other medical collaborators also provides more in-depth context surrounding specific parameters associated with gait analysis.
+
+3 Results
+
+The comparative examination of traditional and computer vision-driven techniques presented in Sections 1.4, 2 reveals that current vision-based pipelines reproduce spatiotemporal trends but do not yet achieve the biomechanical accuracy or clinical validation of marker-based systems. Rather than viewing these as isolated methods, we draw a clearer picture when considering how articulated pose and shape reconstruction, parameter extraction, and gait interpretation interact to form an end-to-end pipeline.
+
+3.1 Emerging requirements
+
+Across the reviewed literature, three technical requirements consistently surface when evaluated against the biomechanical accuracy limits and clinical validation criteria discussed in Sections 2.1, 2.2: A robust monocular 3D articulated shape and pose reconstruction pipeline, capable of handling varying canine morphologies, occlusion and real world environments, while achieving joint localization and angular accuracy within the soft-tissue artifact bounds required for biomechanically interpretable kinematics (10–20 mm).
+
+A clinically meaningful set of gait parameters, derivable from 3D pose sequences, aligned with clinical metrology instruments and gait assessment standards, ensuring they agree with gold-standard measurement from pressure walkways, motion capture or fluoroscopy.
+
+A move from parts-based to holistic gait analysis, where discrete parameters are integrated to generate an interpretable and clinically-relevant output, enabling correlation with clinical outcomes and CMIs.
+
+These requirements directly reflect the limitations and research gaps exhibited across published literature, and define the minimum methodological and validation criteria that vision-based gait analysis systems must satisfy for clinical applications.
+
+3.2 Trends observed in 2D and 3D pose estimation
+
+The literature shows a clear trend: while 2D pose estimation continues to be an accessible and useful entry point, it fails to preserve critical kinematic detail seen in 3D. For example, parameters involving the spatial orientation of joints cannot be reliably extracted when depth information is missing. This is consistent with Fischer (21), who emphasizes that 2D projections distort limb orientation and can induce false symmetry or stride patterns. In contrast, 3D pipelines such as DigiDogs (49) demonstrate an imperfect monocular reconstruction which can still produce joint trajectories and orientations that permit estimation of clinically relevant 3D kinematic parameters over state-of-the-art 2D approaches. However, angular drift, breed-related shape bias, and generalization failures lead to joint localization and orientation errors that exceed the 10–20 mm biomechanical fidelity range required for clinically interpretable kinematics. The consistent reliance on synthetic data also introduces domain gaps which affect downstream gait interpretation.
+
+Taken together, these trends indicate that future progress depends not only on improving pose accuracy but on creating canine-specific, anatomically grounded 3D priors and more diverse real-world training data, aiming to ensure accuracy remain within the acceptable uncertainty bounds imposed by soft-tissue artifacts.
+
+3.3 Extractable gait parameters
+
+By cross-referencing the gait parameters shown in Table 4 with published pose estimation outputs, a clear delineation emerges: 2D systems reliably extract only spatiotemporal parameters and show limited robustness when estimating parameters such as rotation, pelvic motion or elevation.
+
+3D systems enable a broader set of three-dimensional kinematic parameters (e.g., joint angles, pelvic motion, and inter-limb coordination) that are essential for clinically aligned gait interpretation and analysis.
+
+Although 2D pose estimation can provide the basic spatiotemporal parameters, its accuracy rapidly deteriorates under real-world conditions such as occlusion, variable lighting and viewpoint changes, as highlighted across the literature (38, 52). These limitations lead to joint localization errors that frequently exceed the anatomical uncertainty bounds previously defined, particularly when limbs are partially obscured or when camera placement deviates from standardized setups. As Fischer (21) emphasizes, 2D projections distort depth and joint orientations, making them unsuitable for capturing the full 3D motion required for clinically meaningful gait interpretation and analysis. Together, the evidence clearly suggests that reliable canine gait analysis depends on true 3D skeletal reconstruction or mesh-based representation that can accurately preserve spatial and anatomical relationships, while remaining within acceptable soft-tissue artifact bounds.
+
+3.4 Toward integrated gait analysis
+
+Progressing from vision-based parameter extraction to clinical interpretation in canines represents an area in the current literature that has been explored to a limited extent, particularly with respect to outcome-linked clinical validation. Most studies stop at reporting parameter accuracy or mean joint position error, without demonstrating agreement with gold-standard kinetic measures, fluoroscopy-validated kinematics, or correlation with Clinical Metrology Instruments (CMIs) and veterinarian-assigned lameness grades. A small number of studies provide promising precedents, such as condition-specific classification (52, 81, 88), or lameness detection (79), yet these typically focus on single parameters, controlled environments, or specific camera angles such as lateral views, limiting their ability to capture inter-limb coordination or compensatory movements.
+
+Throughout the literature, it becomes clear that gait analysis in canines is inherently multifaceted. Parameters interact non-linearly, pathologies manifest variably across breeds, and environmental factors (lighting, terrain) influence gait profiles. This level of complexity strongly suggests the need for ensemble or multi-module machine learning frameworks, where different aspects of the gait cycle are analyzed independently and then fused to produce a holistic assessment that supports clinically interpretable, repeatable, and morphology-aware inference across gait cycles and environments.
+
+3.5 Comparative analysis
+
+Pose estimation and reconstruction methods outlined in Section 2.1 provide a view of the current technical landscape as it pertains to extracting data usable for gait analysis. Throughout, we identify outputs from given models, their applicability for extracting gait parameters, and evaluate their applicability in clinical gait analysis. Table 7 presents these methods in a comparative format, specifically comparing accuracy metrics, validation against gold standard methods, breed robustness and extracted parameters. These studies were chosen as representative methods due to their accuracy and applicability to clinical gait analysis. As it pertains to accuracy metrics, there is a clear divide between studies in how they evaluate the performance of their respective models. Most utilize within-dataset error measurements such as MPJPE, PA-MPJPE, and AP, which often cannot be interpreted clinically because the ground truth is not biomechanically validated against gold standard methods such as motion capture or fluoroscopy for joint-center localization. They also do not all follow the same accuracy metric, with skeleton-focused studies commonly reporting MPJPE (or Procrustes-aligned variants), whereas mesh/shape reconstruction approaches more frequently report overlap or surface-based measures (e.g., IoU), reflecting different task objectives and error definitions.
+
+Table 7 Comparative analysis of key methods for vision-based pose estimation and reconstruction, with an emphasis on canines.
+
+Method	Accuracy metric	Gold standard validation	Breed robust	Extracted parameters	
+Lyu et al. (57, 58)	PA-MPJPE: 80.4, MPVPE: 85.7	No	Yes	Shape & skeleton	
+Xu et al. (36)	AP: 79.4 (COCO), 76.8 (AP10K)	No	No	2D keypoints	
+Shooter et al. (49)	MPJPE < 50 mm	No	No	3D keypoints	
+Ruegg et al. (56)	Scan → Mesh: 2.07-3.15 cm	Yes	Yes	Shape, skeleton & ground contacts	
+Ruegg et al. (47)	IoU 75.1%, PCK 82.7%	No	Yes	Shape & skeleton	
+Biggs et al. (46)	IoU: 67.5	No	Yes	Shape & skeleton	
+Due to the scarcity of canine-specific research, this table includes state-of-the-art methods applied to other species also. Studies are compared based on accuracy metrics, validation against gold standard measurements (e.g., motion capture, 3D scanning), breed robustness, and extracted parameters.
+
+Several methods report robustness across breeds and varying morphologies, particularly BARC (47) and BITE (56) which incorporate breed priors as part of their shape and pose optimization framework. Methods that incorporate SMAL templates, such as these, have the benefit of instance-specific reconstruction, rather than a generic shape to represent all animals. BARC has the added feature of automatically detecting ground contacts, which provides an initial set of gait parameters to track gait cycles via foot strikes and lift-offs, enabling the extraction of stance and swing timing.
+
+Table 8 synthesizes vision-based gait analysis studies with applicability to canines, comparing accuracy metrics, clinical validation, robustness to breeds and extracted parameters. These studies were chose as representative methods to show the variety of extracted parameters, alongside their clinical validation and accuracy. Only a subset of these studies report full clinical validation, Feuser et al. (52) validate against the AAEP lameness scale for horses (72), while Palez et al. (81) performed rigorous assessments on canine patients with a subset receiving MRI scans for neurological disorders. Palez et al. also utilized a pressure-sensing walkway during data collection but this was not the primary validation comparator, instead opting for a clinical diagnostic label defined from assessments. Relatively few studies emphasize continuous kinematics such as displacement and range of motion (ROM), both Palez et al. and Liu et al. (79) focus on binary or multi-class classification rather than parametrized gait assessment. Classification-based methods report strong performance but may offer limited clinical interpretability beyond categories, whereas kinematic/spatiotemporal methods provide more clinically meaningful parameters but often face strong constraints from measurement validity. Lastly, breed robustness is generally not reported, leading to a lack of generalization across varying morphologies.
+
+Table 8 Comparative analysis of key vision-based gait analysis studies, with an emphasis on canines via images or video.
+
+Method	Accuracy metric	Clinical validation	Breed robust	Extracted parameters	
+Gill et al. (75)	MedAED (SD): 0.14–0.24	Partial	No	Duty factor, stifle ROM	
+Palez et al. (81)	Acc: 96% (multiclass), 82% (binary)	Yes	Partial	Gait classification	
+Liu et al. (79)	Precision: >0.95, Confidence: >0.96	Partial	No	Binary gait classification	
+Gong et al. (53)	Erel: 2.46% Gait Freq., 2.41% Duty Cycle	No	No	Gait frequency & Duty cycle	
+Feuser et al. (52)	SE: 100% (forelimb), 88.9% (hindlimb-stifle); SP: 100%, 87.5%	Yes	No (Horses)	Head trajectory, stifle displacement	
+Due to the scarcity of canine-specific research, this table includes state-of-the-art methods applied to other species also. Studies are compared based on accuracy metrics, clinical validation status, breed robustness, and extracted gait parameters.
+
+4 Discussion
+
+The reviewed literature shows a rapidly evolving intersection between computer vision, biomechanics and veterinary science, where methodological advances in pose estimation, mesh reconstruction, and gait analysis are starting to enable objective assessment of canine locomotion. Translating these advances from controlled laboratory settings with gold-standard capture to uncontrolled video capture in domestic environments offers unprecedented opportunities for longitudinal and large-scale analysis. Considering this, we also see key limitations in current methods with respect to anatomical fidelity, validation, and clinical applicability. This section synthesizes the key findings from the reviewed literatures, implications for automated canine gait analysis, ethical considerations, future research directions, and the broader significance of computer vision in canine and animal research.
+
+4.1 Main findings from the literature
+
+4.1.1 3D pose is essential for clinically meaningful gait interpretation
+
+While 2D pose estimation continues to be widely used, the literature consistently shows that 2D projections cannot extract the kinematic detail necessary for clinical assessment. Additionally, 2D projections distort depth and joint orientations, resulting in missing compensatory movements and key joint mechanics such as the forelimb pivot being located at the upper level of the scapula, not level with the hip joint, as discussed by Fischer et al. (21). Monocular 3D reconstruction methods, while imperfect, may provide substantially more clinically relevant motion information.
+
+4.1.2 Current datasets limit real-world applicability
+
+Most of the studies review rely on small, homogeneous datasets, often collected under controlled conditions and/or inconsistent breed variation. The larger datasets are typically synthetic in nature, relying on domain adaption to accurately apply to “in the wild” scenarios. This creates a significant domain gap when models are applied to domestic dogs in home or outdoor settings. Breed diversity remains particularly underrepresetned, with exception to methods such as BITE (56) and BARC (47).
+
+4.1.3 Methods are not validated against a clinical applicability framework
+
+Literature based on clinical movement analysis use a number of key performance metrics to establish applicability to clinical applications. Vision-based methods are currently not compared to these metrics, largely due to the difference in disciplines. These metrics, once gathered into an acceptable framework, provide a clearer inter-disciplinary relationship which could be used to validated acceptable error ranges, their relationship with soft-tissue artifact limits, and their implications for kinematic and spatiotemporal parameter extraction.
+
+As previously stated in the context of fluoroscopy-validated soft-tissue artifact limits, ~10–20 mm joint center error from markers is acceptable as it still retains interpretable kinematics. Errors exceeding this approach the magnitude of skin-bone motion itself and indicate a loss of anatomical fidelity. In human studies, acceptable joint-angle error bands are 2–5° (90). As veterinary consensus thresholds are not yet standardized, these currently provide the only available quantitative guideline. Using Minimum Detectable Change (MDC) provides important context as to why these error bounds matter. If a markerless approach produces errors in the same range as the MDC or standard measurement error, pathology-related changes may be indistinguishable from noise, therefore limiting the systems utility for pathology detection or longitudinal monitoring. The lack of validation represents the most substantial gap between academic prototypes and clinically deployable systems.
+
+Beyond pose accuracy and biomechanical fidelity, ensuring that measurements are repeatable under the same conditions is paramount for clinical applicability. Throughout the literature, specifically Koo et al. (91) and Aghapour et al. (92), this is most commonly quantified as the Intraclass Correlation Coefficient (ICC), which evaluates the proportion of total variance due to biological variation, rather than just measurement noise. According to established guidelines, ICC values below 0.5 indicate poor reliability, 0.5–0.75 moderate, 0.75–0.9 good, and above 0.9 excellent reliability. While vision-based literature focuses on accuracy metrics such as MPJPE, clinical viability must be evaluated through extended means such as ICC with confidence intervals and inter-rater reliability.
+
+4.2 Implications for automated canine gait analysis
+
+Together, these findings collectively highlight the primary barrier to progress is not solely improved pose accuracy, but the requirement for frameworks that combine pose, gait parameters and clinical applicability. Several implications are suggested by an analysis of the literature. Firstly, biomechanical interpretability and clinical applicability should be treated as a primary design constraint, rather than a downstream add-on. Common computer vision-based evaluations such as MPJPE, when reported without absolute metric reference, do not provide direct comparison to ground truth or gold-standard measurements such as fluoroscopy or motion capture. Establishing a standard threshold for joint angle error, as in human methods (90), and incorporating validation measures used in veterinary literature, such as ICC and MDC, would therefore allow for a more clinically meaningful assessment of pose estimation and gait analysis systems.
+
+Secondly, model design should either be breed-agnostic or breed-specific, with accurate dataset curation to avoid systemic bias. Current methods such as BITE (56) and BARC (47) have incorporated this as a prior for SMAL-based mesh and skeleton reconstruction, reporting more generalizable applicability. This is essential as varying morphologies lead to an adaptability problem for most models, losing accuracy due to varying coat lengths, body proportions and bone lengths.
+
+Thirdly, a lack of ground-truth datasets makes it difficult to compare the accuracies of different methods or their overall biomechanical precision. The literature has suggested that measurements within ~10–20 mm of joint centers measured with fluoroscopy are sufficient for retaining kinematic accuracy. As such, an accessible motion capture or fluoroscopy dataset would provide comparative reference to known bounds. However, due to high costs and logistical difficulty this may not be feasible, thus utilizing synthetic datasets and augmentation may be a valuable alternative, but insufficient without accuracy for varying coats, lighting, environmental diversity, and natural motion. If synthetic datasets could be further refined to include these, as well as represent varying morphologies, body conditions and accurate biomechanical simulations, then their value would greatly increase. It should be noted however, due to domain gap issues discussed in the literature, moving from synthetic training to real-world inference often introduces systemic bias. As such, more accurate domain adaptation would also be required.
+
+Lastly, models should integrate temporality as context, due to many abnormalities and pathologies manifesting across gait cycles rather than single frames. The literature has presented many varying methods to retrieve biomechanical representations, but few incorporate the temporal consistency and smoothness to reflect actual gait. Looking to methods such as Lab4D (67) may provide key insights into how we may incorporate this temporal cohesiveness into current state-of-the-art methods.
+
+4.3 Ethical considerations
+
+Capturing images or videos of canines in domestic settings for the purpose of gait analysis presents a number of ethical considerations. Videos may inadvertently contain personal identifiable information such as human faces, residential addresses, identity documents, and vehicle registration plates. Before considering specific technical mitigation strategies, the collection and processing of user-uploaded canine videos must be framed within data protection and research ethics frameworks. Principles such as data minimization and purpose limitation would require that only information relevant to gait analysis is retained, while transparency and informed consent drive the usage, clearly communicating how videos are processed, stored, and potentially reused. Key regulatory frameworks such as General Data Protection Regulation (GDPR) and analogous health data protection frameworks like the Health Insurance Portability & Accountability Act (HIPAA), alongside ethical guidelines from bodies such as the American Veterinary Medical Association (AVMA) and Royal College of Veterinary Surgeons (RCVS), should be consulted to inform how such data is gathered, processed and governed. Ethical accountability also extends to the ownership and secondary use of uploaded videos, particularly when such data are repurposed for algorithm training, benchmarking, or shared with third parties, necessitating explicit consent and robust governance to ensure respect for user privacy and autonomy.
+
+Looking to possible technical mitigation strategies, the current technical landscape provides various solutions which can aid in these considerations. Firstly, it is important the flow of data is clear in these scenarios, for example, a system for dog owners would capture a video on the user's device and then upload it to the cloud. The aim should be to restrict any personally identifiable information (PII) from reaching the cloud. This could be accomplished by the use of state-of-the-art segmentation algorithms such as Segment Anything (93) on device, performing a background replacement to show only the dog, as seen in popular video conferencing applications. This can be considered a catch-all solution, but could be made more robust by the use of on-device optical character recognition (OCR) for text detection and then blurring any detected text that may appear, ensuring that no residual PII is transmitted or persisted in back-end storage. These are only possible solutions, but must be reinforced with user-based responsibility. As such, introducing a user-driven video review prior to upload presents a second layer of protection whereby the user can scrub through the video for any information that they would not like uploaded to the cloud. Within this, the previously mentioned methods could also be available by allowing the user to select an object or area to blur. While user reviews provide an additional safeguard, primary ethical responsibility for preventing unintended disclosure of personal data rests with system designers and service providers, in line with privacy-by-design and data protection by default principles. Examples of this can be removing image and video metadata such as GPS and Device ID information.
+
+4.4 Future research directions
+
+A number of promising research avenues arise from the limitations identified. The introduction of ensemble and multi-module learning may compliment how gait is inherently multifaceted, especially considering the weakness of some of the present technologies such as occlusion. Given the common use of synthetic datasets, deeper research into synthetic-to-real domain adaptation, particularly shape adaption and real-world fine-tuning, could narrow the domain gap and provide more reliable models. Once parameter extraction is made more robust, the natural progression is toward diagnostic models for early lameness detection, post-operative recovery monitoring, degenerative disease progression, neurological vs. orthopedic classification, and even service-dog or sports-dog performance evaluation. Due to the variation of research domains in this area, we advocate for increased interdisciplinary collaboration to foster innovation and establish new standards in the field.
+
+4.5 Broader significance of computer vision in canine and animal research
+
+Computer vision has significant potential beyond the technical contributions outlined above. Unlike traditional methods like force plates or motion capture, vision-based systems can objectively observe the subject in their natural environment, providing longitudinal data unavailable through traditional means. This also reduces any false positives that may be indicated during examinations in clinics, hospitals or other areas foreign to the animal. Subtle gait changes often precede clinical symptoms. Automated systems could flag these issues earlier, reducing chronic pain and improving quality of life. This can be further expanded to monitor post-operative treatments or evaluate the effect of medication-based treatments. Together, a clear goal for improved animal welfare and early disease detection can be seen. Wider accessibility and the democratization of gait analysis is evident. Vision-based systems bypass the need for for specialized equipments and operators, allowing smaller clinics, research institutes and even dog owners to assess gait and health objectively. By increasing work into large-scale video datasets, reveal new breed-specific biomechanical patterns may be revealed, informing rehabilitation programs and risk assessments for orthopedic disorders. Lastly, advances in automated canine gait analysis may influence research fields focused on other quadrupeds, including bovine, wildlife and equine health analysis.
+
+4.6 Conclusion
+
+The synthesis of literature demonstrates that automatic canine gait analysis is not just an emerging domain, but a field that is on the edge of revolutionizing how veterinary biomechanics, rehabilitation and animal welfare can be approached. While current progress has been strongest in articulated pose and shape reconstruction and in kinematic parameter extraction, their significance lies in what they allow to now be possible. Vision-based methods offer a path toward objective, accessible, and longitudinal assessment of canine gait, capabilities that traditional methods such as pressure walkways and motion capture systems cannot provide outside specialized environments. Limitations such as imperfect monocular 3D reconstruction, inadequate dataset diversity, and the absence of frameworks that integrate both pose, gait parameters and clinical interpretations define not just obstacles, but a blueprint for maturing the field. Resolving these limitations provides a route for automated gait analysis in canines to transition from academic prototypes to clinically meaningful tools. In doing so, this technology has the potential to detect subtle changes in patients, support evidence-based decision-making for mobility and welfare, alongside democratizing gait assessments. It is clear that clinically validated 3D reconstruction and AI-based gait analysis has deep clinical applicability, but to bridge the gap between this and technical feasibility, a number of technical problems must be solved. Monocular 3D reconstruction methods require better occlusion handling, and either greater breed diversity within datasets or novel breed-agnostic methods, achieving an accuracy within the 10-20 mm joint-center localization bounds for soft tissue artifacts. From here, novel AI-based holistic gait analysis methods, which could utilize ensemble or multi-module machine learning frameworks, must be created. Specifically, these methods must be validated in partnership with clinicians to ensure that outputs are interpretable and clinically-relevant, enabling correlation with clinical outcomes and CMIs. Aligning future research with these identified requirements, the field can move toward reliable, accessible and clinically transformable systems that expand what clinicians, researchers and dog owners can understand about canine movement.
+
+Acknowledgments
+
+Constructive conversations with Professor John Innes and the support of the AniSteps team.
+
+Author contributions
+
+BP: Conceptualization, Data curation, Formal analysis, Writing – original draft, Writing – review & editing, Methodology. TM: Writing – review & editing. LC: Writing – review & editing. GL: Conceptualization, Funding acquisition, Methodology, Project administration, Supervision, Writing – review & editing.
+
+Conflict of interest
+
+The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
+
+Generative AI statement
+
+The author(s) declared that generative AI was used in the creation of this manuscript. Specifically Grammerly and ChatGPT were used solely for the purpose of refining and tidying language to improve clarity and grammatical accuracy. BP acknowledges and accepts full responsibility for the use of Generative AI tools in preparation for this work.
+
+Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.
+
+Publisher's note
+
+All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.
+
+Edited by: Andra-Sabina Neculai-Valeanu, Academy of Romanian Scientists, Romania
+
+Reviewed by: Philip Azariadis, University of West Attica, Greece
+
+Tiago Almeida de Oliveira, State University of Paraíba, Brazil
+
+
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+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Emerg Med Int
+Journal ID: Emerg Med Int
+NLM Journal ID: 101567070
+Journal ID: emi
+
+Emergency Medicine International
+
+ISSN: 2090-2840
+EISSN: 2090-2859
+Publisher: Wiley
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC10432084
+PMID: 37593433
+DOI: 10.1155/2023/9869764
+Article version: 1
+Subjects: Retraction
+
+Retracted: Influence of Aerobic Exercise Load Intensity on Children's Mental Health
+
+International Emergency Medicine emi@hindawi.com
+
+Publication date: 2023
+Electronic publication date: 2023 Aug 9
+Volume: 2023
+Electronic Location ID: 9869764
+Received 2023 Aug 8; Accepted 2023 Aug 8
+Copyright: Copyright © 2023 Emergency Medicine International.
+Copyright year: 2023
+License: This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Retraction of: Influence of Aerobic Exercise Load Intensity on Children's Mental Health 2022 11 6 2022 7827980 Emergency Medicine International 10.1155/2022/7827980 PMC9206579 35726303
+
+Ÿ==============================Ÿ
+This article has been retracted by Hindawi following an investigation undertaken by the publisher [1]. This investigation has uncovered evidence of one or more of the following indicators of systematic manipulation of the publication process:Discrepancies in scope
+
+Discrepancies in the description of the research reported
+
+Discrepancies between the availability of data and the research described
+
+Inappropriate citations
+
+Incoherent, meaningless and/or irrelevant content included in the article
+
+Peer-review manipulation
+
+The presence of these indicators undermines our confidence in the integrity of the article's content and we cannot, therefore, vouch for its reliability. Please note that this notice is intended solely to alert readers that the content of this article is unreliable. We have not investigated whether authors were aware of or involved in the systematic manipulation of the publication process.
+
+Wiley and Hindawi regrets that the usual quality checks did not identify these issues before publication and have since put additional measures in place to safeguard research integrity.
+
+We wish to credit our own Research Integrity and Research Publishing teams and anonymous and named external researchers and research integrity experts for contributing to this investigation.
+
+The corresponding author, as the representative of all authors, has been given the opportunity to register their agreement or disagreement to this retraction. We have kept a record of any response received.
+
+
+1 Zhao S. Influence of Aerobic Exercise Load Intensity on Children’s Mental Health Emergency Medicine International 2022 2022 11 7827980 10.1155/2022/7827980 PMC9206579 35726303
diff --git a/corpus/psychology/text/3524923acce9bc18.txt b/corpus/psychology/text/3524923acce9bc18.txt
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+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: JMIR Res Protoc
+Journal ID: JMIR Res Protoc
+NLM Journal ID: 101599504
+Journal ID: ResProt
+
+JMIR Research Protocols
+
+EISSN: 1929-0748
+Publisher: JMIR Publications Inc.
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC13456303
+PMID: 42574675
+DOI: 10.2196/89576
+Article ID: 89576
+Article version: 1
+Subjects: Scoping Review Protocols, Behavior Change, Mental Health Issues in Adolescence, Parent and Caregiver Education and Behavior Change for Injury/Accident Prevention, Violence including Domestic Violence/Abuse, Nursing Education and Training, Novel and Innovative Approaches to Care Involving Nurses, Protocol
+
+Utilization of Training for Nurses in the Prevention of Adolescent Violence Risk Behaviors: Protocol for a Scoping Review
+
+https://orcid.org/0009-0008-3485-3737 Maryatun Sri SKep, Ns, MKep 1 2
+https://orcid.org/0000-0002-5406-8727 Nurjannah Intansari SKp, MNSc, PhD 3
+https://orcid.org/0000-0001-6439-2304 Pertiwi Ariani Arista Putri SKep, Ns, MAN, DNP 4 *
+1 Doctoral Program, Faculty of Medicine, Public Health and Nursing , Universitas Gadjah Mada , Palembang City , South of Sumatera , Indonesia
+2 Nursing Study Program , Faculty of Medicine, Universitas Sriwijaya , South of Sumatera , Indonesia
+3 Departement of Mental Health and Community Nursing , Faculty of Medicine, Public Health and Nursing, Universitas Gadjah Mada , Yogyakarta , Indonesia
+4 Department of Basic and Emergency Nursing , Faculty of Medicine, Public Health and Nursing, Universitas Gadjah Mada , Jl. Farmako, Sekip Utara Yogyakarta , 55281 , Indonesia , +6287878208878
+Schwartz Amy
+Ariani Arista Putri Pertiwi, SKep, Ns, MAN, DNP, Department of Basic and Emergency Nursing, Faculty of Medicine, Public Health and Nursing, Universitas Gadjah Mada, Jl. Farmako, Sekip UtaraYogyakarta, 55281, Indonesia, +6287878208878; ariani_psik@ugm.ac.id
+Publication date: 2026
+Electronic publication date: 2026 Aug 10
+Volume: 15
+Electronic Location ID: e89576
+Received 2025 Dec 14; Revised 2026 Jun 24; Accepted 2026 Jun 29
+Copyright: Copyright © Sri Maryatun, Intansari Nurjannah, Ariani Arista Putri Pertiwi. Originally published in JMIR Research Protocols (https://www.researchprotocols.org)
+Copyright year: 2026
+License: This is an open-access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work, first published in JMIR Research Protocols, is properly cited. The complete bibliographic information, a link to the original publication on https://www.researchprotocols.org, as well as this copyright and license information must be included.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Keywords: adolescent violence, aggressive behaviour, mental health, nurse education, prevention, scoping review
+
+Ÿ==============================Ÿ
+Abstract
+
+Background
+
+Adolescent violence is a significant public health issue that negatively affects the psychological well-being and social functioning of adolescents. These tendencies generally evolve from problems in anger management and stress tolerance related to inherent or external contributors including familial background, interactions with friends, and school atmosphere. Nurses, particularly in primary health care settings, are strategically positioned to contribute to violence prevention through early identification, intervention, and capacity-building programs for adolescents. However, evidence regarding the implementation of nurse-led violence prevention training, including its effectiveness, training approaches, and contextual influencing factors, remains limited.
+
+Objective
+
+This scoping review will map the nature, content, approach, and effectiveness of educational interventions developed for nurses to prevent violent behavior among adolescent learners in health services.
+
+Methods
+
+The protocol adheres to the Joanna Briggs Institute guidelines and the Arksey and O’Malley framework, including identifying the research question, searching for relevant studies, selecting eligible studies, charting the data, collating and summarizing the findings, and consulting experts. This review will be reported in accordance with the PRISMA extension for Scoping Reviews (PRISMA-ScR) guidelines. Literature searches will be conducted in PubMed, Scopus, ProQuest, and the Cochrane Library, along with gray literature sources including Google Scholar and GreyNet. Studies published in English that focus on educational or training interventions aimed at improving nurses’ capacity to prevent adolescent violence will be included, whereas studies unrelated to nurse-focused interventions or adolescent violence prevention will be excluded. Reviewers will independently conduct study selection and data extraction using a standardized extraction form. Extracted data will include study characteristics, intervention types, implementation strategies, outcomes, and contextual factors. The findings will be synthesized descriptively through narrative summaries and tabulated evidence mapping.
+
+Results
+
+Literature searches across the selected electronic databases were initiated in March 2025 using predefined search terms. Title and abstract screening, as well as preliminary appraisal of eligible studies, were conducted in May 2026 following the Joanna Briggs Institute methodology and PRISMA-ScR guidelines. Full-text screening, data extraction, and thematic analysis are currently ongoing and are expected to be completed by July 2026. The findings of this scoping review are expected to be submitted to a journal by September 2026.
+
+Conclusions
+
+This scoping review will provide a comprehensive evidence map of available training programs, implementation strategies, barriers to utilization, and their impact on nurses’ knowledge, attitudes, and skills related to adolescent violence risk behaviors. The findings are expected to support the scientific foundation for the development of the training model of the Prevention of Adolescent Violence-Risk Behavior (Keterampilan Pencegahan Risiko Perilaku Kekerasan Remaja [Kepolar]) in primary health care and inform policymaking to strengthen health professionals’ capacity in preventing adolescent violent behavior.
+
+Introduction
+
+Background
+
+Adolescence is a unique life stage, associated with extensive biological, cognitive, and social-emotional transitions [1]. Adolescents also begin to move from an egocentric mode of thought to a more abstract and introspective kind [2]. Unfortunately, immature cognitive development tends to make adolescents “thoughtless,“ “irritable,” and “reckless,” accompanied by increases in the risk of violent behaviors as well [1]. Emotional dysregulation and the obsessive quest for autonomy in a context of insufficient cognitive maturity render adolescents susceptible to inappropriate outbursts of anger [3,4].
+
+The World Health Organization defines violence as the intentional use of physical force or power that may result in injury, psychological harm, developmental disruption, or death [5]. Adolescent violent behavior may manifest in various forms, including physical aggression, verbal aggression, threatening behavior, bullying perpetration, fighting, emotional violence, and other externalizing behaviors [6,7]. These behaviors are associated with serious short- and long-term consequences, including physical injury, substance misuse, academic problems, criminal involvement, impaired social functioning, and mental health disorders [8,9]. Violence among adolescents also contributes substantially to the burden experienced by families, schools, health care systems, and communities [10].
+
+Recent evidence indicates increasing trends in peer aggression, physical violence, emotional violence, and other forms of externalizing behavior among adolescents worldwide [11]. A UNESCO (United Nations Educational, Scientific and Cultural Organization) report estimated that approximately one-third of adolescents aged 11‐15 years have experienced involvement in bullying or peer violence within school environments [12]. Over the past year, one-third of students (36%) aged 13‐15 years were involved in a physical fight with another student, and almost one in three (32%) had been physically attacked at least once [13]. A study in Indonesia, the National Survey on the Life Experiences of Children and Adolescents [14], found two in three children and adolescents have experienced violence at least once in their lives, with this figure increasing [15]. These findings highlight the urgent need for early identification, prevention, and intervention strategies targeting adolescents at risk of violent behavior, particularly within community and primary health care settings [16].
+
+Adolescent violent behavior is influenced by multiple interacting internal and external factors. Internal factors include age, sex, impulsivity, emotional regulation, psychological conditions, coping abilities, and spirituality [17,18]. External factors include parenting style, family conflict, peer influence, school climate, exposure to community violence, and broader social environments [19,20]. Conversely, protective factors such as family connectedness, empathy, religiosity, social support, and positive school engagement may reduce the likelihood of violent behavior [21,22]. Understanding these multidimensional influences is important for health care professionals, particularly nurses, in supporting early risk identification, prevention planning, and violence management among adolescents [23].
+
+Health care professionals, especially nurses working in primary health care and community settings, play an important role in preventing and managing adolescent violent behavior [24]. Nurses are often among the first health care providers to identify behavioral problems, aggression, emotional dysregulation, and psychosocial risks in adolescents [25]. Their roles may include early screening and risk assessment, psychoeducation, counseling, emotional regulation support, family involvement, crisis management, and referral coordination. Effective nursing interventions may contribute to reducing aggressive behavior and improving psychosocial and behavioral outcomes among adolescents [26].
+
+Despite the important role of nurses, previous studies indicate that many nurses report insufficient preparedness, limited confidence, and inadequate competencies in managing adolescents with violent or aggressive behavior [27-29]. Limited training in adolescent mental health, violence prevention, behavioral management, and psychosocial intervention may reduce nurses’ ability to provide early detection and appropriate interventions in health care settings [30]. In Indonesia, these challenges may be more pronounced because mental health services in primary health care settings (puskesmas) still predominantly focus on severe mental disorders rather than preventive interventions targeting adolescent behavioral risks [31].
+
+Recent studies suggest that education and training programs for health care professionals, including nurses, may improve confidence, preparedness, communication skills, risk assessment abilities, and management of violent or aggressive behaviors among adolescents [26]. Interactive approaches such as role-playing, simulation, case-based learning, and de-escalation training have been associated with improved competency development and more sustainable behavioral outcomes [32]. However, most violence prevention interventions have primarily focused on school-based or community-based youth programs, whereas evidence specifically examining nurse-targeted training for adolescent violence prevention and management remains limited [33]. Existing studies also commonly position nurses as facilitators or referral agents within broader community or school health initiatives rather than as primary targets of structured competency-based training programs [34].
+
+Implementation of violence prevention training programs is influenced not only by individual competencies but also by institutional and systemic support, including operational guidelines, referral pathways, leadership support, protected intervention time, and intersectoral collaboration [35]. Although adolescent violence may occur across school and community environments, this scoping review specifically focuses on nurse training interventions in the Prevention of Adolescent Violence Risk-Behavior (Keterampilan Pencegahan Risiko Perilaku Kekerasan Remaja [Kepolar]) program implemented within health care and primary health care contexts.
+
+Effective prevention and management of adolescent violent behavior require multidimensional approaches addressing individual, interpersonal, family, community, and societal factors, as described in the social ecological model [36,37]. Nursing interventions and training programs may also be informed by frameworks such as King’s Goal Attainment Theory [38] and Bronfenbrenner’s Ecological Systems Theory [39], which emphasize interactions among adolescents, health care providers, families, and surrounding environments. These theoretical perspectives may support the development of structured nurse training models for adolescent violence prevention within primary health care settings.
+
+Current evidence related to violence prevention interventions remains methodologically heterogeneous, with many studies characterized by small sample sizes, inconsistent outcome measures, and limited reporting transparency. Existing evidence on nurse training interventions for adolescent violence prevention has also not been comprehensively mapped regarding theoretical frameworks, intervention components, implementation strategies, and reported outcomes. Therefore, a scoping review is needed to systematically identify, map, and synthesize available evidence regarding nurse training interventions for adolescent violence prevention and management within primary health care settings.
+
+Objective
+
+This scoping review protocol seeks to offer a more structured and methodical approach for identifying young people who behave violently and ensuring they are referred to nurse education programs so that they may benefit from interventions provided therein. Our protocol is designed to make sure that the review procedure is carried out systematically and reproducibly, thereby reducing any possible bias and increasing methodological transparency as well as scientific trustworthiness.
+
+The purpose of this review is to create an evidence-based training model that can be used by nurses in primary health care centers (puskesmas) to prevent adolescent violent behavior. In particular, this scoping review aims to discern and map the current scientific evidence on training for nurses in adolescent violence prevention regarding theoretic frameworks, the main elements of interventions, and intervention delivery strategies and effects. Finally, risk and protective factors related to adolescent violent behavior will be discussed in this review, as well as the instruments adopted for measuring nurses’ knowledge, attitudes, skills, and self-efficacy. It will offer further evidence of training interventions’ impact on these competences.
+
+Methods
+
+This scoping review protocol follows the methodological guidance developed by Arksey and O’Malley [40], further refined by Levac et al [41], and aligns with the Joanna Briggs Institute methodology for scoping reviews. The review will also be reported in accordance with the PRISMA-ScR (Preferred Reporting Items for Systematic Reviews and Meta-Analyses extension for Scoping Reviews) guidelines. A systematic and iterative review process will be undertaken to comprehensively map existing evidence regarding training and educational interventions for nurses in the prevention of adolescent violence risk behaviors.
+
+The review process will consist of six stages: (1) identifying the research questions; (2) developing eligibility criteria; (3) systematically identifying and selecting relevant studies; (4) charting and extracting data using a standardized extraction form; (5) collating, summarizing, and reporting the findings through descriptive narrative synthesis and evidence mapping; and (6) conducting expert consultation to strengthen the interpretation and applicability of the findings. We will conduct literature searches in PubMed, Scopus, ProQuest, and the Cochrane Library, as well as gray literature sources including Google Scholar and GreyNet. Two independent reviewers will perform study screening and data extraction, with disagreements resolved through discussion or consultation with a third reviewer when necessary.
+
+Protocol Registration and Reporting Information
+
+This protocol has been registered in the Open Science Framework. The final report will be prepared in accordance with the PRISMA-ScR checklist to ensure transparency and completeness throughout all stages of the review.
+
+Research Questions
+
+This scoping review seeks to map and synthesize the existing evidence regarding nurse training programs for the prevention of adolescent violent behavior in primary health care settings.
+
+The main research question guiding this review is “What evidence exists regarding training programs for nurses in the prevention of adolescent violent behavior in primary health care settings?”
+
+The review will further address the following subquestions:
+
+What risk and protective factors associated with adolescent violent behavior are reported in the literature?
+
+What types of training or educational programs for nurses related to adolescent violence prevention have been described?
+
+What theoretical frameworks, intervention components, and delivery strategies are used in these training programs?
+
+What instruments or assessment tools have been used to evaluate nurses’ knowledge, attitudes, skills, self-efficacy, or competencies related to adolescent violence prevention?
+
+What outcomes or reported impacts of nurse training programs related to adolescent violence prevention have been described in the literature?
+
+Eligibility Criteria
+
+The eligibility criteria for this scoping review were developed using the Population-Concept-Context (PCC) framework recommended by the Joanna Briggs Institute for scoping reviews (Table 1). The population of interest includes nurses and nursing personnel involved in providing care for adolescents who exhibit violent behavior. The concept focuses on violence prevention training interventions designed to enhance nurses’ capacity in managing adolescent violent behavior. These interventions may include educational programs, de-escalation training, communication skills training, simulation-based learning, and other strategies aimed at improving nurses’ knowledge, attitudes, competencies, confidence, preparedness, self-efficacy, and experiences in managing violent behavior among adolescents (Textbox 1). Comparators, where applicable, may include usual care, routine nursing practice without specific violence prevention training, health care services without active nurse involvement in violence prevention, or pre–post comparisons evaluating the effects of training interventions. The context of this review encompasses health care settings, community services, school-based health services, and primary health care facilities, including public health centers (puskesmas).
+
+Table 1. Population-Concept-Context framework.
+
+PCC	Description	
+Population	Nurses or nursing personnel involved in adolescent violence prevention and management	
+Concept	Training programs, educational interventions, simulation-based learning, de-escalation training, communication training, and competency development related to adolescent violence prevention	
+Context	Primary health care settings, community health care services, school health services, and other health care settings where nurses provide adolescent health services	
+
+Textbox 1. Inclusion and exclusion criteria.
+
+Inclusion criteria
+
+Studies involving nurses or nursing personnel in training or educational interventions related to adolescent violence prevention or management
+
+Studies conducted in health care, community, or school health settings
+
+Studies describing theoretical frameworks (eg, social ecological model, goal attainment theory, or other relevant models)
+
+Qualitative, quantitative, mixed methods studies, reviews, and relevant gray literature
+
+Publications in English or Indonesian
+
+Studies published between 2000 and 2024
+
+Exclusion criteria
+
+Studies focused exclusively on psychiatric disorder treatment without relevance to violence prevention or risk behavior management
+
+Studies without involvement of nurses or nursing personnel
+
+Editorials, opinion pieces, commentaries, and conference abstracts without full text
+
+Studies without accessible full text
+
+The review will consider qualitative, quantitative, and mixed methods studies, as well as review articles and relevant gray literature published in English or Indonesian between 2000 and 2024. Editorials, commentaries, opinion papers, conference abstracts without full text, and studies not related to violence prevention training for nurses in the context of adolescent violent behavior will be excluded. Studies eligible for inclusion are those that discuss violence prevention training, intervention programs, or related educational strategies for nurses in the context of adolescent violent behavior management. Editorials, commentaries, opinion papers, conference abstracts without full text, and studies not relevant to violence prevention training for nurses managing adolescent violent behavior will be excluded from the review.
+
+Population
+
+Although scoping reviews do not primarily aim to evaluate the effectiveness of interventions, the PCC framework was used to provide additional clarification regarding the focus of this review. The population of interest includes nurses or nursing personnel involved in adolescent violence prevention and management within primary health care, community health care, school-based services, or other health care settings.
+
+Intervention
+
+The included interventions of this scoping review are training and education initiatives that enhance nurses’ competencies regarding the prevention of violence in adolescents. These may include modules on emotional regulation, conflict resolution, early detection of violence risk, and communication strategies for managing adolescents. The training can be delivered through workshops, seminars, simulation-based learning, online courses, or blended methods. Some studies may also include the use of digital communication media as part of training delivery such as mobile apps, web-based platforms, social media, educational games, or interactive tools to support nurses in health promotion, emotional management, and psychosocial education for adolescents.
+
+Context
+
+The context of this review encompasses primary health care settings, community health care services, school health services, and other health care settings where nurses provide adolescent health services and are involved in violence prevention and management activities.
+
+Outcomes
+
+Because the objective of this scoping review is to map the breadth of existing evidence, outcomes will not be predefined as eligibility criteria. Instead, all reported outcomes associated with nurse training interventions for adolescent violence prevention will be charted during data extraction. These may include outcomes related to nurses (eg, knowledge, attitudes, competencies, confidence, and self-efficacy), adolescents (eg, behavioral and psychosocial outcomes), and implementation outcomes (eg, feasibility, acceptability, and sustainability).
+
+Identification of Relevant Studies
+
+A comprehensive literature search will be conducted to identify studies relevant to violence prevention training programs for nurses in the context of adolescent violent behavior management. Electronic databases to be searched include PubMed, Scopus, CINAHL, ProQuest, Web of Science, and ScienceDirect. Gray literature sources, including Google Scholar, institutional repositories, reports, and theses, will also be searched to identify additional relevant evidence. The search strategy is detailed in the next section.
+
+Search Strategy
+
+The search strategy will be developed in accordance with the objectives and research questions of this scoping review. Searches will be conducted using a combination of controlled vocabulary terms, including MeSH and free-text keywords related to nurses, violence prevention, adolescent violent behavior, and training or educational programs. Reference lists of included studies will also be screened manually to identify additional eligible articles.
+
+Keywords and phrases such as “violence prevention,” “aggression management,” “de-escalation training,” “nurse,” “nursing staff,” “adolescent,” “youth,” and “training program” will be combined using Boolean operators such as AND and OR. Quotation marks will be used for exact phrases where appropriate, and search strategies will be adapted according to the syntax and indexing systems of each database.
+
+Filters and limits applied during the search process will include publication years between 2000 and 2024, articles published in English or Indonesian, and studies available in full text when accessible. The search process and study selection procedure will be presented using a PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) flow diagram.
+
+To ensure transparency and reproducibility, the complete PubMed search strategy for one electronic database is provided in Multimedia Appendix 1 and reported according to the PRISMA-S (Preferred Reporting Items for Systematic Reviews and Meta-Analyses Literature Search Extension) recommendations.
+
+Study Selection
+
+All retrieved records will be imported into EndNote (Clarivate; version 20) and subsequently uploaded into Rayyan (Rayyan Systems Inc; version 2024) for screening and duplicate removal. Two reviewers will independently screen titles and abstracts according to the eligibility criteria. Full-text articles of potentially relevant studies will then be assessed independently by the same reviewers. Disagreements at any stage will be resolved through discussion, and where consensus cannot be reached, a third reviewer will be consulted. The study selection process will be reported using a PRISMA-ScR flow diagram.
+
+Data Charting and Extraction
+
+A standardized data charting form will be developed to systematically extract and organize relevant information from the included studies. The form will be pilot-tested on a small number of studies and refined iteratively throughout the review process to ensure consistency and relevance to the review objectives and research questions.
+
+The extracted data will include author(s), year of publication, country of study, study design, study objectives, participant characteristics, health care or community setting, characteristics of the training or educational program, theoretical frameworks, delivery methods, duration of intervention, implementation strategies, measurement or assessment tools, and reported findings related to nurses’ competencies in adolescent violence prevention (Table 2). Information related to barriers, facilitators, implementation experiences, and recommendations for practice or future research will also be extracted where available.
+
+Table 2. Data extraction variables.
+
+Variable	Description	
+Study title	Full title of the article	
+Authors and year	Author(s) and year of publication	
+Country and context	Study setting, country, and health care/community context	
+Study design	Qualitative, quantitative, mixed methods, review	
+Population	Nurses or nursing personnel involved in adolescent violence prevention or care	
+Participant characteristics	Age group, professional role, sample size (if available)	
+Type of intervention	Description of training or educational intervention	
+Theoretical framework	Underlying theories or models (eg, social ecological model, goal attainment theory)	
+Training method	Mode of delivery (workshop, simulation, online, blended learning, etc)	
+Duration and frequency	Length and frequency of intervention	
+Implementation strategy	How the training was delivered and supported	
+Outcome measures	Nurses’ knowledge, attitudes, skills, self-efficacy, or other reported outcomes	
+Measurement tools	Instruments or scales used (if available)	
+Key findings	Main results as reported in the study	
+Barriers and facilitators	Factors influencing implementation or effectiveness	
+Study limitations	Limitations reported by authors	
+
+Data charting will be conducted independently by two reviewers using the standardized form. Any discrepancies in the extracted data will be resolved through discussion and consensus, with consultation from a third reviewer if necessary. The extracted data will be reviewed regularly to ensure accuracy, completeness, and alignment with the objectives of the scoping review.
+
+Data Synthesis
+
+Data will be summarized in narrative and tabular forms to map the extent, characteristics, and distribution of the existing evidence regarding violence prevention training programs for nurses in the context of adolescent violent behavior management. Consistent with the purpose of a scoping review, the synthesis will focus on describing and mapping available evidence rather than evaluating intervention effectiveness.
+
+Descriptive analysis (frequencies and percentages) will be conducted for quantitative data where appropriate, while qualitative findings will be synthesized using thematic analysis following the 6-phase approach proposed by Braun and Clarke [42]. The analysis will involve six iterative phases: (1) familiarization with the extracted data, (2) generation of initial codes, (3) searching for potential themes, (4) reviewing and refining themes, (5) defining and naming themes, and (6) producing the narrative synthesis. Themes will be developed inductively to map intervention characteristics, implementation strategies, barriers, facilitators, and reported outcomes related to nurse training for adolescent violence prevention. The synthesis process will also examine the characteristics of training programs, educational components, delivery methods, theoretical frameworks, assessment approaches, and reported findings related to nurses’ competencies in adolescent violence prevention.
+
+The findings will be presented in narrative summaries, evidence tables, and thematic groupings aligned with the objectives and research questions of the review. Quality appraisal will not be performed, as it is not mandatory for scoping reviews and the primary aim of this review is to comprehensively map the existing literature.
+
+Presentation and Reporting of Results
+
+Results will be presented according to the objectives and research questions of the review, including characteristics of training programs, educational components, delivery methods, theoretical frameworks, assessment approaches, implementation strategies, and reported findings related to nurses’ competencies in adolescent violence prevention. The synthesis will discuss the extent, nature, and limitations of the existing evidence and provide implications for nursing practice, policy, and future research.
+
+The study selection process will be presented using a PRISMA-ScR flow diagram, while the review findings will be summarized in narrative form and supported by evidence tables and thematic groupings where appropriate.
+
+Consultation Process
+
+Validity of the findings, missing evidence, and interpretation of results will be addressed through an expert consultation involving psychiatric nursing, adolescent psychology, and public health experts. Expert input will be included in the final synthesis to increase the relevance and utility of the review.
+
+Ethical Considerations
+
+As this is a review study, we use secondary data collected from previously published studies and therefore do not need any formal ethical approval. However, all procedures will be conducted in accordance with research ethics guidelines, such as following citation rules and acknowledging intellectual property rights. If the results are later to be used as the basis for a human study, ethical approval shall be sought before collecting data.
+
+Results
+
+Literature searches across the selected electronic databases were initiated in March 2025 using predefined search terms. Title and abstract screening, as well as preliminary appraisal of eligible studies, were conducted in May 2026 following the Joanna Briggs Institute methodology and PRISMA-ScR guidelines. Full-text screening, data extraction, and thematic analysis are currently ongoing and are expected to be completed by July 2026. The findings of this scoping review will be submitted to a journal by September 2026.
+
+This scoping review is expected to systematically map and synthesize the existing evidence regarding nurse training programs for the prevention of adolescent violent behavior in primary health care settings. The review findings will be organized in accordance with the objectives and research questions of the study, particularly focusing on the identification of risk and protective factors associated with adolescent violent behavior, the characteristics of nurse training and educational programs, and the theoretical frameworks underpinning these interventions. This scoping review is expected to provide a comprehensive map of existing evidence regarding nurse training interventions for adolescent violence prevention, including characteristics of interventions, theoretical foundations, implementation approaches, and reported outcomes. The findings will inform the development of the Kepolar model and support future nursing practice, policy, and research.
+
+The Kepolar model will subsequently be further developed and tested in the researcher’s (SM) doctoral dissertation. Moreover, the review is expected to contribute to practical and policy recommendations aimed at strengthening the promotive and preventive roles of nurses in puskesmas settings, thereby supporting adolescent mental health promotion and violence prevention efforts in Indonesia.
+
+Discussion
+
+This scoping review is expected to provide a comprehensive mapping of existing evidence regarding nurse training interventions for adolescent violence prevention and management within primary health care and community health care settings. This scoping review protocol concentrates on training targeting primary health care nurses to reduce the risk of violent behavior in adolescents, a direction that turns the focus from interventions exclusively aimed at adolescents toward equipping frontline health workers to be proactive regarding violence prevention. Early results from the international literature discuss that education and training for health care workers, including nurses, can improve confidence, readiness, communication skills, and practical competencies concerning risk assessment and management of violent situations (eg, de-escalation and referral screening) [43]. However, there remains relatively little direct evidence regarding the effectiveness of nurse-targeted training in reducing adolescent violence, with considerable heterogeneity in study designs, intervention characteristics, and outcome measures [26]. The review is also anticipated to demonstrate that evidence specifically focusing on structured nurse-targeted training for adolescent violence prevention remains limited compared with broader school-based or youth-focused violence prevention programs.
+
+Recent evidence underscores the critical role of multilevel interventions (eg, individual, family, school, health care system, and community levels) in accordance with the social ecological model [44]. Several assessed programs have primarily targeted adolescents through school-based life skills education, peer support interventions, and community psychosocial programs, demonstrating improvements in social competence, emotional regulation, knowledge, and risk-taking behaviors. Nevertheless, relatively few studies specifically examine nurse-targeted training, particularly within primary health care settings, where nurses may function as frontline screeners, facilitators, referral coordinators, and providers of psychosocial support. The present scoping review extends prior work by specifically focusing on nurse-targeted training interventions within health care and primary health care settings. This focus is particularly relevant in Indonesia and other low- and middle-income countries, where primary health care centers (puskesmas) often function as the first point of contact for adolescent health services and community mental health support.
+
+The literature indicates that training programs incorporating theoretical foundations (eg, trauma-informed care, ecological approaches, and life skills frameworks), ongoing supervision, and interactive learning modalities such as simulation, role-playing, communication exercises, de-escalation training, and case-based learning may result in greater competency acquisition and more sustainable behavioral change among health care providers [32]. In addition, multisession interventions with longer duration may provide more sustained effects compared with single-session workshops [45]. Accordingly, this review may help identify important intervention characteristics, including theoretical underpinnings, training content, delivery methods, implementation strategies, and duration of training programs.
+
+The findings of this review may also help clarify several important competencies and components that should be considered in nurse training programs for adolescent violence prevention and management. Core competencies may include early identification of violence risk factors, communication and therapeutic relationship skills, emotional regulation support, de-escalation techniques, behavioral assessment, trauma-informed care, crisis intervention, family engagement, referral coordination, and interprofessional collaboration. Existing literature also suggests that effective training programs often incorporate interactive and practice-based approaches such as simulation, role-playing, case discussions, and reflective learning activities rather than relying solely on didactic lectures [32,45,46].
+
+In addition, nurse training programs may require adaptation to local health care contexts, particularly within primary health care systems such as puskesmas in Indonesia, where nurses frequently manage adolescents with limited mental health resources and multidisciplinary support. Therefore, training programs may benefit from incorporating culturally appropriate approaches, practical referral algorithms, community-based case management strategies, and implementation guidance relevant to resource-limited settings. These findings may support the future development of more structured, competency-based, and contextually appropriate nurse training models for adolescent violence prevention.
+
+Institutional and systemic support including operational guidelines, referral pathways, leadership endorsement, protected implementation time, and intersectoral collaboration between health care services, schools, and child protection agencies have been identified as important determinants of training implementation and effectiveness [35,45]. Therefore, the focus on puskesmas in this protocol is considered particularly relevant because primary health care centers may function as coordination hubs connecting health care, educational, family, and community sectors in adolescent violence prevention efforts. However, in the absence of broader structural and organizational support, individual-level training alone may have limited impact. Accordingly, mapping studies that evaluate implementation-related constructs such as feasibility, acceptability, adherence, and sustainability may provide important insights for future intervention development and implementation.
+
+The majority of previous studies have evaluated training outcomes primarily at the provider level, including knowledge, attitudes, confidence, preparedness, and self-efficacy [32,47], while relatively fewer studies have assessed adolescent-level outcomes such as violent incidents, psychosocial functioning, school engagement, school attendance, or mental health indicators. Both provider-level and adolescent-level outcomes are considered within this protocol through the inclusion of studies evaluating nursing competencies as well as intervention impacts on adolescents. Importantly, improvements in nurses’ competencies alone may not necessarily reduce adolescent violence unless broader contextual issues including school culture, policy support, cross-sector partnerships, and health care infrastructure are also addressed [48]. The findings of this scoping review may therefore support policymakers and health care administrators in designing integrated adolescent violence prevention strategies that combine workforce development with broader system-level strengthening.
+
+Current systematic reviews and experimental studies focusing on violence prevention interventions remain methodologically heterogeneous, with many studies characterized by small sample sizes, inconsistent outcome measures, and limited reporting transparency. Among nurse training studies, many employ pre–post or qualitative evaluative designs, requiring cautious interpretation regarding intervention effectiveness. In addition, this review may identify considerable methodological heterogeneity across studies, including differences in study design, intervention components, measurement instruments, and reported outcomes [47]. As such, this scoping review represents an important initial step toward systematically identifying and synthesizing the nature, scope, and characteristics of current evidence before future large-scale intervention and implementation studies are conducted.
+
+Recent research has also explored innovative training modalities, including online learning platforms, blended learning approaches, digital educational modules, and virtual reality simulation training, to improve communication and de-escalation skills among health care workers [46]. Early evidence suggests that these approaches may increase engagement and facilitate skill acquisition, although long-term effectiveness and sustainability remain under investigation [46,48]. Future studies should also consider the use of standardized outcome measures to improve comparability across interventions. Further research is also needed to explore culturally appropriate and context-specific training models applicable to primary health care systems in Indonesia and other low- and middle-income countries.
+
+Several limitations identified in the international literature are also relevant to this protocol, including the limited availability of high-quality evidence specifically evaluating nurse training for adolescent violence prevention, substantial heterogeneity in terminology and outcome measures across studies, and contextual differences requiring adaptation of interventions to local health care systems and resource availability. This scoping review seeks to address some of these limitations through the inclusion of peer-reviewed literature, gray literature, qualitative studies, and instrument validation studies to provide a broader and more comprehensive evidence mapping.
+
+The findings of this scoping review will be disseminated through publication in peer-reviewed journals, presentations at national and international scientific conferences, and communication with health care stakeholders and policymakers. Dissemination activities may also include practical outputs such as stakeholder discussions, educational materials, implementation recommendations, policy briefs, and evidence-informed guidance to facilitate the translation of findings into nursing practice and adolescent mental health services. This scoping review protocol also has several strengths. It follows internationally recognized methodological frameworks, including the Joanna Briggs Institute methodology and Arksey and O’Malley framework, and includes both peer-reviewed and gray literature to support comprehensive evidence mapping. Another strength of this review is its focus on adolescent violence prevention within primary health care contexts, an area that remains relatively underexplored in existing literature. However, as a scoping review, this study will not formally assess the methodological quality or risk of bias of included studies. In addition, heterogeneity across study designs, intervention approaches, and outcome measures may limit comparability across studies.
+
+This scoping review protocol aims to systematically map and synthesize evidence regarding nurse training interventions for adolescent violence prevention and management within primary health care settings. Ultimately, this review may support future research, nursing practice, and policy development related to adolescent violence prevention within community and primary health care systems.
+
+Supplementary material
+
+10.2196/89576 Multimedia Appendix 1 Full PRISMA-S search strategies.
+
+10.2196/89576 Checklist 1 PRISMA-ScR checklist.
+
+Acknowledgments
+
+The authors would like to acknowledge the organizational support for this review from Gadjah Mada University and Sriwijaya University. We are also thankful for the financial assistance received from the Center for Higher Education Funding and the Indonesia Endowment Fund for Education, as acknowledged in decree 01637/J5.2.3./BPI.06/ 9/2022 (awardee ID202209091542). We also thank Dr Lutfan Lazuardi, the Director of Health Policy and Management in the Faculty of Medicine, Public Health, and Nursing at Universitas Gadjah Mada, Indonesia, for their suggestions in conducting this scoping review.
+
+Generative artificial intelligence tools were used solely to assist with language editing and improvement of manuscript readability. All intellectual content, interpretation of findings, methodological decisions, and final manuscript revisions were performed and verified by the authors, who take full responsibility for the content of this manuscript.
+
+Abbreviations
+
+Kepolar Keterampilan Pencegahan Risiko Perilaku Kekerasan Remaja (Prevention of Adolescent Violence-Risk Behavior)
+
+MeSH Medical Subject Headings
+
+PCC Population-Concept-Context
+
+PRISMA Preferred Reporting Items for Systematic Reviews and Meta-Analyses
+
+PRISMA-S Preferred Reporting Items for Systematic Reviews and Meta-Analyses Literature Search Extension
+
+PRISMA-ScR Preferred Reporting Items for Systematic Reviews and Meta-Analyses Extension for Scoping Reviews
+
+UNESCO United Nations Educational, Scientific and Cultural Organization
+
+Funding: This study was supported by the Indonesian Educator Scholarship Program (Beasiswa Pendidikan Indonesia [BPI]) administered by the Center for Higher Education Funding and the Indonesia Endowment Fund for Education (LPDP), award number 01637/J5.2.3./ BPI.06/9/2022. The funding body had no role in the design, conduct, writing, or decision to publish this protocol.
+
+Authors’ Contributions: SM designed and wrote the manuscript. IN provided advice and reviewed the manuscript. AAPP helped write and proofread the manuscript and will review the screening process selection on Rayyan. All authors read and approved the final manuscript.
+
+Data Availability: No primary datasets were generated or analyzed during this protocol study. The search strategies, extraction forms, and materials developed for the review will be made available as supplementary materials and through the Open Science Framework repository upon completion of the review. Any additional materials may be made available from the corresponding author upon reasonable request.
+
+Conflicts of Interest: None declared.
+
+
+References
+
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+8. Bellis MA Hardcastle K Hughes K Wood S Nurse J Preventing violence, promoting peace: a policy toolkit for preventing interpersonal, collective and extremist violence Commonwealth Secretariat 2017 URL https://phwwhocc.co.uk/wp-content/uploads/2020/08/Preventing-Violence-Promoting-Peace-Full-report.pdf Accessed 29-07-2026
+9. Smith SG Zhang X Basile KC Merrick MT Wang J Kresnow M et al National intimate partner and sexual violence survey: data brief—updated release National Center for Injury Prevention and Control (U.S.). Division of Violence Prevention 2018 URL https://stacks.cdc.gov/view/cdc/60893 Accessed 29-07-2026
+10. Novaco RW Anger Kazdin AE Encyclopedia of Psychology Oxford University Press 2000 170 174 doi 10.1037/10516-061
+11. Claussen C Matejko E Exner-Cortens D Exploring risk and protective factors for adolescent dating violence across the social-ecological model: a systematic scoping review of reviews Front Psychiatry 2022 13 933433 doi 10.3389/fpsyt.2022.933433 Medline 36339863 PMC9630934
+12. New UN report shows countries failing to protect children against violence UNESCO Jun 18 2020 URL https://www.unesco.org/en/articles/new-un-report-shows-countries-failing-protect-children-against-violence Accessed 29-07-2026
+13. Behind the numbers: ending school violence and bullying UNESCO 2019 URL https://www.unicef.org/media/66496/file/behind-the-numbers.pdf Accessed 29-07-2026
+14. Widiningsih Y Mother’s violent behavior in children equality 2020 6 2 11 doi 10.22373/equality.v6i2.7648
+15. Kurniasari A Widodo N Husmiati H et al PREVALENSI KEKERASAN TERHADAP ANAK LAKI-LAKI DAN ANAK PEREMPUAN DI INDONESIA [Article in Indonesian] SKA Sep 1 2017 6 3 doi 10.33007/ska.v6i3.740
+16. Silva M da Milbrath VM Santos B dos Bazzan JS Gabatz RIB Freitag VL Nursing care for child/adolescent victims of violence: integrative review Rpesq:cuidfundamOnline 2020 115-123 115 123 doi 10.9789/2175-5361.rpcfo.v12.7102
+17. Stuart GW Laraia MT Principles and Practice of Psychiatric Nursing Mosby Publication 2000 ISBN 978-0323012546
+18. Palupi AO Purwanto E Noviyani DE Pengaruh religiusitas terhadap kenakalan remaja [Article in Indonesian] Educ Psychol J 2013 2 1 1 10 URL https://garuda.kemdiktisaintek.go.id/documents/detail/486495 Accessed 29-07-2026
+19. Álvarez-García D Núñez Pérez JC Dobarro González A Rodríguez Pérez C Risk factors associated with cybervictimization in adolescence Int J Clin Health Psychol 2015 15 3 226 235 doi 10.1016/j.ijchp.2015.03.002 Medline 30487840 PMC6224863
+20. Massarwi AA Khoury-Kassabri M Serious physical violence among Arab-Palestinian adolescents: the role of exposure to neighborhood violence, perceived ethnic discrimination, normative beliefs, and, parental communication Child Abuse Negl 01 2017 63 233 244 doi 10.1016/j.chiabu.2016.11.002 Medline 27884509
+21. Vagi KJ Rothman EF Latzman NE Tharp AT Hall DM Breiding MJ Beyond correlates: a review of risk and protective factors for adolescent dating violence perpetration J Youth Adolesc Apr 2013 42 4 633 649 doi 10.1007/s10964-013-9907-7 Medline 23385616 PMC3697003
+22. Dubow EF Huesmann LR Boxer P et al Exposure to political conflict and violence and posttraumatic stress in Middle East youth: protective factors J Clin Child Adolesc Psychol 2012 41 4 402 416 doi 10.1080/15374416.2012.684274 Medline 22594697 PMC3387283
+23. Ferreira A Maravilha A Fluttert F et al Risk management of aggressive behaviors in mental health units for adolescents: a scoping review Encyclopedia 2025 5 3 144 doi 10.3390/encyclopedia5030144
+24. Core competencies in adolescent health and development for primary care providers: including a tool to assess the adolescent health and development component in pre-service education of health-care providers World Health Organization 2015 URL https://iris.who.int/server/api/core/bitstreams/44a2934c-6e86-4436-85fd-bb8339ae6a1b/content Accessed 29-07-2026
+25. Akinwale DO Bello CB Elemile MG Adolescent health issues: the role of public health nurses Journal of Integrative Nursing 2023 5 1 59 65 doi 10.4103/jin.jin_40_22
+26. Brandão Neto W Pinheiro HVS Araújo N de B et al Core competences of school nurses for the development of anti-bullying strategies: protocol for a scoping review Nurs Rep Nov 13 2024 14 4 3505 3514 doi 10.3390/nursrep14040255 Medline 39585146 PMC11587460
+27. Galindo NA Gonçalves CF Neto NM Santos SC Santana CR Alexandre AC Child and youth violence under the perspective of nursing J Nurs UFPE Online 2017 11 doi 10.5205/reuol.10263-91568-1-RV.1103sup201714
+28. Alsafy NN Alhendal ES Alhawaj SH El-Shazly MK Kamel MI Knowledge of primary care nurses regarding domestic violence Alexandria Journal of Medicine Jun 1 2011 47 2 173 180 doi 10.1016/j.ajme.2011.02.002
+29. Dönmez A Yeşil Y Evaluation of nurses’ and midwives’ knowledge and attitudes towards recognizing violence against women Afr J Reprod Health Feb 28 2024 28 2 116 124 doi 10.29063/ajrh2024/v28i2.11 Medline 38425273
+30. Hoffmann U Clemens V König E Brähler E Fegert JM Violence against children and adolescents by nursing staff: prevalence rates and implications for practice Child Adolesc Psychiatry Ment Health Nov 6 2020 14 1 43 doi 10.1186/s13034-020-00350-6 Medline 33292414 PMC7648387
+31. Sahriana NIM Peran kader kesehatan jiwa dalam program kesehatan jiwa komunitas di masyarakat [Dissertation in Indonesian] Surabaya Universitas Airlangga 2018 URL https://repository.unair.ac.id/78476/2/TKP%2095_18%20Sah%20p.pdf Accessed 25-10-2025
+32. Dafny HA Waheed N Cabilan CJ et al Effectiveness of interventions for the prevention or management of workplace violence in student nurses during clinical placement: a systematic review J Adv Nurs Mar 2025 81 3 1142 1171 doi 10.1111/jan.16357 Medline 39078141 PMC11810489
+33. Eldred E Devries K Nelson KA et al A systematic review and equity analysis of school-based violence prevention interventions evaluated in randomised controlled trials BMC Public Health 01 28 2026 26 1 681 doi 10.1186/s12889-025-26142-1 Medline 41593599 PMC12922353
+34. Agatha EZ Yosep I Hernawaty T et al Beyond the trauma: a scoping review of nursing interventions for improving psychological well-being in adolescents bullying victims BMC Nurs 07 25 2025 24 1 973 doi 10.1186/s12912-025-03642-4 Medline 40713664 PMC12297714
+35. Vijh R Exner-Cortens D Madigan S Noel M Adolescent dating violence prevention in healthcare settings: systematic scoping review Trauma Violence Abuse Oct 29 2025 15248380251381811 doi 10.1177/15248380251381811 Medline 41163319
+36. Supartini Y Tambunan ES Suheri T Ningsih R Pengembangan Model Deteksi Dini Kekerasan Pada Remaja Sebagai Upaya Meningkatkan Kemampuan Dalam Mendeteksi Adanya Kekerasan Pada Remaja [Article in Indonesian] QJK 2022 16 2 82 95 doi 10.36082/qjk.v16i2.792
+37. Global status report on violence prevention 2014 World Health Organization 2014 URL https://www.undp.org/sites/g/files/zskgke326/files/publications/UNDP-GVA-violence-2014.pdf Accessed 29-07-2026
+38. King IM King’s theory of goal attainment Nurs Sci Q 1992 5 1 19 26 doi 10.1177/089431849200500107 Medline 1538850
+39. Bronfenbrenner U Morris PA The ecology of developmental processes Damon W Lerner RM Handbook of Child Psychology: Theoretical Models of Human Development 5th John Wiley & Sons 1998 993 1028 ISBN 9780470147658
+40. Arksey H O’Malley L Scoping studies: towards a methodological framework Int J Soc Res Methodol Feb 2005 8 1 19 32 doi 10.1080/1364557032000119616
+41. Levac D Colquhoun H O’Brien KK Scoping studies: advancing the methodology Implement Sci Sep 20 2010 5 69 doi 10.1186/1748-5908-5-69 Medline 20854677 PMC2954944
+42. Braun V Clarke V Using thematic analysis in psychology Qual Res Psychol 01 2006 3 2 77 101 doi 10.1191/1478088706qp063oa
+43. Brenig D Gade P Voellm B Is mental health staff training in de-escalation techniques effective in reducing violent incidents in forensic psychiatric settings? - A systematic review of the literature BMC Psychiatry Apr 12 2023 23 1 246 doi 10.1186/s12888-023-04714-y Medline 37046228 PMC10099889
+44. Steeger CM Combs KM Buckley PR et al Substance use prevention during adolescence: study protocol for a large-scale cluster randomized trial of Botvin High School LifeSkills Training Contemp Clin Trials Feb 2023 125 107049 doi 10.1016/j.cct.2022.107049 Medline 36521631
+45. Jackson DI Maa T Luna J Huang Y Fristad MA Sezgin E Challenges and opportunities in healthcare workplace violence training: a qualitative study of staff experiences J Workplace Behav Health Oct 2 2025 40 4 641 654 doi 10.1080/15555240.2025.2474055
+46. Peddle M Jackson M Searby A Alexander L Influence of simulation on the knowledge, skills, and confidence of entry-to-practice nursing students to recognise and respond to occupational violence and aggression: A scoping review Nurse Educ Today Mar 2026 158 106939 doi 10.1016/j.nedt.2025.106939 Medline 41319445
+47. Somani R Muntaner C Hillan E Velonis AJ Smith P A systematic review: effectiveness of interventions to de-escalate workplace violence against nurses in healthcare settings Saf Health Work Sep 2021 12 3 289 295 doi 10.1016/j.shaw.2021.04.004 Medline 34527388 PMC8430427
+48. Clay CJ Hochmuth JM Wirth O Virtual reality training to reduce workplace violence in healthcare Issues Ment Health Nurs 01 2025 46 1 2 11 doi 10.1080/01612840.2024.2429712 Medline 39761223 PMC11774209
diff --git a/corpus/psychology/text/372d452db11f55e1.txt b/corpus/psychology/text/372d452db11f55e1.txt
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@@ -0,0 +1,3 @@
+The Intellectual Justice Scale: Measuring How Fairly People Engage With Knowledge
+
+Intellectual justice, the disposition to engage fairly with knowledge and those who produce it, has received growing attention in philosophy and education, yet no validated self-report measure exists. We developed and validated the Intellectual Justice Scale (IJS), a 9-item measure with three factors (Testimonial Justice, Hermeneutical Justice, and Intellectual Action) grounded in Fricker’s framework of intellectual injustice. An initial item pool was refined through expert review and pilot testing. In Study 1 (N = 404), exploratory factor analysis supported a three-factor structure, with independent statistical and conceptual item selection converging on the same nine items. In Study 2 (N = 401), confirmatory factor analysis supported good model fit, and the IJS showed expected associations with intellectual humility, personality traits, and social justice attitudes while remaining empirically distinguishable from each. These findings offer the first validated self-report measure of intellectual justice attitudes, providing researchers with a tool to study individual differences.
diff --git a/corpus/psychology/text/3742843a8b20ba9a.txt b/corpus/psychology/text/3742843a8b20ba9a.txt
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@@ -0,0 +1,3 @@
+Limited Information Model Fit Test of Binary Item Response Theory Model with Missing Responses
+
+Even though missing data are prevalent in applications of item response theory (IRT), there has been a lack of research on the global model fit of IRT models with missing data. This study proposes two limited information fit statistics under full information maximum likelihood estimation for binary IRT models, related to the M_2 statistics of Maydeu-Olivares and Joe (2005). For a baseline model, we choose a log-linear model up to pairwise interaction effects based on the observations that M_2=0 with df=0 for this model under complete data as the first- and second-order model-implied marginals exactly recover those of sample and that two-parameter logistic IRT models are special cases of the model. We develop a computationally efficient generalized expectation-maximization algorithm (Dempster et al., 1977) to estimate the log-linear model under missing data. The two proposed statistics are motivated by G^2_dif of Fuchs (1982) and D_m of Rubin (1987) in multiple imputation, referred to as G^2_dif and \tilde{M}_2. Due to exponentially increasing cells (i.e., two to the power of the number of items), we discuss poor man's data augmentation of Wei and Tanner (1990) for \tilde{M}_2. We show that the two proposed statistics perform well throughout a simulation study and an application to PISA mathematics achievement data, among which \tilde{M}_2 shows the most promising result. We complete the study by discussing several important topics for the global model fit of IRT models under missing data.
diff --git a/corpus/psychology/text/37c9f664e7256f63.txt b/corpus/psychology/text/37c9f664e7256f63.txt
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@@ -0,0 +1,586 @@
+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Health Promot J Austr
+Journal ID: Health Promot J Austr
+NLM Journal ID: 9710936
+Journal ID: HPJA
+
+Health Promotion Journal of Australia
+
+ISSN: 1036-1073
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC13123304
+PMID: 42047464
+DOI: 10.1002/hpja.70190
+Article ID: HPJA70190
+Article ID: 5341005
+Article version: 1
+Subjects: Review, Review
+
+Impact of Different Types of Sedentary Behaviour on Cognitive Function in Older Adults: A Systematic Review
+
+de Jesus Silva Tawan Ricardo https://orcid.org/0009-0008-1063-9525 1
+Damião Eduarda Pereira https://orcid.org/0000-0002-1576-0809 1
+Barbosa Vanessa Santos https://orcid.org/0009-0007-6210-8913 2
+de Matos Alcantara Lara https://orcid.org/0000-0003-2332-0296 1
+dos Santos Rafaela Gomes https://orcid.org/0000-0001-7361-0078 2
+Junior Jair Sindra Virtuoso https://orcid.org/0000-0001-7602-1789 1 jair.junior@uftm.edu.br
+
+1 Graduate Program in Physical Education Federal University of Triângulo Mineiro (UFTM) Uberaba Minas Gerais Brazil
+2 Department of Education (DEDC 10) State University of Bahia (UNEB) Teixeira de Freitas Bahia Brazil
+* Correspondence:
+Jair Sindra Virtuoso Junior (jair.junior@uftm.edu.br)
+
+Electronic publication date: 2026 Apr 28
+Print publication date: 2026 Jul
+Volume: 37
+Electronic Location ID: e70190
+Revised 2026 Mar 28; Received 2025 Dec 22; Accepted 2026 Apr 11
+Copyright: © 2026 The Author(s). Health Promotion Journal of Australia published by John Wiley & Sons Australia, Ltd on behalf of Australian Health Promotion Association.
+License: This is an open access article under the terms of the http://creativecommons.org/licenses/by/4.0/ License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Keywords: cognition, cognitive ageing, life style, older adults, sedentary behaviour
+Figure count: 1
+Table count: 8
+Page count: 18
+
+source-schema-version-number: 2.0
+cover-date: July 2026
+details-of-publishers-convertor: Converter:WILEY_ML3GV2_TO_JATSPMC version:6.7.6 mode:remove_FC converted:28.04.2026
+
+T. R. de Jesus Silva , E. P. Damião , V. S. Barbosa , L. de Matos Alcantara , R. G. dos Santos , and J. S. V. Junior , “Impact of Different Types of Sedentary Behaviour on Cognitive Function in Older Adults: A Systematic Review,” Health Promotion Journal of Australia 37, no. 3 (2026): e70190, 10.1002/hpja.70190.
+
+Handling Editor: Carmel Williams
+
+Ÿ==============================Ÿ
+ABSTRACT
+
+Issue Addressed
+
+Sedentary behaviour (SB) is a relevant determinant of health in ageing, yet its effects on cognitive function remain inconclusive. The literature often treats SB as a homogeneous exposure, without considering that different sedentary activities may differentially affect cognitive domains. Accordingly, this study sought to identify how distinct types of SB influence cognition in older adults.
+
+Methods
+
+A systematic review was conducted and registered in PROSPERO (CRD42025637160), following PRISMA guidelines. Observational studies published between 2010 and 2025 were included if they involved participants aged 60 years or older and examined the relationship between specific types of SB and cognitive domains. Searches were performed in PubMed/MEDLINE, Web of Science and Scopus. Two independent reviewers carried out study selection, data extraction and quality assessment using Joanna Briggs Institute tools.
+
+Results
+
+The search yielded 1795 records, resulting in the inclusion of 13 studies encompassing 43 902 participants. Findings were heterogeneous: passive SB, particularly, television viewing, was more frequently associated with poorer cognitive performance. In contrast, cognitively stimulating sedentary activities involving complex tasks—such as reading, playing games and computer use—were positively associated with memory, executive function and processing speed. Some studies further suggested that cognitive engagement may mitigate potential negative effects of SB.
+
+Conclusions
+
+The findings indicate that the impact of SB on cognition depends more on the type of activity performed than on total sedentary time, underscoring the importance of context and mental demand.
+
+So What?
+
+Identifying which types of SB are beneficial or harmful may inform health promotion strategies, encouraging older adults to replace passive SB with cognitively stimulating sedentary activities, thereby supporting healthier cognitive ageing.
+
+1 Introduction
+
+Human lifestyles undergo continuous changes depending on adopted habits, directly impacting individual health [1], particularly, among older adults, whose routines often change abruptly according to physical, social and economic conditions [2]. When distinguishing the time allocated to daily activities such as work, sleep, eating, leisure and physical activity, it is observed that better adjustments in daily routines positively influence life expectancy [3, 4].
+
+Nevertheless, time spent in sedentary behaviour (SB) is also part of the overall routine [5]. Recent studies have highlighted concerns regarding excessive time spent in this type of behaviour, due to its harmful effects on health and psychosocial determinants [6, 7]. However, when addressing the effects of SB on cognition in older adults, the evidence remains inconclusive. A systematic review with meta analysis demonstrated a positive association between higher levels of SB and increased risk of cognitive decline [8]. On the other hand, Dillon et al. [9] emphasise that the effects of SB depend on the context in which it occurs, suggesting that different types of SB may exert distinct impacts on cognitive domains.
+
+Concurrently, cognitive function comprises multiple subdomains such as language, memory, executive function and attention, each supported by specific neural circuits and susceptible to different influences throughout ageing [10]. Therefore, the stimulation or decline of each subdomain depends on a variety of factors, including the type of activity performed, its complexity and the time devoted to it. Evidence suggests that different patterns of cognitive engagement may either mitigate or accentuate cognitive changes in older adults, reinforcing the dynamic and contextually modulated nature of cognition at this stage of life [11].
+
+Considering that most of the literature treats SB as a single entity, without accounting for the various contexts in which it occurs, this study helps to identify which types of SB have a greater impact on cognitive activity. Thus, the guiding question of this review is: What is the impact of different types of SB on specific cognitive domains in older adults? Accordingly, the objective of this study is to systematically analyse the impact of different contexts of SB, such as watching television, use of electronic devices, reading, games, religious activities, among others, on different cognitive domains in older adults.
+
+2 Methods
+
+This systematic review was registered in the International Prospective Register of Systematic Reviews PROSPERO (CRD42025637160) and followed the recommendations of the Preferred Reporting Items for Systematic Reviews and Meta Analyses PRISMA [12].
+
+3 Eligibility Criteria
+
+This review included studies whose participants were community‐dwelling older adults aged 60 years or older [13]. Eligible studies were required to report exposure to SB in specific domains, such as television viewing, computer use, reading time, games or similar activities and to provide explicit information on at least one cognitive domain, including memory, language, orientation or other domain‐specific cognitive outcomes.
+
+Studies that included populations with a mean age below 60 years were eligible only when results were stratified by age, allowing extraction of data exclusively for participants aged 60 years or older.
+
+Studies were excluded if they focused on institutionalised or residential care populations, participants with diagnosed dementia or moderate to severe cognitive impairment or clinical samples selected based on specific neurological or psychiatric conditions. In addition, studies were excluded if they did not specify the SB domain assessed, if they reported only total sedentary time or weekend sedentary time or if they evaluated only overall cognitive decline or global cognition defined as a composite score across multiple cognitive domains.
+
+4 Search Strategy and Sources
+
+Searches were conducted in the PubMed/MEDLINE, Web of Science and Scopus databases. When applicable, filters were applied to restrict publication dates between 2010 and 2025. The search strategy was based on three key concepts: sedentary behaviour, cognitive function and older adults, using controlled vocabulary and free‐text terms combined with Boolean operators to broaden retrieval (Appendix A).
+
+Only studies published from 2010 onwards were included to ensure conceptual and methodological consistency with the contemporary definition of SB. From this period, studies more frequently distinguished SB from physical inactivity, differentiated specific sedentary activities and used more standardised and validated measurement approaches, improving comparability across findings.
+
+5 Study Selection
+
+Observational studies including cohort, case control and/or cross‐sectional designs published over the last 15 years were selected. These studies assessed the impact of different types of SB activities on cognitive function in older adults with a mean age equal to or greater than 60 years. Initially, titles and abstracts were independently screened in pairs, followed by full text assessment for inclusion in the systematic review.
+
+6 Data Collection Process and Data Extraction
+
+Two authors TRJS and EPD performed the study selection and identified studies based on titles and abstracts. Duplicate articles and those that did not meet the selection criteria were removed. The remaining articles were reviewed in full text by the same authors to determine eligibility. Any discrepancies and or doubts regarding the manuscripts were resolved by a third reviewer VSB. Both authors TRJS and EPD conducted the search, extracted files to the Rayyan Systematic Review platform and performed selection based on the predefined criteria. The software indicated that the researchers were fully aligned and identified only two conflicts among the studies.
+
+TRJS and EPD independently extracted data from all included articles using a customised extraction table developed by the reviewers in a Microsoft Excel spreadsheet 2024. The following general information was extracted: (1) first author name and year of publication; (2) study design, age range and number of participants; (3) country; (4) study objective in relation to SB and the outcome.
+
+For SB, the following information was extracted: (1) measurement instrument; (2) SB domain or activity performed; (3) type of exposure assessment; (3) data collection procedure; (4) statistical methods and confounding factors. For the assessment of cognitive function, the following aspects were examined: (1) cognitive function domain or domains; (2) instrument used; (3) data collection procedure; (4) association with the SB domain. Regarding cognitive domains, some terminologies were standardised in this manuscript due to heterogeneity across studies.
+
+To improve clarity regarding the intended evaluation, studies assessing immediate and delayed memory operational terms were standardised as short‐term and long‐term memory theoretical terms. In addition, given the complexity of assessing a single domain without interference from others, some studies indicated that the instrument assessed more than one cognitive function, such as executive function and processing speed or working memory and short term memory.
+
+7 Assessment of Risk of bias and Quality of Evidence
+
+Two authors TRJS and EPD assessed the quality of the articles using two tools appropriate for different study designs, both developed by the same international centre for health evidence research, the Joanna Briggs Institute JBI [14]. The quality of included cohort and or case control studies was assessed using a checklist composed of 11 questions [15]. For cross sectional and analytical studies, a critical appraisal checklist composed of eight questions was used [16]. Both tools included response options of yes, no or unclear. For studies that presented both cross sectional and longitudinal analyses included in this review, the risk of bias was assessed separately for each study design according to the appropriate methodological tool.
+
+Two evaluators TRJS and EPD independently used a Microsoft Excel spreadsheet 2024 to estimate study quality. The assessment considered three possible classifications for each item evaluated: low risk, unclear risk and high risk. The evaluators applied the following scoring criteria to determine study quality in cross sectional and cohort studies: low risk of bias if 70% of responses were scored as yes, unclear risk if 50%–69% of responses were scored as yes and high risk of bias if fewer than 50% of responses were scored as yes [17].
+
+8 Results
+
+The initial search yielded a total of 1795 manuscripts. For analysis, titles and abstracts were first screened. Subsequently, full text articles that potentially met the inclusion criteria were reviewed in detail. After these stages, 13 manuscripts that fulfilled the eligibility criteria were included (Figure 1). One study [18] appeared to meet the inclusion criteria based on title and abstract screening; however, the full text could not be accessed despite attempts to retrieve it from complementary databases and through contact with the authors. As a result, this record did not proceed to the full‐text eligibility assessment and was not included in the review.
+
+FIGURE 1 Flow diagram of the manuscript screening process.
+
+9 Study Characteristics
+
+Among the studies included in this systematic review, seven presented an exclusively cross sectional design, two adopted a cohort design and four combined cross sectional and longitudinal analyses within the same manuscript. The age range varied, with mean or median values between 51 and 90 years or older. In studies whose total sample included individuals below the age threshold defined for the review ≥ 60 years, only results stratified for the older adult subgroup were considered in the analyses. Accordingly, the final synthesis comprised data from 43 902 participants.
+
+The specific objectives of the studies varied, mainly due to the inclusion of different outcome variables. Nevertheless, with regard to SB and cognitive function, all studies investigated the association between one or more SB domains and indicators of cognitive performance, encompassing executive function, language, memory and other relevant constructs (Table 1).
+
+TABLE 1 Main characteristics of the included studies.
+
+References	Study design	Age range (mean and SD/CI)	n	Study objective	
+Coelho et al. (2020) [19]	Cross‐sectional	74.6 (± 9.0)	75	To examine the relationship between sedentary time and cognitive ability using a robust assessment of cognitive abilities;
+
+To determine whether the association between sedentary time and executive function is different among individuals who engage in regular physical activity compared to those who are inactive.
+
+	
+Edwards and Loprinzi (2017) [20]	Cross‐sectional	69.9 (69.3–70.4)	2.472	Examine the independent association of SB and cognitive function in older adults, as well as whether or not physical activity attenuates this potential association.	
+Hu et al. (2025) [21]	Cohort (prospective)	70.8 (±5.7)	517	To investigate the association between mentally active SB and cognitive function in rural older Chinese across different levels of education.	
+Kesse‐Guyot et al. (2014) [22]	Cohort	65.6 (±4.5)	2.430	To examine the association between individual and clustered lifestyle behaviours and later cognitive functioning.	
+Kesse‐Guyot et al. (2012) [23]	Cross‐sectional and cohort	65.6 (±4.5)	2.179	To estimate the associations between different SBs and cognitive performance in healthy older adults.	
+Maasakkers et al. (2021) [24]	Cross‐sectional and cohort a	67 (±9.0)	6.687	Evaluate how subjective TV time and objectivelymeasured SB are associated with each other, but also how they are crosssectionally and longitudinally (4‐year follow‐up period) associated with global and domain‐specific cognitive outcomes in healthy older adults.
+
+Examine the reverse association between cognitive decline and future SB, we investigated the bidirectionality of the relation between SB and cognition.
+
+	
+Mellow et al. (2022) [25]	Cross‐sectional	65.6 (±3.0)	384	To understand how 24‐h time‐use composition is associated with cognitive function across a range of domains in healthy older adults and whether the level of recreational physical activity, amount of TV watching or the quality of sleep impact these potential associations.	
+Moreira et al. (2022) [26]	Cross‐sectional	61 (58–66)	6.505	To verify the association between SB and performance on cognitive function tests in middle‐aged and elderly adults.	
+Olanrewaju et al. (2020) [27]	Cross‐sectional and cohort (prospective)	63.5 (±9.2)	8.163	To explore the cross‐sectional associations between reported sedentary behaviours and cognitive function at baseline Wave 1 (sitting time) and Wave 3 (television viewing time);
+
+To explore the longitudinal associations between baseline sedentary behaviours and cognitive changes at 4‐year (Waves 1–3) and 2‐year follow‐up (Waves 3–4) in community dwelling adults 50 years and older, while accounting for well‐established socio‐economic, behavioural and health‐related confounders.
+
+	
+Palazuelos‐González et al. (2025) [28]	Cross‐sectional	51 (±8.8) b	11.087 b	To examine the association between time spent in physical activities, SB and sleep with executive functioning and to estimate the influence of reallocating time from SB to other activities on executive functioning.	
+Rosenberg et al. (2015) [29]	Cross‐sectional	83.6 (±6.4)	307	Examined the relationships between objective and self‐reported sedentary time and health indicators among older adults residing in retirement communities.	
+Wingood et al. (2024) [30]	Cross‐sectional and cohort	≥ 65	2.244	To describe the types and amount of SB performed by older adults with and without impaired orientation, memory and executive function;
+
+To examine how participating in different types and amounts of SB at baseline impacts longitudinal changes in orientation, memory and executive function.
+
+	
+Zhou et al. (2022) [31]	Cross‐sectional	≥ 80	852	I Identify distinct subgroups of oldest old adults based on six domains of SB (watching TV, using a computer/tablet, talking to friends or family members, doing hobby or other activities, transportation and resting/napping);
+
+III Compare health‐related outcomes across identified subgroups, using the National Health and Aging Trends Study (NHATS) dataset.
+
+	
+Abbreviations: CI: confidence interval; SD: standard deviation.
+
+a The assessment of methodological quality considered only the cross‐sectional design, as the study used specific SB domains rather than total sedentary time alone.
+
+b Results were analysed exclusively in the age stratum of 60 years or older.
+
+Additionally, a wide diversity was observed in terms of the countries in which the studies were conducted. Four were carried out in the United States [20, 29, 30, 31], two in Ireland [24, 27], two in France [22, 23], one in the Netherlands [28], one in China [21], one in Australia [25], one in Canada [19] and one in Brazil [26].
+
+10 Assessment of SB
+
+Most studies (77%; 10 of 13) used only subjective methods to assess SB through standardised questionnaires or single questions [19, 20, 21, 22, 23, 26, 27, 28, 30, 31]. In contrast, 23% of the studies (3 of 13) combined objective measures using accelerometry with questionnaires [24, 25, 29]. However, in these studies that employed accelerometers, only the subjective data were analysed due to the need to assess the context of SB.
+
+The most frequently investigated domain was television viewing, reported in 85% of the studies (11 of 13) [20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31]. In addition, 62% (8 of 13) examined computer, tablet or Internet use [19, 20, 23, 25, 28, 29, 30, 31]. Other less frequent domains included reading, hobbies, games and sedentary time spent driving or as a passenger in a motor vehicle.
+
+All studies (100%) administered questionnaires in person with interviewers, demonstrating methodological standardisation in this aspect. In studies that included accelerometry (23%), devices were worn for periods ranging from 6 to 7 days [24, 25, 29].
+
+Regarding statistical methods, considerable analytical heterogeneity was observed among the included studies. Linear regression, either simple or multiple, was the predominant approach, used in 54% of the studies (7 of 13) [19, 20, 24, 26, 27, 28, 31], although this method has limitations in modelling complex relationships between behavioural variables and cognitive domains. Other studies employed analysis of covariance (ANCOVA) [22, 23, 25] or linear mixed effects models [21, 29], the latter being more appropriate for the analysis of repeated measures and for accounting for within‐subject dependence over time.
+
+Beyond these approaches, some studies applied more sophisticated statistical methods, including isotemporal substitution models [28], which allow estimation of counterfactual effects by reallocating time between different behaviours; structural equation modelling [19], which enables the assessment of latent relationships between cognitive constructs and components of SB and more recent analyses based on χ 2 tests with Bonferroni correction and discrete time competing risk models [30], thereby expanding the ability to capture associations in scenarios with multiple competing outcomes (Table 2).
+
+TABLE 2 Characteristics of SB assessment and analytical approaches used.
+
+References	Measurement instrument	SB domain or activity performed	Type of exposure assessment	Data collection procedure	Statistical methods	
+Coelho et al. (2020) [19]	LASA‐SB (Longitudinal Ageing Study Amsterdam—SB)	Watching television, napping, reading, listening to music, socialising and engaging in hobbies.	Subjective	Interviewer‐administered questionnaire (in person).	Correlation analyses and multiple linear regression	
+Edwards and Loprinzi (2017) [20]	Self‐reported data from NHANES	Watching television or videos or using a computer outside of work.	Subjective	Interviewer‐administered questionnaire (in person).	Multivariable linear regression.	
+Hu et al. (2025) [21]	Single question	Card games or mahjong; chess or checkers; calligraphy, painting, reading or writing during leisure time.	Subjective	Interviewer‐administered questionnaire (in person).	Linear mixed‐effects models.	
+Kesse‐Guyot et al. (2014) [22]	Modifiable Activity Questionnaire (MAQ)—French version	SB was assessed as the average daily time spent watching television at home.	Subjective	Interviewer‐administered questionnaire (in person).	Analysis of covariance (ANCOVA); structural equation modelling (SEM); principal component analysis (PCA)	
+Kesse‐Guyot et al. (2012) [23]	MAQ Questionnaire (Modifiable Activity Questionnaire)—French version	Computer use, television viewing and reading	Subjective	Interviewer‐administered questionnaire (in person).	Analysis of covariance (ANCOVA).	
+Maasakkers et al. (2021) [24]	GENEActiv accelerometer plus a single question on television viewing time	Total sedentary time and time spent watching television.	Objective and subjective	Accelerometer (wrist‐worn for 7 days).
+
+Interviewer‐administered questionnaire (in person).
+
+	Longitudinal mixed models (bidirectional associations).	
+Mellow et al. (2022) [25]	Triaxial accelerometer (model not specified) and multimedia activity recall for children and adults (MARCA)	Television viewing and total SB.	Objective and subjective	Accelerometer (waist‐worn for 7 days);
+
+Interviewer‐administered questionnaire (in person).
+
+	Multiple linear regression models;
+
+Analysis of covariance (ANCOVA).
+
+	
+Moreira et al. (2022) [26]	Single question on total SB and screen time	Total sedentary time and screen time (television, video games, computers, tablets, smartphones, etc.).	Subjective	Interviewer‐administered questionnaire (in person).	Linear regression	
+Olanrewaju et al. (2020) [27]	International Physical Activity Questionnaire (IPAQ) and a single question on television viewing (TILDA data)	Total sitting time and time spent watching television on weekdays.	Subjective	Interviewer‐administered questionnaire (in person).	Linear regression analyses (cross‐sectional and longitudinal).	
+Palazuelos‐González at al (2025) [28]	Self‐reported	Time spent watching television.	Subjective	Interviewer‐administered questionnaire (in person).	Multivariable linear regression and isotemporal substitution analysis.	
+Rosenberg et al. (2015) [29]	GT3X accelerometer and SB Questionnaire (SBQ)—modified version	Television viewing, computer or internet use, reading, socialising, transportation, hobbies and group activities.
+
+For analysis, SB was aggregated as total sedentary time, but television viewing was analysed separately.
+
+	Objective and subjective	Accelerometer (waist‐worn for 6 days);
+
+Interviewer‐administered questionnaire (in person).
+
+	Linear mixed‐effects models.	
+Wingood et al. (2024) [30]	Self‐reported	Watching television, computer use, socialising, hobbies, transportation, eating and resting.	Subjective	Interviewer‐administered questionnaire (in person).	χ 2 tests and t‐tests with Bonferroni correction (Objective 1); Discrete‐time competing risk models (Objective 2)	
+Zhou et al. (2022) [31]	Subjective questionnaire (SB Questionnaire—SBQ)	Television viewing; computer or tablet use; socialising with friends or family; engaging in hobbies; transportation.	Subjective	Interviewer‐administered questionnaire (in person).	Latent profile analysis (LPA); Linear and logistic regression analyses.	
+
+Among the cognitive domains most frequently investigated, memory was the most commonly assessed overall, accounting for 76.9% (10 of 13) of citations across studies. However, the included studies associated SB with one or more memory subsystems. Accordingly, there was variation in the examination of this domain, including assessments of short‐term and long‐term memory, as well as semantic and phonemic memory.
+
+Executive function was the second most frequently evaluated domain, with a prevalence of 53.8% (7 of 13). One study assessed processing speed as an extension of executive function [20]. The remaining domains were investigated less frequently, with proportions ranging from 15.3% (2 of 13) to 7.7% (1 of 13).
+
+In the analysis of the included studies (n = 13), a predominance of instruments aimed at assessing memory and executive function was identified. Among the most frequently used tests, the 10 word list stands out, applied in different versions and contexts, including the CERAD protocol, as a standalone measure or integrated into cognitive batteries, and employed in several studies [19, 20, 21, 24, 26, 27, 30, 31]. This instrument was widely used to measure short term and long term memory, constituting the most frequent method for the assessment of these cognitive domains.
+
+Another group of widely used instruments consisted of verbal fluency tests, both semantic, such as category based tasks including animal naming and phonemic, based on letter generation, employed in several studies [22, 23, 24, 26, 27]. These tests were relevant for measuring semantic and phonemic verbal memory and language related components, including lexical access, retrieval speed and semantic organisation. Trail Making Tests A and B were also used in several studies [22, 23, 26, 29], particularly, to assess cognitive flexibility, sustained attention, processing speed and components of executive function.
+
+In addition, other instruments were used less frequently but remain relevant for cognitive assessment. These included forward and backward Digit Span tests, used to measure working memory and attention [22, 23]; the Digit Symbol Substitution Test (DSST), applied by Edwards and Loprinzi [20] to assess processing speed and aspects of executive function and the Ruff Figural Fluency Test (RFFT), employed by Maasakkers et al. [24] to measure non‐verbal fluency and cognitive flexibility. More comprehensive cognitive batteries were also identified, such as the CERAD [26], the CANTAB [25], the Mini‐Mental State Examination (MMSE) [20] and the TICS‐10 [21], designed to assess global cognition and multiple cognitive domains.
+
+11 Associations With SB
+
+Time spent watching television was the SB domain most consistently associated with poorer cognitive outcomes, reported in 61.5% of the included studies (8 of 13) [19, 20, 22, 24, 26, 27, 28, 31]. However, this association was not uniform. Two studies by Rosenberg et al. [29] and Mellow et al. [25] did not identify a relationship between television viewing time and cognitive performance across the different domains evaluated. In contrast, the study by Wingood et al. [30] was the only one to demonstrate a potential protective effect of television viewing time on memory performance.
+
+Computer or internet use showed a positive association with better performance in memory and executive functions in 23% of the studies (3 of 13) [19, 23, 26]. In addition, other studies observed that cognitively stimulating sedentary activities, such as card games, hobbies, reading and other behaviours considered mentally active, were associated with better performance in specific domains, including orientation, attention and short‐term and long‐term memory. In contrast, SBs classified as mentally passive were associated with poorer outcomes in several cognitive subdomains [21, 31].
+
+All included studies adjusted their analyses for sociodemographic variables, with particular emphasis on age, sex and educational level, which were the most frequently applied adjustments. Other commonly considered factors, reported in more than 70% of the studies, included body mass index, physical activity level, smoking, alcohol consumption, presence of chronic diseases, depressive symptoms and sleep quality (Table 3).
+
+TABLE 3 Characteristics of cognitive function assessment and corresponding associations with SB.
+
+References	Cognitive function domain(s) assessed	Measurement instrument or test	Association with the SB domain	Confounding factors	
+Coelho et al. (2020) [19]	– Executive function;
+
+– Short‐ and long‐term memory.
+
+	– BRIEF‐A, Stroop, Tower of Hanoi, LEGO/Mega Blocks, Snap;
+
+– Logical memory.
+
+	Greater time spent watching television, napping and engaging in sedentary hobbies was associated with poorer executive function, with only napping being associated with memory; other forms of SB (such as attending church and driving) did not impact cognition.	Age, level of physical activity and sex.	
+Edwards and Loprinzi (2017) [20]	– Executive function and processing speed.
+
+	Digit symbol substitution test (DSST)	SB (television, videos or computer use) of at least 5 h per day was associated with poorer performance; however, the association lost statistical significance after adjustment for physical activity.	Age, sex, body mass index, race, smoking, physical activity and coronary artery disease.	
+Hu et al. (2025) [21]	– Orientation;
+
+– Attention;
+
+– Short‐ and long‐term memory;
+
+– Global cognition.
+
+	Telephone Interview for Cognitive Status (TICS‐10); – Spatial orientation (current day, month and year);
+
+– Serial subtraction (serial 7 s);
+
+– 10‐word list;
+
+– Sum of all tests.
+
+	Mentally active SB (card games, time spent playing mahjong and or reading or painting) was positively associated with cognitive subdomains, with stronger associations observed among illiterate individuals.	Age, sex, educational level, income, marital status, sleep, physical activity, body mass index, alcohol consumption and smoking.	
+Kesse‐Guyot et al. (2014) [22]	– Working memory or short‐term memory;
+
+– Mental flexibility;
+
+– Long‐term memory;
+
+– Semantic verbal memory;
+
+– Phonemic verbal memory.
+
+	– Forward and backward Digit Span;
+
+– Trail Making Test (TMT);
+
+– RI‐48 test;
+
+– Animal naming;
+
+– Phonemic fluency (letter P).
+
+	SB (watching television for more than 1 h per day) was negatively associated with verbal memory in the unadjusted model; however, this association lost statistical significance after adjustment.	Age, sex, educational level, body mass index, physical activity, depressive symptoms and chronic diseases.	
+Kesse‐Guyot et al. (2012) [23]	– Phonemic verbal memory;
+
+– Semantic verbal memory;
+
+– Long‐term memory;
+
+– Working memory or short‐term memory;
+
+– Mental flexibility.
+
+	– Phonemic fluency test (letter P);
+
+– Semantic fluency test (animals);
+
+– RI‐48 test (free and cued recall test);
+
+– Forward and backward Digit Span;
+
+– Trail Making Test (TMT Part B).
+
+	Computer use was positively associated with verbal memory and executive function, even after 6 years, whereas television viewing was negatively associated with executive function in cross‐sectional analyses.	Age, sex, educational level, marital status, occupation, alcohol consumption, smoking, physical activity, depression, antioxidant supplementation and body mass index.	
+Maasakkers et al. (2021) [24]	– Short‐ and long‐term memory;
+
+– Semantic verbal memory;
+
+– Global cognition.
+
+	– 10‐word list;
+
+– Animal naming;
+
+– Mini‐Mental State Examination (MMSE).
+
+	A weak negative correlation was observed between television viewing time and memory, which was explained by confounding factors. No longitudinal associations were found between television viewing time and the outcome.	Age, sex, educational level, depression, body mass index, comorbidities, moderate to vigorous physical activity, sleep, mobility and self‐rated health.	
+Mellow et al. (2022) [25]	– Short‐term memory;
+
+– Long‐term memory;
+
+– Executive function;
+
+– Processing speed.
+
+	Cambridge Automated Neuropsychological Test Automated Battery (CANTAB); – Word list;
+
+– Word list and Paired Associates Learning;
+
+– Multitasking test;
+
+– Reaction time.
+
+	The study found no significant effect of television viewing time on cognitive function, including memory, executive function and processing speed.	Age, sex, educational level, place of data collection, smoking status, sleep and recreational physical activity.	
+Moreira et al. (2022) [26]	– Short‐ and long‐term memory;
+
+– Language;
+
+– Executive function.
+
+	CERAD test battery; – 10‐word list;
+
+– Semantic fluency test (flora) and phonemic fluency test (letter A);
+
+– Trail Making Test (Part B).
+
+	Greater sedentary time in occupational screen use was positively associated with performance on memory, language and executive function tests, with variations between men and women.	Age, sex, educational level, race or ethnicity, income, depression, body mass index, physical activity, smoking and alcohol consumption.	
+Olanrewaju et al. (2020) [27]	– Short‐ and long‐term memory;
+
+– Semantic verbal memory.
+
+	– 10‐word list;
+
+– Animal naming.
+
+	Greater time spent watching television was associated with poorer performance in verbal memory and fluency, particularly among adults aged 65 years or older who watched television for at least 3.5 h per day after 2 years.
+
+	Age, sex, social class, employment status, physical activity, loneliness, obesity, depression, disabilities and chronic diseases.	
+Palazuelos‐González et al. (2025) [28]	– Executive function
+
+	– Ruff figural fluency test (RFFT)
+
+	Time spent watching television was negatively associated with executive function; replacing this time with physical activities (sports, work and leisure) was associated with improved executive function.	Age, sex, educational level, occupation, depression, anxiety, chronic diseases, body mass index, smoking, alcohol consumption, diet and social contacts	
+Rosenberg et al. (2015) [29]	– Visual search and perceptual speed;
+
+– Executive function.
+
+	– Trail Making Test (Part A);
+
+– Trail Making Test (Part B).
+
+	Weak association: self‐reported SB aggregated across contexts was related to better performance on Trail Making Test Part A, whereas television viewing time showed no significant association.	Age, sex, educational level, marital status, fear of falling, pain, stress, depression, sleep, physical activity and chronic diseases.	
+Wingood et al. (2024) [30]	– Orientation;
+
+– Short‐ and long‐term memory;
+
+– Executive function.
+
+	– Spatial orientation (current day, month and year);
+
+– 10‐word list;
+
+– Clock drawing test.
+
+	Older adults who engage more frequently in cognitively active SB (computer use and hobbies) show a lower risk of impairment in orientation and memory, whereas passive SB, except for television viewing for more than 3 h per day in longitudinal analyses, do not provide cognitive protection.	Age, sociodemographic characteristics, self‐rated health, physical function and educational level.	
+Zhou et al. (2022) [31]	– Short‐term memory.
+
+	– 10‐word list.
+
+	Mentally passive SB (television viewing and napping) were associated with poorer cognition, particularly short‐term memory, whereas mentally active behaviours (hobbies and computer use) were associated with better cognitive performance.	Age, sex, race, educational level and marital status.	
+
+12 Risk of Bias
+
+The assessment of risk of bias in cross sectional studies (n = 11) showed variation between low, moderate and high risk (Appendix B). Approximately 45% (5 of 11) of the studies were classified as having low risk of bias [23, 26, 27, 28, 29], suggesting methodological consistency across different evaluated domains.
+
+Another 45% (5 of 11) presented moderate risk [19, 20, 25, 30, 31], mainly due to limitations related to the clarity of inclusion criteria, characterisation of the sample and context, validity and reliability of exposure measures and definition of the diagnostic criteria used. In contrast, the study by Maasakkers et al. [24] was classified as having high risk of bias due to relevant shortcomings across the domains.
+
+Overall, the domains most consistently well evaluated were those related to control of confounding factors D6, validity and reliability of outcomes D7 and adequacy of statistical analysis D8, in which most studies were classified as having low risk of bias. Conversely, the weakest points were concentrated in the domains of inclusion criteria D1, description of sample and context D2, validity and reliability of exposure D3 and objective criteria for the condition D4, where a higher frequency of moderate and high risk was observed. Minor inconsistencies were also noted in the domain of identification of confounding factors D5 (Appendix C).
+
+Taken together, the results indicate that although most studies present satisfactory methodological quality, relevant limitations persist, particularly, those related to clarity and precision in the measurement of different SB domains and in the assessment of cognitive conditions. These methodological weaknesses may compromise the robustness of effect estimates and influence the interpretation of the observed associations between SB and cognitive function. The assessment of risk of bias in cohort studies demonstrated that all were classified as having low risk of bias [21, 22, 23, 24, 27, 30] (Appendix D), indicating adequate methodological consistency across the main evaluated domains.
+
+Overall, the domains with the best performance were group comparability (D1), identification of and strategies to control confounding factors (D4 and D5) and adequacy of statistical analysis (D11), all of which were predominantly rated as having low risk of bias. In contrast, the most critical points were identified in the domains of validity and reliability of exposure measurement (D3), validity and reliability of outcome measurement (D7) and completeness of follow up (D9), which showed a higher proportion of moderate risk (Appendix E). Thus, although the reviewed cohort studies generally present satisfactory methodological quality, there remains a need for greater rigour in the measurement of exposures and outcomes, as well as clearer reporting of follow up procedures and associated losses.
+
+13 Discussion
+
+This study systematically analysed the impact of different contexts of SB, such as watching television, use of electronic devices, reading or playing games, on different cognitive domains in older adults. The findings of this review demonstrate that the impact of SB on cognitive function in older adults strongly depends on the type of activity performed during sedentary time.
+
+It was observed that mentally passive SB, such as watching television and napping, tends to be negatively associated with cognitive outcomes, particularly, in domains related to memory and executive function. In contrast, mentally active behaviours, including computer use, reading and other cognitively stimulating activities, showed positive associations with cognitive performance or with a smaller decline in performance over time.
+
+Time spent watching television is one of the most prevalent SB domains in the context of leisure, especially among older adults. The study by Bertuol et al. [32] showed that between 2006 and 2016 older adults in Brazil presented nearly twice the prevalence of this behaviour compared with adults, largely due to resistance to other technologies. Although television viewing has been negatively associated with several physical health determinants because of physiological factors [33], its relationship with brain functioning is complex due to multifactorial influences of biological, psychological and social nature [34].
+
+Consistent with the findings of the present review, Xu et al. [35] observed that time spent watching television was negatively associated with long‐term cognitive function, particularly, among individuals with central nervous system diseases such as dementia, stroke and Parkinson disease. Conversely, Cegolon and Jenkins [36] demonstrated that cognitively stimulating activities, such as computer use, games, reading and other mentally active tasks, were associated with preservation of cognitive performance, in line with the theoretical principle of use it or lose it, according to which continuous engagement in mental activities contributes to the maintenance and strengthening of cognitive functions.
+
+This association is multi‐faceted. From a neurophysiological perspective, excessive time spent on certain screens compromises grey matter volume, which is responsible for information processing [37, 38]. However, television screen time differs from computer use in terms of cognitive stimulation, as the former is less demanding of working memory, planning and problem solving, directly influencing cortical activation, synaptic stimulation and the release of neurotrophic factors that are essential for dendritic maintenance [39].
+
+Additionally, from psychological and social perspectives, mentally passive behaviours may lead to low motivation, depressive symptoms, social isolation and reduced community engagement [40, 41, 42]. Thus, cognition, as a central component of brain activity, both influences and is influenced by mental and social factors and is shaped according to the level of neurobiological stimulation that allows the preservation of cognitive subdomains [43].
+
+Nevertheless, cognitive abilities, although interacting in complex ways and functioning in an integrated and dynamic manner, also present domain‐specific functioning and perform distinct tasks [44]. For this reason, some outcomes in the studies included in this systematic review reveal distinct interactions with different SB domains, depending on the context in which they occur and the activity performed [21, 22, 30].
+
+Tasks that rely on executive function involve planning, decision making, cognitive flexibility and execution of daily activities [45]. Accordingly, this ability is related to physical activity, which, by engaging neurobiological and behavioural mechanisms inherent to bodily movement, positively impacts the brain system [46]. This relationship explains the inclusion of physical activity as a confounding factor in some studies.
+
+In contrast, language, memory and orientation require not only factors such as educational level, sex and age, which influence performance on many cognitive assessment tests, but also individual repertoire and participation in activities that stimulate these abilities at different levels [47]. This further supports the argument regarding the complexity of SB types and their multiple facets.
+
+Although this review focused on the context and type of SB, time spent in these activities is also relevant. Evidence suggests that longer durations of mentally passive behaviours, especially television viewing, are more consistently associated with poorer cognitive outcomes, while shorter or moderate engagement shows weaker associations [48, 49]. However, heterogeneity in time measurement and categorisation across studies prevented direct comparisons and dose–response analysis. Thus, findings reflect qualitative differences between SB domains rather than precise exposure thresholds.
+
+Regarding risk of bias, an initial individual assessment of each manuscript was conducted, followed by an integrated analysis of the domains most susceptible to methodological weaknesses. A large proportion of studies presented relevant limitations in the measurement of SB and in the definition of cognitive conditions, as well as insufficient transparency regarding inclusion and exclusion criteria. In longitudinal studies, gaps were also identified in the description and handling of follow up losses, which may compromise the internal validity of the estimates.
+
+The use of validated instruments with adequate psychometric properties reflects greater methodological rigour [50]. In order to minimise estimation errors related to self‐reported measures or cognitive tests, the instruments used need to be tested and compared with others to confirm their reliability and accuracy [51]. Likewise, studies must clearly report sample characteristics to avoid misinterpretations and potential distortions.
+
+In addition, this review revealed marked heterogeneity regarding the countries of origin of the studies. It is well recognized that daily behaviours and habitual practices vary substantially across different cultural contexts [52]. Thus, although all manuscripts included older adult populations, the ways in which individuals engage in SB and cognitively active behaviours reflect specific sociocultural characteristics, such as gender norms, educational levels and access to digital technologies, which directly influence the relationship between SB and cognitive performance [53]. These contextual factors should be carefully considered when interpreting and comparing the observed associations.
+
+In light of this scenario, the findings of this study have important scientific implications. They highlight the need for strategies aimed at reducing time spent in passive forms of SB, favouring their substitution with cognitively stimulating activities. Furthermore, they reveal gaps that create opportunities for the development of digital and leisure based interventions focused on active mental engagement. Finally, they underscore the urgency of studies with greater methodological robustness, particularly longitudinal and experimental designs, to elucidate causal relationships between SB and cognitive function.
+
+An important limitation of this review is that the search strategy focused on SB terms, which may have led to the exclusion of studies examining cognitively engaging leisure activities that are not explicitly framed in terms of sitting time. Consequently, the findings should be interpreted within the context of SB research rather than cognitively stimulating activities per se. Another limitation is that SB domains were predominantly assessed through self‐report, which may be affected by recall bias, particularly for habitual and prolonged activities, potentially influencing the observed associations.
+
+14 Conclusion
+
+The findings of this systematic review indicate that SB is consistently associated with cognitive function in older adults, but this relationship strongly depends on the type of activity performed during sedentary time. Time spent watching television was the most extensively investigated domain and showed a negative association with cognition in a large proportion of studies, particularly with memory and executive function, suggesting that mentally passive SB may contribute to the decline of certain cognitive functions during ageing.
+
+In contrast, sedentary activities considered mentally active, such as computer use, reading, card games and hobbies, were associated with better cognitive performance, indicating that cognitive engagement during sitting time may play a protective role in brain function. Despite the predominance of subjective methods for measuring SB, the consistency of findings across different countries and study designs reinforces the relevance of the context in which SB occurs, rather than focusing solely on total sedentary time. However, methodological heterogeneity and limitations in the validity and precision of exposure measures still warrant caution in the interpretation of the findings.
+
+Overall, the results support the hypothesis that not all SB is equally harmful to cognition. Engagement in cognitively stimulating activities, even while sitting, may mitigate some of the negative effects associated with prolonged sedentary time. Therefore, health promotion strategies aimed at healthy ageing should not only seek to reduce total exposure to SB but also encourage the replacement of passive SB with cognitively active activities.
+
+Funding
+
+The authors have nothing to report.
+
+Ethics Statement
+
+The authors have nothing to report.
+
+Conflicts of Interest
+
+The authors declare no conflicts of interest.
+
+Acknowledgements
+
+The authors would like to thank the researchers who contributed to the development of this study and to the Coordination for the Improvement of Higher Education Personnel—Brazil (CAPES)—Funding Code 001 and to the Research Support Foundation of the State of Minas Gerais (FAPEMIG). The Article Processing Charge for the publication of this research was funded by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior ‐ Brasil (CAPES) (ROR identifier: 00x0ma614).
+
+Data Availability Statement
+
+Data sharing not applicable to this article as no datasets were generated or analysed during the current study.
+
+Appendix A See Table A1
+
+TABLE A1 Search strategy for study selection.
+
+PubMed/Medline	
+#1	(‘Aged’[Mesh]) OR (senior) OR (old person) OR (older age) OR (older person) OR (older adult) OR (elderly) OR (elderly population)	
+#2	(‘Sedentary Behaviour’[Mesh]) OR (Sedentary Lifestyle) OR (sitting time) OR (sedentary time)	
+#3	(‘Cognition’[Mesh]) OR (performance cognitive) OR (cognitive function)	
+#4	#1 AND #2 AND #3	
+Scopus	
+TITLE‐ABS‐KEY((‘Older Adults’ OR ‘Aged’ OR ‘elderly’ OR ‘sênior’ OR ‘older age’ OR ‘old person’ OR ‘elderly population’ OR ‘older person’) AND (‘Sedentary Behaviour’ OR ‘Sitting time’ OR ‘sedentary time’ OR ‘Sedentary Lifestyle’) AND (‘Cogniton’ OR ‘Cognitive Function’ OR ‘Performance Cognitive’))	
+Web of Science	
+‘Older Adults’ OR ‘Aged’ OR ‘Elderly’ OR ‘Senior’ OR ‘Older Age’ OR ‘Old Person’ OR ‘Elderly Population’ OR ‘Older Person’ AND ‘Sedentary Behaviour’ OR ‘Sitting Time’ OR ‘Sedentary Time’ OR ‘Sedentary Lifestyle’ AND ‘Cognition’ OR ‘Cognitive Function’ OR ‘Cognitive Performance’	
+Abbreviation: tw, text word.
+
+Appendix B See Table B1
+
+TABLE B1 Risk of bias for cross‐sectional studies.
+
+	
+Abbreviations: D1: clear inclusion criteria; D2: description of sample and context; D3: validity and reliability of exposure; D4: objective criteria for the condition; D5: identification of confounding factors; D6: control of confounding factors; D7: validity and reliability of outcomes; D8: adequate statistical analysis.
+
+Low: Unclear: High:
+
+Appendix C See Table C1
+
+TABLE C1 Risk of bias by domain assessed in cross‐sectional studies.
+
+	
+
+Appendix D See Table D1
+
+TABLE D1 Risk of bias for cohort studies.
+
+	
+Abbreviations: D1: similarity of groups and recruitment from the same population; D2: uniform measurement of exposure for all groups; D3: validity and reliability of exposure measurement; D4: identification of confounding factors; D5: strategies to control confounding factors; D6: absence of the outcome at the start of the study or exposure; D7: validity and reliability of outcome measurement; D8: adequate follow‐up time for outcome occurrence; D9: completeness of follow‐up and description of losses; D10: strategies to address incomplete follow‐up; D11: adequate statistical analysis.
+
+Low: Unclear: High:
+
+Appendix E See Table E1
+
+TABLE E1 Risk of bias by domain assessed in cohort studies.
+
+	
+
+
+References
+
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+26 P. d. A. Moreira , S. M. A. de Matos , F. J. G. Pitanga , et al., “Association Between Sedentary Behavior and Cognitive Performance in Middle‐Aged and Elderly Adults: Cross‐Sectional Results From ELSA‐Brasil,” International Journal of Environmental Research and Public Health 19, no. 21 (2022): 14234.36361115 10.3390/ijerph192114234 PMC9654160
+27 O. Olanrewaju , A. Koyanagi , M. Tully , N. Veronese , and L. Smith , “Sedentary Behaviours and Cognitive Function Among Community Dwelling Adults Aged 50+ Years: Results From the Irish Longitudinal Study of Ageing,” Mental Health and Physical Activity 19 (2020): 100344.
+28 R. Palazuelos‐González , R. C. Oude Voshaar , S. la Bastide‐van Gemert , and N. Smidt , “Time Spent in Physical Activities, TV Watching and Sleep and Its Association With Executive Functioning in Middle Age and Older Adults: An Isotemporal Substitution Analysis,” Mental Health and Physical Activity 28 (2025): 100668.
+29 D. E. Rosenberg , J. Bellettiere , P. A. Gardiner , V. N. Villarreal , K. Crist , and J. Kerr , “Independent Associations Between Sedentary Behaviors and Mental, Cognitive, Physical, and Functional Health Among Older Adults in Retirement Communities,” Journals of Gerontology. Series A, Biological Sciences and Medical Sciences 71, no. 1 (2015): 78–83.26273024 10.1093/gerona/glv103 PMC4861254
+30 M. Wingood , N. M. Gell , D. E. Rosenberg , G. J. Stoddard , and E. D. Bouldin , “Associations of Cognitively Active Versus Passive Sedentary Behaviors and Cognition in Older Adults,” Journal of Physical Activity & Health 21, no. 9 (2024): 928–938.39084614 10.1123/jpah.2024-0003 PMC11545599
+31 W. Zhou , K. E. Webster , P. T. Veliz , and J. L. Larson , “Profiles of Sedentary Behaviors in the Oldest Old: Findings From the National Health and Aging Trends Study,” Aging Clinical and Experimental Research 34, no. 9 (2022): 2071–2079.35676552 10.1007/s40520-022-02157-1
+32 C. Bertuol , K. S. da Silva , A. M. Gerage , et al., “Tempo excessivo de televisão e fatores associados em adultos e idosos da região Sul do Brasil: mudanças após uma década,” Cadernos de Saúde Coletiva 33 (2025): e33010251.
+33 E. C. Lopes , L. M. Cândido , R. A. Rosa , et al., “Tempo de televisão, obesidade e doenças cardiovasculares em idosos brasileiros: Pesquisas Nacionais de Saúde 2013 e 2019,” Ciência & Saúde Coletiva 28 (2023): 3169–3181.37971001 10.1590/1413-812320232811.12692022
+34 E. A. Rodrigues , A. J. Djiberou Mahamadou , and S. Moreno , “The Impact of Lifestyle Factors on Trajectories of Cognitive Subtypes in the Older Adult Population,” Scientific Reports 15, no. 1 (2025): 31744.40877588 10.1038/s41598-025-91171-0 PMC12394718
+35 C. Xu , Z. Cao , Z. Lu , Y. Hou , Y. Wang , and X. Zhang , “Associations Between Recreational Screen Time and Brain Health in Middle‐Aged and Older Adults: A Large Prospective Cohort Study,” Journal of the American Medical Directors Association 25, no. 8 (2024): 104990.38642587 10.1016/j.jamda.2024.03.010
+36 A. Cegolon and A. Jenkins , “Older Adults, Cognitively Stimulating Activities and Change in Cognitive Function,” International Journal of Lifelong Education 41, no. 4–5 (2022): 405–419.
+37 R. J. Dougherty , T. D. Hoang , L. J. Launer , D. R. Jacobs , S. Sidney , and K. Yaffe , “Long‐Term Television Viewing Patterns and Gray Matter Brain Volume in Midlife,” Brain Imaging and Behavior 16, no. 2 (2022): 637–644.34487279 10.1007/s11682-021-00534-4 PMC8898315
+38 A. A. Mercadante and P. Tadi , “Neuroanatomy, Gray Matter,” in StatPearls (StatPearls Publishing, 2025), http://www.ncbi.nlm.nih.gov/books/NBK553239/.31990494
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diff --git a/corpus/psychology/text/38cc90a0861d301e.txt b/corpus/psychology/text/38cc90a0861d301e.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d61bbcb8eea20a5d67af419afd97b62509ca8e4c
--- /dev/null
+++ b/corpus/psychology/text/38cc90a0861d301e.txt
@@ -0,0 +1,3 @@
+Monocular stereopsis, pinholes, and the perils of classroom theorizing:  A response to McIntosh (2025).
+
+Monocular stereopsis is a compelling perceptual effect wherein viewing a picture of a 3-dimensional scene with one eye through an aperture generates a perceptual impression of depth similar to binocular stereopsis. Here I provide a critique of a recently published report on the topic in the journal i-Perception (McIntosh, 2025).  In the report, the author claims to adjudicate on explanations of the monocular stereopsis effect and the phenomenology of stereopsis more broadly construed.  The author suggests, based on an informal test comparing pinhole and aperture viewing of a picture during a fifteen-minute classroom lecture break, that the monocular-aperture effect is best explained by a 100-year-old description of the phenomenon. I show that McIntosh’s report reveals a lack of understanding of the modern empirical facts and theoretical concepts relevant to this scientific debate and neglects the rudimentary demands of conducting an interpretable perceptual test.
diff --git a/corpus/psychology/text/3e30cd389eb307ac.txt b/corpus/psychology/text/3e30cd389eb307ac.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e0d953ca88e16e4f38f0d56d5f9f293b4837272a
--- /dev/null
+++ b/corpus/psychology/text/3e30cd389eb307ac.txt
@@ -0,0 +1,77 @@
+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: PLoS One
+Journal ID: PLoS One
+NLM Journal ID: 101285081
+Journal ID: plos
+
+PLOS One
+
+EISSN: 1932-6203
+Publisher: PLOS
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC12654873
+PMID: 41296764
+DOI: 10.1371/journal.pone.0337819
+Article ID: PONE-D-25-61700
+Article version: 1
+Subjects: Correction
+
+Correction: Experiences, impacts and mental health functioning during a COVID-19 outbreak and lockdown: Data from a diverse New York City sample of college students
+
+López-Castro Teresa
+Brandt Laura
+Anthonipillai Nishanthi J.
+Espinosa Adriana
+Melara Robert
+Electronic publication date: 2025 Nov 26
+Publication date: 2025
+Volume: 20
+Issue: 11
+Electronic Location ID: e0337819
+Copyright: © 2025 López-Castro et al
+Copyright year: 2025
+Copyright holder: López-Castro et al
+License: This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Erratum for: Experiences, impacts and mental health functioning during a COVID-19 outbreak and lockdown: Data from a diverse New York City sample of college students 16 4 7 4 2021 e0249768 PLoS ONE 10.1371/journal.pone.0249768 PMC8026074 33826654
+Figure count: 0
+Table count: 1
+Page count: 3
+
+Ÿ==============================Ÿ
+In the Abstract, there are errors in the fourth sentence. The correct sentence is: Findings highlight significant impediments to multiple areas of students’ daily life during this period (i.e., home life, work life, social environment, and emotional and physical health) and a proportion of students endorsing clinically significant levels of depression (36.1%) and generalized anxiety (26.5%).
+
+In the Students’ mental health functioning during the COVID-19 pandemic subsection of the Results, there are errors in the third sentence of the first paragraph. The correct sentence is: Thirty-six percent of students exceeded the cut-off score for the PHQ, indicating severe symptoms of depression in the past 2 weeks, and 26.5% reported severe symptoms of anxiety in the same time period.
+
+In the Psychological functioning during lockdown subsection of the Discussion, there are errors in the first three sentences of the first paragraph. The correct sentences are: Our findings pertaining to the mental health during this prolonged confinement are concerning and support the body of research chronicling the psychological toll of pandemics [1]. Clinically significant levels of stress, anxiety, and depression were reported at rates similar to prior published data on COVID-19-affected populations, which have ranged from 15% to 48% for depression and 6 to 51% for anxiety [2]. The similarity of our study’s rates of depression (36.1%) and anxiety (26.5%) to those of prior COVID-19 work is important because the pandemic-related exposures and impacts reported by our sample appear to differ by an order of magnitude, most notably in infection and mortality exposure.
+
+In the Psychological functioning during lockdown subsection of the Discussion, a sentence was omitted. After the sixth sentence, the following sentence should be included: Nevertheless, that the depression and anxiety prevalence in this “hard hit” sample generally converges with other COVID-19 samples suggests a potential plateauing of the pandemic’s negative emotional impact.
+
+There are errors in Table 4. In the Mean score (SD) row, the values in the DASS-21 Stress column should be 11.84 (9.60), the values in the DASS-21 Anxiety column should be 7.90 (8.23), the values in the DASS-21 Depression column should be 12.41 (10.74), the values in the PHQ-9 column should be 9.42 (6.56), and the values in the GAD-7 column should be 7.03 (5.95.) In the Exceeded cut-off, N (%) row, the values in the PHQ-9 column should be 328 (36.1) and the values in the GAD-7 row should be 241 (26.5.) Please see the correct Table 4 here.
+
+There are errors in the S1 Table. In the 1. DASS-21 Stress row, the values in the M column should be 11.84 and the values in the SD column should be 9.60. In the 2. DASS-21 Anxiety row, the values in the M column should be 7.90 and the values in the SD column should be 8.23. In the 3. DASS-21 Depression row, the values in the M column should be 12.41 and the values in the SD column should be 10.74. In the 4. PHQ-9 row, the values in the M column should be 9.42 and the values in the SD column should be 6.56. In the 5. GAD-7 row, the values in the M column should be 7.03 and the values in the SD column should be 5.95. Please see the correct S1 Table here.
+
+10.1371/journal.pone.0337819.t004 Table 4 Mental health of the surveyed student sample (N = 909).
+
+	DASS-21 Stress	DASS-21 Anxiety	DASS-21
+
+Depression	PHQ-9	GAD-7	PC-PTSD-5	MPSS Total	
+Mean score (SD)	11.84 (9.60)	7.90 (8.23)	12.41 (10.74)	9.42 (6.56)	7.03 (5.95)	2.73 (1.42)	5.26 (1.32)	
+Exceeded cut-off, N (%)	–	–	–	328 (36.1)	241 (26.5)	43 (4.7)	554 (60.9)	
+DASS-21, Depression, Anxiety, and Stress Scale-21; PHQ-9, Patient Health Questionnaire-9; GAD-7, Generalized Anxiety Disorder-7; PC-PTSD-5, Primary Care-PTSD Screen for DSM-5; MPSS, Multidimensional Scale of Perceived Social Support.
+
+Supporting information
+
+S1 Table Means, standard deviations, and correlations with 95% confidence intervals of mental health measures.
+
+(DOCX)
+
+
+Reference
+
+1 López-Castro T , Brandt L , Anthonipillai NJ , Espinosa A , Melara R . Experiences, impacts and mental health functioning during a COVID-19 outbreak and lockdown: Data from a diverse New York City sample of college students. PLoS One. 2021;16(4):e0249768. doi: 10.1371/journal.pone.0249768 33826654 PMC8026074
diff --git a/corpus/psychology/text/3ece7b99e392b837.txt b/corpus/psychology/text/3ece7b99e392b837.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a04a1e3084c66c43a970b4f43f318c8b65504b0b
--- /dev/null
+++ b/corpus/psychology/text/3ece7b99e392b837.txt
@@ -0,0 +1,320 @@
+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Syst Rev
+Journal ID: Syst Rev
+NLM Journal ID: 101580575
+
+Systematic Reviews
+
+EISSN: 2046-4053
+Publisher: BMC
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC13041137
+PMID: 41761373
+DOI: 10.1186/s13643-026-03143-8
+Article ID: 3143
+Article version: 1
+Subjects: Protocol
+
+Comparative efficacy and acceptability of sleep interventions for children and adolescents with autism spectrum disorders: a protocol for a systematic review and network meta-analysis
+
+http://orcid.org/0000-0002-5358-5263 Sakata Masatsugu m.sakata@med.nagoya-cu.ac.jp
+1 2 3
+http://orcid.org/0000-0002-8717-0832 Ostinelli Edoardo G. 4 5 6
+http://orcid.org/0000-0002-5500-9964 Yamamoto Ryuichiro 7
+http://orcid.org/0000-0001-5757-971X Oi Hitomi 3 8
+http://orcid.org/0000-0001-6706-4912 Kikuchi Shino 2 9
+http://orcid.org/0000-0003-1125-3145 Toyomoto Rie 2 10
+http://orcid.org/0000-0002-2992-195X Nakajima Shun 3
+http://orcid.org/0000-0001-6910-3591 Ohashi Kei 1
+http://orcid.org/0000-0001-5696-9900 Nogimura Akane 1
+http://orcid.org/0009-0003-3951-2222 Yamada Rie 1
+http://orcid.org/0000-0001-7002-3695 McLay Laurie 11
+http://orcid.org/0000-0003-2159-3776 Furukawa Toshi A. 12
+http://orcid.org/0000-0003-3140-5038 Nagai Yukiyo 1
+http://orcid.org/0000-0002-5271-9346 Yamada Atsurou 1
+1 https://ror.org/04wn7wc95 grid.260433.0 0000 0001 0728 1069 Department of Neurodevelopmental Medicine, Nagoya City University Graduate School of Medicine, Nagoya, Japan
+2 https://ror.org/02kpeqv85 grid.258799.8 0000 0004 0372 2033 Department of Health Promotion and Behavioral Sciences, Kyoto University Graduate School of Medicine/School of Publich Health, Kyoto, Japan
+3 https://ror.org/02956yf07 grid.20515.33 0000 0001 2369 4728 International Institute for Integrative Sleep Medicine (WPI-IIIS), Tsukuba Institute for Advanced Research (TIAR), University of Tsukuba, Tsukuba, Japan
+4 https://ror.org/052gg0110 grid.4991.5 0000 0004 1936 8948 Department of Psychiatry, University of Oxford, Oxford, UK
+5 https://ror.org/052gg0110 grid.4991.5 0000 0004 1936 8948 Oxford Precision Psychiatry Lab, National Institute for Health Research Oxford Health Biomedical Research Centre, University of Oxford, Oxford, UK
+6 https://ror.org/04c8bjx39 grid.451190.8 0000 0004 0573 576X Oxford Health NHS Foundation Trust, Oxford, UK
+7 https://ror.org/03y8n3k44 grid.444357.5 0000 0004 0370 2606 College of Sociology, Department of Psychology and Humanities, Edogawa University, Nagareyama, Chiba Japan
+8 https://ror.org/029smmd76 grid.443635.3 0000 0004 0375 3497 Department of Psychological Sciences, University of Human Environments, Matsuyama, Japan
+9 https://ror.org/04wn7wc95 grid.260433.0 0000 0001 0728 1069 Core Laboratory, Center for Psycho-Oncology and Palliative Care, Nagoya City University Graduate School of Medical Sciences, Nagoya, Japan
+10 https://ror.org/03fvwxc59 grid.63906.3a 0000 0004 0377 2305 Department of Health Policy, National Center for Child Health and Development, Tokyo, Japan
+11 https://ror.org/03y7q9t39 grid.21006.35 0000 0001 2179 4063 Faculty of Health, Child Well-Being Research Institute, University of Canterbury, Christchurch, New Zealand
+12 https://ror.org/02kpeqv85 grid.258799.8 0000 0004 0372 2033 Kyoto University Office of Institutional Advancement and Communications, Kyoto, Japan
+Electronic publication date: 2026 Feb 27
+Publication date: 2026
+Volume: 15
+Electronic Location ID: 116
+Received 2024 Dec 18; Accepted 2026 Feb 22
+Copyright: © The Author(s) 2026
+Copyright year: 2026
+License: Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Keywords: Developmental disorders, Sleep disturbances, Melatonin, Orexin, Behavior therapy, Chronotherapy, Light therapy, Matless technology, Weighted blanket
+issue-copyright-statement: © BioMed Central Ltd., part of Springer Nature 2026
+
+Ÿ==============================Ÿ
+Background
+
+Children and adolescents with autism spectrum disorder (ASD) frequently experience sleep problems. Although various pharmacological, behavioral, and physical interventions have demonstrated efficacy in improving sleep among children with ASD, the relative effectiveness of these interventions remains unclear.
+
+Methods
+
+We will conduct a systematic literature search to identify randomized controlled trials that evaluate the efficacy of pharmacological (e.g., melatonin), psychological (e.g., cognitive behavioral therapy), and physical (e.g., bright light therapy) interventions for sleep problems in children with ASD. We will search PubMed, PsycINFO, Cochrane CENTRAL, major trial registries, and regulatory agency websites. We will assess the Cochrane Risk of Bias 2.0 (RoB 2.0) tool for primary outcome and the Risk Of Bias due to Missing Evidence in Network meta-analysis (ROB-MEN) tool for the bias due to missing network evidence. A network meta-analysis (NMA) will be performed to compare the included interventions. The primary outcome will be sleep onset latency, while secondary outcomes will include other sleep variables, all-cause dropouts, and sleep disturbances assessed using standardized measures. We will assess confidence in NMA(CINeMA).
+
+Discussion
+
+Our NMA aims to provide evidence-based insights into the effectiveness of sleep interventions for clinicians, children with ASD, and their caregivers. This information will help guide treatment decisions and improve the quality of life for children with ASD and their families.
+
+Systematic review registration
+
+PROSPERO CRD42024592795.
+
+Supplementary Information
+
+The online version contains supplementary material available at 10.1186/s13643-026-03143-8.
+
+Background
+
+Sleep disturbances represent one of the most commonly reported problems among children and adolescents (henceforth, children) with autism spectrum disorder (ASD), affecting between 37 to 93% of children [1]. Children and adolescents with ASD tend to experience higher rates of sleep problems such as bedtime resistance, prolonged sleep onset latency, short sleep duration, sleep-related anxiety, and daytime sleepiness compared to their non-autistic peers [2]. These sleep problems often persist into adulthood [3]. In addition, impaired sleep quality is associated with the severity of social dysfunction, sensory sensitivity, and internalizing and externalizing behavior problems in children with ASD [4]{Du, 2023, Neurometabolite levels in the brains of patients with autism spectrum disorders: A meta-analysis of proton magnetic resonance spectroscopy studies (N = 1501)}.
+
+Recent systematic reviews demonstrate the efficacy of melatonin [5] and behavioral interventions such as stimulus control, extinction, or reinforcement for sleep problems among children with ASD [6]. Emerging evidence also demonstrates the effectiveness of cognitive behavioral therapy (CBT) for these children [7]. Improvement in sleep following intervention has been shown to result in secondary improvement in stereotypic behavior, internalizing and externalizing behavior problems, and quality of life [8], underscoring the importance of effective sleep intervention.
+
+The American Academy of Neurology (AAN) developed a comprehensive practice guideline based on its systematic review, recommending the combination of melatonin and cognitive behavioral therapy (CBT) or melatonin alone as interventions for bedtime resistance, sleep onset latency, sleep continuity, and total sleep time (Williams Buckley et al., 2020). However, the comparative efficacy and acceptability of each intervention is unclear. The recommendations of the AAN were based on a series of pairwise meta-analyses of each intervention compared with control condition and, therefore, cannot inform the relative effects of each intervention approach. A recent network meta-analysis focusing on the general pediatric patient population showed that light therapy is effective for sleep onset latency (SOL), an evidence-based psychological intervention (EBPI) that includes CBT and parental intervention for wake-after-sleep onset (WASO), and EBPI plus light therapy for total sleep time (TST) compared to control condition [9]. Still, there are several challenges in applying these results to children with ASD. First, the comparative effectiveness of different sleep interventions for the ASD population remains unclear. Second, psychological and behavioral interventions have distinct therapeutic mechanisms and may have varying effects depending on the child's characteristics. As such, they should be separate into one category to inform clinical decision-making pragmatically. It is also inappropriate to classify the various control conditions used in these studies into one node because different control conditions, e.g. placebo, treatment as usual or waiting list, lead to different efficacy estimates [10]. Third, since 2020, there has been an exponential increase in clinical trials of sleep interventions for people with ASD, warranting analyses and syntheses that reflect recent data in the 2020 s [11, 12].
+
+To address these issues, we hereby plan a network meta-analysis (NMA) of sleep intervention for children and adolescents with ASD.
+
+Aim
+
+We will investigate the comparative efficacy and acceptability of pharmacological, psychological, behavioral, and physical interventions for disrupted sleep in children and adolescents with autism spectrum disorder (ASD).
+
+Methods
+
+The protocol follows the Preferred Reporting Items for Systematic Reviews and Meta-Analyses Protocols (PRISMA-P) [13] and extension statement for network meta-analysis [14] where relevant for protocols. We prospectively registered this protocol to PROSPERO (CRD42024592795).
+
+Data sources
+
+Criteria for considering studies for this review
+
+Study design
+
+We will incluonde all randomized ctrolled trials of sleep-focused interventions compared with other types of intervention or control conditions for children and adolescents with ASD.
+
+Participants
+
+Participants will be children and adolescents under 24 years of age, of any gender, who meet diagnostic criteria for ASD or meet the thresholds of clinically relevant ASD traits using a standardized screening scale. Studies allowing participants with comorbid conditions (e.g., epilepsy, intellectual disabilities, attention deficit hyperactivity disorders, major depressive disorders, anxiety disorders, and obsessive–compulsive disorders) will be included. Still, we will test the influence of their inclusion in sensitivity analyses.
+
+Interventions and controls
+
+We will select interventions from the practice guidelines of the American Academy of Neurology [15] and a recent network meta-analysis on sleep intervention for general pediatric populations [9]. All pharmacological, psychological, behavioral, and physical interventions will be considered eligible. Pharmacological interventions (i.e., medications) will include oral melatonin, orexin receptor antagonists, antipsychotics, and other hypnotic medications used to treat sleep disturbances. Psychological and behavioral interventions refer to those that are underpinned by psychological theories and/or principles of applied behavior analysis and will include cognitive behavioral therapy for sleep problems, parent education, parental training, and chronotherapy. Physical interventions involve modification to the physical environment to primarily result in physiological (as opposed to behavioral) changes, including bright light therapy, Sound-to-Sleep mattress technology, and weighted blankets. We will treat any combined intervention (e.g., CBT + melatonin) as a distinct node in the network meta-analysis if it is evaluated as a separate arm in the original study. This applies to both within-category (e.g., CBT + parent education) and cross-category (e.g., behavioral + pharmacological) combinations.
+
+The control conditions will include a pill placebo, attention/psychological placebo, no treatment, treatment as usual, and waiting list. When the placebo, no treatment or treatment as usual are used while waiting to receive intervention, such arms will be classified as the waiting list. We will include any psychological and behavioral intervention format, including self-help learning with or without guidance, internet or human-administered programs, face-to-face, hybrid or remote, and group or individual. Table 1 shows a list of included interventions and control conditions. Table 1 Definition of interventions and control conditions
+
+Names	Description	
+Pharmacological intervention	
+Oral melatonin	A hormone naturally produced by the pineal gland that is often used as a supplement to regulate circadian rhythms and manage sleep disorders. We will include melatonin receptor agonists such as ramelteon	
+Orexin receptor antagonist	A class of drugs that function by inhibiting the activity of orexins, neurotransmitters that play a key role in maintaining wakefulness	
+Other hypnotic medication	Other medications that purpose to improve sleep such as benzodiazepines and trazodone	
+Psychological and behavioral intervention	
+Cognitive behavioral therapy	Structured programs help individuals identify and replace thoughts and behaviors that maintain sleep problems with habits that promote sound sleep, including sleep restriction, stimulus control, cognitive restructuring, sleep/wake rescheduling, and mindfulness. These programs may include written, digital, or in-person information delivered individually or in groups	
+Parent education and training	Provide parent psychoeducation about child sleep, including sleep hygiene, sleep scheduling, and contingency management. This may include written, digital, or in-person information delivered in individual or group format	
+Chronotherapy	Chronobiological intervention gradually shifts sleep and wake times to adjust the sleep schedule to align with desired or socially acceptable times	
+Physical or environmental interventions	
+Bright light therapy	Chronobiological intervention that adjusts sleep time by stimulating cells in the retina, which connects to the hypothalamus, the brain region controlling human circadian rhythms	
+Adapted mattress technology	Mattress technology uses embedded acoustic resonators to transmit gentle sound waves, aiming to improve sleep quality	
+Weighted blanket	Blankets, often filled with materials like plastic pellets or glass beads, to apply gentle, deep-pressure stimulation across the body to promote relaxation and sleep onset	
+Control conditions	
+Pill placebo	Often, sugar pills or treatments without active ingredients can elicit therapeutic effects through the power of belief and expectation and are used in clinical trials	
+Psychological/attention placebo	Control conditions that could generate expectation intervention effects for trial participants, such as health education, sleep hygiene, or relaxation training	
+Usual care	Typical continuous care or treatment in the context of each healthcare system	
+Waiting list	Conditions that provide delayed intervention after outcome collection	
+
+Search methods for identification of studies
+
+We will conduct a comprehensive literature search in PubMed, PsycINFO, Cochrane CENTRAL, major trial registries, and regulatory agency websites with the American Academy of Neurology's revised search strings (Table 2) until the most current date. A medical librarian from Nagoya City University Kawasumi Library, with experience in supporting systematic reviews, peer-reviewed our search strategy in accordance with the PRESS (Peer Review of Electronic Search Strategies) guideline [16] (see Supplementary information). Table 2 Search strings for PubMed, Cochrane CENTRAL, and PsycINFO
+
+PubMed	(((autis*[tiab] OR asperger*[tiab] OR "pervasive development* disorder*"[tiab] OR "Child Development Disorders, Pervasive"[Mesh]) AND ("Sleep Wake Disorders"[Mesh] OR sleep*[tiab] OR circadian*[tiab])) AND (randomized controlled trial[pt] OR controlled clinical trial[pt] OR randomized[tiab] OR placebo[tiab] OR "drug therapy"[sh] OR randomly[tiab] OR trial[tiab] OR groups[tiab])) AND (child*[tiab] OR adolescent*[tiab] OR youth*[tiab] OR "young adult*"[tiab] OR "Child"[Mesh] OR "Adolescent"[Mesh] OR "Young Adult"[Mesh])	
+Cochrane CENTRAL	((autis* OR asperger* OR ("pervasive developmental disorders" OR "pervasive developmental disorder" OR "pervasive development disorders" OR "pervasive development disorder")):ti,ab,kw OR [mh "Child Development Disorders, Pervasive"]) AND ([mh "Sleep Wake Disorders"] OR (sleep* OR circadian*):ti,ab,kw) AND ([mh child] OR [mh Adolescent] OR [mh "Young Adult"] OR (child* OR adolescent* OR youth* OR (young NEXT adult*)):ti,ab,kw))	
+PsycINFO	((autis* OR asperger* OR "Pervasive Developmental Disorder" OR "Autism Spectrum Disorder") AND (sleep* OR circadian* OR insomnia) AND (randomized controlled trial OR controlled clinical trial OR randomized OR placebo OR "drug therapy" OR trial OR groups) AND (child* OR adolescent* OR youth* OR "young adult*"))	
+
+We will use a combination of index and free terms relating to sleep interventions and autism spectrum disorder with filters for randomized clinical trials. We will impose no date, language, or publication status restriction and include dissertations, conference abstracts, and trial registries. We will check the reference lists of identified studies and review articles for additional potentially eligible records.
+
+Data collection and analysis
+
+Selection of studies
+
+Two reviewers will independently screen titles and abstracts from the potential studies, classify them as “retrieve” vs. “not retrieve,” and retrieve the full-text publications for the studies identified as potentially relevant. Two reviewers will screen the full text independently and select eligible studies that meet the inclusion criteria. We will resolve disagreements through discussion between pairs or consult with a third reviewer if necessary. We will calculate the kappa for inter-rater reliability of full-text screening. We will identify duplicate publications. We will record details in a PRISMA flow diagram. We will utilize Covidence to facilitate both the title and abstract screening as well as the full-text screening processes.
+
+Data items
+
+Two reviewers will independently extract the data from each study's eligible arms in the Covidence. Any disagreement will be resolved through discussion or with a third person if necessary. We will abstract the following information.Characteristics of the studies
+
+We will extract trial registration ID, number of arms, treatment or control arm, number of each arm, year of publication, country, study site (single or multi-center), study design (individual or cluster), population characteristics (mean age, number of female participants), the definition of ASD, intervention type(pharmacological, psychological and behavioral, or physical), the definition of inclusion, intervention (content, delivery format, duration), duration of follow-up.
+
+Risk of bias
+
+Two reviewers will assess the risk of bias for the primary outcome in each domain of the Cochrane Risk of Bias 2.0 tool (RoB2) [17]. The RoB2 tool is specifically designed for randomized controlled trials and evaluates five key domains of potential bias: (1) bias arising from the randomization process, (2) bias due to deviations from intended interventions, (3) bias due to missing outcome data, (4) bias in the measurement of the outcome, and (5) bias in the selection of the reported result. Each domain will be assessed using signaling questions that guide the reviewers in categorizing the risk of bias as “low risk,” “some concerns,” or “high risk.” These domain-specific judgments will then be used to determine the overall risk of bias for each study.
+
+If disagreements arise between the two reviewers during the assessment process, a structured approach will be taken to resolve them. The reviewers will discuss the points of contention, referencing the RoB2 guidance document and study-specific information to reach a consensus. In cases where consensus cannot be achieved, a third reviewer with expertise in systematic reviews and bias assessment will be consulted to make a final determination.
+
+To ensure the reliability of the assessments, inter-rater agreement will be calculated using Cohen’s kappa statistic. This statistical measure will provide an objective evaluation of the consistency between the reviewers’ judgments and highlight any potential areas where further refinement of the assessment process might be required.
+
+In addition to assessing the risk of bias at the study level, we will evaluate bias at the network level using the Risk of Bias due to Missing Evidence in Network Meta-Analysis (ROB-MEN) tool [18]. The ROB-MEN tool addresses the risk of bias introduced by missing studies or network connections in the meta-analysis. It evaluates whether the evidence available in the network is sufficiently robust and representative to support reliable conclusions. By combining RoB2 assessments with ROB-MEN evaluations, we aim to ensure a comprehensive and transparent appraisal of bias that enhances the credibility and robustness of our findings.
+
+Data to calculate effect sizes
+
+We will calculate the between-group standardized mean difference (SMD) by dividing the differences in the change score from baseline to post-intervention of the continuous outcomes by the observed SD of the endpoint scores (preferred) or by dividing the differences in the endpoint scores by the observed SD of the endpoint scores. We will calculate the odds ratio (OR) for all-cause dropouts from the study.
+
+Primary outcome and secondary outcomes
+
+The primary outcome is sleep onset latency (SOL) measured by sleep diary at short-term (post-intervention) periods. There are various possible indicators for sleep problems in ASD. However, we consider difficulty falling asleep to be an indicator that covers a wide range of problems, including insomnia, sleep resistance, and delayed sleep phase. We prioritize patients' self-report SOL and other reports if patients' self-reports are not available.
+
+Secondary outcomes include acceptability, defined as all-cause dropouts from the study, wake after sleep onset (WASO), total sleep time (TST), waking time (WT), and other sleep disturbances assessed by standardized measures at a short-term period. We define sleep disturbance widely, including insomnia, circadian sleep phase problems, and sleep resistance or phobias. Sleep disturbances should be evaluated using validated scales such as the Sleep Disturbance Scale for Children (SDSC) [19], the Children's Sleep Habits Questionnaire (CSHQ [20]), the Children’s Report of Sleep Pattern-Sleepiness Scale (CRSPSS [21]) and the Insomnia Severity Index (ISI) [22].
+
+We investigate the effects of intervention for all sleep variables(SOL, WASO, TST, and WT) at the long-term periods(up to six-month follow-up). To maintain interpretability and avoid bias due to time-point heterogeneity, short-term and long-term outcomes will be analyzed separately and not pooled in the same analysis.
+
+We will calculate SMD as reported by the original authors, who followed the intention-to-treat principle as closely as possible. We will calculate the OR by assuming all non-reported cases as dropouts.
+
+Statistical analyses
+
+We will use R (latest version, R Foundation, Vienna, Austria) (R Core Team, 2020) package “NMA” [23], which implements frequentist contrast-based network meta-analysis methods, for primary analyses. The package is publicly available at https://cran.r-project.org/web/packages/NMA/.
+
+We assume a random-effect model considering clinical and methodological heterogeneities in intervention effects among studies. We will create a network diagram for each outcome and examine the network's transitivity, inconsistency, and heterogeneity.
+
+We will examine transitivity in the network by comparing the distribution of important potential effect modifiers across the comparisons, including gender, age, baseline severity of autistic symptoms, and psychiatric and physical comorbidities. We will examine heterogeneities by comparing common τ2 of a network meta-analysis against their empirical distributions [24, 25]. In the case of substantive heterogeneity, we will explore their sources through the pre-planned subgroup analyses. We will investigate inconsistency in the network using the local test of inconsistency (the side-splitting test (König et al., 2013)) and the global test of inconsistency (the design-by-treatment inconsistency model [26].
+
+Certainty of evidence
+
+We will assess the certainty of evidence in network estimates of the primary outcome using Confidence in Network Meta-Analysis(CINeMA [27]). CINeMA evaluates six domains of confidence in network meta-analysis: within-study bias, reporting bias, indirectness, imprecision, and heterogeneity. We will use the developers’ web application to assess CINeMA [28].
+
+Publication bias
+
+We will assess small study-effect bias by visually inspecting asymmetry in the contour-enhanced funnel plot (all active interventions against the controls, including the treatment as usual and the waiting list) and performing Peters’ test [29].
+
+Subgroup analyses
+
+We will conduct subgroup analyses and meta-regressions to examine the impact of age on the outcomes, as developmental differences between younger children, adolescents, and young adults with autism spectrum disorder (ASD) may influence treatment response. Participants will be categorized into predefined age groups (e.g., children under 10 years, adolescents aged 10–17 years, and young adults aged 18–24 years), and the results will be compared to assess age-related effect modifications.
+
+To ensure credibility, we will apply the ICEMAN tool to evaluate the plausibility, consistency, independence, and robustness of the observed subgroup effects [30]. We will verify that findings are supported by prior evidence, consistent across studies, free from confounding by other modifiers, and adequately powered for analysis. Results will be presented as pooled effect estimates with confidence intervals, with meta-regressions assessing age as a continuous variable for deeper insights. Findings will be reported in line with PRISMA and ICEMAN guidelines to ensure transparency and reliability, aiding in clinically meaningful conclusions.
+
+Sensitivity analyses
+
+We will conduct sensitivity analyses by excluding studies with a high risk of bias (RoB2), studies without a clinical diagnosis of ASD, studies with more than 50% of participants having comorbidity, studies not targeted sleep disorders other than insomnia (e.g. circadian rhythm sleep–wake disorders).
+
+We will compare results from the full dataset and the restricted dataset using forest plots to assess the impact of study quality on network estimates.
+
+Patient and public involvement
+
+There was no patient or public involvement in preparing this study plan.
+
+Discussion
+
+Our systematic review and NMA will contribute to the existing body of evidence by synthesizing data on sleep interventions' comparative efficacy and acceptability for ASD children. This work addresses critical gaps in understanding which interventions yield the most significant improvements in sleep outcomes, an area of substantial importance given the high prevalence of sleep disturbances in this population and their impact on overall functioning and quality of life.
+
+By leveraging the power of network meta-analysis, we can integrate direct and indirect evidence to provide a comprehensive overview of the available interventions. The CINeMA framework allows us to systematically evaluate the evidence's certainty, considering domains such as within-study bias, reporting bias, and transitivity. This rigorous approach ensures that our findings are methodologically sound, highly transparent, and interpretable for stakeholders.
+
+Our NMA will empower patients, clinicians, caregivers, and policymakers with robust, evidence-based insights to guide intervention choices tailored to the unique needs of individuals with ASD. By identifying interventions with the highest certainty of evidence and most significant clinical relevance, we aim to improve both short- and long-term outcomes, addressing a critical unmet need in the care of this vulnerable population.
+
+Despite the strengths of this protocol, several limitations should be acknowledged. First, clinical and methodological heterogeneity across included studies may affect the consistency and generalizability of network estimates. Second, the risk of selective or incomplete outcome reporting in original trials may introduce bias into our synthesis. Third, this protocol was developed without direct involvement of patients, caregivers, or other stakeholders, which may limit the relevance of certain outcomes or interpretations. We will address these concerns through sensitivity analyses and transparent reporting practices.
+
+Supplementary Information
+
+Supplementary Material 1: PRISMA-P 2015 Checklist.
+
+Supplementary Material 2: Appendix 1. PRESS Guideline — Search Submission& Peer Review Assessment.
+
+Acknowledgements
+
+We thank Ms. Minako Tahara, medical librarian at Nagoya City University Kawasumi Library, for her expert review and valuable advice on the development of the electronic search strategies.
+
+Authors’ contribution
+
+Conception or design of the work: MS, EGO, RyY, HO, SN, LM, TAF. Drafting the work: MS. Revising it critically for important intellectual content: SK, RiT, KO, AN, RN, YN, AY.
+
+Funding
+
+Not applicable.
+
+Data Availability
+
+Not applicable.
+
+Declarations
+
+Competing interests
+
+MS, AN, RiY, KO, YN, and AY MS are employed in the Department of Neurodevelopmental Medicine, Nagoya City University Graduate School of Medicine, which is an endowment department supported by the City of Nagoya. MS has received a personal fee from SONY outside the submitted work. EGO is supported by NIHR Applied Research Collaboration Oxford and Thames Valley at Oxford Health National Health Service Foundation Trust, by the NIHR Oxford Cognitive Health Clinical Research Facility, by the NIHR Oxford Health Biomedical Research Centre (BRC-1215–20005), by the Brasenose College Senior Hulme Scholarship, and has also received research and consultancy fees from Angelini Pharma. The Sleep Research Institute of Edogawa University, to which RyY belongs, is collaborating with PARAMOUNT BED CO., LTD. and receiving research funding. SN has received research funding from Nomura Real Estate, S'UIMIN Inc., and Mitsubishi Electric Corporation outside the submitted work. TAF reports personal fees from Daiichi Sankyo, DT Axis, Micron, Shionogi, SONY and UpToDate, and a grant from DT Axis and Shionogi, outside the submitted work; In addition, TAF has a patent 7448125 and a pending patent 2022–082495, and has licensed intellectual properties for Kokoro-app to Mitsubishi-Tanabe. AY has received speaker’s fees from Takeda Pharmaceutical Co., Ltd.; lecture fees from the Mental Care Association Japan and Asamidori-no-Kai, a social welfare corporation; manuscript fees from Igaku-Shoin Co., Ltd., Arcmedium Co., Ltd., and Chugai Igaku-Sha Co., Ltd.; and advisory fees and compensation as an expert member from Snom Co., Ltd.
+
+Publisher’s Note
+
+Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
+
+
+References
+
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+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Biomimetics (Basel)
+Journal ID: Biomimetics (Basel)
+NLM Journal ID: 101719189
+Journal ID: biomimetics
+
+Biomimetics
+
+EISSN: 2313-7673
+Publisher: Multidisciplinary Digital Publishing Institute (MDPI)
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC13024012
+PMID: 41892122
+DOI: 10.3390/biomimetics11030199
+Article ID: biomimetics-11-00199
+Article version: 1
+Subjects: Article
+
+Bio-Inspired Blade Cascades: Numerical Predictions Versus Experimental Measurements
+
+https://orcid.org/0000-0003-0460-7558 Totu Andrei-George 1 2 *
+Crunțeanu Daniel-Eugeniu Conceptualization Methodology Validation Formal analysis Investigation Writing – review & editing Supervision 1
+https://orcid.org/0000-0003-2506-8637 Isvoranu Dragoș Conceptualization Methodology Validation Investigation Data curation Writing – original draft Writing – review & editing Supervision 1 *
+Alexeev Alexander Academic Editor
+Meng Xue Guang Academic Editor
+1 “Elie Carafoli” Department of Aerospace Science, Polizu Campus, National University of Science and Technology POLITEHNICA Bucharest, Splaiul Independenței 313, 060042 Bucharest, Romania; daniel.crunteanu@upb.ro
+2 Gas Turbines COMOTI, National Research and Development Institute, 220D Iuliu Maniu, 061126 Bucharest, Romania
+* Correspondence: andrei_george.totu@upb.ro (A.-G.T.); ddisvoranu@gmail.com (D.I.)
+Electronic publication date: 2026 Mar 9
+Publication date: 2026 Mar
+Volume: 11
+Issue: 3
+Electronic Location ID: 199
+Received 2026 Jan 29; Revised 2026 Feb 25; Accepted 2026 Mar 6
+Copyright: © 2026 by the authors.
+Copyright year: 2026
+License: Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Keywords: bio-inspired, serrations, noise, blade cascade, spectra, SPL (sound pressure level)
+
+Funding: This research received no external funding.
+
+Ÿ==============================Ÿ
+This work presents a numerical–experimental validation of aeroacoustic predictions for bio-inspired leading edge serrated blade cascades. Transient simulations were carried out on a four-blade cascade using several turbulence modeling strategies commonly applied in broadband noise analysis—Spalart–Allmaras (SA), k−ω SST, k−ε, Scale-Adaptive Simulation (SAS), and Large Eddy Simulation (LES)—for assessing their capability to reproduce measured spectra. Multiple timestep resolutions were tested to ensure temporal accuracy. The comparison indicates that below 900 Hz, interaction noise is difficult to evaluate for such applications, whereas in the range from 0.9 to 5 kHz the turbulent jet–blade interaction is clearly captured. In the low-frequency regime (<1 kHz), the SA, SAS, and k−ω SST models exhibit similar behavior, while at higher frequencies SAS provides the closest agreement with experimental results, albeit with a slight tendency to overestimate at the upper end of the spectrum. LES demonstrates a satisfactory performance in reproducing the baseline response. The validation of numerical simulations with experimental results has been achieved, and a complex analysis using pressure measurements on the blade surface for a four-blade cascade configuration shows that turbulent formations lose their coherence quite significantly across several frequency bands. Overall, the results confirm that numerical simulations can reproduce the dominant experimental trends, while emphasizing the model-dependent trade-offs in predicting the acoustic benefits of bio-inspired leading edge serrations.
+
+1. Introduction
+
+Noise emissions from turbomachinery and compact aerodynamic devices remain a critical barrier to environmental compliance and societal acceptance. Stricter community noise limits and increasingly ambitious sustainability targets push designers toward solutions that reduce both tonal and broadband components [1,2] without compromising aerodynamic efficiency, structural integrity, or manufacturability [3,4,5]. Within this context, cascades of blades operating under turbulent inflow—typical of rotor–stator interactions, fans, compressors, or mixer–ejector configurations—are recurrent sources of broadband noise driven by unsteady loading and edge–turbulence interactions [5,6,7,8,9,10].
+
+Conventional noise mitigation strategies span geometric and materials-based treatments, such as sweep and lean, skew, trailing edge thickness minimization, porous or compliant surfaces, and acoustic liners, as well as active flow control approaches based on periodic blowing or plasma actuators [8,11,12,13,14,15]. While effective in targeted regimes, these solutions often come with trade-offs, including added weight and complexity, efficiency penalties, narrowband effectiveness, or sensitivity to off-design operation. As a result, attention has shifted toward bio-inspired concepts that rely on flow physics mechanisms observed in nature [4,13,16,17,18,19] and aim for broadband efficacy with minimal actuation or maintenance overhead.
+
+Several bio-inspired motifs have contributed to aerodynamic and aeroacoustic design. Owl-inspired trailing edge serrations [20,21] disrupt spanwise coherence and reduce scattering efficiency at the trailing edge. Humpback whale leading edge tubercles [22,23,24] modulate stall progression and lift distribution. Shark skin riblets [25,26,27] reduce drag through streamwise alignment and near-wall vortex management. Figure 1 shows adaptations from nature that can be considered as a starting point for the design of quieter blades/stages. Building on these ideas, leading edge serrations have emerged as a promising option for mitigating inflow–edge interaction noise. In silent flight, owls rely on a multi-element edge treatment system: high amplitude, small pitch, comb-like structures near the leading edge, together with downstream micro-structures, reduce coherent scattering by promoting spanwise phase variation and broadband decorrelation of surface pressure fluctuations. From an engineering standpoint, leading edge serrations can be interpreted as a “manufacturable abstraction” of this strategy, aiming to reduce the spanwise coherence of unsteady loading before it is converted into noise. While the serration shape used in many studies (including the present one) may appear conventional, the biomimetic aspect is primarily functional rather than geometric. In practice, the spanwise-varying phase decorrelates the impingement of turbulent eddies, redistributes the relevant wavenumber content, and weakens the coherent unsteady forces responsible for sound generation. In cascades, where a turbulent jet/wake or any sort of incoming turbulence interacts with the blade row, this decorrelation is particularly valuable because it can limit the constructive build-up of unsteady loading across adjacent passages.
+
+The advantages of leading edge serrations include their broadband noise potential attenuation, purely passive operation, and compatibility with existing cascade architectures. Nevertheless, limitations must be acknowledged. Aerodynamic penalties may arise from increased wetted area and local curvature, which affect loss coefficients and intended flow deflection [31]. Sensitivity to Reynolds number and inflow properties, such as turbulence intensity and integral length scale, can shift the effective frequency band [32,33]. Structural and manufacturing complexity is expected to increase with serration amplitude and wavelength, while unintended spectral features may emerge when serration spacing interacts with coherent structures in the inflow. Successful application therefore requires a careful balance between acoustic benefit and aerodynamic cost. From a biomimetics perspective, this balance is not merely a design compromise but a functional translation constraint: the geometry must remain manufacturable and aerodynamically acceptable while still enforcing the measurable spanwise decorrelation of leading edge pressure fluctuations.
+
+The transition from a straight-edged blade to a serrated leading edge is typically parameterized by serration amplitude (relative to chord), wavelength (relative to chord), and (local) blade skew, together with operational parameters such as Reynolds number, Mach number, incidence, turbulence intensity, and the ratio between incident turbulence length scale and serration wavelength. Prior studies suggest that the strongest decoherence benefits occur when incoming turbulence scales are commensurate with the serration wavelength, while far-field spectral trends tend to scale with Strouhal number [34,35]. These considerations provide motivation for systematic parametric exploration at a reduced scale before committing to full-scale implementation.
+
+Performance assessment methods can be grouped into analytical models [8,25,36,37,38], numerical simulations [8,19,20,21,22,23,29,32,35,39,40], and experimental techniques [7,24,27,31,33,36]. Analytical and semi-empirical formulations for leading edge noise predict far-field spectra from wall pressure or inflow statistics and capture first-order parametric trends, while their serration-extended variants introduce spanwise phase modulation to represent decorrelation. These methods are computationally inexpensive but depend strongly on modeling assumptions. Computational approaches based on steady RANS provide reliable low-cost aerodynamics but lack fidelity for broadband spectra [14,19,29,41]. Unsteady approaches, such as URANS, SAS, DES, and LES, increasingly resolve the unsteady flow content responsible for noise radiation, with far-field prediction obtained through acoustic analogies such as Ffowcs Williams–Hawkings (FW-H). Accuracy depends on turbulence modeling, grid resolution near edges, numerical dissipation, and temporal resolution. On the experimental side, cascade wind-tunnel campaigns remain the benchmark for validation, combining steady and time-resolved pressure measurements, wake development, and far-field microphone data to quantify both aerodynamic performance and aeroacoustics output. In this context, reduced-scale testing represents a powerful and time-efficient path to evaluating serrated concepts. Results at laboratory scale can be regarded as satisfactory, and thus transferable to higher technology readiness levels, when they demonstrate consistent broadband noise reduction without unacceptable aerodynamic penalties and when they prove to be robust to variations in turbulence intensity, length scale, incidence, and Reynolds number, without introducing new adverse spectral features. When these conditions are met, small-scale findings can be scaled to full-size applications through similarity-based methods/algorithms, supported by complementary simulations or tests.
+
+The present study addresses the numerical–experimental validation of bio-inspired leading edge serrated cascades. Reduced-scale experiments provide controlled conditions and a high spatial resolution, while a range of turbulence modeling strategies—Spalart–Allmaras, k−ω SST, k−ε, SAS, and LES (whose formulations are very well covered in [41,42,43])—are evaluated in transient simulations with varying timestep resolutions. The focus is on their capability to reproduce measured spectra and to capture the dominant mechanisms of jet–blade interaction noise. Comparisons with experiments indicate that interaction noise is negligible at low frequency and clearly captured at higher frequencies (over 2 kHz). While Spalart–Allmaras and k−ω SST reproduce the low-frequency regime, SAS achieves the closest overall agreement in the mid-to-high frequency range, albeit with slight overestimation, and LES satisfactorily reproduces the baseline response at a higher computational cost. These findings highlight model-dependent trade-offs, clarify temporal resolution requirements, and confirm the relevance of numerical simulations as predictive tools for the aeroacoustic benefits of bio-inspired leading edge serrations. Beyond far-field SPL reduction, serrations are expected to modify the spanwise pressure distribution (on the leading edge). To quantify this effect, spanwise coherence and the associated coherence length are introduced. This choice is directly aligned with the biomimetic design objective, since leading edge serrations are intended to reduce spanwise coherence as the primary pathway to broadband noise suppression. The present work is intended as a preliminary validation step for the CFD workflow, setting a certain level of confidence at a reduced scale before transferring the methodology to a more representative, near-full-scale compressor/turbine configuration.
+
+2. Materials and Methods
+
+2.1. Experimental Approach
+
+Experiments were conducted in an anechoic facility, designed to satisfy ISO 3745 [44] free-field conditions. The chamber has a volume of approximately 1200 m3 (15 m × 10 m × 8 m) with wall absorption ≈99% in the 150 Hz–20 kHz band [45]; the compressor was located outside the chamber and connected via a 20 m flexible duct to the in-room test section, arranged diagonally to minimize curvature of the supply line. Free-field conditions were ensured by placing the measurement devices sufficiently far from reflecting boundaries and by operating above the room’s effective cut-on frequency; the residual influence of reflections was minimized by the high absorption treatment and the diagonal arrangement of the rig. The measurement procedure follows the intent of ISO 3745 in providing an essentially free-field environment over a reflecting plane within the frequency range used for the present comparisons. Two Class 1 sound level meters (Acoem Fusion, Limonest, France) were used, positioned on a 1 m radius circular arc as in Figure 2. The quasi-axial microphone was placed at approximately 10° relative to the jet axis to remain in the acoustic far field while avoiding direct exposure to the high-velocity jet core and associated pressure “contamination”. The 90° microphone complements this view by capturing lateral radiation, which is typically more sensitive to loading noise directivity. Raw signals were sampled at 50 kHz. The dataset comprises two operating conditions: self-noise, with flow generated only by the convergent nozzle, and interaction noise, in which a 3D-printed rectangular turbulence grid was inserted in the nozzle to intensify inflow fluctuations and promote jet–blade interaction. The 3D-printed turbulence grid had a nominal cell of 20 × 20 mm and 4.5 mm thickness and was placed ~300 mm upstream of the leading edge. The 3D-printed grid acts as a passive turbulence generator that increases turbulence intensity and sets an integral length scale upstream of the cascade, thereby reproducing a representative interaction noise inflow condition. This controlled inflow enables a consistent experimental reference for validating the turbulence model dependence of the predicted spectra, particularly in the 2–5 kHz band where turbulence–leading edge interaction dominates. Data were processed in dBFa (ACOEM) using FFT in 10–20,000 Hz with 1.25 Hz resolution, Hanning windowing, 50% overlap, and RMS estimation.
+
+The cascade comprised four vanes mounted downstream of the convergent nozzle. Two geometries were assessed at an incidence angle of 15°: a baseline blade with a straight leading edge and a bio-inspired blade with triangular leading edge serrations. The serrations were rounded-tip cutouts with amplitude equal to 20% of the chord and 15 mm pitch; other geometric parameters, including chord and vane spacing, followed the configuration described in [45].
+
+The test used as experimental data in the comparative analyses performed in the manuscript is part of a larger testing campaign where both leading edge and trailing edge serrations were tested. Trailing edge serrations tend to work well in reducing self-noise, while those placed on the leading edge are effective in reducing interaction noise. Before each type of geometry, the consistency of the reference blade spectra (for all AoAs analyzed) was checked to ensure repeatability. On the aerodynamic side, an L-shaped Pitot tube was used to reconfirm that the fluid velocity is consistent (the air source only has an on–off function, without speed variation). The microphone signals were recorded for approximately 30 s for each test condition, and the acoustic results were obtained from time-averaged spectral estimates to improve spectral convergence and reduce the variance (finite sample variability) of the broadband jet–blade interaction noise [45].
+
+2.2. Numerical Approach
+
+The computational domain mirrored the experimental arrangement and was divided into two regions. The near-field region (77 mm × 75 mm inlet zone and 62 mm × 220 mm box around blades) was for resolving the cascade and the inlet zone used a predominantly structured mesh (Figure 3) around solid boundaries—the four blades, the side walls, and the top and bottom of the first domain (the one containing the blades)—with near-wall spacing chosen to achieve y+ ≈ 1 (a first layer thickness of ~10−5 m). A velocity inlet boundary condition was used for the vane section upstream area with a mean speed of 50 m/s, turbulence intensity Tu = 10%, and integral length scale Λ = 2.5 mm, representing the interaction noise condition produced experimentally by the physical grid. The outer region extended to around 3 m in length and 3.22 m width to include virtual microphone points coincident with the experimental sensor locations (1 m radius at 10° and 90° relative to the longitudinal axis of the test setup). For a medium size mesh (close to 4 M elements), near-blade domain elements are limited to a maximum size of ~1.25·10−4 m and for the outer go up to ~2.5·10−2 m (global mesh size). Far-field boundaries (set as atmospheric pressure inlets on the side walls, as well as a pressure outlet on the outflow area as shown in Figure 3) were set non-reflecting to avoid acoustic contamination of the spectra. Five turbulence modeling strategies commonly used for broadband aeroacoustics were evaluated on both geometries: Spalart–Allmaras (SA), k−ω SST, k−ε, Scale-Adaptive Simulation (SAS), and Large Eddy Simulation (LES). Transient solutions were initialized from a statistically steady state obtained with a 1 ms physical time step; stabilization was verified by monitoring the temporal evolution of prms and dp/dt until stationarity. The unsteady runs then proceeded with a time step Δt = 10−5 s for 1800–2000 time steps and up to 20 inner iterations per step (to ensure that spectral roll-off and peak locations were not artifacts of under-resolved unsteadiness).
+
+The FW-H formulation described in [46] and Equation (1) were used for noise prediction:(1) ∂2p′∂t2−c02∇2p′=c02∂2∂xi∂xjTijHf−c02∂∂xiPijnj+ρuiun−vnδf+∂∂tρ c02un−vn δf
+
+with H(f)—the Heaviside function (unity outside the body), δ(f)—the Dirac distribution on the moving surface S, outward normal ni, flow velocity ui (with un=uini) and surface normal speed vn. Compressive and Lighthill stress tensors are written in Equation (2):(2) Pij=pδij+ρuiuj−τij,    Tij=Pij−c02ρδij
+
+where τij is the viscous stress tensor. For a fixed, impermeable surface (vn=un=0 on S), the thickness (monopole) term in Equation (1) vanishes and the dipole reduces to −∂xi[p ni δ(f)]. ANSYS Fluent implements the FW-H post-processing in Farassat’s Formulation 1A (time-domain integrals—surface formulation [19,46]), evaluating the time-domain surface integrals in Equations (3)–(5) at specified observer points. For an observer at x, let R=x−y, R=R, r=R/R, M=U/c0 the material Mach vector of the surface, Mr=M·r, and define the loading vector Li=Pijnj with Lr=Liri. Using retarded time τr (all bracketed quantities evaluated at τr), we can write(3) p′(x,t)=pT′(x,t)+pL′(x,t)
+
+(4) pT′x,t=∫Sρ0vn−un4πR1−MrretdS
+
+(5) pL′(x,t)=∂∂t∫SLr4πc0R1−MrretdS+∫SLr4πR21−Mr2retdS
+
+For rigid, impermeable surfaces un=vn=0, the thickness term pT′ is zero and the radiation is purely loading noise. These relations correspond to the formulation in [22] and are consistent with the tensor definitions in Equation (2). Two source-surface options are available: impermeable (the solid blade and walls) and permeable (a control surface in the flow). In the impermeable case typically used here, the thickness term Equation (4) is zero and only the loading term Equation (5) contributes; quadrupole volume sources from Lighthill’s tensor are not included by the FW-H post-processor (they would require separate modeling). Practically, the workflow is: (i) select the FW-H surface(s) (blades/near-blade shroud), (ii) define observers at 1 m and 10°/90°, (iii) run the transient with Δt = 10−5 s, and store the surface data needed for Equation (5), (iv) let Fluent assemble p′(t) at each observer from the retarded-time integrals. Frequency-domain SPL is then obtained by FFT of p′(t) using the same windowing and overlap as the experiment. Statistical stationarity was assessed by monitoring pressure and pressure gradient signals at multiple locations until their mean and RMS values stabilized over several flow-through times. Given the inflow velocity and the streamwise extent of the computational domain, the incoming flow crossed more than 80% of the domain length prior to the start of unsteady data acquisition, which is consistent with accepted practices for establishing steady or statistically stationary conditions in cascade simulations.
+
+2.3. Unsteady Derived Metrics
+
+To quantify the three-dimensional structure of the unsteady surface pressure field along the leading edge, we evaluated the magnitude-squared coherence of the pressure fluctuations measured at discrete spanwise locations. For each point i, as in Figure 4 (corresponding to the nearest surface mesh node at various z positions), the fluctuating component was obtained as in Equation (6), followed by a linear detrending to remove slow drift in the quasi-static pressure signal. The acquisition files report only the spanwise coordinate z, hence the present analysis quantifies coherence strictly as a function of Δz along the leading edge line. This is appropriate for a first-order “spanwise coherence” assessment, because the principal design intent of leading edge serrations is to modify interaction mechanisms distributed along the span. The spanwise direction corresponds to the blade height direction, while the streamwise direction is aligned with the incoming flow at the leading edge (as the pressure term from the fluctuating pressure coefficients [47]).(6) pit′=pit−pit¯
+
+The magnitude-squared coherence between two locations i and j was computed in the frequency domain as in [48] as follows:(7) γijf2=Gijf2Giif· Gjjf
+
+where Giif and Gjjf are auto power spectral densities (PSDs) and Gijf is the cross power spectral density (CPSD). Spectral estimates were obtained using Welch’s averaging (Hanning window, 50% overlap, NFFT = 512), consistent across baseline and serrated configurations to ensure comparability. Since the points were placed along the leading edge at known spanwise coordinates z (provided in the simulation related pressure variation export file), the separation for a pair is Δzij=zj−zi. To obtain relevant metrics, coherence was computed over user-defined frequency bands f1, f2 and over all pairs as follows:(8) γ2¯(Δz; f1, f2) = mediani<j, Δzij=Δz [ medianf∈f1,f2γij2f]
+
+A two-stage median aggregation is employed: first across frequency bins within each band to mitigate the effect of narrowband spectral spikes, and subsequently across all sensor pairs sharing the same spanwise separation Δz. This strategy provides increased robustness relative to single-reference coherence and prevents bias associated with a particular spanwise location. A compact length scale was extracted by fitting an exponential decay model, commonly used to represent spanwise decorrelation of wall pressure fluctuations. A compact length scale was extracted by fitting the following exponential decay model, commonly used to represent spanwise decorrelation of wall pressure fluctuations (as in [49] or [50]):(9) γ2f, Δz≈exp−2ΔzLzf
+
+For each frequency band, Lz was estimated from all available Δzij,γ2ij¯ pairs via a least-squares slope through the origin after logarithmic linearization as follows:(10) y = −12·lnγ2≈ ΔzLz → Lz = ΔzT · yΔzT · Δz−1
+
+To prevent numerical artifacts, γ2 was clipped to the interval [10−6, 0.999999] prior to the logarithm. In addition, frequency bins where PSD energy was too low (e.g., more than 60 dB below the channel’s PSD maximum) were discarded to avoid coherence values dominated by numerical noise rather than physical correlation. The parameters defining the characteristic lengths of coherence are defined in various forms, with variants found in the literature that also take into account the parameters of the boundary layer (momentum or displacement thickness) [47,48,49,50,51].
+
+3. Results
+
+A grid convergence (mesh independence) study was performed by varying the mesh size from 0.68 M nodes and 1.71 M elements (coarse) to 5.18 M nodes and 13.4 M elements (cine) using the same setup (boundary conditions) as in Figure 3. An intermediate (medium) grid (2.12 M nodes, 4.11 M elements)—offering the best compromise between spectral fidelity and computational cost—was adopted for the turbulence model comparison. Figure 5 presents normalized time histories of the pressure time derivative dp/dt (top) and static pressure p (bottom) at the two numerical receivers (≈10° and 90°), from coarse to fine grids (the signals were normalized to the maximum value). After initialization, both records reach statistically stationary conditions and display periodic content that anticipates the fluid–structure interaction seen later. The phase and amplitude envelope are consistent across meshes, with modest amplitude differences—slightly larger at mic 1—suggesting that the near-observer unsteady loading is captured, while mesh effects are concentrated in the low–mid frequencies. These signals therefore indicate that the temporal resolution is adequate and that the serrated configuration promotes repeatable, spanwise-modulated fluctuations at the observers; the forthcoming SPL/PSD comparisons can thus focus on quantifying how turbulence models distort the sub-kilohertz region versus their mid-band alignment with the measurements.
+
+Verification runs performed during mesh convergence checks (based on SPL/PSD) indicated consistent trends at both receivers: for mic1 (rec1), the coarse grid systematically overestimated the low–mid band, with a broad elevation up to 1 kHz, whereas the medium grid reproduced the experimental interaction noise spectra more faithfully over 1–5 kHz range; the fine grid did not deliver systematic improvements and introduced pronounced undulations and local peaks (notably near 1.5–3 kHz) absent from the measurements. For the lateral microphone, the coarse grid again overshot the 0.5–1 kHz region, the medium grid remained closest to the data across most of the band, and the fine grid tended to sit higher and comparatively flat with a notch near 2 kHz. These trends justify adopting the medium grid for turbulence model comparisons.
+
+The results for baseline and serrated configurations are presented in Figure 6 (run on Fluent 2021 R1). Multiple combinations of timestep sizes and turbulence models were tested, with the corresponding data extracted and processed to obtain the acoustic sound pressure level (SPL) spectrum. Unless otherwise indicated in the figure, the simulations used the medium mesh, were initialized from a stabilized solution (1 ms), and advanced for approximately 1500–1800 time steps. The SPL was derived by converting the numerically obtained PSD following the FFT. Overall, the model predictions are broadly consistent, with model-dependent features over certain frequency ranges—most notably at low frequencies (<1 kHz)—and close agreement in the band of interest (2–5 kHz), particularly for the SAS model, which is relatively inexpensive computationally.
+
+Regarding the contributors to noise, a distinction can be made between the influence of the near-blade region (mainly dipole sources) and that of the outer domain (quadrupole sources corresponding to unbounded flow); the total perceived noise results from the combined effect of both. Solely to quantify the relative contribution of each, Figure 7 overlays the spectra computed for three acoustic source scenarios—near-blade domain, outer domain, and the combined case—sampled at the same receiver locations as in the preceding figures. For this analysis, the k−ω SST model was used with a time step of Δt = 10−5 s, and results were obtained after just over 500 time steps.
+
+The PSD overlays (Figure 7) indicate that the near-blade region controls the spectrum across almost the entire band starting from the sub kiloHertz region. The outer domain contribution decays rapidly with frequency and becomes secondary as viscous dissipation suppresses wake-borne fluctuations (which was to be expected for a relatively low Reynolds numbers). The combined spectra essentially collapse onto the near-blade curves, for both angles, confirming that aeroacoustics content is dominated by the flow physics (such as separation, unsteady loading, and local edge interactions) in the immediate vicinity of the blades. This aligns with the observation that improving near-wall resolution (y+ ≈ 1) and controlling temporal accuracy in that region are the two ingredients responsible for high spectral fidelity.
+
+Figure 8a–d provides complementary perspectives of the same unsteady loading indicator (dp/dt). The blade-attached views in Figure 8a,c highlight the spatial distribution of strong loading events along the leading edge, whereas the axial plane cuts in Figure 8b,d show how these events travel downstream too. Compared to the baseline case (Figure 8a,b), the serrated configuration (Figure 8c,d) exhibits a visibly shorter spanwise continuity and reduced streamwise persistence of high-amplitude dp/dt patches. This spatial fragmentation is consistent with serration-induced phase modulation at the leading edge, which weakens the coherent accumulation of unsteady forces and supports the spectral reductions observed in the interaction noise band.
+
+The iso-surfaces (Figure 9) provide a three-dimensional view of the unsteady structures. In the baseline case, the dp/dt field forms large, contiguous lobes that extend over several passages, suggestive of spanwise-correlated loading. In the serrated case, the same threshold (dp/dt = 2·10−4 Pa/s) yields narrower, broken-up lobes that are segmented by the serration influence, with noticeably reduced lateral continuity. This topological change is consistent with serration-induced phase variation at the leading edge: the impinging turbulent eddies are decorrelated in the spanwise direction, which limits the constructive accumulation of unsteady forces and promotes more rapid downstream decay of the energetic structures. The qualitative differences between iso-surfaces Figure 9a,b thus reinforce the spectral evidence reported earlier—namely, that interaction noise content is governed by near-blade dynamics and is mitigated when spanwise coherence is disrupted.
+
+The integrated aerodynamic loads reinforce this picture (Table 1). For all models, the serrated configuration carries higher axial (X) and lift-like (Y) loadings than the baseline (e.g., SA and k−ω SST show an X-force of roughly 1.9–2.4 N and Y-force of ~4–5.3 N), and more modest in SAS/LES. This systematic uplift in load is compatible with the pressure distribution: stronger LE pressure gradients and spanwise modulation around the serration geometry translate into enhanced unsteady loading, which is precisely the mechanism expected to feed the measured interaction noise band. The fact that SAS and LES predict smaller load increments aligns with their tendency to distribute energy over a broader range of resolved scales, consistent with the closer spectral agreement observed in the 2–5 kHz region.
+
+The magnitude-squared coherence γ2 ∈ [0, 1] directly measures the fraction of linearly correlated fluctuations shared by two locations at a given frequency. Values close to 1 indicate strongly coherent, phase-consistent content, whereas values close to 0 indicate decorrelated fluctuations or content dominated by uncorrelated turbulence. Pressure fluctuations were recorded at 11 surface probes along the leading edge for both the baseline and serrated configurations (shown schematically in Figure 4).
+
+The extracted coherence length, Lz, provides a single-number characterization of how quickly correlation decays along the span; a larger Lz indicates spanwise-extended coherent structures, while a smaller Lz implies rapid decorrelation (Figure 10c,d). In practical terms, Lz can be interpreted as a descriptor for the spanwise “source size” over which unsteady loading may add constructively and thus contribute efficiently to far-field radiation; in turn, a reduced Lz is consistent with weakened spanwise content and reduced potential for coherent summation. In the baseline configuration, the generally low coherence levels suggest that the leading edge pressure field is dominated by locally generated, weakly correlated turbulent structures rather than by spanwise-extended features. In contrast, the serrated leading edge introduces a geometric modulation that can redistribute coherence: while it is intended to reduce broadband coherence of the incoming interaction, it may also imprint coherence features at specific spanwise scales associated with the serration wavelength, which can appear as localized peaks and a more repeatable fitted Lz (as also suggested in [46] by plotting the coherence parameter for various LE treatments). When coherence decays rapidly and remains close to zero over most spanwise separations, the fitted coherence length becomes sensitive to statistical fluctuations. This behavior is therefore interpreted as an indicator of weak spanwise organization rather than as a numerical artifact.
+
+The results shown in Figure 10 were obtained by post-processing the simulated pressure signals with an in-house GNU Octave code (v9.2.0), following the procedure described in the Section 2. Each dataset covers approximately 0.5 s of simulated time (about 5000 samples at Δt = 1 × 10−4 s). For each probe location along the leading edge, the pressure time series was first converted to a fluctuating signal by removing its temporal mean and applying linear detrending. The auto- and cross-power spectral densities (PSD/CPSD) were then computed using Welch’s method (also called the averaged periodogram method, with Hanning windowing, 50% overlap, NFFT = 512). The magnitude-squared coherence was then evaluated for all probe pairs from these spectra. To improve statistical robustness, coherence values were band-averaged over predefined frequency intervals and further aggregated across all probes sharing the same spanwise separation Δz using median statistics. This procedure reduces the sensitivity to narrowband spectral peaks, numerical noise, and spatial bias associated with a fixed reference location, enabling a consistent comparison between the baseline and serrated leading edge cases.
+
+4. Discussion
+
+The observed differences between turbulence models can be interpreted in terms of their respective treatment of unsteady scales and eddy viscosity adaptation. Models such as k−ω SST tend to retain higher modeled turbulence levels near the leading edge, which explains their elevated low-to-mid frequency content. In contrast, SAS dynamically reduces eddy viscosity in regions of resolved unsteadiness, allowing partial scale resolution and a redistribution of energy toward higher frequencies. LES further extends this trend by resolving a broader portion of the turbulent spectrum, although at a significantly higher computational cost. These distinctions clarify why models may converge in the interaction noise band (1–3 kHz) while diverging outside of it.
+
+For the baseline case at the 10° receiver position (Figure 6a), temporal resolution remains the decisive factor. The coarse time step (LES, Δt = 10−4 s) produces a noisy, poorly converged spectrum with spurious elevations around the 0.5–1.5 kHz band, whereas refining to Δt = 10−5 s regularizes the spectrum and brings LES closer to the experimental interaction noise slope beyond 1–2 kHz. Under the same Δt, SAS and k−ω SST offer comparable fidelity in the mid–high band; SAS tends to run slightly high in the few-hundred-hertz region and slightly low above ~5 kHz, while k−ω SST sits marginally under the experiment below 1 kHz but tracks well toward 2–8 kHz. In short, the ranking is unchanged: with adequate Δt, LES does not systematically outperform SAS or k−ω SST for the band of interest.
+
+For the serrated geometry at the 10° receiver position (Figure 6b), the models reproduce the broadband character with distinct biases by frequency. The k−ω SST model remains generally above the measurements in the 0.5–2 kHz interval, while Spalart–Allmaras follows the experimental decay more closely beyond ~2 kHz. SAS is elevated at low frequencies (<~700 Hz) and shows localized underestimation around ~1 kHz; LES aligns well in the midband once Δt is tightened, with small deficits at the highest frequencies. The complementary PSD view (Figure 6c) corroborates these tendencies: SAS concentrates more energy at low frequencies, k−ω SST exhibits a higher PSD plateau over 1–3 kHz, and LES/SA sit lower in that range, consistent with their closer SPL match above 2 kHz. At 90° (Figure 6d), the angular sensitivity is evident. The k−ω SST model underestimates the 0.6–1.5 kHz hump seen in the experiment but approaches the envelope beyond ~2 kHz; SAS carries excess low-frequency levels and introduces localized peaks not present in the data; SA tracks the mid–high-frequency decay reasonably well but retains isolated over- and undershoots. LES tends to underpredict the midband yet converges toward the experimental slope at higher frequencies. The PSD comparison at 90° (Figure 6e) confirms this picture: SAS places disproportionate energy at low frequencies, k−ω SST is comparatively elevated over ~3–10 kHz, and LES takes an intermediate position with the smallest midband overfit among the models.
+
+Overall, the obtained SPL and PSD spectra reinforce the main conclusions: interaction noise content is captured by all unsteady models once Δt is sufficiently small (observed for other time steps but more time-consuming); SAS and k−ω SST provide the most consistent agreement in the 2–5 kHz band that governs jet–blade interaction, with angle-dependent nuances; LES approaches the correct envelope with refined Δt but does not deliver a systematic advantage for the present runtime envelope; and the spectral energy distributions (Figure 6c,e) explain the observed SPL biases—low-frequency excess for SAS, 1–3 kHz elevation for k−ω SST, and comparatively balanced midband energy for LES/SA at 10°, with shifts at 90° that justify multi-angle validation.
+
+Table 1 reports instantaneous surface-integrated blade loads (representative sample from the unsteady simulations after ~2000 time steps), not time-averaged or RMS values; therefore, they are used only as a supporting indicator, while model ranking is based primarily on spectral agreement with the measurements. Taking LES as the reference for physical fidelity, SAS is the closest model in Table 1, with deviations relative to LES of +10.3%/−0.4% (baseline X/Y) and −2.4%/+4.4% (serrated X/Y), whereas SA and k−ω SST show larger deviations (up to ~31%). This is consistent with the expected behavior of turbulence closures for leading edge interaction noise problems: LES resolves the large energy-containing eddies that drive unsteady blade loading, while URANS eddy–viscosity models may smooth part of the inflow–blade interaction; SAS partially recovers resolved unsteady content and therefore remains closer to LES.
+
+Regarding TKE values in regions of interest integrated on the blades, a slight increase in values compared to the reference was observed, exceeding 30%, and at the domains’ interface (exit from the blade area), these values averaged over the surface were double those of the reference in the case of serrations. The same setup can be leveraged for the following deeper—but fully complementary—analyses: wall pressure RMS maps on the blades and along the leading edge, spanwise wall pressure coherence γ2(f, Δz) to quantify the decoherence introduced by the serration pitch, and FFT-based spectra of the axial/transverse force fluctuations (CL′(f); CD′(f)) to connect energy peaks directly to the interaction noise band. These additions would further consolidate the link between near-blade pressure gradients, integrated loading, and far-field spectra, while keeping the central conclusion (leading edge serrations can be credibly assessed with numerically affordable models for early-stage design and down-selection).
+
+The interaction noise band targeted in this work lies in the kilohertz range, where turbomachinery blades commonly have strong components and where design changes (such as leading edge serrations) are expected to alter the source coherence and effective radiating area. Therefore, reporting coherence metrics in 0.9–5 kHz, and highlighting 1.6–3 kHz as a BPF-adjacent band, provides a mechanism-oriented complement to SPL spectra. It should be noted that below 1000 Hz, the pressure fluctuates quite inconsistently in the reference case, although there is data in the literature suggesting a decoupling also for straight leading edges as the distance from the reference increases [46,51]. We expected a lower coherence between sources at the serration peak and root [46], as is the case in Figure 10b. In [52], it is noted that the flow regime also affects the correlation parameters, especially at Reynolds numbers close to 105 (this issue being remedied at higher speeds).
+
+Several tendencies emerge from the presented results. The presence of interaction noise above ~1 kHz is captured by all unsteady models, while model ranking is angle-dependent: at 10° (quasi-axial), SAS/k−ω SST track the experimental spectra well and SA often matches the high-frequency roll-off; at 90° laterally, k−ω SST is generally the closest, with SA and SAS showing localized peaks that the experiment does not consistently exhibit. Importantly, no persistent narrowband tones appear in the measurements for the serrated case, and the simulations reflect this broadband character when time integration is sufficiently resolved. Unsteady relevant parameters were plotted from representative LES cases (here at Δt = 10−4 s, t ≈ 50 ms) to visualize the fluctuating field build-up; they are not intended to replace the time-resolved spectral analysis used for quantitative validation. Nevertheless, the observed patterns—the concentration of dp/dt near the leading edge, the fragmented spanwise structure with the presence of serrations, and triggered faster downstream attenuation—are fully consistent with the SPL/PSD trends and with the mentioned aerodynamic loads. The same computational setup can be extended to time-averaged unsteady statistics (e.g., wall pressure RMS plots) and spanwise correlation along the leading edge; however, even in the present form the figures already support the central mechanism by which leading edge serrations (a bio-inspired solution) reduce the effective coherence of unsteady loading and, consequently, the broadband radiation.
+
+Beyond the presented configuration, the main value of this work is the transferability of the validation workflow rather than a result tied to a single cascade. The same approach can be applied to other interaction noise problems—e.g., rotor–stator stages, fan/OGV systems, or compressor/turbine cascades—by preserving the key similarity parameters that govern the flow–blade mechanism (Mach and Reynolds numbers, incidence, and, most importantly, the relation between the dominant inflow length scales and the serration wavelength, together with a consistent Strouhal-based scaling of the frequency band of interest). In practice, the results provide a route for other studies: the use of a numerically affordable model (unsteady SAS or k−ω SST) with a time step sufficiently small to resolve the interaction band and to play with various serration designs/parameters and operating points/flow conditions; LES can be used for a limited set of cases where finer-scale content or detailed near-field statistics are required; coherence metrics (γ2 and the derived metrics such as coherence length) can contribute to verify that the intended mechanism—the reduced spanwise coherence of unsteady loading—is actually achieved. This combination makes it easier to down-select designs at laboratory scale and then carry the most promising candidates toward more representative turbomachinery geometries with reduced risk and fewer costly iterations.
+
+5. Conclusions
+
+The study shows that bio-inspired leading edge serrated cascades can be modeled with mid-cost turbulence closures, making routine broadband assessments practical. In the band where jet–blade interaction governs radiation (≈2–5 kHz), SAS and k−ω SST reproduce the experimental spectral slope and level with a consistency comparable to—and often indistinguishable from—LES under comparable runtime constraints. This means that the approach is not only feasible but operationally convenient: engineers can screen serrated designs without committing to the computational expense of full LES.
+
+The near-blade region—unsteady separation and inflow–edge interaction—dominates radiation across most of the spectrum, while the outer-domain contribution decays rapidly with frequency, especially at the relatively low Reynolds number considered here. This explains why achieving accurate near-wall dynamics and temporal resolution leads to the largest gains in predictive fidelity and why the conclusions hold at both microphones despite their different perspectives.
+
+A limitation of the current coherence implementation is that probe locations are described only by z; therefore, the analysis captures spanwise decorrelation but cannot isolate potential streamwise/chordwise effects introduced by local geometric features. Nevertheless, the reported metrics are sufficient to support design down-selection because they provide an interpretable, geometry-sensitive mechanism indicator in the same frequency ranges where the acoustic benefit is observed.
+
+Taken together, the findings are relevant and encouraging for design practice. They show that leading edge serration concepts can be evaluated using computationally efficient turbulence models that reproduce the measured spectral trends in the interaction noise band, thereby enabling rapid design iteration and evidence-based down-selection. This study achieves consistent experiment–simulation agreement over the 2–5 kHz range, clarifies model performance with clear angular sensitivity, and confirms that the dominant acoustic sources are localized to the near-blade region. These results support the practical adoption of leading edge serrations in early-stage workflows and motivate targeted LES only when additional scale resolution is demonstrably required.
+
+Acknowledgments
+
+The raw experimental data used for comparison were obtained with the help of INCDT COMOTI’s Research and Experiments Center in the field of Acoustic and Vibrations (ACUVIB) staff and facility.
+
+Author Contributions
+
+Conceptualization, A.-G.T., D.-E.C. and D.I.; methodology, D.-E.C. and D.I.; validation, A.-G.T., D.-E.C. and D.I.; formal analysis, D.-E.C.; investigation, A.-G.T., D.-E.C. and D.I.; data curation, A.-G.T. and D.I.; writing—original draft preparation, A.-G.T. and D.I.; writing—review and editing, A.-G.T., D.-E.C. and D.I.; supervision, D.-E.C. and D.I. All authors have read and agreed to the published version of the manuscript.
+
+Institutional Review Board Statement
+
+Not applicable.
+
+Informed Consent Statement
+
+Not applicable.
+
+Data Availability Statement
+
+The codes used in the additional processing of data are available upon reasonable request.
+
+Conflicts of Interest
+
+The authors declare no conflicts of interest.
+
+Figure 1 Adaptations identified in nature as potential inspiration for designing new blades: (a) owl adaptation [28]; (b) humpback whale tubercles [29]; (c) shark skin riblets [30].
+
+Figure 2 Experimental setup.
+
+Figure 3 Computational domain and mesh.
+
+Figure 4 Leading edge points for baseline and serrated geometry.
+
+Figure 5 Steady solution and mesh independence (LES, dt = 10−4).
+
+Figure 6 Comparative spectra: (a) various combinations on baseline geometry (10° direction); (b) various models on serrated geometry (10° direction, dt = 10−5 s); (c) PSD on serrated geometry (10° direction, dt = 10−5 s); (d) various models on serrated geometry (90° direction, dt = 10−5 s); (e) PSD on serrated geometry (90° direction, dt = 10−5 s).
+
+Figure 7 Acoustic sources’ influence.
+
+Figure 8 Comparative dp/dt, LES, dt = 10−4 s, t ≈ 50 ms: (a) baseline (blade distribution); (b) baseline (axial plane distribution); (c) serrations (blade distribution); (d) serrations (axial plane distribution).
+
+Figure 9 Iso-contours (dp/dt = 2 · 10−4 Pa/s, LES): (a) baseline; (b) serrations.
+
+Figure 10 Spanwise coherence analysis: (a) band-averaged spanwise coherence, baseline; (b) band-averaged spanwise coherence, serrations; (c) coherence length Lz, (fit from all pairs) baseline; (d) coherence length Lz (fit from all pairs), serrations.
+
+biomimetics-11-00199-t001_Table 1 Table 1 Aerodynamic loading on blades (instant averaged values on surface after ≈2000 time steps).
+
+Model	Geometry	Force on X (Axial)	Force on Y (⟂ to Axis)	
+Spalart	serr	5.175 N	15.959 N	
+	bsln	2.738 N	11.908 N	
+k−ω SST	serr	4.845 N	16.616 N	
+	bsln	2.637 N	11.273 N	
+SAS	serr	4.505 N	15.298 N	
+	bsln	4.188 N	14.218 N	
+LES	serr	4.614 N	14.650 N	
+	bsln	3.797 N	14.275 N	
+
+Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.
+
+
+References
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diff --git a/corpus/psychology/text/41ab3d373d6c754b.txt b/corpus/psychology/text/41ab3d373d6c754b.txt
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+Updating rigor in psychological mixed methods research: A systematic methodological guidance review
+
+Mixed methods research (MMR) is increasingly used in psychology, yet strengthening rigor remains challenging because of fragmented guidance and new approaches in MMR practice such as co-creation, open science, and emerging technologies. We conducted a preregistered systematic methodological review to investigate (1) how rigor is defined and conceptualised in the context of MMR and (2) what strategies are used to ensure or demonstrate rigor in MMR? Searches of databases, preprint archives, leading mixed methods journals, citation networks, reporting guidelines, journal instructions to authors, empirical psychology articles, and methodological textbooks yielded 345 included sources. From these sources, we extracted 236 interpretations of rigor definitions and 1,698 rigor strategies. The definitions were synthesized into four interdependent components: critical reflection, consistent set-up within and across study strands, grounding in paradigmatic and theoretical foundations, and meaningful integration. The extracted strategies were consolidated into 90 unique practices organized across 10 research-lifecycle categories: assembling, framing, reflecting, co-creating, designing, collecting, analysing, integrating, concluding, and reporting. Findings indicate that rigor in MMR cannot be reduced to applying separate quantitative and qualitative quality criteria or to compliance with a universal checklist. Instead, rigor depends on coherent, context-sensitive methodological decision-making. The definition and strategies provide psychologists with a flexible blueprint for designing, conducting, evaluating, and reporting rigorous MMR.
diff --git a/corpus/psychology/text/41fe12589de2e003.txt b/corpus/psychology/text/41fe12589de2e003.txt
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+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Front Psychiatry
+Journal ID: Front Psychiatry
+NLM Journal ID: 101545006
+Journal ID: Front. Psychiatry
+
+Frontiers in Psychiatry
+
+EISSN: 1664-0640
+Publisher: Frontiers Media SA
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC12957251
+PMID: 41788649
+DOI: 10.3389/fpsyt.2026.1648067
+Article version: 1
+Article version:
+Subjects: Study Protocol
+
+Traditional Chinese medicine interventions for post-stroke emotional disorders: a protocol for network meta-analysis of randomized controlled trials
+
+Chao Yuqiao 1 2 Conceptualization Data curation Formal analysis Methodology Software Writing – original draft
+Li Bai 1 3 Conceptualization Investigation Software Writing – original draft
+Xie Zhaozhan 2 Conceptualization Software Writing – original draft
+Jia Hongling 1 * Funding acquisition Project administration Supervision Writing – review & editing
+Zhang Yongchen 2 * Project administration Supervision Writing – review & editing
+1 The Second Affiliated Hospital of Shandong University of Traditional Chinese Medicine , Jinan ,  China
+2 College of Acupuncture and Tuina, Shandong University of Traditional Chinese Medicine , Jinan ,  China
+3 Second School of Clinical Medicine, Shandong University of Traditional Chinese Medicine , Jinan ,  China
+* Correspondence: Hongling Jia, jiahl1969@163.com; Yongchen Zhang, zhangyc58@sina.com
+Electronic publication date: 2026 Feb 18
+Publication date: 2026
+Volume: 17
+Electronic Location ID: 1648067
+Received 2025 Jun 16; Accepted 2026 Jan 7; Revised 2026 Jan 3
+Copyright: Copyright © 2026 Chao, Li, Xie, Jia and Zhang.
+Copyright year: 2026
+Copyright holder: Chao, Li, Xie, Jia and Zhang
+License: This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Keywords: network meta-analysis, post-stroke emotional disorders, study protocol, systematic review, traditional Chinese medicine
+
+Funding: The author(s) declared that financial support was received for this work and/or its publication. Clinical Research Project of Shandong University of Traditional Chinese Medicine(LCKY202424); Clinical Study on the Efficacy of Xiangqi (Nape Seven-Needle) Therapy in High-Risk Stroke Population (B-2022006).
+
+Figure count: 1
+Table count: 3
+Equation count: 0
+Reference count: 61
+Page count: 12
+
+section-at-acceptance: Mood Disorders
+
+Ÿ==============================Ÿ
+Background
+
+Post-stroke emotional disorders (PSED), primarily encompassing depression, anxiety, and their comorbid conditions, are common and serious complications of stroke. PSED has a high prevalence, significantly reduces patients’ quality of life, impedes neurofunctional recovery, and increases the risk of stroke recurrence and mortality. While modern medical treatments are effective, they are generally limited by slow onset, suboptimal response rates, and side effects, and often target a single pathological mechanism, making them inadequate to address the complex interplay of multiple mechanisms characteristic of PSED. Traditional Chinese Medicine (TCM) demonstrates potential advantages through multi-target regulation and relatively good safety. However, the relative efficacy ranking of its numerous therapeutic approaches still lacks robust evidence-based support.
+
+Methods
+
+This study plans to conduct a network meta-analysis (NMA), systematically searching multiple Chinese and English databases and grey literature since the 21st century, including PubMed, Embase, Cochrane CENTRAL, Web of Science, CNKI, CBM, VIP, Wanfang, and ClinicalTrials. Randomized controlled trials (RCTs) comparing different TCM therapies with conventional Western medicine or placebo control for adult PSED will be included. The primary outcome measures include the total clinical effective rate and changes in standardized scale scores. Study screening, data extraction, and risk of bias assessment will be independently completed by two researchers, and any discrepancies will be resolved through discussion or third-party arbitration. A random-effects NMA model based on the Bayesian statistical framework will be constructed to quantify the efficacy differences among different TCM interventions. Additionally, subgroup analyses will be conducted based on PSED types and TCM syndrome patterns to further explore the heterogeneity of efficacy. This study will also comprehensively evaluate the transitivity assumption, heterogeneity, and inconsistency, and use the GRADE framework to grade the quality of evidence. The study protocol strictly follows the PRISMA-P and NMA guidelines and has been registered on the PROSPERO platform.
+
+Results
+
+This NMA will synthesize direct and indirect evidence to quantify effect sizes and rank probabilities of diverse TCM interventions for PSED. Key outputs will include:1. Pairwise comparisons among TCM interventions and between each TCM intervention versus control groups; 2. The ranking of the efficacy of each TCM intervention measure in improving the symptoms of PSED; 3. Subgroup analyses of treatment effects stratified by PSED subtypes and TCM syndrome patterns; 4. Evidence certainty ratings for all effect estimates using the GRADE framework.
+
+Conclusion
+
+This study expects to rigorously conduct a network meta-analysis that will, for the first time within the TCM syndrome differentiation and treatment framework, systematically compare the relative efficacy of multiple TCM therapies for PSED, quantifying their effect sizes and optimal ranking probabilities. The results will provide clinicians with evidence-based hierarchical selection criteria for “acupuncture-Chinese herbal medicine-integrated therapy”, addressing the current evidence gap in TCM-based decision-making for PSED. This protocol emphasizes the critical importance of subgroup analyses by PSED subtypes and TCM syndrome patterns, aiming to establish the foundation for more precise and individualized integrated Chinese-Western treatment regimens. Public preregistration enhances research transparency and result credibility, promotes the production of high-quality TCM evidence and its international recognition, ultimately serving to optimize clinical management and improve prognosis in PSED patients.
+
+Systematic Review Registration
+
+https://www.crd.york.ac.uk/prospero/, identifier CRD420251069356.
+
+1 Introduction
+
+Post-stroke emotional disorders (PSED) represent prevalent neuropsychiatric complications following stroke, predominantly manifesting as depression, anxiety, and their comorbid conditions (1). Epidemiological studies indicate their prevalence correlates with time course and gender; specifically, the 1-year aggregate prevalence of post-stroke anxiety (PSA) approximates 29.3% (2), while post-stroke depression (PSD) exhibits a 2-year incidence ranging from 11% to 41% (3). PSED not only significantly diminishes patients’ quality of life but also impedes neurological rehabilitation, exacerbates cognitive impairment, and reduces treatment adherence. These effects substantially increase stroke recurrence risk and mortality (4), thereby establishing a vicious cycle of “brain injury → emotional dysfunction → clinical deterioration”. This complex pathophysiology underscores the imperative for comprehensive exploration of pathogenic mechanisms and targeted interventions.
+
+Based on the aforementioned clinical risks, modern medical research has revealed that the pathogenesis of PSED involves synergistic interactions among multiple mechanisms (5). Stroke directly damages monoaminergic pathways in the brainstem, such as the raphe nuclei and locus coeruleus, leading to reduced synthesis of serotonin (5-HT), norepinephrine (NE), and dopamine (DA). This impairs patients’ ability to regulate emotions (6). Additionally, ischemia and hypoxia trigger massive glutamate release, which induces calcium overload and excitotoxicity through NMDA and AMPA receptors. This ultimately results in neuronal death in the prefrontal cortex and limbic system, while suppressing the production of brain-derived neurotrophic factor (BDNF) (7–9).This process further activates microglia, prompting the release of pro-inflammatory cytokines such as IL-1β and TNF-α. These cytokines not only directly inhibit monoamine synthase activity but also increase cortisol secretion by activating the hypothalamic-pituitary-adrenal (HPA) axis, thereby accelerating monoamine neurotransmitter depletion (10). Simultaneously, stroke-induced sympathetic hyperactivity causes intestinal ischemia and gut dysbiosis. Metabolic products from pathogenic bacteria enter the brain via the circulatory system and vagus nerve, exacerbating central inflammation and reducing the conversion of tryptophan to 5-HT (11). Infiltration of peripheral neutrophils releases matrix metalloproteinase-9 (MMP-9), which disrupts the blood-brain barrier and facilitates the spread of inflammation within the brain. The resulting burst of reactive oxygen species (ROS) forms a positive feedback loop with glutamate excitotoxicity. Together, these factors suppress hippocampal neurogenesis and synaptic plasticity. These mechanisms are interlinked: glutamate excitotoxicity exacerbates oxidative stress; inflammation aggravates monoamine imbalance; dysregulation of the gut-brain axis and systemic inflammation mutually reinforce each other. Ultimately, this cascade leads to functional collapse of the prefrontal-limbic network, driving persistent worsening of emotional disorder symptoms. Currently, pharmacological treatments for PSED include monoaminergic system modulators, glutamatergic system modulators, and gamma-aminobutyric acid (GABA) system modulators (5, 12). Monoaminergic system modulators encompass drugs with two distinct mechanisms: one involves monoamine reuptake inhibitors (SSRIs, SNRIs, and TCAs) that directly elevate monoamine levels in the synaptic cleft by blocking 5-HT/NE reuptake, thereby improving mood and motivation (13, 14); the other comprises noradrenergic and specific serotonergic antidepressants (NaSSAs) that selectively block α2-adrenergic receptors along with 5-HT2 and 5-HT3 receptors, promoting NE and 5-HT release while activating 5-HT1A receptors (15). Both ultimately increase brain monoamine neurotransmitter levels. However, SSRIs and SNRIs exhibit limitations including delayed onset, suboptimal response rates, and potential increased risk of cerebral hemorrhage (16, 17). Compared to SSRIs, TCAs demonstrate higher adverse reaction rates in elderly patients and may cause cardiac suppression, resulting in lower safety; consequently, they are no longer recommended as first-line therapeutics (18). Although NaSSAs are not associated with severe adverse reactions, they tend to induce sedative effects, and concomitant use with other sedative-hypnotic agents should be avoided. Glutamatergic system modulators can rapidly alleviate depressive symptoms in treatment-resistant post-stroke depression(PSD) by blocking NMDA receptors (19), but their clinical application is substantially limited by risks of hallucinogenic effects, addiction potential, and long-term neurotoxicity. Gamma-aminobutyric acid (GABA) system modulators, specifically benzodiazepines (BZDs), function as positive allosteric modulators of GABAA receptors. They enhance endogenous GABA binding efficacy, promoting chloride channel opening and influx, which induces neuronal hyperpolarization and inhibition. This effect is particularly pronounced in key anxiety-regulating brain regions such as the amygdala, where they mediate rapid anxiolytic effects by suppressing neuronal hyperexcitability. Prolonged use, however, may cause dependence, tolerance, and withdrawal symptoms. A systematic review further highlighted BZDs’ association with elevated overall mortality risk (20). Although numerous pharmacological options exist, all exhibit significant side effect limitations, and crucially, current drugs predominantly target single mechanistic pathways, failing to address PSED’s multi-mechanistic pathophysiology.
+
+Within this context, TCM demonstrates multi-pathway regulatory advantages through comprehensive therapies including compound formulations, acupuncture, and other treatment modalities. Research indicates that Chinese herbal compounds and acupuncture therapy can ameliorate PSED via multiple mechanisms: regulating neurotransmitters, mitigating neuronal damage, suppressing hypothalamic-pituitary-adrenal (HPA) axis hyperactivity, reducing immune-inflammatory responses, and modulating gut microbiota. Studies have shown that the “Tongdu Tiaoshen(Unblocking Governor Vessel and Regulating Mind)” acupuncture technique, primarily targeting acupoints Baihui (GV20), Shuigou (GV26), Shenting (GV24), and Dazhui (GV14), effectively alleviates ultrastructural damage in the hippocampal CA1 region of post-stroke depression(PSD) model rats, and this intervention increases hippocampal levels of neurotransmitters NE, 5-HT, and DA while improving depressive-like behaviors (21). Electroacupuncture elevates hippocampal expression of BDNF, TrkB, and cAMP response element-binding protein (CREB) in PSD model rats, enhancing synaptic activity (22). Acupuncture significantly reduces serum levels of CRH, ACTH, and CORT in PSED patients, correcting HPA axis dysregulation and exerting anxiolytic and antidepressant effects (23). Electroacupuncture at Baihui (GV20), Shenting (GV24), Zusanli (ST36), and Yanglingquan (GB34) downregulates serum pro-inflammatory cytokines IL-1β, IL-6, and TNF-α, attenuating inflammatory responses and promoting hippocampal neural repair (24, 25). Sun demonstrated that “Tiaoshen Yunshu(Mind-Regulating and Pivot-Moving)” acupuncture increases the relative abundance of Lactobacillus and Bifidobacterium while reducing Escherichia coli and Enterococcus in PSD patients, and this technique upregulates beneficial microbial metabolites SCFAs, elevates neuroprotective gut-derived butyrate concentrations, ameliorates cerebral neuroinflammation, and effectively alleviates depressive states (26). Regarding Chinese herbal compounds, studies reveal that Si-Ni-San inhibits excessive NMDAR activation in the dorsal raphe nucleus (DRN), balancing 5-HTergic and GABAergic neuronal activity to improve anxiety-depression-like behaviors in adolescent mice (27). Xiao-Yao-San bidirectionally regulates gene expression in the hippocampus and amygdala, modulates cerebral neurotransmitters including DA, NE, and 5-HT, inhibits M1 polarization of hippocampal microglia to exert anti-inflammatory effects, and promotes hippocampal neurogenesis (28). Additionally, multiple compound formulations such as Gui-Pi-Tang, Chaihu-Shugan-San, and Xingnao Jieyu Capsules demonstrate efficacy in ameliorating negative emotions including anxiety and depression. For non-pharmacological and non-invasive therapies like music intervention, clinical studies indicate that the “Jue-note” in Five-Element Music therapy soothes liver stagnation, regulates emotional states, and improves heart rate variability to enhance autonomic nervous function. This intervention regulates qi-blood dynamics, reduces serum cortisol levels, and alleviates anxiety symptoms. Furthermore, Jue-note music increases serum superoxide dismutase (SOD) while decreasing malondialdehyde (MDA) levels, exerting antioxidant effects that improve depressive symptoms and sleep disorders (29).
+
+Notably, although TCM demonstrates multi-target regulatory advantages against PSED’s complex pathophysiology and numerous clinical observations indicate its overall adverse reaction rate is generally lower than that of Western pharmaceuticals (30, 31), hierarchical efficacy ranking among TCM therapies remains unsupported by high-level evidence due to therapeutic diversity and the TCM-specific paradigm of syndrome differentiation-based treatment. To address this critical gap, NMA serves as a quantitative methodology capable of globally evaluating comparative effectiveness across multiple interventions by synthesizing direct and indirect evidence (32).Within this study context, while head-to-head clinical trials comparing different TCM therapies are lacking, NMA enables indirect comparisons when pairwise interventions share common comparator arms, thereby integrating all therapies within a unified effect size framework. This indirect evidence-based approach has become essential for evidence synthesis and clinical decision-making in healthcare (33), particularly valuable for overcoming limitations of traditional direct comparisons—especially when clinicians require identification of the “optimal single therapy” from multiple treatment options (32).Through NMA, systematic comparisons of effect sizes among acupuncture, Chinese herbal medicine, and other interventions—while preserving TCM’s syndrome differentiation principle—can establish an evidence-based decision-making framework for developing hierarchical integrated Chinese-Western therapeutic protocols.
+
+2 Materials and methods
+
+This study rigorously adheres to the PRISMA-P guidelines for framework development and will comply with PRISMA-NMA standardized reporting requirements during the results presentation phase (34, 35) (Supplementary Files 1, 2). To further enhance the decision-support value of the research, we incorporate the Indirect Treatment Comparison/Network Meta-Analysis Study Questionnaire issued by the International Society for Pharmacoeconomics and Outcomes Research (ISPOR). This tool systematically evaluates clinical relevance, methodological credibility, and evidence translation efficiency to improve evidence interpretation capabilities for clinicians and health policy-makers (36). The study protocol has been prospectively registered on the PROSPERO international platform for systematic reviews (Registration ID: CRD420251069356). All protocol amendments will be updated in real-time through the platform’s version control functionality, ensuring transparent and traceable research conduct.
+
+2.1 Search strategy
+
+This study will systematically search the Cochrane Central Register of Controlled Trials (CENTRAL), Embase, PubMed, Web of Science, and four major Chinese databases(China National Knowledge Infrastructure (CNKI), Chinese Biomedical Literature Database (CBM), VIP Chinese Science and Technology Journal Database (VIP), and Wanfang Database). Additionally, we will search the ClinicalTrials.gov registry for unpublished complete clinical trial data, while extending to grey literature, international conference proceedings, and reference lists of included studies and existing systematic reviews. To ensure evidence completeness, corresponding authors and principal investigators will be proactively contacted to supplement incompletely reported data in primary studies or obtain raw data from unpublished research. This strategy aims to minimize publication bias and construct a comprehensive evidence network. All randomized controlled trials (RCTs) published since the inception of the 21st century (January 1, 2000, onward) investigating TCM interventions for post-stroke emotional disorders will be comprehensively collected. The search strategy employs a combination of Medical Subject Headings (MeSH) and free-text terms, with search syntax adapted to each database’s indexing rules and controlled vocabularies. For English databases, using PubMed as an example, a structured search syntax was constructed using Boolean operators; the specific search strategy is detailed in Table 1. For Chinese databases, using CNKI as an example, its search strategy is shown in Table 2. To ensure accurate correspondence between Chinese and English search terms, bilingual researchers familiar with the field verified and refined the candidate terms with reference to the Chinese Medical Subject Headings (37) and the built-in subject heading systems of databases such as CBM and CNKI, to identify the most precise and commonly used controlled vocabulary. Subsequently, another independent reviewer back-translated the finalized Chinese subject terms into English and compared them with the original English terms to ensure conceptual consistency and minimize semantic bias. The search strategies for other Chinese databases were adapted based on the CNKI search strategy, modifying the syntax according to the requirements of each database’s search engine while keeping the core set of search terms unchanged.
+
+Table 1 Search strategy for the PubMed database.
+
+Number	Search items	
+#1	Stroke[MeSH Terms] OR Stroke[Title/Abstract] OR Cerebrovascular Accident[Title/Abstract] OR CVA[Title/Abstract]	
+#2	Mood Disorders[MeSH Terms] OR Mood Disorders[Title/Abstract] OR Emotional Disorders[Title/Abstract] OR Affective Disorders[Title/Abstract]	
+#3	Post-Stroke Depression[MeSH Terms] OR (Post-Stroke Depression) OR (Depression after Stroke)	
+#4	Post-Stroke Anxiety[MeSH Terms] OR (Post-Stroke Anxiety) OR (Anxiety after Stroke)	
+#5	Acupuncture[MeSH Terms] OR Acupuncture[Title/Abstract] OR Needle Therapy[Title/Abstract] OR Acupressure[Title/Abstract] OR Acupoint Stimulation[Title/Abstract]	
+#6	Traditional Chinese Medicine[MeSH Terms] OR Traditional Chinese Medicine[Title/Abstract] OR TCM[Title/Abstract] OR Herbal Medicine[Title/Abstract] OR Chinese Herbal Medicine[Title/Abstract]	
+#7	Massage[MeSH Terms] OR Massage[Title/Abstract] OR Manipulative Therapy[Title/Abstract] OR Manual Therapy[Title/Abstract] OR Bodywork[Title/Abstract]	
+#8	Traditional Exercises[Title/Abstract] OR (Traditional Exercises) OR (Qigong) OR (Tai Chi)	
+#9	Randomized Controlled Trial[MeSH Terms] OR Randomized Controlled Trial[Title/Abstract] OR RCT[Title/Abstract] OR Randomized Study[Title/Abstract] OR Clinical Trial[Title/Abstract]	
+#10	#2 OR #3 OR #4	
+#11	#5 OR #6 OR #7 OR #8	
+#12	#1 AND #10 AND #11	
+
+Table 2 CNKI search strategy.
+
+Number	Search items	Logic	Search field	
+#1	Stroke + Apoplexy + Cerebrovascular Accident	OR	Subject	
+#2	Mood Disorders + Emotional Disorders + Depression + Anxiety + Post-Stroke Depression + Post-Stroke Anxiety	OR	Subject	
+#3	Traditional Chinese Medicine + Traditional Chinese Medicine (TCM) + Chinese Herbal Medicine + Acupuncture + Electroacupuncture + Scalp Acupuncture + Needling + Qigong + Tai Chi + Baduanjin + Five-Element Music	OR	Subject	
+#4	Randomized Controlled Trial + RCT + Randomized Control + Clinical Controlled Trial	OR	Subject	
+#5	#1 AND #2 AND #3 AND #4	AND		
+
+2.2 Eligibility criteria
+
+2.2.1 Inclusion criteria
+
+1) Study Population
+
+Diagnostic Criteria: Stroke diagnosis must comply with the 2024 AHA/ASA Guidelines for the Primary Prevention of Stroke (38) or the Chinese Guidelines for Cerebrovascular Disease Prevention and Treatment (2024) (39).
+
+Emotional Disorder Diagnosis: Depression: Meets DSM-5/ICD-10 criteria for depressive episode, with SDS score ≥ 53 or HAMD-17 score ≥ 8; Anxiety: GAD-7 score ≥5 or HAMA score ≥ 7; Mixed Type: Concurrent depressive and anxiety symptoms with HADS mean score ≥ 8.
+
+Disease Course: Emotional disorders emerging between 2 weeks and 1 year post-stroke.
+
+Age: 18–75 years, no gender restrictions.
+
+2) Interventions
+
+TCM Intervention Types: Chinese Herbal Medicine: Compound formulas; single herbs; proprietary Chinese medicines;
+
+Acupuncture: Body acupuncture; scalp acupuncture; electroacupuncture;
+
+Other Therapies: Qigong; Tai Chi; Baduanjin; Five-Element Music therapy;
+
+Combination Therapies: TCM integrated with Western medicine; multimodal TCM approaches.
+
+Intervention Details: Treatment frequency and duration must be reported; herbal formulas require specification of decoction methods and dosages.
+
+3) Comparator Groups
+
+Control Types:
+
+Active Control: Conventional Western therapy (e.g., pharmacotherapy, cognitive behavioral therapy).
+
+Negative Control: Placebo (e.g., sham acupuncture, herbal placebo).
+
+No-Intervention Control: Basic stroke care only (e.g., aspirin, rehabilitation).
+
+Permitted Co-Interventions: Control groups may receive foundational stroke treatments (e.g., antiplatelet agents).
+
+4) Outcome Measures
+
+Primary Outcomes:
+
+Clinical Response Rate: Total effective rate; (To control for heterogeneity, only studies that explicitly define the total effective rate will be included. The definition must be based on standardized scales recognized in this study and must clearly report the thresholds for “marked improvement” and “improvement.” Studies using self-defined criteria, vague definitions, or failing to report the specific calculation method will be excluded).
+
+Standardized Scale Scores: Pre-post treatment differences in HAMD-17, HAMA, SDS, GAD-7, or HADS scores.
+
+Secondary Outcomes:
+
+Quality of Life: Changes in scores assessed by standardized QoL instruments, including but not limited to the 36-Item Short Form Health Survey (SF-36), the Stroke-Specific Quality of Life Scale (SS-QOL), or the WHO Quality of Life-BREF (WHOQOL-BREF).
+
+5) Study Design
+
+Design: Parallel-group randomized controlled trials (RCTs) with intervention duration ≥4 weeks.
+
+Sample Size: ≥20 participants per group to minimize bias.
+
+Publication Period: Studies published between January 2000 and May 2025 (excludes methodologically immature early studies and obsolete therapies).
+
+Language: Chinese or English publications.
+
+2.2.2 Exclusion criteria
+
+1) Study Population
+
+Severe cognitive impairment or aphasia precluding assessment cooperation;History of psychiatric disorders (e.g., schizophrenia, bipolar affective disorder);Substance abuse (e.g., alcohol dependence);Pre-existing unresolved emotional disorders prior to stroke onset (to avoid confounding efficacy evaluation).
+
+2) Interventions
+
+Non-traditional TCM methods (e.g., infrared “acupuncture,” unvalidated device-based therapies);Interventions lacking TCM theoretical basis (e.g., proprietary Chinese medicines administered without syndrome differentiation).
+
+3) Outcome Measures (Outcomes)
+
+Sole use of non-validated or self-designed assessment tools; Failure to distinguish stroke-related emotional disorders from other complications (e.g., fatigue, pain) in outcome reporting.
+
+4) Study Design
+
+Non-controlled studies; Duplicate publications or inaccessible full texts.
+
+2.3 Data collection and analysis
+
+2.3.1 Study selection
+
+This study will implement a standardized literature management workflow: Retrieved citations will undergo automated and manual deduplication in EndNote 2025, with the deduplicated library subsequently uploaded to the Covidence platform (40). Within this system, two independent reviewers will conduct preliminary title/abstract screening for all records; a randomly selected 10% subset will undergo dual independent screening to quantify inter-rater agreement via Kappa statistics (target κ≥0.8), with discrepancies resolved through consensus discussion, while the remaining records will be screened independently. Studies passing initial screening will proceed to full-text assessment, wherein corresponding authors of publications with incomplete data will be contacted for supplementation; all exclusion decisions will be categorically documented in Covidence per PRISMA-P standards, automatically generating auditable exclusion records. The platform’s built-in functionality will ultimately export a PRISMA 2020-compliant flow diagram to dynamically visualize the screening process (41) (provisional diagram: Figure 1). For data extraction, customized Covidence electronic forms will facilitate dual independent data entry, automatically flagging discordant entries for arbitration until consensus is achieved, ensuring dataset accuracy and methodological transparency.
+
+Figure 1 PRISMA flow chart of study selection process. *Consider, if feasible to do so, reporting the number of records identified from each database or register searched (rather than the total number across aall databases/registers). **If automation tools were used, indicate how many records were excluded by a human and how many were excluded by automation tools.
+
+Flowchart illustrating the process of study identification and screening. It is divided into two methods: databases/registers and other methods. The left side shows records identified, removed, screened, and assessed, leading to inclusion in the review. The right side shows records from other sources, with similar screening and exclusion steps. The chart includes placeholder numbers and advises reporting specific data when feasible.
+
+2.3.2 Data extraction process
+
+Dual Independent Extraction: Two reviewers will independently extract data using a structured extraction template encompassing:
+
+Study Characteristics: Authors, publication year, journal, country, funding sources.
+
+Design Information: Intervention types, comparator groups, total study duration, diagnostic criteria.
+
+Sample Characteristics: Sample size per group, age/gender/racial composition.
+
+Outcome Metrics: Baseline and post-intervention scale scores (HAMD-17, HAMA, SDS, GAD-7, HADS, SF-36, SS-QOL, WHOQOL-BREF).
+
+TCM Syndrome Patterns: With reference to the TCM syndrome classification in the Guidelines for the Integrated Clinical Diagnosis and Treatment of Mental Disorders - Post-Stroke Mental Disorders (42), a standardized syndrome reference table will be developed to serve as the basis for data extraction and subsequent subgroup analysis, as shown in Table 3.
+
+Table 3 Diagnostic criteria for traditional chinese medicine (TCM) syndrome patterns.
+
+TCM syndrome pattern	Diagnostic criteria	
+Gan Yu Qi Zhi Zheng
+(Liver Qi Stagnation)	Core symptoms: Mental depression, emotional unrest; Distending pain in chest and hypochondrium (no fixed location); Epigastric stuffiness and belching
+Secondary symptoms: Anorexia, irregular defecation; Thin greasy tongue coating; Wiry pulse (Xian Mai)
+Key Points for Syndrome Differentiation: Meets ≥2 core symptoms + ≥1 secondary symptom	
+Qi Yu Hua Huo Zheng
+(Qi Stagnation Transforming into Fire)	Core symptoms: Sudden facial paralysis, slurred speech, limb clumsiness (even hemiplegia); Irritability, easy anger; Distending pain in chest and hypochondrium; Bitter and dry taste in mouth
+Secondary symptoms: Headache, red eyes, tinnitus; Acid regurgitation, constipation; Red tongue with yellow coating; Rapid wiry pulse (Xian Shu Mai)
+Key Points for Syndrome Differentiation: Meets ≥2 core symptoms + ≥1 secondary symptom	
+Tan Meng Qing Qiao Zheng
+(Phlegm Obscuring the Clear Orifices)	Core symptoms: Sudden syncope, unconsciousness;Locked jaw, clenched fists, limb spasticity; Absence of defecation and urination; Pale complexion, dark lips
+Secondary symptoms: Mental trance, poor memory, drowsiness; Dizziness, cold limbs; Profuse phlegm; Dark tongue with white greasy coating; Deep slippery pulse (Chen Hua Mai)
+Key Points for Syndrome Differentiation: Meets ≥2 core symptoms + ≥1 secondary symptom	
+Xin Pi Liang Xu Zheng
+(Heart-Spleen Deficiency)	Core symptoms: Excessive worrying, mental restlessness; Palpitations, timidity- Dizziness, fatigue
+Secondary symptoms: Insomnia, amnesia; Pale complexion, poor appetite; Pale tongue with thin white coating; Thin weak pulse (Xi Ruo Mai)
+Key Points for Syndrome Differentiation: Meets ≥2 core symptoms + ≥1 secondary symptom	
+Gan Shen Yin Xu Zheng
+(Liver-Kidney Yin Deficiency)	Core symptoms: Emotional unrest, palpitations, amnesia; Dizziness, tinnitus, soreness of waist and knees
+Secondary symptoms: Insomnia, dreaminess; Five-center heat (palms, soles, chest), night sweats; Dry mouth and throat; Red tongue with little fluid; Thin weak or deep thin pulse (Xi Ruo/Chen Xi Mai)
+Key Points for Syndrome Differentiation: Meets ≥2 core symptoms + ≥1 secondary symptom	
+Yu Xue Nei Zu Zheng
+(Blood Stasis Blockage)	Core symptoms: Mental depression, irritability; Headache, insomnia, amnesia;Chest and hypochondrium pain, Local cold or heat sensation in body
+Secondary symptoms: Purple dark tongue (with ecchymoses/petechiae); Wiry or unsmooth pulse (Xian/Se Mai)
+Key Points for Syndrome Differentiation: Meets ≥2 core symptoms + ≥1 secondary symptom	
+Bold text includes three parts: 1) the description of core diagnostic criteria (Core symptoms); 2) the description of secondary diagnostic criteria (Secondary symptoms); 3) the syndrome differentiation rules (Key Points for Syndrome Differentiation). Among them, the core symptoms are the key indicators to distinguish different syndrome types and determine the syndrome differentiation result.
+
+Follow-up Data: Scale scores categorized by endpoint: short-term (≤90 days), mid-term (91–364 days), and long-term (>364 days).
+
+Consistency Validation: Inter-rater agreement will be quantified using the Kappa statistic (κ≥0.8 required). If the naming of syndrome patterns in the included studies varies, two TCM clinical experts will perform a consensus classification based on the above diagnostic criteria, preferentially assigning them to the syndrome type with the highest match to core symptoms. Studies that cannot be clearly classified will be included in an “other syndrome patterns” subgroup or excluded. In case of any other disagreements, a third reviewer will arbitrate to reach a consensus.
+
+2.3.3 Data management and export
+
+All extracted data will undergo cross-verification and organization within the Covidence literature management platform, with final exportation in structured.csv format to support subsequent statistical analysis.
+
+2.3.4 Intervention group classification
+
+Intervention group classification will be completed during the data extraction phase. The intervention groups in each trial will be categorized according to the following classes: the TCM interventions will be classified as follows: Chinese herbal compound formulas with clearly defined compositions and syndrome differentiation basis; acupuncture therapies conforming to the STRICTA reporting guidelines (43); integrated TCM therapies; and other TCM therapies. Control condition types are classified as: conventional Western medicine treatment, where the categories of anti-affective disorder drugs included in this study are based on evidence-based therapeutic agents recommended by the American Psychiatric Association medication guidelines (44), including selective serotonin reuptake inhibitors (SSRIs, e.g., sertraline, fluoxetine), serotonin-norepinephrine reuptake inhibitors (SNRIs, e.g., venlafaxine), and tricyclic antidepressants (TCAs, e.g., amitriptyline), etc.; placebo control; and no-treatment control. If classification discrepancies cannot be resolved by a third-party reviewer, consultation will be sought with the project advisory group, comprising TCM clinical experts and psychiatric specialists, to determine the final classification through consensus.
+
+This study will generate a network plot to visualize the available evidence structure. This plot will depict all possible direct comparisons between interventions, with the thickness of the connecting lines between nodes, or numerical annotations, reflecting the number of included studies or sample size for each comparison pair. The reference node will be set as the active control condition, and different intervention combinations will be presented as distinct nodes (45). This figure will intuitively display the connectivity of the evidence network and the comparison pathways, providing a topological basis for subsequent statistical analysis. To address the potential issue of sparse network connectivity resulting from overly granular classification, we will adhere to the principle of “clinical similarity first.” Based on clinical criteria of “similarity in therapeutic principle” and “similarity in herbal composition or acupoint selection,” two reviewers will independently assess and subsequently submit cases for arbitration by an expert advisory panel to merge similar interventions into a single node.
+
+2.3.4 Risk of bias assessment
+
+Studies passing full-text screening will undergo risk of bias assessment. This assessment will be independently performed by two reviewers using the Cochrane Risk of Bias tool on the Covidence platform (46). The tool assesses key domains including the method of random sequence generation, allocation concealment, blinding of participants and personnel, blinding of outcome assessors, completeness of outcome data, and risk of selective outcome reporting.
+
+2.3.5 Summary measures
+
+The summary measures for this study will report scores for anxiety, depression, comorbid conditions and quality of life. For studies employing continuous data, the effect size between treatment groups will be presented as the mean difference (MD). The mean difference will be calculated as the follow-up score minus the baseline score (with some studies directly reporting the difference). Any study unable to provide any two of the following—baseline data, change values, or follow-up data—will be excluded. Furthermore, studies failing to report the standard deviation (SD) of the score change or the follow-up SD (or where this cannot be calculated from confidence intervals or standard errors) will also be excluded. These criteria aim to reduce the risk of bias while maintaining the informational integrity of the evidence network. Data will also be summarized via treatment rankings and the surface under the cumulative ranking curve (SUCRA) to aid in interpreting the relative effectiveness of all intervention types within the network.
+
+2.3.6 Transitivity assessment
+
+To validate the effectiveness of indirect comparisons within the network meta-analysis (NMA) and ensure the scientific validity and clinical plausibility of comparative results across different interventions, a table of trial characteristics that may act as effect modifiers will be compiled from the collected data. This table will include: ① Stroke-related factors (severity, type); ② PSED-related factors (time of onset, subtype); ③ Patient-related factors (age, sex, cognitive function); and ④ Co-interventions. By analyzing whether the distribution of potential effect modifiers is balanced across studies, this approach will assess whether these factors introduce heterogeneity that interferes with treatment effects, thereby supporting the evaluation of the transitivity assumption (47, 48). If clinically significant imbalances in key factors are identified, this will be explicitly noted in the interpretation of indirect comparisons and will serve as the basis for conducting pre-planned meta-regression or subgroup analyses.
+
+2.3.7 Data synthesis
+
+The primary objective of data synthesis in this study is to compare the efficacy differences among different Traditional Chinese Medicine (TCM) therapies. As network meta-analysis (NMA) can compensate for the lack of direct evidence through indirect estimations, it is suitable for achieving this objective. Currently, no head-to-head clinical trials have been conducted between distinct TCM therapies; therefore, studies will be pooled for analysis according to the intervention group classifications defined above. If quantitative synthesis of study results is infeasible, findings will be presented through a descriptive systematic review. All quantitative analyses will be performed using Stata 18 and RStudio software.
+
+2.3.8 Pairwise meta-analysis
+
+If included studies provide direct comparison data between different Traditional Chinese Medicine (TCM) interventions, an exploratory pairwise meta-analysis will be performed. A random-effects model will be employed for analysis, with forest plots used to display individual study results and pooled effect sizes; separate independent analyses will be conducted for each primary outcome measure. Publication bias and small-study effects will be assessed using funnel plots and Egger’s regression test. If significant bias is detected (Egger’s test P < 0.10), the trim-and-fill method will be applied to adjust effect size estimates (49).
+
+2.3.9 Subgroup analysis
+
+Given that this study examines the effectiveness of diverse Traditional Chinese Medicine (TCM) interventions for post-stroke emotional disorders (PSED), subgroup analyses will be implemented as follows: First, studies will be stratified into subgroups according to distinct PSED types. Subsequently, meta-regression models will be applied to perform further subgroup analyses incorporating variations in 1) forms of TCM interventions, 2) TCM syndrome patterns, 3) treatment durations, or 4) outcome data types, among other factors. These analyses will quantify inter-subgroup differences and test their statistical significance.
+
+2.3.10 Network meta-analysis
+
+Given that the transitivity assumption holds, we will conduct subgroup-specific random-effects network meta-analyses for PSED subtypes and TCM syndrome patterns (where data volume permits) using the “gemtc” package (version 1.0.2) in R 4.3.1 software under a Bayesian framework with non-informative priors. The NMA model will account for treatment effect correlations in multi-arm trials, comparing acupuncture, moxibustion, tuina, Chinese herbal medicine, traditional mind-body exercises (e.g., Tai Chi, Qigong), and other TCM therapies. Results will be presented in tables showing pairwise effect sizes between all interventions within each subgroup alongside probability rankings for optimal interventions (including mean ranks, 95% credible intervals, and surface under the cumulative ranking curve values). Model convergence will be evaluated using the Gelman-Rubin statistic, with values <1.1 indicating adequate convergence (50, 51).
+
+2.3.11 Sensitivity, heterogeneity, inconsistency, and evidence quality assessment
+
+The robustness of findings will be verified by testing different priors and comparing fixed-effect versus random-effects models to exclude influences from key assumptions or data selections. Given the heterogeneity arising from inconsistent definitions of the total clinical effective rate, we will construct a primary analysis model and a sensitivity analysis model and compare the consistency of effect estimates and intervention rankings between the two models to test the robustness of the results concerning this outcome measure. If substantial differences are observed, they will be highlighted in the results and discussion sections.
+
+According to Cochrane guidelines, I² and τ² statistics will be used to assess heterogeneity. If significant statistical heterogeneity or clinical imbalance in effect modifiers is identified, meta-regression analysis will be conducted to explore potential sources. The pre-specified effect modifiers will serve as candidate covariates. Random-effects meta-regression models will be used to examine the associations between these continuous or categorical covariates and the treatment effect size. This analysis will first be conducted within direct comparisons that have a sufficient number of studies. If the network structure and data permit, we may also employ network meta-regression within a Bayesian framework to evaluate the influence of covariates on the relative effects across the entire network.Publication bias, small-study effects, and related uncertainties will be detected and quantified through funnel plots and Egger’s regression. Since included studies may contain both two-arm and multi-arm trials, design inconsistency and loop inconsistency will be evaluated using the design-by-treatment interaction model; if inconsistency is detected within the network, closed loops will undergo further examination (52). The certainty of evidence for treatment effect estimates derived from the network meta-analysis will be assessed using a four-step approach specifically designed for NMA (53, 54). First, all direct comparisons within the network will be rated using the five standard GRADE domains. Second, for indirect comparisons, the certainty will be based on the assessment of the two contributing direct comparisons, with a focus on evaluating transitivity by comparing the distribution of potential effect modifiers across the trials forming the indirect comparison. If clinically important imbalances that threaten transitivity are identified, the evidence will be downgraded for indirectness. Third, for the mixed evidence derived from the NMA model, the assessment will start from the higher certainty rating between the available direct and indirect evidence. Network inconsistency will then be evaluated globally using the design-by-treatment interaction model. If significant and unexplained inconsistency is detected, downgrading will be applied. Finally, the certainty of evidence for each comparison will be categorized as high, moderate, low, or very low. Pre-specified operational downgrading criteria are as follows: For imprecision, downgrading will be considered if the 95% credible interval crosses a pre-defined minimal important difference or spans both the null value and a clinically important effect. For inconsistency, downgrading will be considered if evidence from direct comparisons shows a heterogeneity indicator I² > 50% with non-overlapping confidence intervals across studies, or if the P-value from network inconsistency tests is < 0.05. For indirectness, a clinically relevant imbalance in the distribution of key effect modifiers among the trials underlying an indirect comparison will serve as a basis for downgrading. Given that traditional rank probabilities based on any non-zero effect difference may be fragile and could overstate clinical superiority (54), a sensitivity analysis will be conducted to test the robustness of treatment rankings. This involves setting a series of thresholds representing minimal clinically important differences (e.g., for continuous outcomes: SMD = 0.2, 0.5, 0.8; for dichotomous outcomes: RR = 0.9, 0.8, 0.7) and recalculating the probability of each intervention being optimal. This analysis will evaluate the robustness of ranking results against clinical significance criteria.
+
+3 Discussion
+
+Stroke, ranked as the second leading cause of death globally and the third cause of mortality and disability worldwide (55), imposes a compound burden due to its high disability rate coupled with comorbid emotional disorders. Approximately 33%-50% of survivors develop affective disorders such as depression and anxiety (56). PSED severely impair patients’ quality of life across psychological, functional, and social adaptation dimensions, creating a vicious cycle with brain injury that doubles the risk of stroke recurrence and mortality. Consequently, early identification and intervention are critical for disrupting this cycle and improving prognosis. Currently, TCM demonstrates unique and significant advantages in managing PSED. By establishing a multidimensional regulatory network targeting “neuro-immuno-metabolic” pathways, TCM addresses the complex interplay of mechanisms underlying PSED through multi-target interventions (57, 58). Early TCM interventions not only effectively halt disease progression but also play a vital preventive role, substantially enhancing patient outcomes. Research indicates that early acupuncture treatment accelerates angiogenesis, promotes neuronal regeneration, and effectively inhibits apoptosis (59). For patients unable to tolerate herbal decoctions, non-pharmacological therapies such as acupuncture and Five-Element Music Therapy offer greater clinical flexibility and safety as viable alternatives. Furthermore, guided by TCM syndrome differentiation theory, treatments can be precisely tailored to match individual symptom profiles, ensuring targeted therapeutic efficacy. Finally, surveys reveal that TCM interventions provide superior cost-effectiveness ratios compared to conventional Western treatments, with patients reporting higher satisfaction levels post-treatment (60).
+
+However, the very characteristics of TCM—diverse therapeutic approaches, multi-target regulation, and syndrome differentiation-based treatment—render clinical research in this field exceptionally complex and lacking in large-scale randomized controlled trials. Although TCM has demonstrated promising outcomes in certain disease areas, these factors impede the depth of evidence-based research on TCM interventions. Network meta-analysis (NMA), by quantifying effect sizes and ranking probabilities across multiple TCM interventions, can provide clinicians with a hierarchical selection basis for “acupuncture-Chinese herbal medicine-integrated therapy,” thereby filling the evidence gap in clinical decision-making. Nevertheless, previous TCM NMAs have predominantly focused on comparing different interventions. Given the distinctive nature of TCM syndrome differentiation and treatment, clinical studies on PSED involve varied approaches to syndrome-specific treatment. Prior TCM NMAs have not addressed efficacy comparisons across different syndrome patterns. This protocol proposes a more refined NMA design that incorporates both TCM interventions and syndrome patterns, thereby addressing the previous neglect of syndrome-specific analysis in TCM NMAs. Although this protocol proposes subgroup analysis based on TCM syndrome patterns with the aim of exploring evidence for “treating the same disease with different methods,” it also faces methodological challenges. First, heterogeneity in diagnosis and incomplete reporting are major obstacles. Despite establishing reference criteria, the included RCTs may employ different syndrome differentiation systems or report patterns only cursorily, which could lead to classification errors and residual confounding. Second, the fragmentation of sample sizes may result in a limited number of studies and patients within each syndrome subgroup, thereby reducing statistical power and making it difficult to detect true subgroup effects. These factors imply that TCM syndrome patterns are more likely to serve as effect modifiers in this NMA, rather than as absolute criteria capable of clearly delineating patient subgroups. Consequently, the results of the subgroup analysis should be interpreted as exploratory and hypothesis-generating, not as confirmatory conclusions. Nonetheless, conducting this analysis is crucial, as it represents a necessary attempt to integrate the individualized treatment philosophy of TCM into the population-based framework of evidence synthesis. Regardless of whether the results show significant differences between syndromes, this study will provide critical baseline evidence and methodological reference for future, more rigorously designed clinical trials aimed at validating the efficacy advantage of “syndrome differentiation and treatment”. Concurrently, publishing this protocol holds significance in constructing a complete chain of evidence-based research. Pre-registration compels researchers to lock the PICO elements from the outset, preventing outcome-driven analysis. Protocol registration ensures traceability in the evidence generation process, significantly reducing the risk of the “file drawer effect” (61). This process inherently adheres to the FAIR data principles, establishing an internationally compliant evidence pool for TCM’s complex intervention system. It offers direction and reference for future researchers conducting other TCM NMAs. The adoption of more rigorous evidence-based methodologies will further enhance TCM’s persuasiveness within the internationally recognized evidence hierarchy, facilitating the integration of traditional medicine achievements into global stroke management guidelines.
+
+3.1 Prospects
+
+As TCM techniques continue to be explored, developed, and refined in the future, clinical research on TCM for PSED will become more detailed, robust, and comprehensive. With the conduct of more high-quality clinical studies and the expansion of data volume, subsequent quantitative analysis via NMA will enable the identification of the most suitable TCM treatment regimens for specific syndrome patterns based on TCM characteristics. This approach will maintain the advantages of TCM’s holistic view and syndrome differentiation-based treatment while constructing an internationally recognized evidence system. Ultimately, this will achieve the goal of “articulating TCM efficacy in modern scientific terms,” promoting TCM’s greater contribution within the global health system.
+
+Author contributions
+
+YC: Conceptualization, Data curation, Formal analysis, Methodology, Software, Writing – original draft. BL: Conceptualization, Investigation, Software, Writing – original draft. ZX: Conceptualization, Software, Writing – original draft. HJ: Funding acquisition, Project administration, Supervision, Writing – review & editing. YZ: Project administration, Supervision, Writing – review & editing.
+
+Conflict of interest
+
+The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
+
+Generative AI statement
+
+The author(s) declared that Generative AI was not used in the creation of this manuscript.
+
+Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.
+
+Publisher’s note
+
+All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.
+
+Supplementary material
+
+The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fpsyt.2026.1648067/full#supplementary-material
+
+Edited by: Magdalena Sowa-Kućma, University of Rzeszow, Poland
+
+Reviewed by: Shanchun Su, Duke University, United States
+
+Xin Geng, First Affiliated Hospital of Kunming Medical University, China
+
+
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+22 Ma YD Sun XW Yun F . Effects of acupoints electric stimulation on behavior and neurotransmitters in rats with post-stroke depression. JCAM. (2022) 38:44–50. doi: 10.19917/j.cnki.1005-0779.022210
+23 Zuo YC Lou BD Liu K Gao YY . Effect of electro-needling acupoints of pericardium meridian on blood ACTH and cort in treatment of post-stroke depression. JCAM. (2023) 39:53–7. doi: 10.19917/j.cnki.1005-0779.023073
+24 Yong Y Wang K . Electroacupuncture attenuates neuropathic pain and comorbid negative behavior: the involvement of the dopamine system in the amygdala. Front Neurosci. (2021) 15:657507. doi: 10.3389/fnins.2021.657507, PMID: 34025342 PMC8137986
+25 Cai W Ma W Wang GT Shen WD . Effects of electroacupuncture on serum expression of interleukin-1β, interleukin-6, and tumor necrosis factor-α in rats with post-stroke depression. Chin J Integr Med Cardio-Cerebrovasc Dis. (2019) 17:3515–8. doi: 10.12102/j,issn.1672-1349.2019.22.014
+26 Sun Y Gao Y Wang RZ Sun YZ . Effect of tiaoshen yunshu acupuncture on intestinal flora and its metabolites and related neurotransmitters in treatment of post-stroke depression: A randomized control trial. JCAM. (2024) 40:33–8. doi: 10.19917/j.cnki.1005-0779.024007
+27 Cao K Zhong J Wang S Shi Y Bai S Zhao J . SiNiSan exerts antidepressant effects by modulating serotonergic/GABAergic neuron activity in the dorsal raphe nucleus region through NMDA receptor in the adolescent depression mouse model. J Ethnopharmacol. (2024) 328:118040. doi: 10.1016/j.jep.2024.118040, PMID: 38479542
+28 Shi BY Rao ZL Luo J Liu XB Fang Y Cao HJ . Protective effect and mechanism of Xiaoyao San on lipopolysaccharideinduced hippocampal neurons injury. Chin J Chin Mater Med. (2019) 44:781–6. doi: 10.19540/j.cnki.cjcmm.20181101.003, PMID: 30989892
+29 Zhang P Chang XQ . Observation on the rehabilitation efficacy of auricular point pressing with beans combined with jue-tone music therapy in elderly patients with hypertension complicated by depression. Shanxi Med J. (2023) 52:716–9. doi: 10.3969/j.issn.0253-9926.2023.09.018
+30 Chan YY Lo WY Yang SN Chen YH Lin JG . The benefit of combined acupuncture and antidepressant medication for depression: A systematic review and meta-analysis. J Affect Disord. (2015) 176:106–17. doi: 10.1016/j.jad.2015.01.048, PMID: 25704563
+31 Yang NN Lin LL Li YJ Li HP Cao Y Tan CX . Potential mechanisms and clinical effectiveness of acupuncture inDepression. Curr Neuropharmacol. (2022) 20:738–50. doi: 10.2174/1570159X19666210609162809, PMID: 35168522 PMC9878952
+32 Greco T Biondi-Zoccai G Saleh O Pasin L Cabrini L Zangrillo A . The attractiveness of network meta-analysis: a comprehensive systematic and narrative review. Heart Lung Vessel. (2015) 7:133–42., PMID: 26157739 PMC4476767
+33 Biondi-Zoccai G Abbate A Benedetto U Palmerini T D’Ascenzo F Frati G . Network meta-analysis for evidence synthesis: What is it and why is it posed to dominate cardiovascular decision making? Int J Cardiol. (2015) 182:309–14. doi: 10.1016/j.ijcard.2015.01.023, PMID: 25585376
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+36 Jansen JP Trikalinos T Cappelleri JC Daw J Andes S Eldessouki R . Indirect treatment comparison/network meta-analysis study questionnaire to assess relevance and credibility to inform health care decision making: an ISPOR-AMCP-NPC good practice task force report. Value Health. (2014) 17:157–73. doi: 10.1016/j.jval.2014.01.004, PMID: 24636374
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+39 National Health Commission of the People’s Republic of China . Guideline for prevention and treatment of cerebrovascular disease(2024 edition). Chin J Magn Reson Imaging. (2025) 16:1–8.
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+61 Page MJ Moher D Bossuyt PM Boutron I Hoffmann TC Mulrow CD . PRISMA 2020 explanation and elaboration: updated guidance and exemplars for reporting systematic reviews. BMJ. (2021) 372:n160. doi: 10.1136/bmj.n160, PMID: 33781993 PMC8005925
diff --git a/corpus/psychology/text/4a247a6bdffd04b5.txt b/corpus/psychology/text/4a247a6bdffd04b5.txt
new file mode 100644
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--- /dev/null
+++ b/corpus/psychology/text/4a247a6bdffd04b5.txt
@@ -0,0 +1,80 @@
+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: BMC Psychiatry
+Journal ID: BMC Psychiatry
+NLM Journal ID: 100968559
+
+BMC Psychiatry
+
+EISSN: 1471-244X
+Publisher: BMC
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC10668440
+PMID: 38001402
+DOI: 10.1186/s12888-023-05367-7
+Article ID: 5367
+Article version: 1
+Subjects: Correction
+
+Correction: Incidence rates of treated mental disorders before and during the COVID-19 pandemic—a nationwide study comparing trends in the period 2015 to 2021
+
+Jensen Pia pia.jensen@fhi.no
+1 2
+Engdahl Bo 3
+Gustavson Kristin 1 2
+Lund Ingunn Olea 1 2
+Pettersen Johanne Hagen 1 2
+Madsen Christian 4
+Hauge Lars Johan 5
+Knudsen Ann Kristin Skrindo 4
+Reneflot Anne 5
+Brandlistuen Ragnhild Eek 6
+Ask Helga 1 2
+Nesvåg Ragnar 1
+1 https://ror.org/046nvst19 grid.418193.6 0000 0001 1541 4204 Department of Mental Disorders, Norwegian Institute of Public Health, Oslo, Norway
+2 https://ror.org/01xtthb56 grid.5510.1 0000 0004 1936 8921 Department of Psychology, University of Oslo, Oslo, Norway
+3 https://ror.org/046nvst19 grid.418193.6 0000 0001 1541 4204 Department of Physical Health and Ageing, Norwegian Institute of Public Health, Oslo, Norway
+4 https://ror.org/046nvst19 grid.418193.6 0000 0001 1541 4204 Centre for Disease Burden, Norwegian Institute of Public Health, Bergen, Norway
+5 https://ror.org/046nvst19 grid.418193.6 0000 0001 1541 4204 Department of Mental Health and Suicide, Norwegian Institute of Public Health, Oslo, Norway
+6 https://ror.org/046nvst19 grid.418193.6 0000 0001 1541 4204 Department of Child Health and Development, Norwegian Institute of Public Health, Oslo, Norway
+Electronic publication date: 2023 Nov 24
+Publication date: 2023
+Volume: 23
+Electronic Location ID: 874
+Copyright: © The Author(s) 2023
+License: Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated in a credit line to the data.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Erratum for: Incidence rates of treated mental disorders before and during the COVID-19 pandemic—a nationwide study comparing trends in the period 2015 to 2021 23 13 9 2023 668 BMC Psychiatry 10.1186/s12888-023-05157-1 PMC10500922 37704941
+issue-copyright-statement: © BioMed Central Ltd., part of Springer Nature 2023
+
+Ÿ==============================Ÿ
+Correction: BMC Psychiatry (2023) 23:668
+
+10.1186/s12888-023-05157-1
+
+Following the publication of the original article [1], the authors identified errors in the Discussion section. The updated sentence is given below, and the change has been highlighted in bold typeface.
+
+The sentence currently reads:
+
+In primary- and specialist health care, the observed incidence rate among 18–24-year-olds in 2021 was more than 140% higher than predicted.
+
+The sentence should read:
+
+In primary- and specialist health care, the observed incidence rate among 18–24-year-olds in 2021 was more than 40% higher than predicted.
+
+The original article [1] has been corrected.
+
+The online version of the original article can be found at 10.1186/s12888-023-05157-1.
+
+Publisher’s Note
+
+Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
+
+
+References
+
+1. Jensen, BMC Psychiatry. (2023) Incidence rates of treated mental disorders before and during the COVID-19 pandemic—a nationwide study comparing trends in the period 2015 to 2021 (2023) 23:668 10.1186/s12888-023-05157-1.10.1186/s12888-023-05157-1 PMC10500922 37704941
diff --git a/corpus/psychology/text/4a450a4ac4109411.txt b/corpus/psychology/text/4a450a4ac4109411.txt
new file mode 100644
index 0000000000000000000000000000000000000000..77c4c131f0de647449a9f53c06040d09292fac37
--- /dev/null
+++ b/corpus/psychology/text/4a450a4ac4109411.txt
@@ -0,0 +1,461 @@
+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Biophys J
+Journal ID: Biophys J
+NLM Journal ID: 0370626
+
+Biophysical Journal
+
+ISSN: 0006-3495
+EISSN: 1542-0086
+Publisher: The Biophysical Society
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC13335156
+PMID: 42249612
+DOI: 10.1016/j.bpj.2026.06.005
+Article ID: S0006-3495(26)00413-3
+Article version: 2
+Subjects: Articles
+
+Curvature-based machine-learning method for automated segmentation of dendritic spines
+
+Geraldo Abdel Kader A. 1
+Chirillo Michael A. 2
+Harris Kristen M. 3
+Fai Thomas G. tfai@brandeis.edu 4 ∗
+1 Department of Mathematics, Brandeis University, Waltham, MA, USA
+2 Department of Biological Sciences, University of Rhode Island, Kingston, RI, USA
+3 Department of Neuroscience, University of Texas at Austin, Austin, TX, USA
+4 Department of Mathematics and Volen Center for Complex Systems, Brandeis University, Waltham, MA, USA
+∗ Corresponding author tfai@brandeis.edu
+Print publication date: 2026 Jul 21
+Electronic publication date: 2026 Jun 5
+Volume: 125
+Issue: 14
+First page: 3604
+Last page: 3619
+Received 2025 Dec 29; Accepted 2026 Jun 2
+Copyright: © 2026 The Author(s)
+Copyright year: 2026
+License: This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+CURVATURE-BASED MACHINE LEARNING METHOD FOR AUTOMATED SEGMENTATION OF DENDRITIC SPINES 8 12 2025 2025.12.04.692360 bioRxiv 10.64898/2025.12.04.692360 PMC12713589 41427309
+
+Editor: Guoyou Huang.
+
+Ÿ==============================Ÿ
+Recent advances in connectomics have been led by high-resolution reconstruction of large volumes of neural tissues using electron microscopy (EM), providing unprecedented insights into brain structure and function. Dendritic spines—dynamic protrusions on neuronal dendrites—play crucial roles in synaptic plasticity, influencing learning, memory, and various neurological disorders. However, current spine-analysis methods often rely on manual annotation of subcellular features, limiting their ability to handle the complexity of spines in dense dendritic networks. This paper introduces a novel automated computational framework that integrates discrete differential geometry, machine learning, and 3D image processing to analyze dendritic spines in these intricate environments. By generating distributions of spine morphology from high-resolution images including many thousands of spines, our approach captures subtle variations in spine shapes, offering a nuanced understanding of their roles in synaptic function. This framework is tested on multiple EM datasets with the aim of enhancing our understanding of synaptic plasticity and its alterations in disease states. The proposed method is poised to accelerate neuroscience research by providing a scalable, objective, and comprehensive solution for spine analysis, uncovering insights into the role of spine geometry for neural function.
+
+Significance
+
+We develop a deep-learning method to probe key aspects of the structure of neuronal dendritic spines and formulate a series of neural-network geometries that improve spine detection. The training data consist of manually segmented dendritic segments from hippocampal area CA1 of juvenile rats. We validate the method by applying the trained model to data obtained from published reconstructions of spiny dendrites and demonstrate that our method successfully learns key features of neuronal structure. By taking this step toward the automation of spine segmentation, we are able to obtain statistical information on individual synaptic structures and correlations between their geometries.
+
+Introduction
+
+Recent advances in electron microscopy (EM) and connectomics have made it possible to reconstruct astonishingly large volumes of neural tissue at nanometer resolution.1,2 These breakthroughs have opened new opportunities for studying brain microstructures, particularly dendritic spines, dynamic protrusion on dendrites where most excitatory synapses in the brain occur. The morphology of dendritic spines—encompassing shape, size, and density—is highly plastic and closely tied to fundamental neurological processes such as learning and memory.3,4,5,6,7
+
+Quantitative studies have shown that fine-scale geometric features of spines, including head volume, neck length, and curvature, are strongly associated with synaptic strength, developmental state, and functional specialization.8,9,10 Changes in spine structure have also been linked to drug abuse, environmental influences, and a wide range of neurodevelopmental, neurodegenerative, and psychiatric disorders.11,12,13
+
+Accurate detection and analysis of dendritic spines in three-dimensional (3D) reconstructions is therefore essential for advancing our understanding of synaptic organization and plasticity. However, spine identification remains challenging due to their heterogeneous morphologies, dense clustering, and local curvature variations. Manual annotation is highly time intensive and impractical for large-scale datasets, underscoring the need for automated and reliable computational methods. Several segmentation approaches have been proposed in recent years,14,15,16,17,18,19,20,21,22 yet challenges remain in achieving both accuracy and scalability.
+
+In particular, many existing 3D convolution neural-network (CNN)-based methods23,24,25 operate directly on voxel representations, which require dense volumetric grids and therefore scale poorly to large EM datasets. This voxel dependence leads to substantial memory overhead, slow inference, and difficulty capturing fine geometric details such as thin spine necks. More broadly, large EM volumes contain millions of surface elements, creating significant computational constraints for voxel-level processing or repeated high-resolution inference. Together, these challenges underscore the need for automated approaches that incorporate geometric cues and remain robust across large, heterogeneous datasets.
+
+To address these challenges, we introduce a method for automated spine segmentation that combines discrete differential geometry with deep learning. Our framework begins by preprocessing 3D reconstructions of dendritic segments to smooth the triangulated mesh, reduce noise, and enhance surface quality. From the resulting meshes, we extract geometric descriptors such as Gaussian and mean curvature along with additional features including distances from the dendritic shaft skeleton and clustering-based descriptors. Together, these features provide a rich representation of both local and global morphology.
+
+Building on this geometric foundation, we developed a series of deep neural-network (DNN) architectures to evaluate how feature enrichment impacts segmentation performance. The baseline model, DNN1, relies primarily on curvature-based descriptors. DNN2 extends this by incorporating distance-to-skeleton features, improving the separation of spines from shafts. Finally, DNN3 integrates a set of enriched geometric and topological descriptors, enabling the network to capture subtle morphological variations and complex spine arrangements. This progression of models demonstrates how systematically incorporating new features enhances both training convergence and segmentation accuracy.
+
+In this work, we use deep learning to generate a dataset consisting of over 500 segmented spines and analyze the distributions of spine neck diameter, spine area, and spine volume along with their correlations. The resulting distributions address a fundamental biological question of how form and function are related in dendritic spines.3,26
+
+Materials and methods
+
+In this section, we employ differential geometry to design a DNN architecture for the segmentation of dendritic spines. As a first step, we analyze how curvature can contribute to the characterization of dendritic morphology. Building on this analysis, we then develop and explore a DNN that leverages the geometric properties of dendrites to achieve accurate segmentation. For convenience, a summary table of the symbols and variables used throughout the materials and methods section is provided in Table S1.
+
+Dendritic morphology analysis using discrete differential geometry
+
+Segmentation of dendritic shafts and spines can be guided by their differential geometric properties, particularly Gaussian and mean curvature. These curvature measures capture local shape variations that distinguish the roughly cylindrical shaft from protruding spines. However, raw curvature values obtained directly from EM reconstructions are often noisy due to the sectioning process and mesh irregularities. To address this, we first smooth the dendritic triangulated surface mesh using discrete differential-geometry techniques, then compute curvature values, and finally enhance these through image-processing filters. This three-step process—smoothing, curvature computation, and enhancement—provides robust geometric descriptors that form the basis for accurate segmentation.
+
+Mean and Gaussian curvature
+
+In this section, we motivate the use of Gaussian and mean-curvature values as key variables for segmenting the dendritic shaft. In the study of dendritic morphology, the shaft is typically modeled as an approximately cylindrical structure from which spines protrude. The discrete mean H and Gaussian curvatures K computation details are provided in Section S5.
+
+The Gaussian curvature provides insight into the surface’s shape at different points. At hyperbolic points, where the surface curves in opposite directions (saddle-like), the Gaussian curvature is negative. Conversely, at elliptical points, where the surface curves uniformly in the same direction (dome-like), the Gaussian curvature is positive. This contrasts with the cylindrical shaft, along which the Gaussian curvature is zero. Applying these principles to dendritic morphology, we observe that, along the spine neck and at the intersection between the neck of a spine and the dendritic shaft, the surface exhibits a saddle shape, leading to negative Gaussian curvature. On the other hand, the spine head, with its more spherical or dome-like structure, exhibits positive Gaussian curvature.
+
+The mean curvature further characterizes the surface. On a concave surface, the mean curvature is positive, while, on a convex surface, it is negative. This distinction helps to identify regions of significant shape change. For instance, at the transition from the dendritic shaft to the spine neck, the surface is concave, leading to relatively positive mean curvature. In contrast, the spine head, which is a convex region, has relatively negative mean curvature.
+
+These curvature measures are most useful for segmentation when the triangular mesh is sufficiently smooth, as smoothness preserves the overall geometry of the dendritic branches while reducing discretization noise. Under these conditions, the curvature fields more accurately capture the cylindrical shape of the dendritic shaft and the geometric deviations introduced by spine necks and spine heads. As a result, the smoothed curvature values provide a more reliable representation of the underlying morphology, which is valuable in distinguishing the shaft from protruding spines.
+
+Smoothing the triangulated surface mesh
+
+To analyze the triangulated surface of the dendritic mesh, we first address the inherent roughness introduced by the EM sectioning process. We apply discrete differential-geometry techniques—specifically a discrete approximation of mean-curvature (Willmore) flow—to smooth the triangular surface mesh.
+
+We define kbend as the bending coefficient of the surface. The curvature energy over the surface A is(1) Wbend(X)=kbend2∫AH2(X)dA,
+
+and the associated bending force is obtained as the negative gradient of this energy:(2) Fbend(X)=−∇XWbend(X).
+
+The surface is then evolved by a gradient-descent step,(3) ∂∂tX=Fbend(X),
+
+which produces a smoothed version of the mesh. In practice, this smoothing is implemented using standard discrete differential-geometry operators. Although the mesh consists of discrete triangles, smoothing is well defined: each vertex exchanges curvature information only with the vertices in its 1-ring neighborhood (the set of triangles directly adjacent to it), as illustrated in Figure S1. Updating each vertex using curvature information from its neighbors provides a discrete analog of smoothing on a continuous surface. This suppresses high-frequency numerical noise introduced by the discretization while preserving the underlying geometric structure of the dendritic mesh. Further numerical details, following the approach of Wu et al.,27 are provided in Section S5.
+
+The results of performing this smoothing are illustrated in Figure 1, where we compute the Gaussian and mean curvature of a segment of spiny dendrite. The data were obtained from high-resolution 3D EM reconstructions of dendritic segments in the CA1 region of the hippocampus from P21 rats. Slices were subjected to in vitro theta-burst stimulation to induce long-term potentiation (LTP) or to control stimulation, as described elsewhere.28,29,30 Comparing the curvature before and after smoothing, we observe that the processed mesh exhibits a more easily interpretable profile of the dendritic surface, which can be exploited to improve the accuracy of spine-shaft segmentation.Figure 1 Effect of curvature smoothing on dendritic meshes. The plots labeled (init) and (smooth) show the initial dendritic curvature and the curvature after smoothing, respectively. The plots labeled mean and gauss correspond to the mean curvature and Gaussian curvature of a segment of dendrite. Smoothing enhances the curvature profile, producing a more easily interpretable pattern in the mesh that can be effectively leveraged to improve segmentation accuracy. For visualization, Gaussian curvature values are thresholded to remain within an absolute value of 45, while the mean curvature is constrained within an absolute value of 15, thereby highlighting the most relevant mesh faces. The triangular mesh is obtained from CA1 dendritic reconstructions.28,29,30
+
+Enhancement of curvature through image processing
+
+Here, we provide an intuition for using image-processing techniques to enhance the mean and Gaussian curvature values. The goal is to emphasize regions of the surface with significant curvature changes, which are more likely to correspond to dendritic shafts or spines, thereby facilitating segmentation. This forms the foundation for the machine-learning methods that will be developed in the segmentation algorithm.
+
+First, let us define the following sigmoidal function, which is often used in image processing to normalize and enhance contrast:ζ(x)=11+exp(−x).
+
+This transformation maps all real values into the interval (0, 1). For large positive x, ζ(x) → 1, while, for large negative x, ζ(x) → 0. Around x = 0, the function has its steepest slope, which enhances small variations near zero and makes them more distinguishable.
+
+Applying this transformation to the mean curvature H and the Gaussian curvature K, we obtain(4) H˜=ζ(aHH+bH),K˜=ζ(aKK+bK),
+
+where aH, bH, aK, and bK are empirically chosen parameters used to emphasize specific geometric features of the dendritic mesh. For example, in the neck region of a spine, we expect relatively high negative Gaussian curvature. By appropriately choosing aK and bK, these negative values are pushed toward the lower end of the sigmoid, making them stand out more clearly during segmentation.
+
+In contrast, along the cylindrical shaft, the Gaussian curvature is close to zero. Proper tuning ensures that values near zero are mapped consistently with the shaft so that these regions are correctly identified. For mean curvature, which distinguishes concave and convex regions, the transformation highlights transitions: concave regions (positive mean curvature) are enhanced toward higher sigmoid values, while convex regions (negative mean curvature) are mapped toward lower values.
+
+In practice, within this paper, the quantities H˜ and K˜ are not computed explicitly. Their formulation serves only to motivate the use of a DNN as an approximation function for the segmentation task, with a sigmoidal activation used in the output layer. Figure 3 shows the spine and shaft probability outputs of the DNN that will be examined next. These results demonstrate a substantial improvement in segmentation quality compared to the manually tuned baseline. The overall processing pipeline—from mesh smoothing and geometric feature extraction to DNN-based prediction—is summarized in the flowchart shown in Figure S2.Figure 2 DNN1 architecture used to segment the dendrite shaft. The input layer consists of the mean curvature H and the Gaussian curvature K, computed after smoothing, and their squares. The network includes four hidden layers, each with 50 neurons and ReLU activation functions. The output layer employs a sigmoidal activation function.
+
+Figure 3 Visualization of geometric-based and learned probability representations used for dendritic spine segmentation. The part labeled “sigmoid” shows the sigmoid of a linear combination of mean intensity and Gaussian curvature, which highlights the neck region and serves as a handcrafted baseline cue for segmentation. The parts labeled “probability shaft” and “probability spine” display the class-specific probability outputs of the network DNN3 for shaft and spine, respectively. Compared with the sigmoid representation, the learned probabilities provide a clearer and more discriminative separation of spine and shaft regions. The triangular mesh is obtained from CA1 dendritic reconstructions.28,29,30
+
+DNN approach for spine and shaft analysis
+
+In the previous section, we provided an intuitive explanation of how segmentation can be enhanced using image-processing techniques. We then introduced empirical filtering parameters that can improve segmentation quality. Instead of manually selecting these parameters and explicitly computing H˜ and K˜, we can leverage DNNs to learn an optimal segmentation approximation function based on H and K. At the same time, DNNs allow us to incorporate non-linearities that further enhance segmentation performance.
+
+We analyze three different DNN architectures. The first network is designed to support the second by assisting in the extraction of the shaft skeleton, while the third network relies solely on external Python libraries for skeletonization. Machine-learning methods have also been employed for dendrite segmentation of dendritic spines obtained from confocal reconstruction images using CNNs.20 In this work, we adopt a simple DNN architecture inspired by the physics-informed neural-network (PINN) model,31,32,33,34,35,36,37,38 which has been widely applied to approximate ordinary and partial differential equations. These models leverage their well-known ability to serve as universal function approximators.37 Given the geometrical characteristics of the dendritic triangular mesh, this approximation capability of DNNs constitutes a fundamental tool in our algorithm. Here, we present the architectures that produced the best results among the different trials.
+
+DNN (DNN1) using the Gaussian and mean curvature
+
+As for the sigmoidal function (4) introduced in the previous section, various model parameters require fine-tuning to enhance the shaft segmentation process. Rather than manually selecting these parameters and computing H˜ and K˜, we train a DNN in a two-step procedure.
+
+We first train a DNN, denoted as DNN1, whose architecture is illustrated in Figure 2. The input layer receives both the mean curvature H and the Gaussian curvature K values of the dendritic triangular mesh (after smoothing), together with their squared terms to capture higher-order variations. The input features are preprocessed such that the Gaussian curvature values and their squared terms are thresholded to remain within an absolute value of 45. Specifically, for K = (K1, K2, …, Km), we enforce Ki ∈ [−45, 45]. We then compute Ki2 and threshold its value to the range [0, 45]. Similarly, the mean-curvature values and their squared terms are constrained within an absolute value of 15, following the same procedure as in the Gaussian curvature case.
+
+These thresholds are applied because curvature values can sometimes become very large, and such extreme values do not significantly improve prediction accuracy but can instead cause instability during training and inference. To further reduce instability, any NaN values, if present, are replaced with the average of the corresponding curvature values.
+
+The network consists of four hidden layers, each containing 50 neurons with Rectified Linear Unit (ReLU) activation functions to introduce non-linearity.38 The output layer employs a sigmoid activation function, as described in section enhancement of curvature through image processing, to classify vertices into dendritic shafts and spines.
+
+The segmentation produced by DNN1 is not fully satisfactory, as regions within spines are sometimes misclassified as part of the shaft. This misclassification arises because certain spines regions exhibit relatively flat curvature, making them appear similar to shaft regions.
+
+Skeletonization
+
+In this section, we describe that the process used to obtain the skeletonization of dendritic meshes is an image-processing technique that reduces binary shapes to thin, single-pixel-wide lines while preserving their topological structure and connectivity.39,40
+
+The first step in building the skeleton is to ensure that the mesh is watertight, meaning that it forms a completely closed surface with no gaps, holes, or disconnected edges. A watertight mesh guarantees a well-defined interior and exterior, which is essential for reliable geometric processing and for preserving the topological structure during skeletonization. To achieve this, we wrap the existing mesh using the algorithm described in Section S6.1. This procedure converts the surface into a uniformly sampled point cloud, estimates and orients normals, and then applies Poisson surface reconstruction to generate a closed, watertight representation.
+
+In addition to Poisson reconstruction, we also evaluated the alpha-wrap method provided by PyMeshLab,41 which is based on the classical α-shape formulation.42 Alpha wrapping produces well-behaved closures and can preserve fine geometric detail; however, in our experiments, it was substantially slower than Poisson surface reconstruction for meshes of this size and resolution. For this reason, we adopted Poisson reconstruction as our primary wrapping method. For completeness, the alpha-wrap implementation is also included in Section S6.1.
+
+Once a watertight mesh is obtained, we compute its skeleton using the scikit-image skeletonization package, which implements algorithms from Lee et al. and Zhang and Suen.39,40 Further implementation details are provided in Section S6. This simplified representation captures the essential branching geometry of dendrites for subsequent segmentation and morphological analysis.
+
+DNN (DNN2) using shaft skeleton
+
+We can enhance dendritic spine-shaft segmentation by incorporating the shaft skeleton. This involves using the distance between the shaft-skeleton vertices and the dendritic branch as an additional input to the DNN. For this purpose, we use the shaft segmented with DNN1 together with the skeletonization procedure outlined in section skeletonization.
+
+To begin, we consider the shaft-segmented meshes obtained from DNN1. Since this mesh results from the dendritic branch after spine regions have been segmented, it is no longer watertight. Therefore, we apply the procedure described earlier to make the mesh watertight. Once the shaft mesh skeletonization is completed, we compute the distance D between the shaft skeleton and the dendritic-branch mesh vertices. Here, for each vertex Xl, l ∈ {1, 2, …, n} in the dendritic triangular mesh with n vertices, and {V1, V2, …, Vv} the set of shaft-skeleton vertices, we compute the Euclidean norm:(5) Dl=min1≤j≤vVj−Xl2,D=D1,D2,…,Dn.
+
+With this additional information, we develop an improved DNN, DNN2, whose architecture is shown in Figure S3. This model is similar to DNN1 except that it incorporates the new input feature. As in the earlier model, the input layer receives both the Gaussian and mean-curvature values of the dendrite, along with the squared values of these curvatures as additional features. The network consists of four hidden layers, each containing 50 neurons with ReLU activation functions to introduce non-linearity. The output layer employs a sigmoid activation function, as discussed in section enhancement of curvature through image processing, to classify vertices into dendritic shafts or spines.
+
+Dendrite spine-shaft segmentation using dendritic-branch regions (DNN3)
+
+To improve segmentation accuracy, we introduce a DNN (DNN3) that incorporates regional information from dendritic-branch segments. These segments are derived from the dendrite skeleton, which serves as a structural reference for spatial organization.
+
+For this model, once the skeleton is extracted, we compute the shortest distance from each mesh vertex to its nearest skeleton point. These distances are then clustered using the k-means algorithm to partition the dendritic mesh into multiple regions. This regional segmentation enables us to distinguish between different parts of the dendrite shaft, spine neck, and spine head—regions that are critical for accurate classification.
+
+As shown in Figure 4, to capture variations in dendritic morphology, we apply k-means clustering with multiple values of k. We denote these segmentation features by Sk, where k ∈ {2, 3, …, 10} corresponds to the number of clusters. In particular, the value of each feature Sk is given by the corresponding cluster label. Therefore, this model incorporates nine additional scalar features. In this study, we explore values of k ranging from 2 to 10 to provide a multi-scale representation of regional structure.Figure 4 Additional features used in the DNN training. The plot labeled “gauss−sq” and “mean−sq” show, respectively, the square of the Gaussian and mean curvature of the dendrite. The plot labeled “length sh. skl. vert.” indicates the distance from the shaft skeleton to the dendritic mesh vertices, denoted by D. The plot labeled “kmean−k” illustrates the k subdivision from k-means clustering, corresponding to the set Sk. The triangular mesh is obtained from CA1 dendritic reconstructions.28,29,30
+
+In addition to these region-based segmentation features, we incorporate Gaussian curvature and its squared value as geometric descriptors. These measures are particularly effective for identifying neck regions, as discussed in earlier sections. We intentionally exclude mean curvature as we have observed that the mean-curvature input increases the probability of misclassifying all dome-like regions as spines, leading to false positives. By omitting mean curvature and focusing on more discriminative features, DNN3 achieves improved segmentation performance compared to the baseline models.
+
+Note that, in practice, the k-means algorithm is not deterministic because its initial values depend on a random seed. To mitigate this and obtain consistent region assignments, we perform 50 independent clustering runs and select the labeling corresponding to the run with the lowest final k-means inertia. Since inertia measures the within-cluster compactness optimized by k-means, choosing the run with minimal inertia yields the most stable and coherent clustering among all runs. This procedure effectively filters out seed-dependent fluctuations and provides reproducible region assignments without requiring post hoc consensus voting.
+
+We also considered using the silhouette score as an alternative selection criterion; however, computing silhouette values for all vertices is prohibitively expensive due to the large number of mesh vertices. For this reason, inertia-based selection offered a practical and computationally efficient solution.
+
+Loss function
+
+We use the binary cross-entropy (BCE) to compute the loss function, and its derivation is presented below.
+
+Let us consider a set of m dendritic meshes, denoted as D=(D1,D2,…,Dm), where each mesh Di consists of ni vertices. For the training set, we assume that each Di has a ground-truth classification matrix Yi∈{0,1}ni×2, which represents the classification of vertices in Di in one-hot encoding, such thatYi,j=(0,1)ifvertexjofDibelongstothedendriticshaft,(1,0)otherwise.
+
+We define Y = (Y1, Y2, …, Ym) as the set of all annotation matrices. Next, we define the set of mean-curvature vectors for all dendritic meshes as H = (H1, H2, …, Hm) and the set of Gaussian curvature vectors as K = (K1, K2, …, Km). For each mesh Dj, j ∈ {1, 2, …, m}, the mean-curvature vector is given by Hj=(H1,j,H2,j,…,Hnj,j), and the Gaussian curvature vector by Kj=(K1,j,K2,j,…,Knj,j), where Hi,j and Ki,j denote the mean and Gaussian curvatures of Dj at vertex i, for i ∈ {1, 2, …, nj}.
+
+Additionally, we define the distance vector D = (D1, D2, …, Dm), representing the distances between the central curve and the vertices, as well as additional structural descriptors Sk, where k ∈ {2, 3, …, 10}. For each mesh Dj, we write Sjk=(S1,jk,S2,jk,…,Snj,jk).
+
+We now define the feature vector for vertex i of mesh j asZi,j=Hi,j,Hi,j2,Ki,j,Ki,j2,Di,j,Si,j2,Si,j3,…,
+
+and the corresponding feature matrix for dendritic mesh Dj asZj=Hj,Hj2,Kj,Kj2,Dj,Sj2,Sj3,….
+
+Our objective is to find a functionfθ:Zj↦Yj∈[0,1]nj×2,∀j∈{1,2,…,m},
+
+that best approximates the ground-truth classification by minimizing the following loss function:L=minθfθ(Z)−Y,
+
+where ‖·‖ denotes an appropriate norm measuring the discrepancy between the predicted and actual classifications. In particular, we use a weighted sum of the BCE, which encourages a more balanced optimization process. The BCE formula is given byBCE(y,yˆ)=−y⁡log(yˆ)+(1−y)log(1−yˆ).
+
+The final loss function is defined asLθ=1m∑j=1m1nj∑i=1njBCE(Yi,j,fθ(Zi,j))⋅wj2.
+
+Here the weights wj is empirically determined.
+
+Note that the mean curvature H and Gaussian curvature K used during training are computed after smoothing the curvature fields on the triangular dendritic-branch meshes. The sole purpose of this smoothing is to obtain stable and interpretable curvature estimates that enhance the segmentation performance during training. As described in section smoothing the triangulated surface mesh, smoothing the curvature improves the readability of the curvature profile and reduces noise-driven artifacts. Thus, the smoothing step in our pipeline serves only as a feature-enhancement operation, not as a geometric modification of the underlying dendrite.
+
+Importantly, all manual annotations were performed on the actual, unsmoothed dendritic branches, ensuring that the ground-truth labels correspond to the true biological geometry. During training, the network is therefore supervised to segment the real dendritic shaft and spine structures. After training, all dimensional measurements and quantitative analyses are performed on the original triangulated meshes, not on the smoothed versions.
+
+Spine and shaft detection
+
+After the training step of the algorithm, the next stage of spine-shaft segmentation involves applying the model for classification as well as performing additional post-processing steps to first isolate the shaft and then the spines. In this section, we analyze the processes required to obtain a reliable segmentation.
+
+Grouping dendritic mesh parts into connected vertices
+
+After training the DNN, the first step is to classify the vertices of a given test dendritic mesh into shaft and spine categories. The resulting classification can then be grouped into connected components of spine vertices and shaft vertices.
+
+As a consequence of the sigmoidal activation function applied to the final layer, the output of the DNN is a probability matrix Y¯=fθ(Z)∈[0,1]n×2, where each row corresponds to a vertex and contains the probabilities of that vertex being classified as a spine, X˜spine (first column greater than the second), or a shaft, X˜shaft (second column greater than or equal to the first). Formally, we define(6) X˜spine={XiϵD|bY¯(i,1)>aY¯(i,0)},X˜shaft={XiϵD|bY¯(i,1)≤aY¯(i,0)}.
+
+Here, a and b are user-defined weighting parameters that control the decision boundary. In our experiments, we fixed b = 0.81 and initially set a = 3. If the resulting segmentation produced too many shaft labels, we increased a; if too many spine labels were produced, we decreased a. This adjustment allowed us to fine-tune the spine-shaft separation based on the model’s output distribution.
+
+Next, we describe how to group the predicted dendritic parts—classified as either spine or shaft —into subgroups of connected components. Let each vertex Xi have an associated set of neighboring vertices denoted by Ni:Ni=Xj|Xjisinthe1-ringneighborhoodofXi.
+
+We define a connected group of vertices Gi⊆D such that, for any pair Xp,Xq∈Gi, there exists a path of vertices Xi1,Xi2,…,Xim∈X˜part satisfyingXi1=Xp,Xim=Xq,Xiℓ∈Niℓ−1forallℓ=2,…,m.
+
+Here, X˜part denotes the set of vertices classified as a given part type; either X˜spine for spines or X˜shaft for shafts. The subset of part-classified vertices within this group is thenY˜parti=Xj∈X˜part|Xj∈Gi.
+
+Finally, the complete set of part-classified vertices Y˜part can be decomposed into disjoint set of connected vertices, where connectivity is defined by neighborhood overlap:Y∼part=Y∼partii.
+
+Spine-shaft detection
+
+Using the subgroups defined above of connected components, we now define the segmentation of the dendritic mesh into spines and shaft. Let Y˜shaft denote the set of connected components classified as shaft. In practice, some of these components may actually be parts of spines, so it is crucial to separate them from the true shaft set for accurate segmentation.
+
+To achieve this, we identify the largest connected component in Y˜shaft and designate it as the entire shaft. All remaining connected components in Y˜shaft are then assumed to belong to spines.
+
+The set of vertices belonging to the shaft is defined asYshaft0=argmaxY˜shafti⊂X˜shaftY˜shafti,
+
+where · denotes the cardinality of the set.
+
+Once the entire shaft is defined, spine segmentation proceeds by removing the shaft vertices from the dendrite vertex set, reclassifying them as spine vertices, and then reapplying the connected-component grouping process described in section grouping dendritic mesh parts into connected vertices to the remaining vertices. The set of segmented spines is defined asYspine=Yspineii,
+
+where each individual spine component is given byYspinei=Xj∈D∖Yshaft0|Xj∈Gi.
+
+Dataset description
+
+This section describes the datasets of dendritic segments used for training and testing our algorithm. To mitigate overfitting, the training and testing sets were independent and originate from different animals. This separation ensures that the model learns generalizable features of dendritic structures rather than memorizing patterns specific to a single specimen. Table S3 provides a consolidated overview of the datasets used for training and testing, including their sources, annotation strategy, and selection criteria.
+
+Training dataset
+
+The training dataset used as ground truth in this paper comprises six high-resolution 3D EM reconstructions of dendrites from the CA1 region of the hippocampus from rats at postnatal day 21 (P21), an immature developmental stage. Brain slices from these animals either underwent in vitro theta-burst stimulation to induce LTP or received control stimulation, as described elsewhere.28,29,30
+
+For the training dataset, the meshes were manually annotated by experts, where spine and shaft segmentations were performed on all six dendritic-branch reconstructions. Each spine was stored as an individual .obj file in watertight format. The mesh corresponding to the shaft of each dendritic segment was provided separately, along with the complete mesh of the dendritic segment. Because spine and shaft meshes were stored independently, we wrapped the spines and shaft with a tight mesh from the exterior in order to generate a unified dendritic mesh using the algorithm in Section S6.1. We then used the independent spine meshes to label the constituent parts of the new wrapped dendritic mesh. To achieve this, we employed a KD-tree-based nearest-neighbor search to map spine vertices to the wrapped dendritic mesh. Specifically, for each set of spine vertices in the individual dataset vertices, we queried a KD tree built from the wrapped dendritic mesh vertices to identify all branch vertices within a radius threshold rth:vertices_appr=listsetnp.concatenatekdtree.query_radius(vertices,rth).
+
+Here, query_radius returns the indices of dendrite mesh vertices that lie within a distance rth of each spine vertex. By aggregating these indices, we obtain the set of dendrite vertices corresponding to the annotated spine regions on the wrapped mesh. This mapping step allows us to merge the spine and shaft meshes into a single labeled dendritic mesh, which is then used for both training and validation.
+
+Training data augmentation
+
+Only six dendritic branches are available for training, so we expanded the dataset by applying a series of geometric transformations. First, we computed the principal-component analysis (PCA) of each mesh and projected its vertices onto the corresponding PCA plane. We then applied random scaling to the vertices in two separate steps, introduced random rotations in two additional steps, and added random translations. These transformations produced four augmented versions of each original mesh, resulting in a total of 30 dendritic branches available for training and validation. Of these, 22 branches were used for training, and the remaining eight were used for validation.
+
+Testing dataset
+
+For testing, we used data from the axon-spine coupling study, which includes a complete nanoconnectomic 3D reconstruction of hippocampal neuropil obtained via serial EM.43 This dataset contains four independent annotations—two performed by each of two annotators44—providing detailed segmentation of dendritic spines. Out of 151 meshes, we selected 28 spiny dendritic branches for testing based on annotation consensus. Specifically, we included only those meshes where two or more annotators agreed on the presence of at least one dendritic spine. Additionally, for each spine mesh identified by the annotators, we retained only those meshes that were consistently labeled as spines by at least two of the selected annotations. This ensured that the testing set reflected a high-confidence subset of spiny dendritic structures.
+
+It is important to note that some structures exhibiting spine-like morphology were not annotated as spines in the test set for two reasons. First, biologically, the presence of a synaptic area in the spine head is essential for defining a spine. Thus, even if a mesh appears spiny, it is not considered a spine if no synapse is present. Second, some meshes were excluded due to incomplete reconstruction—parts of the spine may have been cut off or lost during imaging.
+
+In contrast, the training dataset does not apply as strict criteria for spine identification as the test set. As a result, the testing dataset introduces additional segmentation challenges that are not reflected in the training data. Our algorithm does not explicitly account for these differences, which may influence performance.
+
+Independent dataset
+
+In addition to the training and testing datasets, we also used dendritic segments from the large-scale nanoconnectomic EM reconstruction of mouse neocortex by Kasthuri et al.1 This dataset provides densely reconstructed neuropil at nanometer resolution but does not include manual spine or shaft annotations. We therefore use it solely for qualitative visualization (Figure 6) to demonstrate that our method generalizes to independently acquired EM volumes. These data are not used for training, validation, or quantitative evaluation.
+
+Results
+
+This section presents a comprehensive evaluation of our algorithm’s performance in segmenting dendritic shafts and spines. We first describe the identification of dendritic shafts using geometric properties and a neural-network-based approach. We then assess the ability of the algorithm to segment dendritic spines, highlighting both its strengths and limitations.
+
+Figure 6 illustrates the predicted dendritic shafts and spines from datasets from Kasthuri et al.,1 demonstrating that our method successfully identifies spines along the dendritic shaft by leveraging geometric properties such as Gaussian and mean curvature. However, misclassification can occur when the dendritic structure deviates significantly from the idealized cylindrical shape, underscoring the need for further improvements to the method.
+
+DNN prediction results analysis
+
+In this section, we present and analyze the prediction results of the three DNNs, DNN1, DNN2, and DNN3. The methodology is outlined in section dendrite spine-shaft segmentation using dendritic-branch regions (DNN3), and the evaluation here focuses on four key metrics: the training loss, the dice similarity coefficient (DICE), the Jaccard index intersection over union (IoU), and the area under the receiver operating characteristic curve (AUC).
+
+Analysis of the performance
+
+The training loss curves for the three models are shown in Figure S4. Among the three models, DNN2 achieves the most effective convergence, reaching a minimum loss of approximately 2.44, closely followed by DNN3 with a minimum loss of about 3.56. In contrast, the baseline architecture DNN1 shows the weakest convergence, with a substantially higher final loss of 6.73 throughout training. These results highlight the importance of the additional features and architectural refinements incorporated into DNN2 and DNN3 for improving optimization stability.
+
+To quantitatively assess segmentation accuracy, we computed the IoU, DICE, and AUC scores between predicted and annotated vertices for the dendritic shaft and spines on both the training and test sets. The performance curves are presented in Figure S5. For DNN2, the IoU converges to average values of approximately 0.70 for the shaft and 0.81 for the spines, with corresponding DICE scores of about 0.88 and 0.92, respectively. DNN3 achieves comparable performance across both IoU and DICE metrics, whereas DNN1 lags behind with average IoU values of 0.55 (shaft) and 0.75 (spines), along with lower DICE scores overall. The AUC curves further support these trends: both DNN2 and DNN3 maintain consistently high AUC values throughout training, while DNN1 again shows weaker discriminative performance. Importantly, the similarity between training and testing curves across all metrics indicates good generalization and minimal overfitting.
+
+Overall, these results demonstrate a clear progression in performance from DNN1 to DNN3. The incorporation of additional geometric and topological features in DNN2 and DNN3 substantially improves convergence and segmentation accuracy, underscoring the value of feature enrichment in dendritic spine detection.
+
+Dendritic spine detection analysis
+
+Following dendritic shaft segmentation, we applied the spine detection algorithm described in section spine-shaft detection to identify spines. For each detected spine, we computed the IoU to evaluate segmentation accuracy. In addition, we calculated the IoU for the union of all detected spines to assess overall performance. We then computed accuracy, precision, recall, and F1 score to further quantify classification performance.
+
+The segmentation results produced by the DNN models are shown in Figure 5. A clear qualitative progression is evident from DNN1 to the more advanced architectures DNN2 and DNN3. The DNN1 model frequently misclassifies portions of the shaft as spines, resulting in fragmented and noisy predictions. Incorporating additional geometric features—such as the distance to the shaft skeleton—allows DNN2 to reduce these errors and produce a more coherent separation between shaft and spine regions. Building on this, DNN3 integrates richer geometric and topological descriptors, enabling it to capture subtle curvature variations and resolve complex spine clusters more effectively. These improvements are visible not only in the 3D mesh renderings but also in the 2D slice, where the highlighted region clearly shows the reduction in mislabeling from DNN1 to DNN3. Overall, the predicted segmentations from DNN3 align most closely with the expert annotation. These qualitative trends are consistent with the quantitative results in Table S4, where both DNN2 and DNN3 outperform DNN1 across all evaluation metrics.Figure 5 Comparison of segmentation results obtained using DNN1, DNN2, and DNN3. The first three columns correspond to the predictions from DNN1, DNN2, and DNN3, respectively, and the final column shows the expert spine annotation used as ground truth. The top row displays the 3D mesh representations, while the bottom row shows 2D slices of the same regions. In the meshes, red vertices indicate correct spine predictions that match the annotation, sky-blue vertices represent shaft regions misclassified as spines, and yellow vertices represent spine regions misclassified as shaft. DNN1 produces noisier results with more misclassifications, particularly in clustered regions. DNN2 reduces shaft-to-spine errors, and DNN3 achieves the most accurate segmentation overall, with fewer misclassifications and the closest agreement with the expert annotation. The slice highlights the region where mislabeling is most apparent, especially for DNN1 and DNN2. The triangular mesh is obtained from CA1 dendritic reconstructions.28,29,30
+
+Quantitative evaluation and analysis
+
+We evaluated segmentation performance using multiple complementary metrics, including AUC, precision, recall, and F1 score, computed under both IoU and DICE criteria, each with standard and union variants. These results, summarized in Table S4, enable a detailed comparison between our geometric-informed models (DNN1, DNN2, DNN3) and established CNN baselines (U-Net, VoxNet, VGG16-FCN). Details on the training procedures and evaluation of the three CNN models are provided in Section S9. The weighting parameters used in the geometric-informed models are specified in Equation 6, where the values of a for each model are listed and the parameter b is fixed at 0.81.
+
+Among the CNN baselines, U-Net achieves the highest AUC (0.792), indicating strong global discriminative ability. However, AUC alone does not fully capture fine-scale segmentation quality. When examining precision, recall, and F1 score under the IoU and DICE criteria, the geometric-informed model DNN3 consistently delivers the strongest performance. Under the IoU-union metric, DNN3 attains the highest recall (0.873) and F1 score (0.845), indicating that it captures spine regions more completely than both the CNN baselines and the other geometric-informed variants. Its DICE-union performance is even stronger, with an F1 score of 0.857 and a recall of 0.895.
+
+In contrast, DNN1 and DNN2 exhibit more limited recall, particularly under the standard variants of IoU and DICE, where both models tend to miss a substantial fraction of true spines despite maintaining moderate to high precision. VoxNet and VGG16-FCN perform noticeably worse across all metrics, with lower AUC values (0.682 and 0.466, respectively) and substantially reduced F1 scores, especially under the IoU criterion. These results highlight the limitations of intensity-based CNN architectures when applied to thin, high-curvature structures such as dendritic spines.
+
+The union variants of IoU and DICE consistently yield higher recall and F1 scores across all models, reflecting their ability to more fairly evaluate clustered or contiguous spine regions. This is particularly relevant in dense dendritic environments, where individual spine boundaries may be ambiguous. Under these more biologically meaningful metrics, DNN3 shows the clearest advantage, outperforming all baselines by a substantial margin.
+
+Overall, the quantitative results demonstrate a clear progression in performance from DNN1 to DNN3, with DNN3 providing the most reliable and complete segmentation of dendritic spines. The strong performance of DNN3 under both IoU and DICE—especially in the union variants—underscores the value of incorporating geometric curvature cues for accurate spine-shaft segmentation.
+
+Dendrite spine segmentation without smoothing
+
+In the segmentation of dendrite triangular meshes, curvature smoothing is typically required. However, when the number of vertices is large—more than 200,000—the process becomes computationally expensive, taking more than 20 h to produce a smooth mesh. We note that, by using DNN3, the computational time can be reduced by performing segmentation without smoothing while still achieving a level of accuracy comparable to that obtained with smoothing.
+
+We evaluated the effectiveness of curvature smoothing with DNN3 on both the training and test datasets and compared the accuracy. The computed accuracy for the test dataset is 0.658 (with and without smoothing), while, for the training dataset, it is 0.704 with smoothing and 0.780 without smoothing. These results show that smoothing the curvature of the triangular mesh when using DNN3 is unnecessary, and segmentation may even perform better without it.
+
+This phenomenon may be due to the fact that the nine region-based segmentation features Sk enable the DNN to detect the neck area without requiring an enhanced curvature profile produced by smoothing. When we tested the same process on other DNN models, the accuracy was zero in both cases.
+
+Application to dendritic surface meshes with many vertices
+
+We next use our algorithm to segment the spines of a dendritic mesh dataset containing a large number of vertices and multiple branches.
+
+In particular, the dataset we study is from the reconstruction of a sub-volume of mouse neocortex.1 We analyzed a dendritic mesh with 5,387,879 vertices and 10,777,005 faces. This dendritic mesh is about 13.42 times larger than the training dataset used in the previous sections (401,371 vertices and 802,750 faces). While most of the training and testing datasets contain only one main dendritic branch with attached spines, this dataset has nine branches with multiple spines. This highlights how much more complex these dataset is compared to the training and testing data.
+
+Because this dataset is relatively large, the segmentation process differs slightly from that used in training. Computations were performed on a MacBook Pro with an Apple M4 Max chip and 64 GB of memory. When we attempted to segment the large dendritic mesh directly, the process failed due to computational constraints. Therefore, we reduced the size of the mesh using the simplification algorithm described in Section S6.2. The mesh was simplified to nearly the size of the largest training dataset, given (about 449,109 vertices and 900,000 faces), and we then proceeded with the same testing process as before.
+
+The segmentation results are shown in Figure 6. Overall, DNN3 achieves the strongest performance, correctly labeling the majority of spines across the dendritic mesh. However, it still misclassifies a small region of the shaft as spines, as illustrated in Figure 6C. This error likely arises from local geometric similarities between the shaft surface and spine neck regions, particularly where the mesh bends or narrows.Figure 6 Comparison of segmentation results obtained using DNN1, DNN2, and DNN3 on a large-scale nanoconnectomic EM reconstruction of mouse neocortex. In all parts, blue indicates the dendritic shaft mesh, while red highlights the segmented spines. The top part shows the full dendritic segment with predictions from the three models. All models correctly identify the majority of spines, but notable differences emerge upon closer inspection. Three boxed regions highlight areas of disagreement, which are shown in detail in the bottom parts. (A) Spine meshes that DNN1 incorrectly labels as shaft. (B) Dendritic sub-branches that DNN2 misclassifies as spines. (C) A similar misclassification pattern for DNN3, where local curvature and branching geometry lead to spurious spine predictions. Reconstruction taken from Kasthuri et al.1
+
+In contrast, DNN1 also performs reasonably well and produces few large false-positive spine regions. However, closer inspection of Figure 6A shows that DNN1 frequently misclassifies spine necks as shaft, and in some cases entire spines are labeled as shaft. These errors are consistent with the limited feature set used by DNN1, where Gaussian and mean curvature alone do not provide sufficient spatial context for reliable spine-shaft discrimination.
+
+Finally, DNN2 exhibits the weakest performance on this dataset. It correctly identifies spines in only a subset of regions while misclassifying large contiguous portions of the spines as shaft. This behavior suggests that the combination of shaft-skeleton distance, Gaussian curvature and mean-curvature features are insufficient to capture the complex local geometry present in this large-scale reconstruction.
+
+Dendritic spine morphologic parameters
+
+In this section, we use the segmentation results obtained from our algorithm to compute several morphological parameters of the dendritic meshes in both the training and testing datasets. These parameters include the neck diameter, head diameter, and spine length.
+
+The computation of head and neck diameters was performed using the spine skeleton. This skeleton was obtained by identifying the closest point of the triangular mesh skeleton to each vertex of the segmented spine mesh. To determine the neck and head diameters, we considered each segmented spine’s triangular mesh. For each vertex, we computed the shortest distance to its nearest skeleton point, as described in Equation 5, while computing D. This procedure yielded a thickness profile along the spine. The neck radius was then defined as the minimum of these computed averages, starting from the skeleton vertices closest to the dendritic shaft. Conversely, the head diameter was defined as the maximum computed distance, measured from the skeleton vertices at the farthest point from the shaft.
+
+Additionally, to compute the length of the spine, we used the spine skeletonization and interpolated additional points along the skeleton using a spline technique. This interpolation increases the accuracy of the computed distances by smoothing and interpolating along the dendritic spine skeleton.45,46,47 Additional details are provided in Section S7. The spine length was then computed as the sum of Euclidean distances between consecutive interpolated points:L=∑i=1N−1‖Vi+1−Vi‖2,
+
+where Vi denotes the i-th interpolated vertex.
+
+The distribution of morphological parameters in the training and large dendritic mesh datasets is shown in Figure 7. In the first column, the head diameter is plotted against the neck diameter of dendritic spines, while in the second column the spine volume is plotted against the spine area, with a colormap encoding spine length. For clearer visualization, some outliers were removed. Marginal histograms of head and neck diameters are also included to facilitate interpretation.Figure 7 Distributions of morphological properties. Properties obtained using DNN3 from the training dataset44 (top row) and the large dendritic mesh dataset1 (bottom row). In the first column, spine head diameter is plotted against spine neck diameter, while, in the second column, spine volume is plotted against spine area. The colormap encodes spine length.
+
+Quantitatively, the segmented training dataset contains 210 spines, with an average neck diameter of 0.166 ± 0.0969 μm, an average head diameter of 0.512 ± 0.101 μm, and an average spine length of 1.35 ± 0.694 μm. The average spine volume is 0.122 ± 0.121 μm3 and the average spine area is 2.30 ± 1.83 μm2, yielding an average area-to-volume ratio of 12.9. Importantly, the relationship between spine volume and area is very strong, as reflected by a high coefficient of determination (R2 = 0.916).
+
+In contrast, the segmented large dendritic mesh dataset contains 562 spines, with an average neck diameter of 0.148 ± 0.0787 μm, an average head diameter of 0.661 ± 0.164 μm, and an average spine length of 5.57 ± 5.34 μm. The average spine volume is 0.090 ± 0.085 μm3 and the average spine area is 1.53 ± 1.15 μm2, yielding an average area-to-volume ratio of 13.9. Here too, the relationship between spine volume and area remains strong, with a coefficient of determination of R2 = 0.847.
+
+Discussion
+
+In this work, we developed and evaluated three geometric-informed DNN architectures for dendritic shaft and spine segmentation. Our results demonstrate a clear progression in performance from the baseline DNN1 to the enhanced models DNN2 and DNN3, with DNN3 achieving the strongest overall segmentation accuracy. By incorporating curvature-based and topology-aware features, these models substantially improve both training stability and predictive performance, particularly in regions with dense spine clusters or complex branching patterns.
+
+A key advantage of the geometric-informed approach is its computational efficiency relative to volumetric 3D CNNs. CNN-based models require dense voxel representations that scale cubically with resolution, making them memory intensive and slow when applied to high-resolution EM reconstructions. In contrast, our geometric models operate directly on mesh-derived features, avoiding voxelization and enabling faster inference on large or irregular geometries. As a result, DNN3 not only surpasses all CNN baselines in accuracy but also scales more effectively to high-resolution meshes, making it the preferred choice for detailed EM datasets where preserving fine structural detail is essential.
+
+The resulting distributions of spine size and shape connect directly to the fundamental biological question of how form determines function in dendritic spines.3,26 In previous work,48,49 we identified the neck radius as a key parameter controlling endocytic membrane trafficking and dendritic spine maintenance. The distributions generated here suggest that there are roughly bimodal distributions of spine neck diameters, which we conjecture may correspond to distinct physiological states in which vesicle entry is up- or downregulated. Although spine area and volume are observed to be positively correlated, as are the spine length and head diameter, we found only weak correlations between neck diameter and the other morphological properties of the spine (Figure 7). This suggests the possibility that the spine neck diameter functions as an independent geometrical switch to support physiological states of individual spines, such as growth, stability, or atrophy.
+
+Limitations in spine group segmentation
+
+Despite its overall promise, our algorithm encounters challenges in segmenting spines with complex morphologies and spatial arrangements. Below, we discuss three key failure cases, illustrated in Figure 8. The consistently high precision suggests that, when a spine is detected, it is almost always correct (few false positives). However, the moderate recall for IoU alone indicates that some spines are missed (false negatives), potentially affecting downstream morphological analyses. The substantial performance improvement with union-based IoU suggests that a more inclusive segmentation strategy enhances detection reliability.Figure 8 Examples of misclassification encountered during spine segmentation. Blue indicates the shaft mesh, while other colors indicate spine meshes that were misclassified. (A–D) Cases where multiple spines were incorrectly merged and classified as a single spine. (E) A region of the dendritic shaft that was mistakenly labeled as a spine. (F) A fraction of a spine that was only partially labeled. These examples highlight the challenges of accurately separating spines in dense clusters. The triangular mesh is obtained from CA1 dendritic reconstructions.28,29,30
+
+Dendritic spines frequently appear in dense clusters, complicating their segmentation. These spine groups are two or more spines whose vertices are directly connected, and, after the shaft is removed, they still group together. Figure 8 shows a region containing tightly packed spines where the algorithm struggles to distinguish individual structures due to overlapping curvature features. This limitation highlights the need for improved clustering-based segmentation techniques or the integration of additional geometric descriptors capable of differentiating individual spines in high-density regions.
+
+Misclassification of dendritic shaft regions as spines
+
+Another failure mode involves the erroneous classification of dendritic shaft regions as spines, as depicted in Figure 8F. This misclassification likely stems from local curvature variations that resemble spine-like features. To mitigate this issue, we propose the incorporation of spatial continuity constraints, contextual neighborhood information, or multi-scale curvature analysis to better distinguish dendritic shafts from true spine structures.
+
+Scalability and large-dataset limitations
+
+A further limitation arises from the scale of the datasets used in training and evaluation. High-resolution 3D EM reconstructions of dendritic segments generate extremely large meshes, often containing millions of vertices. Processing such datasets requires substantial computational resources, both in terms of memory and runtime. This constraint limits the feasibility of applying our method to very large-scale reconstructions or to entire brain regions without significant preprocessing or downsampling. Moreover, the need to balance mesh resolution with computational efficiency may lead to the loss of fine structural details, particularly in thin spine necks or small protrusions. Addressing this limitation will require the development of more efficient algorithms, parallelized implementations, or hierarchical multi-resolution approaches that can scale to increasingly large datasets while preserving biologically relevant detail.
+
+Outlook
+
+Overall, our findings highlight the potential of feature-enriched geometric learning for robust dendritic spine detection. By improving segmentation accuracy, computational efficiency, and scalability, these models provide a strong foundation for downstream morphological analyses and quantitative studies of synaptic connectivity. Continued refinement of geometric descriptors, multi-resolution strategies, and post-processing methods will further enhance the reliability and applicability of this framework to increasingly large and complex neural reconstructions.
+
+By automating the segmentation of dendritic spines using a deep-learning approach specialized to the distinctive geometries of dendritic spines, this work makes it possible to analyze data at greater scale, setting the stage for future research on the relationship between dendritic spine form and function. In future work, we plan to look at spatial correlations between dendritic spine position along the dendritic shaft and to explore changes in spine shape that occur throughout development, including during long-term potentiation50 and in Parkinson’s disease51 and other disorders.
+
+Data availability
+
+To make these methods widely accessible, we have posted an open-source code repository on GitHub (GitHub:curvature-based-dendrite-segmentation), with the trained model, training data, and validation data made available in a linked repository (Zenodo: https://doi.org/10.5281/zenodo.19593999).
+
+Acknowledgments
+
+We acknowledge Myles Joyce for help with spine segmentation. This work was supported by 10.13039/100000001 NSF Technology Hub #1707356, NSF NeuroNex2 #2014862, NSF award 2219894, and NIH grants R01MH095980 and R56MH139176 to K.M.H. and NIH grant T32 NS007292 to A.K.A.G. We acknowledge use of the Brandeis High Performance Computing Cluster (HPCC), which is partially supported by the 10.13039/100000001 NSF through DMR-MRSEC 2011846 and OAC-1920147.
+
+Author contributions
+
+A.K.A.G. designed research, developed code, performed analysis, made figures, and wrote the manuscript. M.A.C. designed research and wrote the manuscript. K.M.H. designed research and wrote the manuscript. T.G.F. designed research, performed analysis, and wrote the manuscript.
+
+Declaration of interests
+
+The authors declare no competing interests.
+
+Supplemental citation
+
+References 52,53,54,55,56,57,58,59,60,61,62,63,64,65,66 appear in the supplemental information.
+
+Supplemental information
+
+Document S1. Figures S1–S6, Tables S1–S4, and supplemental materials and methods
+
+Document S2. Article plus supplemental information
+
+Supplemental information can be found online at https://doi.org/10.1016/j.bpj.2026.06.005.
+
+
+References
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@@ -0,0 +1,467 @@
+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Sci Rep
+Journal ID: Sci Rep
+NLM Journal ID: 101563288
+
+Scientific Reports
+
+EISSN: 2045-2322
+Publisher: Nature Publishing Group
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC13233853
+PMID: 42236829
+DOI: 10.1038/s41598-026-54158-z
+Article ID: 54158
+Article version: 1
+Subjects: Article
+
+Torsional strength and deformation characteristics of HSC deep beams reinforced with cross-inclined stirrups
+
+Fawzi Rehab rehabfawzy373@gmail.com
+1
+Asker Hamed S. 2
+Yousef Ahmed M. 2
+1 https://ror.org/0481xaz04 grid.442736.0 0000 0004 6073 9114 Department of Civil Engineering, Delta University for Science and Technology, Mansoura, Egypt
+2 https://ror.org/01k8vtd75 grid.10251.37 0000 0001 0342 6662 Department of Structural Engineering, Mansoura University, Mansoura, Egypt
+Electronic publication date: 2026 Jun 4
+Publication date: 2026
+Volume: 16
+Electronic Location ID: 17322
+Received 2026 Mar 6; Accepted 2026 May 18
+Copyright: © The Author(s) 2026
+Copyright year: 2026
+License: Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Keywords: Cross-inclined stirrups, Deep beams, Torsion, Torsional deformation characteristics, High-strength concrete (HSC)
+Keywords: Engineering, Materials science
+
+Funding: Delta University for Science and Technology Open access funding provided by The Science, Technology & Innovation Funding Authority (STDF) in cooperation with The Egyptian Knowledge Bank (EKB).
+
+issue-copyright-statement: © Springer Nature Limited 2026
+
+Ÿ==============================Ÿ
+The findings of this paper provide essential knowledge for the effective and economical design of deep beams subjected to pure torsion. As a result, this paper studies the torsional behavior of nine high-strength concrete (HSC) deep beams reinforced by cross-inclined stirrups. The test parameters comprised stirrup type (conventional stirrups and cross-inclined stirrups), inclination angle (45 and 60 degrees), stirrup spacing (100, 150, and 200 mm), the main longitudinal bars (4∅12 and 4∅18), and the side longitudinal bars (without and 4∅12). Torsional moment capacity, crack pattern, twisting angle, strain on longitudinal and transverse reinforcement, and torsional deformation characteristics in terms of stiffness and ductility were used to evaluate the tested beams’ torsional response. Test results clearly indicated that using the cross-inclined stirrup reinforcement improved the evaluated deep beams with conventional stirrups’ torsional capacity, stiffness, ductility, and overall performance. Reducing stirrup spacing from 200 to 100 mm increased torsional capacity by 49% for conventional stirrups and 65% for cross-inclined stirrups. An ABAQUS three-dimensional finite element model was built to evaluate the model’s ability to replicate the experimental beams’ torsional behavior. A theoretical model for ultimate torque calculation was also created. Compared to experimental findings, numerical and theoretical investigations were satisfactory.
+
+Introduction
+
+Historically, torsion in reinforced concrete (RC) structures is commonly neglected, and its impacts was included in the safety factor instead of conventionally designed structures, resulting in brittle shear-torsion failures. As a result, torsional strength is essential in current designs, especially in complex structures like curved girders, spiral staircases, and beams subjected to eccentric or dynamic loads1–5. Large structures such as bridges, offshore constructions, and multistory buildings frequently utilize deep beams as structural components. They stand out due to their significant depth relative to their span and their narrow width. According to ACI 318–20256 and ECP 203–20207, deep beams have spans up to four times their depth or concentrated load regions within twice the depth from supports. Despite their increasing use in modern structures, research into their torsional behavior is limited, and current standards, such as the ACI 318–20256, do not provide specific requirements for deep beams under torsional loads, despite their significance. For instance, transfer girders with significant eccentricity in multistory structures produce torsional moments due to offset load paths8. Alongside, curving bridge girders and edge beams in bridge engineering often experience torsion owing to load eccentricity produced by geometry, especially under asymmetric traffic conditions9,10. Similarly, ring deep beams in circular tanks or domes undergo torsion as a principal effect resulting from circumferential load distribution11.
+
+Deep beams, unlike shallow beams, generate nonlinear strain distributions, rendering common stress analysis methods ineffective12–14. Yousef et al.15 asserted that span-to-depth ratios led to varying crack patterns, stress distributions, and torsional stiffness. The deep beam with an L/h ratio of 1 had an ultimate torque 54% greater than that of the beam with an L/h ratio of 4, despite equivalent reinforcing. In addition, deep beams demonstrate high torsional resistance to cracks compared to shallow beams, since a reduction in the L/h ratio limits crack formation. In other words, the crack width of shallow beams expands and propagates more significantly throughout the span. Moreover, deep beams demonstrated enhanced torsional stiffness after cracking due to their geometric configuration, unlike shallow beams. Consequently, further research into the torsional behavior of deep beams is necessary.
+
+The ultimate strength of reinforced concrete elements subjected to torsion can be predicted using two main theories. Skew bending theory served as the foundation for the old building codes from 1971 to 19816,17, whereas the new building codes have been based on truss model theory since 1995. The space truss analogy theory describes reinforced concrete beams under torsion in two phases: before cracking, the concrete section behaves like a thin-walled tube, with constant shear flow resisting the torsional moment. After cracking, the beam is modeled as a space truss, with inclined concrete strips handling compression and longitudinal bars and stirrups handling tension to resist the torsional forces18–20.
+
+Although considerable research has been performed to improve the torsional performance of reinforced concrete beams, the majority of studies have concentrated on conventional vertical stirrups in shallow beams, employing advanced materials such as Ultra-High-Performance Concrete (UHPC) and Ultra-High Performance Fiber Reinforced Concrete (UHPFC), which have augmented cracking resistance and post-cracking behavior through fiber bridging mechanisms21,22. Externally bonded and internally reinforced FRP systems enhance torsional resistance of UHPC tubular beams by confining and distributing stress23,24. Hybrid strengthening methods such as FRP with strain-hardening cementitious composites (SHCC) or fiber meshes have improved ultimate capacity, stiffness, and energy absorption25. These advanced methodologies enhance torsional performance, although cost may limit their use.
+
+According to previous studies, the use of High-Strength Concrete (HSC) beams generally exhibits higher torsional strength and cracked stiffness compared to normal-strength concrete (NSC) beams26–28. According to Ibrahim T. Mostafa et al.29, when the web reinforcement ratio and configuration are identical, the HSC specimens exhibit greater torsional strength and stiffness both before and after cracking compared to the NSC specimens. A. M. Yousef30 conducted experiments on deep beams that responded to pure torsion and discovered that enhancing the concrete compressive strength from fcu = 35.1 MPa to 80.7 MPa significantly boosts the observed cracking torsional strength by approximately 44% and marginally increases the ultimate torsional strength by around 20%.
+
+Whilst other studies highlighted the benefits of employing spiral stirrups as torsional reinforcement in place of closed stirrups31,32. This method is particularly valued for its cost-effectiveness compared to other approaches, such as those involving steel fibers, glass fiber reinforced polymer sheets, and external prestressing techniques. A. Ibrahim et al.33 studied the torsional behavior of concrete beams reinforced with inclined spiral stirrups. The findings indicated that these stirrups improved the torsional capacity by approximately 16% compared to conventional closed stirrups. Additionally, the study revealed that this method resulted in greater twist angles, more ductile failure, and an increase in strain energy by about 27%. These findings align with Chalioris and Karayannis’s34 conclusions that rectangular spiral stirrups enhance the torsional capacity of RC beams. Additionally, locked rectangular spirals further enhanced the torsional strength of RC beams.
+
+Implementing spiral stirrups in deep beams is challenging due to their geometric shape. Consequently, this study’s novelty is in demonstrating the impact of an affordable alternative method using high-strength concrete (HSC) and cross-inclined stirrups on deep beams under pure torsion, which has been little addressed in previous studies. The experimental data gathered were subsequently utilized to validate a numerical model created using the ABAQUS simulator. This model is intended to expand the experimental research by broadening the experimental parameters, thereby achieving a thorough comprehension of the torsional behavior of deep beams.
+
+Experimental program
+
+Material properties
+
+For all deep beams, ready-mix of High-Strength Concrete (HSC) was used. The used mix proportions are selected according to ACI 211.4R35 and closely align with previously documented high-strength concrete compositions36,37. The HSC mix proportions, by weight per 1.0 m, were 495 kg ordinary portland cement, 1150 kg gravel, 580 kg natural sand, 154 kg water, and 55 kg silica fume. A superplasticizer with 2.2 percent binder weight was added. The mix achieved a cube compressive strength (fcu) of 91.7 MPa after 28 days, based on a mean of six cube specimens (150 × 150x150 mm) tested according to ASTM C39/C39M38. The average splitting cylinder tensile strength of six cylinder specimens (150 × 300 mm), tested according to ASTM C496/C496M39, was 5.8 MPa. The diameters of steel bars used in the test beams were 8 mm, 12 mm, and 18 mm. Table 1 lists steel bar mechanical properties.Table 1 Mechanical properties of steel bars.
+
+Diameter
+Φ (mm)	Yielding strength
+fy (MPa)	Ultimate strength
+fu (MPa)	Modulus of elasticity
+E (GPa)	
+8	320	453	200	
+12	465	707	210	
+18	465	707	210	
+
+Details of test specimen
+
+The experimental specimens are intended to investigate the impact of the cross-inclined configuration of HSC deep beams on the pure torsional behavior. Nine rectangular HSC deep beams were designed with a length of 1500 mm and a cross-section dimension of 150 × 450 mm2. All of the specimens have the same concrete cover at 20 mm. Each beam was divided into two regions: a pure torsion test region (1000 mm) and a support region (500 mm), as shown in Fig. 1. The two 250 mm extensions at each end were added to simplify the loading system and create torsional moments via eccentric loading arms without reducing specimen span. These dimensions were selected to make the depth-to-ratio equal to 2.22 within the ACI 318–2025’s deep beam classification. In the support region, steel bars were reinforced with 8 mm diameter stirrups spaced at 50 mm to ensure damage occurs in the pure torsion test region. Cross-inclined stirrups are perpendicular as shown in Fig. 1. The variables in these specimens were stirrup spacing (200 – 150 – 100 mm), stirrup type (ordinary closed stirrups – cross-inclined stirrups), inclined stirrup angle (45° – 60°), main longitudinal bars (4 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varnothing$$\end{document} 12 – 4 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varnothing$$\end{document} 18), and side longitudinal bars (without – 4 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varnothing$$\end{document} 12). All these variables, in addition to the ratios of provided longitudinal (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rho}_{L}$$\end{document}) and transverse (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rho}_{T}$$\end{document}) reinforcement based on Eqs. (1, 2, and 3) illustrated in Table 2. In Eq. 2, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f$$\end{document} is equal to 2 for conventional stirrups and 4 for cross-inclined stirrups. The specimens were named such as "DSiLi-ii" or "DCIi-iiLi-ii," where the first letter "D" means deep beam. If the second letter is "S," it indicates ordinary closed stirrups, with the following number representing stirrup spacing; if it is "CI," it denotes cross-inclined stirrups, and the subsequent two numbers indicate the stirrups’ inclination angle and spacing, respectively. The third letter "L" denotes longitudinal steel bars, and the next two digits indicate the main and side longitudinal bar diameters, respectively.Fig. 1 Geometry of the tested deep beams (dimension in mm).
+
+Table 2 HSC deep beams main parameter details.
+
+Specimen	Longitudinal torsional reinforcement	Transverse torsional reinforcement	
+Main long. bars	Side long. bars	\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rho}_{L}$$\end{document}	Inclination angle	Spacing
+(mm)	\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rho}_{T}$$\end{document}	
+DS200L12,12	4 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varnothing$$\end{document} 12	4 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varnothing$$\end{document} 12	1.34	90˚	200	0.39	
+DS150L12,12	4 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varnothing$$\end{document} 12	4 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varnothing$$\end{document} 12	1.34	90˚	150	0.52	
+DS100L12,12	4 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varnothing$$\end{document} 12	4 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varnothing$$\end{document} 12	1.34	90˚	100	0.77	
+DCI45,200L12,12	4 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varnothing$$\end{document} 12	4 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varnothing$$\end{document} 12	1.34	45˚	200	1.03	
+DCI45,150L12,12	4 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varnothing$$\end{document} 12	4 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varnothing$$\end{document} 12	1.34	45˚	150	1.37	
+DCI45,100L12,12	4 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varnothing$$\end{document} 12	4 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varnothing$$\end{document} 12	1.34	45˚	100	2.06	
+DCI60,100L12,12	4 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varnothing$$\end{document} 12	4 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varnothing$$\end{document} 12	1.34	60˚	100	1.74	
+DCI45,100L18,12	4 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varnothing$$\end{document} 18	4 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varnothing$$\end{document} 12	2.18	45˚	100	2.06	
+DCI45,100L12,0	4 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varnothing$$\end{document} 12	–-	0.67	45˚	100	2.06	
+
+1 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\uprho}_{\mathrm{T}}=\frac{{\mathrm{A}}_{\mathrm{T}}{*\uprho }_{0}}{{\mathrm{A}}_{\mathrm{C}\mathrm{P}}*\mathrm{S}}$$\end{document}
+
+2 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\uprho}_{0}=f\left(\frac{{h}_{0}}{\mathrm{sin}\theta }+\frac{{b}_{0}}{\mathrm{sin}{\theta}_{top}}\right)$$\end{document}
+
+3 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\uprho}_{\mathrm{L}}=\frac{{A}_{L}}{ b*h}$$\end{document}
+
+Test set-up and procedure
+
+The test configuration comprises a gravity loading system in which static forces were incrementally delivered using a force-controlled actuator. As illustrated in Fig. 2, a spreader beam was positioned diagonally on two cantilevered arms that were clamped on the specimen to transfer the load to the specimen. The cantilever arms provided the required 450 mm eccentricity. The specimen will therefore experience pure torsion when the jack pushes the spreader beam, as half of the force is transferred to the cantilevered arms. The beam was allowed to move and elongate freely in the longitudinal direction by using two roller supports.Fig. 2 Torsion test set-up.
+
+To get pertinent information on the failure mechanisms of the tested beams, the strains of the longitudinal and transverse steel reinforcements were assessed. The locations of the steel strain gauges are shown in Fig. 2(c). The angle of twist was estimated using two linear variable differential transducers (LVDTs). The LVDTs were used under the cantilever arm (at 350 mm from the specimen’s center line) to record the deflection due to the applied load. Load measurements, deformations, and steel strains were continually monitored and documented using a data acquisition system. The test was performed under displacement control circumstances, with the failure of the specimens designated as the stopping criterion. It is important to note that measurements are documented relative to an initial zero state before loading to clearly isolate the influence of the test setup’s self-weight.
+
+Experimental results and discussions
+
+Cracking and torsional capacity
+
+The cracking and ultimate torsional moments and the associated recorded angles of twist are given in Table 3. The cracking torque varied from 64 to 86% of the ultimate torque. The ultimate torsional capacity is contingent upon variations in the transverse and longitudinal reinforcement ratios. Using inclined stirrups significantly enhances ultimate torque; specifically, when inclined stirrups are used at 60 and 45 degrees, the ultimate torque increases by 3% and 27%, respectively, compared to conventional stirrups, as shown in Fig. 3(a). Which indicates that the ideal inclination angle was 45 degrees, as it was almost perpendicular to the cracks. Reducing the distance between stirrups improves the test beams’ confinement and increases the ultimate torque. For example, compared to the DS200L12,12 beam, the ultimate torque for DS150L12,12 and DS100L12,12 increased by 19 and 49%, respectively. Furthermore, relative to DCI45,200L12,12, it increased by 11 and 65% for DCI45,150L12,12and DCI45,100L12,12, respectively, as illustrated in Fig. 3(b-c). On the other hand, the longitudinal reinforcement has a significant impact on the ultimate torque. Augmenting the longitudinal reinforcement ratio from 0.67 to 1.34 and 2.18%, the torsional capacity increased by 40 and 50%, respectively, as shown in Fig. 3(d).Table 3 Experimental test result.
+
+Specimen	At cracking	At yielding	At ultimate	\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document}
+(˚)	
+Tcr (KN.m)	\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\theta}_{cr}$$\end{document}(rad/m)	Ty (KN.m)	\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\theta}_{y}$$\end{document}(rad/m)	Tu (KN.m)	\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\theta}_{u}$$\end{document}(rad/m)	
+DS200L12,12	14.73	0.0070	17.10	0.033	17.41	0.036	44	
+DS150L12,12	17.08	0.0071	20.30	0.033	20.67	0.037	46	
+DS100L12,12	19.00	0.0084	25.00	0.047	25.90	0.061	52	
+DCI45,200L12,12	17.34	0.0065	19.75	0.017	20.05	0.023	41	
+DCI45,150L12,12	17.90	0.0055	20.92	0.012	22.23	0.026	44	
+DCI45,100L12,12	22.10	0.0050	27.16	0.011	33.00	0.040	44	
+DCI60,100L12,12	20.75	0.0060	25.48	0.025	26.57	0.034	48	
+DCI45,100L12,0	19.97	0.0051	23.50	0.019	23.52	0.019	42	
+DCI45,100L18,12	22.5	0.0048	28.16	0.001	35.19	0.042	47	
+
+Fig. 3 Effect of the tested parameters on the torsional moment capacity.
+
+Crack pattern and mode of failure
+
+Figure 4 displays photographs of the crack patterns at failure for the tested deep beams. The numbers assigned along the cracks in the photographs represent the torsional load (in kN) (gained from the load cell) near the crack’s termination. The testing proceeded until the specimen failed. Stopping criteria were a major decline in the ultimate capacity (20% of the ultimate torque) associated with large torsional cracks that caused stiffness and structural integrity degradation. Figure 5 shows plots of the measured maximum crack width versus torsional moments. The crack width was measured at each loading step using a special microscope and taken at the first visible crack in the midspan of the specimen. The crack pattern of all investigated beams resembles the same pattern, with only minor differences in the number of cracks and crack width due to the various studied parameters. At angles between 41 and 52 degrees with regard to the beam’s horizontal plane, the first crack appeared at the cracking torque moment. The cracks parallel to the initial crack continued to form in a spiral pattern as the load increased. As the applied torsional moment increased, the crack width increased rapidly. Finally, an inclined crack in the pure torsion region grew wider, causing the tested deep beams to fail. The transverse reinforcement has significant effects on the torsional behavior. It is confirmed from the test findings of Fig. 5 that employing cross-inclined stirrups exhibited a significant cracking behavior in contrast to using conventional stirrups. When compared to the DS100L12,12 deep beam, the DCI45,100L12,12 and DCI60,100L12,12 showed the finest and most evenly distributed cracks. Increasing the distance between the stirrups resulted in fewer spiral cracks, as illustrated in Fig. 4. In addition to increasing crack width. In Fig. 5, the crack width of DS200L12,12 was somewhat more than that of DS150L12,12, then DS100L12,12, and the same was true for DCI45,200L12,12, DCI45,150L12,12, and DCI45,100L12,12, respectively. Furthermore, as Fig. 5 illustrates, increasing the longitudinal ratio enhanced the specimens’ behavior and reduced the crack width.Fig. 4 Crack pattern of all tested deep beams.
+
+Fig. 5 Torsional moment-maximum crack width relationship.
+
+Torsional moment versus twist angle curves
+
+Figure 6 illustrates the torque-twist curve for the tested HSC deep beams. First, the curve displays a linear elastic response exhibiting high torsional stiffness prior to cracking, with the concrete section remaining uncracked. Thereafter, the twist of HSC deep beams began to increase swiftly with a slight increase in the torsional moment, marking the beginning of the crack. This phase is distinguished by a decline in stiffness due to the formation of spiral cracks. Finally, the curve attains its maximum capacity. It is confirmed by the test findings in Fig. 6(a) that deep beams with cross-inclined stirrups perform significantly better torsionally than similar beams with conventional stirrups at the same torque. Additionally, it is evident that at the same level of loading, the twist tended to increase as the conventional or spiral reinforcement spacing increased, as shown in Fig. 6(b-c), respectively. Augmenting the ratio of longitudinal bars decreases the angle of twist for the same transverse reinforcement ratio, as illustrated in Fig. 6(d).Fig. 6 Torsional moment–angle of twist relationship.
+
+Torsional moment versus strain curves
+
+The torque versus strain curves for each HSC deep beam’s main longitudinal bar, side longitudinal bar, and stirrup at the midspan are displayed in Fig. 7. The variation of rebar strain and torque for all beams was basically identical. First, the main longitudinal bar, side longitudinal bar, and stirrup all showed minimal and linear strain development. This implies that the torque was mostly resisted by concrete, and the reinforcing bars do not influence the beam’s torsional capacity prior to the initial cracking of the concrete. Once cracking occurs, the strain on reinforcement bars starts to increase immediately. These strains continue to increase, coinciding with the widening of the cracks. As noticed in Fig. 7, the stirrups were the first to yield. This indicates that they were primarily responsible for controlling the first stage of the post-cracking response. Once yielding of the stirrups started, strain increased in the longitudinal reinforcement, specifically in the main longitudinal bars, some of which reached yield, whereas the side longitudinal bars showed lower strains within the elastic range, as seen in Fig. 7(b-c). Cross-inclined stirrups effectively resisted the tensile forces in the beam after cracking, as demonstrated in Fig. 7(a). Their ability to capture cracks was enhanced by their intersection with the diagonal crack, which experienced greater tensile forces during cracking. This effect becomes evident when comparing DS100L12,12 with DCI45,100L12,12 and DCI60,100L12,12; it is clear that 45 degrees is the ideal cross-inclined angle since this angle is perpendicular to the crack. Furthermore, the test findings showed that the effective stirrup strains decreased with decreasing stirrup spacing at the same torque, as shown in Fig. 7(a). The distribution of shear force on additional stirrups intersected by diagonal shear fractures accounts for the reduction in average stirrup strain. Additionally, increasing the area of longitudinal bars reduces the development of strain, as shown in Fig. 7(a).Fig. 7 Torsional moment-strain relationship.
+
+Torsional deformation characteristics
+
+Simultaneous investigations of tests for ductility and stiffness were made to ensure a thorough analysis of the entire behavior under torsion for HSC deep beams. Ductility is the ability to withstand deformation after yielding and failure safety. Torsional stiffness is essential during the serviceability and deformation of the structures. Assessing the different factors assures a comprehensive investigation of strength and deformation properties under pure torsion.
+
+Torsional ductility index
+
+Torsional ductility refers to a reinforced concrete member’s ability to tolerate considerable inelastic deformation and rotation. It can be determined by the torsional ductility index proposed by Bernardo and Lopes40,41. The torsional ductility index is calculated as the ratio of the ultimate angle of twist to the angle of twist at yielding, using the torsional moment-twist response.4 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mu}_{d}=\frac{{\uptheta}_{\mathrm{u}}}{{\uptheta}_{\mathrm{y}}}$$\end{document}
+
+Table 4 illustrates the ductility index values for the tested HSC deep beams. The findings indicated that cross-inclined stirrups with 45˚ boosted ductility for deep beams by 2.80 compared to conventional stirrups, as shown in Fig. 8(a). Based on the findings, the torsional ductility was increased by 1.03 and 1.19 for conventional stirrups and by 1.61 and 2.70 for cross-inclined stirrups when the spacing was decreased from 200 to 150 mm and 100 mm, respectively, as shown in Fig. 8(b-c). Because the internal force redistribution is more effective when the stirrup ratio is higher. As a result, the test beam’s surface had reduced average crack width and spacing, which increased overall deformation prior to crack-instability-caused damage. Figure 8(d) depicts the impact of the longitudinal reinforcement ratio on the HSC deep beam’s ductility index. With a similar stirrup ratio, the longitudinal reinforcement ratio increased from 0.67 to 1.34 and 2.18%, and the ductility index increased by 3.64 and 4.42, respectively. It is important to note that the improvement in ductility from increased reinforcement occurs because all specimens are under the optimum reinforcement limit; exceeding this limit is expected to lead to ductility degradation, which is influenced by prior concrete crushing.Table 4 Torsional deformation characteristics test result.
+
+Specimen	Ductility	\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{f}\mathrm{f}\mathrm{n}\mathrm{e}\mathrm{s}\mathrm{s}$$\end{document}	
+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\upmu}_{\uptheta }$$\end{document}	\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{K}}_{1}$$\end{document}
+(kN.m2/rad)	\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{K}}_{2}$$\end{document}
+(kN.m2/rad)	\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{K}$$\end{document}
+(%)	
+DS200L12,12	1.09	2101.28	92.4	4.40	
+DS150L12,12	1.12	2405.63	120.07	4.99	
+DS100L12,12	1.30	2661.90	131.18	5.80	
+DCI45,200L12,12	1.35	2667.69	164.24	6.16	
+DCI45,150L12,12	2.17	3254.55	211.22	6.49	
+DCI45,100L12,12	3.64	4402.39	311.607	7.08	
+DCI60,100L12,12	1.36	3458.33	207.86	6.01	
+DCI45,100L12,0	1.00	3954.46	254.48	6.44	
+DCI45,100L18,12	4.42	4687.50	341.13	7.28	
+
+Fig. 8 Effect of the tested parameters on the ductility index (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mu}_{d}$$\end{document}).
+
+Torsional stiffness
+
+Torsional stiffness refers to a member’s capacity to withstand twisting under applied torque. Table 4 shows the torsional stiffness of HSC deep beams during loading. The pre-cracking torsional stiffness (K1) represents the stiffness of the test beam during the elastic stage; the torque-twist curve was linear prior to cracking and had the highest value of stiffness, as shown in Table 4. The pre-ultimate torsional stiffness (K2) represents stiffness in the plastic stage, the torque-twist curve was nonlinear, and the tangent slope of the torque-twist curve decreased constantly, as indicated in Table 4. Furthermore, stiffness degradation (K) was used as a comparative indicator for various beam specimens to evaluate the effect of reinforcing arrangement on post-cracking torsional behavior42. This attribute made it simple to check the performance of different types of reinforcement in restraining torsion and retaining stiffness after crack formation. The torsional stiffness was calculated from Eqs. (5), (6), and (7).5 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${K}_{1}=\frac{{\mathrm{T}}_{\mathrm{c}\mathrm{r}}}{{\uptheta}_{\mathrm{c}\mathrm{r}}}$$\end{document}
+
+6 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${K}_{2}=\frac{{\mathrm{T}}_{\mathrm{u}}- {T}_{cr}}{{\uptheta}_{\mathrm{u}}- {\theta}_{cr}}$$\end{document}
+
+7 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K=\frac{{\mathrm{K}}_{2}}{{\mathrm{K}}_{1}}$$\end{document}
+
+The results indicated that employing cross-inclined stirrups with 45˚ increased torsional stiffness by 22%. This improvement was clearly demonstrated in the stiffness degradation values provided in Fig. 9(a). Furthermore, when the spacing of conventional and cross-inclined stirrups was decreased from 200 to 150 mm and 100 mm, the K of HSC deep beams significantly increased, as shown in Fig. 9(b-c). The stiffness deterioration of HSC deep beams improved marginally when the longitudinal reinforcement ratio increased, as seen in Fig. 9(d).Fig. 9 Effect of the tested parameters on the stiffness degradation (K).
+
+Numerical investigation
+
+A three-dimensional nonlinear finite element model is proposed to examine the capability to capture the observed torsional behavior in the experiment of HSC deep beams reinforced by cross-inclined stirrups. For this model, the computer program ABAQUS43 is used.
+
+Numerical data input
+
+Element description
+
+Two primary types of elements were used to produce a 3D FE model of HSC deep beams reinforced with cross-inclined stirrups: solid elements and truss elements.Solid element
+
+Concrete deep beams and cantilever arms are modeled using Solid C3D8R, which has eight nodes with three transitional degrees of freedom. The selection of C3D8R is based on its capacity to specify boundary conditions and specify the concrete property, as well as the contact face. Figure 10(a) shows the parts created. The mesh element was 15 mm × 15 mm × 15 mm for the tested region and 20 mm × 20 mm × 20 mm for the +support region and cantilever arms, as shown in Fig. 10(b). This mesh size was chosen in accordance with a sensitivity analysis to adjust the model according to alternative mesh sizes from 10 to 30 mm for the tested region and the support region, with results compared against experimental data. Thus, the adopted mesh sizes ensure a balance between accuracy and computational efficiency.Fig. 10 Element and mesh configuration of FE model.
+
+b. Truss element
+
+The T3D2 element was determined for modeling reinforcement bars and stirrups, which can only carry compressive or tensile forces. Figure 11 depicts the different reinforcing cages, which were simulated as embedded elements in a concrete block. The steel reinforcement truss element was 15 mm in mesh size.Fig. 11 Different reinforcing configurations of the FE model.
+
+Material modelling
+
+In this paper, a stress-based analysis was conducted for identifying the initiation and development of cracks in casting high-strength concrete. The stress-based formulation is consistent with the Concrete Damaged Plasticity (CDP) model in Abaqus43, which identifies tensile cracking when the maximum primary stress criterion or tensile cracking criteria are violated. With the smeared cracking approach, this formulation allows one to accurately locate regions and orientations that are susceptible to cracking with high geometric accuracy. Nonlinear material behavior was integrated using the Concrete Damaged Plasticity (CDP) model for concrete and elastic–plastic hardening for reinforcement in both tension and compression. For concrete subjected to compression, its stress–strain curve starts off linearly, reaches a strain-hardening region until the peak point, and ends with a softening region. The tensile properties consider fracture energy to reflect the stiffening loss of post-cracked specimens, as shown in Fig. 12. The above procedure was commonly adopted in modeling reinforced concrete numerically in past studies44. The elastic properties of concrete are estimated to have a density of 2200 kg/m3, an elasticity modulus of 41.97 GPa, and a Poisson’s ratio of 0.22. The parameters of the damaged plasticity model of concrete are displayed in Table 5. A perfect bond between concrete and reinforcement was assumed. Reinforcing steel is supposed to have a density of 7859 kg/m3, an elasticity modulus of 210 and 200 GPa for high tensile and mild steel, respectively, and a Poisson’s ratio of 0.30.Fig. 12 Concrete damaged plasticity relationships.
+
+Table 5 Concrete damaged plasticity (CDP) parameter.
+
+Parameter	dilation angle	eccentricity	fbo/fco	K	viscosity	
+Value	43	0.12	1.36	0.67	0.00001	
+
+Boundary conditions
+
+The load was applied on the reference points, which were restricted from translating and rotating in all directions except translation in U2, as illustrated in Fig. 13(a). In addition, the experimental support conditions were replicated using appropriate boundary conditions. Roller supports were defined under each cantilever arm, as shown in Fig. 13(b).Fig. 13 Simply supported boundary condition of model.
+
+Comparison between FEM and experimental test results
+
+The values of all the tested specimens using finite element modeling exhibit strong concordance with the experimental findings. As demonstrated in Table 6, the average difference between finite element (FE) and experimental data was around 90% for the cracking torsional moment and 97% for the ultimate torsional moment. Furthermore, Fig. 14 provides the numerical and experimental torsional moment–angle of twist relationships of the studied deep beams. These evaluations demonstrated that the twist relationships of HSC deep beams reinforced with cross-inclined stirrups are well predicted by the proposed model. Figure 15 indicates that the failure patterns of all FE models for all investigated specimens were identical to that of the same beams investigated experimentally in Fig. 4. As a result, the comparison was considered very effective. The aforementioned findings confirm that the suggested FE models precisely depict the real behavior of HSC deep beams under pure torsion, as the numerical results’ values are strikingly similar to the experimental results.Table 6 Comparisons between experimental and numerical results.
+
+Specimen	Tcr,Num. (KN.m)	Tcr,exp / Tcr,Num	Tu,Num. (KN.m)	Tu,exp /Tu,Num	
+DS200L12,12	16.11	0.91	18.31	0.95	
+DS150L12,12	19.14	0.89	21.75	0.95	
+DS100L12,12	22.80	0.83	27.15	0.95	
+DCI45,200L12,12	19.42	0.89	20.66	0.97	
+DCI45,150L12,12	20.02	0.89	23.27	0.96	
+DCI45,100L12,12	26.10	0.85	34.34	0.96	
+DCI60,100L12,12	20.98	0.99	25.59	1.04	
+DCI45,100L12,0	21.41	0.93	24.90	0.94	
+DCI45,100L18,12	26.10	0.86	36.24	0.97	
+
+Fig. 14 Numerical and experimental torsional moment–angle of twist curves for all tested deep beams.
+
+Fig. 15 FE crack pattern of all tested deep beams.
+
+Ultimate torque proposed model
+
+This study demonstrated that using cross-inclined stirrups in deep beams significantly improved torsional capacity. As a result, the stirrup inclination angle should be accounted in the design equations. To anticipate the torsional capacity, the torsional behavior of a standard RC beam is divided into two regions: the elastic until the first cracking part and the after-cracking part. The differences in response in these places reflect the characteristics of the load-resisting system in each instance.
+
+Cracking torque
+
+The provisions for calculating the cracking torsional moment could be calculated using ACI 318–20256. Equation (8) illustrates the cracking torque load-calculating formula, which is based on thin-walled tube theory. The cracking torsional moment depends on the concrete strength and cross-section. Meanwhile, the influence of steel reinforcement is ignored due to their low stress before cracking.8 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{T}}_{\mathrm{c}\mathrm{r}}=0.33\frac{{A}_{cp}^{2}}{{ P}_{c} }\sqrt{{f}_{c}}$$\end{document}
+
+After cracking torque
+
+Many academics have acknowledged the softened space truss model18 as an approach for calculating ultimate torque in RC beams with longitudinal bars and stirrups. The space truss analysis is predicated on the concept that an internal torque generated by the shear flow q, which develops in the center of a shear flow zone with an effective wall thickness td, resists the exterior torsional moment T. Furthermore, using the stress equilibrium, the following known relationships are produced for calculating the longitudinal and the transverse torsional strengths, TL and TT18,45 in the case of conventional stirrups. The inclination of the diagonal compression struts (cracking angle \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document}) is equal to 45° according to ACI 318–20256. Besides that, this angle matches the average crack angles found in the experiment.9 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{T}}_{\mathrm{L}}=\frac{ 2{A}_{L}{f}_{L}{A}_{o}}{{P}_{o}}\text{ tan}\alpha$$\end{document}
+
+10 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{T}}_{\mathrm{T}}=\frac{ 2 { A}_{T} {f}_{T} {A}_{o} }{S}\mathrm{cot}\alpha$$\end{document}
+
+11 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${A}_{o}=0.85\left(\frac{{h}_{o}}{\mathrm{sin}\theta }*\frac{{b}_{o}}{\mathrm{sin}{\theta}_{top}}\right)$$\end{document}
+
+Chalioris and Karayannis34 proposed a model for calculating ultimate torque using the inclination angle of spiral stirrups depending on the space truss model. In this paper, the ultimate torque of HSC deep beams reinforced by longitudinal bars and cross-perpendicular inclined stirrups was calculated using a formula based on Chalioris and Karayannis. In the instance of specimens with cross-inclined stirrup reinforcement as transverse steel reinforcement, the following equations can be acquired from the equilibrium of a section of the vertical wall of the beam, as displayed in Fig. 16(c). The force equilibrium along the longitudinal direction:Fig. 16 Torsional analysis based on space truss theory.
+
+12 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q{p}_{o}=\left({{A}_{L}f}_{L}+{A}_{IS}{f}_{Is}cos\theta -{A}_{CI}{f}_{CI}cos\theta \right) tan\alpha$$\end{document}
+
+The force equilibrium along the transverse direction:13 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$qs=\left({A}_{IS}{f}_{IS}sin\theta +{A}_{CS}{f}_{CS}sin\theta \right) cot\alpha$$\end{document}
+
+Substituting the shear flow (q) in Eqs. (12) and (13) with the equation of Bredt:14 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q=\frac{T}{ 2{A}_{o}}$$\end{document}
+
+It can be derived:15 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{T}}_{\mathrm{L}}=\frac{ 2{A}_{o} \left({{A}_{L}f}_{L}+{A}_{IS}{f}_{Is}cos\theta -{A}_{CI}{f}_{CI}cos\theta \right) }{{P}_{o}}\text{ tan}\alpha$$\end{document}
+
+16 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{T}}_{\mathrm{T}}=\frac{ 2 {A}_{o}\left({A}_{IS}{f}_{IS}sin\theta +{A}_{CI}{f}_{CI}sin\theta \right) }{S}\mathrm{cot}\alpha$$\end{document}
+
+Finally, the following formula can be used to ascertain the ultimate torque capacity for deep beams reinforced by cross-inclined stirrups:17 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T}_{u}={T}_{cr}+min\left\{\begin{array}{c}{T}_{T}\\ {T}_{L}\end{array}\right.$$\end{document}
+
+Comparison with experimental results
+
+The experimental data and the formula’s calculated results were compared in order to validate the calculation’s accuracy for the proposed formula. As demonstrated in Table 7, the average difference between the proposed and experimental data was around 92% for the ultimate torsional moment, which indicated that the formula proposed in this paper can predict the ultimate torque of deep beams using cross-inclined stirrups accurately.Table 7 Comparisons between experimental and theoretical results.
+
+Specimen	Tcr,Theo. (KN.m)	Tcr,exp / Tcr,Theo.	Tu, Theo. (KN.m)	Tu,exp /Tu,Theo	
+DS200L12,12	10.69	1.85	16.86	1.03	
+DS150L12,12	10.69	1.60	18.92	1.09	
+DS100L12,12	10.69	1.38	23.03	1.12	
+DCI45,200L12,12	10.69	2.07	23.03	0.87	
+DCI45,150L12,12	10.69	1.94	27.14	0.82	
+DCI45,100L12,12	10.69	1.62	35.37	0.93	
+DCI60,100L12,12	10.69	1.67	35.37	0.75	
+DCI45,100L12,0	10.69	1.87	32.61	0.72	
+DCI45,100L18,12	10.69	2.10	35.37	0.99	
+
+Conclusion
+
+Experimental and numerical studies are conducted to investigate the behavior of high-strength concrete (HSC) deep beams with cross-inclined stirrups as transverse reinforcement under pure torsion.By using cross-inclined stirrups, the torsional behavior of HSC deep beams was improved considerably. The optimal value for the inclination angle was 45 degrees, as it was almost perpendicular to the cracks. The torsional capacity was augmented by 27%. Reducing the spacing of conventional stirrups resulted in a 19% and 49% enhancement in torsional capacity. While decreasing the distance between cross-inclined stirrups, the maximum torsional capacity increases by 11% to 65%. The torsional strength was enhanced by boosting the longitudinal reinforcement ratio up to 50%.
+
+The arrangement of reinforcement affects the mode of failure and the crack pattern. Cracks were more distributed when cross-inclined stirrups were used. Cracks were more numerous and narrower when stirrups were spaced closer together. Increasing the longitudinal ratio enhanced the specimens’ behavior and reduced the crack width.
+
+Deep beams with cross-inclined stirrups showed reduced angles of twist at the same levels of torsion, proving improved torsional stiffness. Cross-inclined stirrups effectively resisted tensile stresses, leading to the efficient use of steel reinforcement.
+
+Cross-inclined stirrups significantly improved torsional ductility up to 2.80 compared to conventional closed stirrups. Furthermore, the torsional ductility was increased by 1.03 and 1.19 for conventional stirrups and by 1.61 and 2.70 for cross-inclined stirrups when the spacing was decreased, because the internal force redistribution is more effective when the stirrup ratio is higher. In addition, increasing the longitudinal reinforcement ratio led to an enhancement of the ductility index by 3.64 and 4.42.
+
+Cross-inclined stirrups greatly enhanced stiffness by up to 22% when compared to conventional closed stirrups. Additionally, reducing the spacing between conventional and cross-inclined stirrups significantly increased the stiffness of HSC deep beams. The stiffness deterioration of HSC deep beams improved up to 13% when the longitudinal reinforcement ratio increased.
+
+The non-linear finite element model, which was developed by ABAQUS, has been found to accurately simulate the torsional behavior of the tested deep beams in terms of torsional capacity, torque-twist relationship, and crack pattern; the numerical results obtained by the finite element model were found to match the experimental results. Hence, the reliability of the finite element model could be confirmed for predicting the torsional behavior of HSC deep beams reinforced by cross-inclined stirrups.
+
+The theoretical model based on ACI 318–2025 accurately predicted the torsional capacity of deep beams under pure torsion, with an average agreement rate of 92%.
+
+Finally, this paper is conducted on HSC deep beams with a cross-section of 150 × 450 mm, a clear span of 1000 mm (L/h = 2.22), and a compressive strength of 91.7 MPa. The findings cannot be extended to deep beams whose geometrical shapes, materials, or span-to-depth ratios are different. The findings are confined to particular angles and spacing of cross-inclined stirrups; hence, trends of cross-inclined stirrups should be considered accordingly. The study involved pure torsion, whereas in actual structures, there are other forces such as bending and shear that could make a considerable difference to the structural behavior. The findings are relevant for similar deep beam configurations; however, more research is necessary for wider relevance.
+
+Abbreviations
+
+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${A}_{CI},{A}_{IS}$$\end{document} Area of one legged cross-inclined and inclined stirrups, mm2
+
+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{A}}_{\mathrm{C}\mathrm{P}}$$\end{document} Cross-sectional area of the HSC deep beam, mm2
+
+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${A}_{L}$$\end{document} Area of longitudinal reinforcement, mm2
+
+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${A}_{o}$$\end{document} Area enclosed by the centerline of shear flow path, mm2
+
+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{A}}_{\mathrm{T}}$$\end{document} Area of one-legged stirrup, mm2
+
+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b,h$$\end{document} The width and height of the tested beams, mm
+
+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{b}_{0},h}_{0},$$\end{document} The width and height of the area enclosed by the centerline of the stirrup, mm
+
+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${d}_{c}$$\end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${d}_{t}$$\end{document} The compression and tensile damage property
+
+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${E}_{o}$$\end{document} The modulus of elasticity of concrete, GPa
+
+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${f}_{c}$$\end{document} The compressive strength of HSC, MPa
+
+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{f}_{CI},f}_{Is}$$\end{document} The yield strength of cross-inclined and inclined stirrups, MPa
+
+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${f}_{L }, {f}_{T}$$\end{document} The yield strength of longitudinal and transverse reinforcement, MPa
+
+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{K}$$\end{document} Stiffness degradation (pre-ultimate to pre-crcking torsional stiffness), %
+
+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{K}}_{1}, {K}_{2}$$\end{document} The pre-cracking and pre-ultimate torsional stiffness), kN.m2/rad
+
+Pc The perimeter of HSC deep beam cross-section, mm
+
+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${P}_{o}$$\end{document} Perimeter of centerline of the shear flow in space truss analysis, mm
+
+S The stirrup spacing of the tested beams, mm
+
+Tcr, Ty, Tu Cracking, yielding and ultimate torsional moment, kN.m
+
+Tcr,Num, Tu,Num The numerical cracking and ultimate torsional moment, kN.m
+
+Tcr,Theo., Tu,Theo. The theoretical cracking and ultimate torsional moment, kN.m
+
+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document} Diagonal compression struts angle, ˚
+
+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\theta}_{cr}$$\end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\theta}_{y}$$\end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\theta}_{u}$$\end{document} Cracking, yielding and ultimate twist, mm
+
+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varepsilon}_{c}^{el}$$\end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varepsilon}_{t}^{el}$$\end{document} The compressive and tensile elastic strain, mm/mm
+
+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varepsilon}_{c}^{in}$$\end{document} The compressive inelastic strain, mm/mm
+
+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varepsilon}_{c}^{pl}$$\end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varepsilon}_{t}^{pl}$$\end{document} The compressive and tensile plastic strain, mm/mm
+
+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varepsilon}_{oc}^{el}$$\end{document} The elastic strain corresponding to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sigma}_{co}$$\end{document}, mm/mm
+
+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varepsilon}_{ot}^{el}$$\end{document} The elastic strain corresponding to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sigma}_{to}$$\end{document}, mm/mm
+
+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varepsilon}_{t}^{ck}$$\end{document} The tensile cracking strain, mm/mm
+
+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta$$\end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\theta}_{top}$$\end{document} The front and top inclination angles of stirrups, ˚
+
+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mu}_{d}$$\end{document} Ductility index (ultimate to cracking twist ratio)
+
+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rho}_{L}$$\end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rho}_{T}$$\end{document} Longitudinal and transverse reinforcement ratio, %
+
+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\uprho}_{0}$$\end{document} The perimeter of closed stirrups or cross-inclined stirrups, mm
+
+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sigma}_{co}$$\end{document} The yield compressive stress, N/mm2
+
+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sigma}_{cu}$$\end{document} The ultimate compressive stress, N/mm2
+
+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sigma}_{to}$$\end{document} The tensile stress of concrete at failure, N/mm2
+
+Author contributions
+
+Rehab Fawzi performed the experimental and numerical modeling, analyzed the results, and wrote the original draft. Hamed S. Askar was the main supervisor of the research and reviewed the written work. Ahmed M. Yousef played the main role in the technical review and presentation of the manuscript. All authors approved the final manuscript.
+
+Funding
+
+Open access funding provided by The Science, Technology & Innovation Funding Authority (STDF) in cooperation with The Egyptian Knowledge Bank (EKB). By corresponding author.
+
+Data availability
+
+All data generated or analyses during this study are included in this published article.
+
+Declarations
+
+Competing interests
+
+The authors declare no competing interests.
+
+Publisher’s note
+
+Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
+
+
+References
+
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+Schlaich, J. & Schafer, K. Design and detailing of structural concrete using strut-and-tie models. Struct. Eng. 69(6), 113–125 (1991).
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+20. Lampert P Collins MP Torsion, bending, and confusion-an attempt to establish the facts J. Proc. 1972 69 8 500 504
+Lampert, P. & Collins, M. P. Torsion, bending, and confusion-an attempt to establish the facts. J. Proc. 69(8), 500–504 (1972).
+21. Luat, N. V., & Sang, N. V. Modified space-truss model for predicting the torsional capacity of ultra-high-performance concrete beams. J. Mater. Civ. Eng. 16(01), (2026).
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+23. Zeng JJ Hu X Zhu DH Zhang ZZ Zhao HC Zhuge Y Behavior of FRP-reinforced UHPC tubular beams under torsion Eng. Struct. 2025 343 121064 10.1016/j.engstruct.2025.121064
+Zeng, J. J. et al. Behavior of FRP-reinforced UHPC tubular beams under torsion. Eng. Struct. 343, 121064 (2025).
+24. Hu X Sun HQ Zhu DH Fan TH Zeng JJ Theoretical model for FRP-reinforced UHPC tubular beams under torsion Struct 2025 82 110407 10.1016/j.istruc.2025.110407
+Hu, X., Sun, H. Q., Zhu, D. H., Fan, T. H. & Zeng, J. J. Theoretical model for FRP-reinforced UHPC tubular beams under torsion. Struct 82, 110407 (2025).
+25. Hamoda A Yehia SA Ahmed M Abadel AA Sennah K Patel VI Alghamdi H Torsional strengthening of RC beams with openings using hybrid SHCC–glass fiber mesh composites Build 2025 15 13 2237 10.3390/buildings15132237
+Hamoda, A. et al. Torsional strengthening of RC beams with openings using hybrid SHCC–glass fiber mesh composites. Build 15(13), 2237 (2025).
+26. Rasmussen LJ Baker G Torsion in reinforced normal and high-strength concrete beams Part 1: Experimental test series Struct. J. 1995 92 1 56 62
+Rasmussen, L. J. & Baker, G. Torsion in reinforced normal and high-strength concrete beams Part 1: Experimental test series. Struct. J. 92(1), 56–62 (1995).
+27. Rahal KN Torsional strength of normal and high strength reinforced concrete beams Eng. Struct. 2013 56 2206 2216 10.1016/j.engstruct.2013.09.005
+Rahal, K. N. Torsional strength of normal and high strength reinforced concrete beams. Eng. Struct. 56, 2206–2216 (2013).
+28. Lopes SMR Bernardo LFA Cracking and failure mode in HSC hollow beams under torsion Constr. Build. Mater. 2014 51 163 178 10.1016/j.conbuildmat.2013.10.062
+Lopes, S. M. R. & Bernardo, L. F. A. Cracking and failure mode in HSC hollow beams under torsion. Constr. Build. Mater. 51, 163–178 (2014).
+29. Mostafa IT Mousa S Mohamed HM Benmokrane B Behavior of high-strength concrete (HSC) box girders reinforced with GFRP bars, ties, and spirals under torsion Eng. Struct. 2023 294 116726 10.1016/j.engstruct.2023.116726
+Mostafa, I. T., Mousa, S., Mohamed, H. M. & Benmokrane, B. Behavior of high-strength concrete (HSC) box girders reinforced with GFRP bars, ties, and spirals under torsion. Eng. Struct. 294, 116726 (2023).
+30. Yousef, A. M. Codes provisions for torsion in reinforced normal and high-strength concrete deep beams. In Application of Codes, Design and Regulations: Proceedings of the International Conference held at the University of Dundee, Scotland, UK on 5–7, 617-629 (2005).‏
+31. Hadhood A Gouda MG Agamy MH Mohamed HM Sherif A Torsion in concrete beams reinforced with GFRP spirals Eng. Struct. 2020 206 110174 10.1016/j.engstruct.2020.110174
+Hadhood, A., Gouda, M. G., Agamy, M. H., Mohamed, H. M. & Sherif, A. Torsion in concrete beams reinforced with GFRP spirals. Eng. Struct. 206, 110174 (2020).
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+Cao, X. et al. Experiment study on reactive powder concrete beams using spirals reinforcement under torsion. Eng. Struct. 290, 116361 (2023).
+33. Ibrahim A Askar HS El-Zoughiby ME Torsional behavior of solid and hollow concrete beams reinforced with inclined spirals J. King Saud Univ. Eng. Sci. 2022 34 5 309 321 10.1016/j.jksues.2020.10.008
+Ibrahim, A., Askar, H. S. & El-Zoughiby, M. E. Torsional behavior of solid and hollow concrete beams reinforced with inclined spirals. J. King Saud Univ. Eng. Sci. 34(5), 309–321 (2022).
+34. Chalioris CE Karayannis CG Experimental investigation of RC beams with rectangular spiral reinforcement in torsion Eng. Struct. 2013 56 286 297 10.1016/j.engstruct.2013.05.003
+Chalioris, C. E. & Karayannis, C. G. Experimental investigation of RC beams with rectangular spiral reinforcement in torsion. Eng. Struct. 56, 286–297 (2013).
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+Aïtcin, P. C. High Performance Concrete (CRC press, 1998).
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+Basu, D., Mushtaq, S. M., Sharma, S. & Tripathi, S. Enhancing quality control in the mix design of high-strength concrete using a capacity-based approach. Int. J. Concr. Struct. Mater. 18(1), 78 (2024).
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+Teixeira, M. M. & Bernardo, L. F. A. Ductility of RC beams under torsion. Eng. Struct. 168, 759–769 (2018).
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+Said, M., Salah, A., Erfan, A. & Esam, A. Experimental analysis of torsional behavior of hybrid fiber reinforced concrete beams. J. Build. Eng. 71, 106574 (2023).
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+ABAQUS. Abaqus Analysis User’s Manual, Version 6.9 (Dassault Systems Corp., 2013).
+44. Dok, G., Caglar, N., Ilki, A., Yilmaz, C., & Serdar, A. H. Experimental and numerical investigation on residual behavior of high strength reinforced concrete beams subjected to different impact velocities. Eng. Fail. Anal. 110176 (2025).
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diff --git a/corpus/psychology/text/4e08d301679d3f97.txt b/corpus/psychology/text/4e08d301679d3f97.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a30d587b0a68cd5c996d334ada4b1349ca94b336
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+++ b/corpus/psychology/text/4e08d301679d3f97.txt
@@ -0,0 +1,218 @@
+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Materials (Basel)
+Journal ID: Materials (Basel)
+NLM Journal ID: 101555929
+Journal ID: materials
+
+Materials
+
+EISSN: 1996-1944
+Publisher: Multidisciplinary Digital Publishing Institute (MDPI)
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC13514449
+PMID: 42654619
+DOI: 10.3390/ma19163465
+Article ID: materials-19-03465
+Article version: 1
+Subjects: Article
+
+Designing Ambient Pressure Superconductivity in Li–Mg-Based Hydrides via Transition-Metal Modulation: From Quaternary to Quinary Systems
+
+Wang Xinyu Writing – original draft Data curation Investigation 1
+https://orcid.org/0000-0002-2270-4389 Wei Qun Writing – review & editing Supervision Project administration 1 *
+Luo Jing Data curation Investigation 1
+https://orcid.org/0000-0001-7219-843X Zhang Meiguang Writing – review & editing Resources Funding acquisition 2 *
+Casarejos Enrique Academic Editor
+1 School of Physics, Xidian University, Xi’an 710071, China
+2 College of Physics and Optoelectronic Technology, Baoji University of Arts and Sciences, Baoji 721016, China
+* Correspondence: qunwei@xidian.edu.cn (Q.W.); zhmgbj@126.com (M.Z.)
+Electronic publication date: 2026 Aug 16
+Publication date: 2026 Aug
+Volume: 19
+Issue: 16
+Electronic Location ID: 3465
+Received 2026 Jul 6; Revised 2026 Aug 11; Accepted 2026 Aug 13
+Copyright: © 2026 by the authors.
+Copyright year: 2026
+License: Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Keywords: superconductivity, multicomponent hydrides, electronic characteristics, first-principles calculations
+
+Funding: National Natural Science Foundation of China https://ror.org/01h0zpd94 11965005 11964026 Natural Science Basic Research Plan in Shaanxi Province of China 2026JC-YBMS-0047 2025JC-YBMS-027 2026JC-YBMS-0003 This research was funded by the National Natural Science Foundation of China (Grant Nos. 11965005 and 11964026), the Natural Science Basic Research Plan in Shaanxi Province of China (Grant Nos. 2026JC-YBMS-0047, 2025JC-YBMS-027 and 2026JC-YBMS-0003).
+
+Ÿ==============================Ÿ
+Hydrogen-rich superconductors have emerged as promising candidates for achieving high-temperature superconductivity, yet their practical applications are generally limited by the requirement for high external pressures. In this work, taking the Fm-3-XYZ2H12 structure as a prototype, we constructed a series of LiMgM2H12 quaternary hydrides and the LiMgZrHfH12 quinary hydride. High-throughput screening indicates that the three hydrides, LiMgZr2H12, LiMgHf2H12, and LiMgZrHfH12, are dynamically stable at ambient pressure but thermodynamically metastable. Electron–phonon coupling calculations show that the Tc values of LiMgZr2H12, LiMgHf2H12, and LiMgZrHfH12 reach 87.4, 81.2, and 85.2 K at ambient pressure, respectively, all exceeding the boiling point of liquid nitrogen and demonstrating excellent superconducting properties. Further analysis reveals that, compared with the Ga-based parent Fm-3-XYZ2H12 hydrides, Li substitution markedly reconstructs the electronic-state distribution near the Fermi level and enhances the contribution of H atoms to the density of states near the Fermi level. This promotes the coupling between conducting electrons and high-frequency hydrogen vibrations. Such strong electron–phonon coupling plays a crucial role in their high-temperature superconductivity. These findings provide valuable insights into the theoretical design of high-Tc superconductors under ambient pressure and offer theoretical guidance for future experimental studies in this field.
+
+1. Introduction
+
+Superconductors, owing to their unique physical properties, including zero-resistance electrical transport and perfect diamagnetism, are widely regarded as ideal materials with tremendous potential for applications in low-loss power transmission, high-field magnetic devices, magnetic levitation, and quantum computing. Consequently, the exploration of superconducting materials has remained one of the most challenging frontiers in condensed matter physics and materials science. Since the establishment of the Bardeen–Cooper–Schrieffer (BCS) theory [1], metallic hydrogen has been predicted to be one of the ideal candidate systems for achieving a high superconducting transition temperature (Tc) because of its high-frequency phonon characteristics and strong electron–phonon coupling (EPC) [2]. However, the realization of metallic hydrogen requires extremely high pressures exceeding 400 GPa, making its experimental synthesis nearly unattainable [3,4,5].
+
+To overcome this challenge, Ashcroft proposed the concept of chemical precompression [6], in which metal elements are introduced into the hydrogen lattice to reduce the pressure required for metallization through the internal compressive effect exerted by metal atoms on the hydrogen sublattice. The successful implementation of this strategy has led to the discovery of a series of high-temperature superconducting hydrides, including the binary covalent hydride H3S (203 K at 155 GPa) [7,8], the clathrate superhydrides LaH10 (250–260 K at 170–188 GPa) [9,10], YH6 (224 K at 166 GPa) [11], YH9 (243 K at 201 GPa) [12], and CaH6 (215 K at 172 GPa) [13]. These discoveries have convincingly demonstrated the effectiveness of the chemical precompression strategy in promoting high-temperature superconductivity. However, these representative high-Tc hydrides generally require pressures on the order of hundreds of GPa or even higher to maintain structural stability, which severely limits their synthesizability and potential applications. Therefore, achieving the stabilization of hydrogen-rich compounds at lower pressures, or even under ambient conditions, while preserving excellent superconducting properties has become a critical bottleneck that urgently needs to be addressed in the field of hydrogen-based superconductivity research.
+
+In recent years, the design of multicomponent hydrides has provided a new avenue for reducing the stabilization pressure of hydrides and tuning their superconducting properties. Compared with binary hydrides, ternary, quaternary, and even higher-component hydrides possess richer chemical compositions, local coordination environments, and degrees of freedom in their electronic structures. These features allow the bonding characteristics of the hydrogen sublattice, the density of states near the Fermi level, and phonon softening behavior to be tuned through synergistic interactions among metal elements [14,15,16]. However, for multicomponent hydride systems containing four or more constituent elements, the structural search space expands rapidly as the number of elemental species and possible configurations increases. As a result, conventional crystal structure prediction methods, such as USPEX [17], CALYPSO [18], and AIRSS [19], face substantial computational costs when applied to these multicomponent systems. Recent studies indicate that targeted design using known high-temperature superconducting hydrides as structural templates is an effective strategy for realizing multicomponent hydrides with high Tc at low pressure. For example, Wei et al. [20] designed a series of quaternary hydrides based on the Fm-3m-XZH8 prototype through substitutional doping. Among them, LaThBe2H16, AcBaSi2H16, AcSrSi2H16, and YceBe2H16 exhibit Tc values of 126, 137, 123, and 105 K at 10, 30, 30, and 45 GPa, respectively. Zhao et al. [21] constructed a series of XM3Be4H32 structures based on the LaBeH8 prototype, in which CaTh3Be4H32, ThLa3Be4H32, LaAc3Be4H32, and AcLa3Be4H32 achieve Tc values exceeding 120 K at relatively low pressures. Furthermore, Shi et al. [22] designed the MX3B4H20 family of quaternary hydrogen-rich compounds using the ThBH5 parent structure as the structural template. The Tc values of LaNa3B4H20, ThLa3B4H20, NaTh3B4H20, and LaTh3B4H20 are 143 K (50 GPa), 122 K (40 GPa), 118 K (50 GPa), and 112 K (30 GPa), respectively. These studies demonstrate that quaternary hydrides can effectively reduce the stabilization pressure of hydrides through the synergistic effects of multielement chemical precompression and electronic modulation. Moreover, they substantially expand the materials design space for achieving high-temperature superconductivity at relatively low pressures.
+
+Among hydrogen-rich superconducting systems, A15-type structures have attracted considerable attention because of their highly symmetric framework and the tunable potential for multicomponent alloying [23,24]. Liu et al. [25] proposed a multiregion elemental regulation strategy based on an alloyed A15 framework. By selecting and combining elements from different regions of the periodic table, they constructed a series of quaternary XYZ2H12 hydrides, among which GaAlZr2H12 and GaAlHf2H12 exhibit Tc values of 74 and 69 K at 20 GPa, respectively. Notably, in our previous work [26], LiMgZr2H12 was designed through Li substitutional doping based on the MgZrH6 parent structure. This compound exhibits a Tc of 60.8 K at ambient pressure. A comparison of its superconducting properties with those of the parent structure shows that the required external pressure for structural stabilization is significantly reduced while the Tc is essentially preserved.
+
+Inspired by the above studies, in this work, we constructed a series of LiMgM2H12 (M = 3d, 4d, and 5d transition metals) quaternary hydrides through elemental substitution based on the Fm-3-XYZ2H12 prototype. We performed high-throughput screening of the stability of the obtained compounds at ambient pressure and systematically evaluated their thermodynamic, mechanical, and dynamical stability. Two dynamically stable compounds at ambient pressure were identified: LiMgZr2H12 and LiMgHf2H12. EPC calculations indicate that both compounds are superconductors. LiMgZr2H12 and LiMgHf2H12 exhibit Tc values of 87.4 and 81.2 K at ambient pressure, respectively, both exceeding the liquid-nitrogen temperature and demonstrating excellent superconducting properties. However, existing studies have primarily focused on ternary and quaternary hydride systems, whereas the extension of the elemental substitution strategy to quinary hydrides has rarely been explored. Considering that synergistic effects in multicomponent systems may have an important influence on superconducting properties, the exploration of quinary compounds is of significant scientific importance. Therefore, in this work, we further extend the elemental substitution strategy from quaternary to quinary systems. Based on the LiMgM2H12 structural prototype, two transition metal elements, Zr and Hf, are simultaneously introduced into the A15 framework to construct the quinary hydrogen-rich compound LiMgZrHfH12. Its structural stability, electronic properties, and superconductivity are then systematically investigated. This work advances the study of multicomponent hydride superconducting systems from quaternary to quinary compositions, providing a new research paradigm for compositional design and property regulation of ambient-pressure high-temperature superconducting hydrides. It is of great significance for promoting the development of hydrogen-rich compounds toward practical ambient-pressure superconducting materials.
+
+2. Computational Details
+
+Structural optimizations and subsequent property calculations were performed within the framework of density functional theory (DFT) using the Vienna Ab initio Simulation Package (VASP) [27]. The exchange–correlation functional was approximated using the Perdew–Burke–Ernzerhof (PBE) functional form within the generalized gradient approximation (GGA) [28], while the ion–electron interactions were described by the projector augmented-wave (PAW) method [29]. Structural relaxations were performed with a 600 eV plane-wave cutoff and a 2π × 0.02 Å−1 Monkhorst–Pack k-point mesh [30], achieving force convergence below 1 × 10−3 eV/Å and total energy convergence within 1 × 10−5 eV/atom. The single-crystal elastic constants Cij were extracted from the linear stress–strain responses obtained under small finite deformations [31]. The dynamical stability was examined by the finite-displacement approach, with phonon dispersion curves calculated using the PHONOPY package [32]. Electron–phonon coupling (EPC) calculations were carried out within density-functional perturbation theory as implemented in the Quantum ESPRESSO package [33], employing ultrasoft pseudopotentials with a plane-wave kinetic-energy cutoff of 80 Ry. The self-consistent charge density was obtained using a dense 20 × 20 × 20 k-point mesh, while the EPC constants were evaluated on a 5 × 5 × 5 q-point grid. The superconducting transition temperature Tc was estimated using the Allen–Dynes modified McMillan formula [34,35](1) Tc=ωlogf1f21.2exp−1.041+λλ−μ*−0.62λμ*
+
+where f1 and f2 represent the strong-coupling and shape correction factors, respectively; ωlog denotes the logarithmic average phonon frequency; λ is the dimensionless electron–phonon coupling constant that characterizes the strength of the attractive phonon-mediated interaction; and μ* is the Coulomb pseudopotential describing the effective screened electron–electron repulsion [36,37,38]. The parameter μ* is an empirical parameter that is largely material-independent, with typical values of 0.10–0.13 [39,40,41]. The ωlog and λ were given by:(2) ωlog=exp2λ∫dωωα2Fωlnω
+
+and(3) λ=2∫α2Fωωdω
+
+respectively. Accordingly, λ is determined from the calculated electron–phonon spectral function and thus directly reflects the electron–phonon coupling strength of the system under consideration. The correction factors f1 and f2 are defined as(4) f1=1+λ2.461+3.8μ*323
+
+and(5) f2=1+ω¯2ωlog−1λ2λ2+1.821+6.3μ∗ω¯2ωlog2
+
+respectively, where ω¯2 is the second moment of the normalized weight function, described as(6) ω¯2=2λ∫0ωα2Fωdω
+
+3. Results and Discussion
+
+Using the Fm-3-XYZ2H12 structure as the structural template, we constructed a series of LiMgM2H12 quaternary hydrides with Fm-3 symmetry, as shown in Figure 1a, where M represents 3d, 4d, and 5d transition metals (see Figure 1c). A total of 29 candidate compounds were generated for subsequent systematic screening. We first evaluated their mechanical stability according to the Born stability criteria [42] and excluded the structures that failed to satisfy these criteria. The dynamical stability of the remaining structures was then evaluated through phonon dispersion calculations. Structures exhibiting imaginary phonon frequencies were removed, and two dynamically stable structures at ambient pressure were finally obtained: LiMgZr2H12 and LiMgHf2H12. Based on these two compounds, we further constructed the quinary hydride LiMgZrHfH12 through atomic substitution. This compound was also found to be dynamically stable at ambient pressure. The phonon dispersion curves and crystal structural parameters of these three dynamically stable compounds are presented in Figure 2 and Table 1, respectively.
+
+The thermodynamic stability of hydrides is an important criterion for evaluating their experimental synthesizability. To investigate the thermodynamic stability of LiMgZr2H12, LiMgHf2H12, and LiMgZrHfH12, we systematically compared their decomposition enthalpies with those of known binary, ternary, and quaternary competing phases. As shown in Figure 3, all three compounds are thermodynamically unstable at ambient pressure, whereas LiMgHf2H12 becomes thermodynamically stable above 36 GPa. The energies above the convex hull of these compounds are listed in Table 1, and all are below 0.2 eV atom−1, indicating their metastable nature. Notably, metastability does not necessarily preclude the experimental synthesizability of materials. Statistical analyses based on the Inorganic Crystal Structure Database (ICSD) have shown that approximately 20% of experimentally synthesized materials are metastable [43,44,45]. Recently, Deng et al. [46] developed a pressure-quench protocol and successfully retained the pressure-enhanced superconducting state in bulk tetragonal HgBa2Ca2Cu3O8+δ after decompression to ambient pressure, achieving an ambient-pressure superconducting transition temperature of 151 K. Although cuprate superconductors differ substantially from the phonon-mediated hydrides investigated in this work in terms of their chemical bonding characteristics and microscopic pairing mechanisms, this study demonstrates that metastable superconducting phases can, in some cases, be retained at ambient pressure through pressure quenching. Based on this concept, pressure-assisted synthesis combined with controlled low-temperature decompression or pressure quenching may provide a potential route for the experimental preparation of the hydrides investigated herein. Nevertheless, this analogy offers only conceptual and methodological insights, and its practical feasibility remains to be further verified by future experimental studies.
+
+To investigate the superconducting properties of these three hydrides, their superconducting transition temperatures were determined by solving the Allen–Dynes-modified McMillan equation [34,47], and the corresponding results are listed in Table S1. For a Coulomb pseudopotential parameter μ* of 0.10–0.13, the ambient-pressure Tc values of LiMgZr2H12, LiMgHf2H12, and LiMgZrHfH12 are 82.9–87.4 K, 76.8–81.2 K, and 80.7–85.2 K, respectively. As shown in Figure 4, when μ* = 0.10, the Tc values of all three structures exceed the temperature of liquid nitrogen and are substantially higher than those of their parent compounds, GaMgZr2H12 (Tc = 20 K) and GaMgHf2H12 (Tc = 12 K) [25]. These results indicate that this class of Li–Mg-based multinary hydrides exhibits excellent superconducting properties. Furthermore, Figure 4 also summarizes the key superconducting parameters of these three hydrides. The calculated Tc values exhibit positive correlations with the electron–phonon coupling constant λ, the logarithmic average phonon frequency ωlog, and the density of states at the Fermi level N(EF). Among the three compounds, the average electron gain of hydrogen atoms remains nearly unchanged (approximately 0.51 e per H atom), indicating that the substitution of Zr with Hf primarily modifies the metallic framework rather than directly altering the local bonding environment of hydrogen. In addition, the λ values of these three hydrides are all higher than 2.5, which are substantially larger than those of their parent structures, GaMgZr2H12 (λ = 0.66) and GaMgHf2H12 (λ = 0.57) [25]. This result indicates that the introduction of Li atoms markedly enhances the electron–phonon coupling strength of the system. Specifically, compared with Ga, Li has a lower electronegativity and can more readily transfer electrons to the hydrogen sublattice, thereby enhancing the ionic character of the structure and modifying the electronic filling of the hydrogen framework. This charge redistribution may promote the hybridization between the H-s states and the Zr/Hf-d states near the Fermi level, thereby contributing to the enhancement of electron–phonon coupling and the increase in the superconducting transition temperature. However, Li substitution not only induces charge redistribution but also modifies the lattice structure, local coordination, and chemical bonding environment. Therefore, the observed enhancement in superconducting properties is more likely attributable to the synergistic modulation of lattice structural evolution and electronic degrees of freedom.
+
+To elucidate the microscopic mechanism underlying superconductivity in these hydrides, we calculated the phonon dispersion curves, projected phonon density of states (PHDOS), Eliashberg spectral function α2F(ω), and electron–phonon coupling constant λ for the three hydrogen-rich compounds, as shown in Figure 2. No imaginary phonon modes are observed throughout the Brillouin zone for any of the three compounds, confirming their good dynamical stability at ambient pressure. The EPC analysis shows that the phonon vibrations of LiMgZr2H12, LiMgHf2H12, and LiMgZrHfH12 can be divided into two distinct frequency regions: a low-frequency region dominated by metal atom vibrations and a high-frequency region dominated by hydrogen vibrations. Specifically, the vibrations of Li, Mg, and Zr/Hf atoms mainly contribute to the low-frequency phonon modes below 10 THz, whereas H vibrations dominate the high-frequency region above 10 THz. The Eliashberg spectral function α2F(ω) and electron–phonon coupling constant λ show that H-related phonon modes make the dominant contribution to the total EPC. In all three compounds, the contribution of high-frequency H vibrations to λ exceeds 60%. This indicates that the high-frequency vibrations of light H atoms not only provide high characteristic phonon frequencies but also play a key role in strengthening electron–phonon coupling.
+
+To further elucidate the chemical bonding characteristics and charge transfer behavior of this series of hydrogen-rich compounds, we calculated the electronic localization function (ELF) [48] and performed Bader charge analysis for the three compounds. As shown in Figure 5, high ELF values are observed around the hydrogen atoms, whereas the regions between H and the metal atoms (Li, Mg, Zr, and Hf) exhibit low ELF values. This indicates pronounced charge transfer from the metal atoms to hydrogen, suggesting that the metal–H interactions in these systems are predominantly ionic. In addition, continuous electron localization is observed around neighboring H atoms, indicating that the hydrogen sublattice does not exist as isolated units but forms a relatively stable hydrogen-rich network. The ELF values between adjacent H atoms are all lower than 0.5, suggesting the absence of H–H covalent bonds and reflecting the anionic character of hydrogen. Further comparison of the ELF maps of these three structures reveals that their main differences arise from the transition metal–H interactions. Specifically, the Zr–H interaction is stronger than the Hf–H interaction, giving LiMgZr2H12 more pronounced metal–hydrogen hybridization characteristics. In contrast, LiMgHf2H12 exhibits relatively stronger ionic character, whereas LiMgZrHfH12 lies between the two and shows local bonding inhomogeneity caused by the different chemical environments of Zr and Hf. Such differentiated M–H bonding characteristics may modulate the electronic structure of the system and further influence its electron–phonon coupling behavior.
+
+The Bader charge analysis further shows that Li, Mg, and Zr/Hf all act as electron donors, transferring electrons to the hydrogen framework, whereas the hydrogen atoms serve as electron acceptors, as summarized in Table S2. Specifically, the charge losses of Zr are 1.773 and 1.775 e in LiMgZr2H12 and LiMgZrHfH12, respectively. By comparison, Hf loses 1.800 and 1.802 e in LiMgHf2H12 and LiMgZrHfH12, respectively, indicating that Hf donates slightly more electrons to the hydrogen framework than Zr. This result is consistent with the ELF analysis, demonstrating that the Hf–H interaction is more ionic in nature, whereas the Zr–H region retains more pronounced electron localization and metal–hydrogen orbital hybridization. Notably, the average electron gain of H atoms in the three compounds is close to 0.51 e, exhibiting only weak compositional dependence. This indicates that the substitution of Zr by Hf mainly modulates the local electronic distribution of the metal framework, without significantly altering the overall electronic filling state of the hydrogen sublattice.
+
+Considering that superconducting properties are largely influenced by the distribution of electronic states near the Fermi level, we systematically analyzed the electronic band structures and density of states of the obtained structures to further clarify the effect of electronic structure on superconducting behavior. As shown in Figure 6, multiple bands cross the Fermi level, indicating that all three compounds exhibit metallic behavior. In LiMgZr2H12, LiMgHf2H12, and LiMgZrHfH12, H atoms make the most significant contribution to the density of states near the Fermi level. The electronic states near the Fermi level mainly originate from the hybridization between H-s states and Zr/Hf-d states. In contrast, Li and Mg make only minor direct contributions to the density of states near the Fermi level, indicating that Li and Mg atoms mainly act as electron donors and structural regulating components, rather than directly dominating the electronic states near the Fermi level that are associated with superconducting pairing. By comparison, the projected density of states (PDOS) of the parent Fm-3-XYZ2H12 structures reported in the literature shows that the electronic states near the Fermi level are mainly contributed by Zr/Hf-d, Ga-s, and H-s orbitals, with Zr or Hf atoms making the dominant contribution to the density of states near the Fermi level [25]. This difference indicates that the substitution of Ga by Li reconstructs the composition of electronic states near the Fermi level. As a result, the electronic states near the Fermi level change from being dominated by transition-metal d states in the parent structures to an electronic structure characterized by a dominant H-s contribution. According to the phonon-mediated BCS theory [49], H-dominated electronic states at the Fermi level are generally favorable for enhancing electron–phonon coupling and ultimately improving the superconducting transition temperature. This explains why the Li-based structures in this work exhibit superior superconducting performance compared with their Ga-based parent structures.
+
+To comprehensively evaluate the overall performance and potential application value of superconducting materials, Pickard et al. proposed a superconducting figure of merit S [50]. This metric simultaneously considers the transition temperature Tc of a material and the applied pressure required to achieve this temperature, thereby assessing the feasibility of superconducting systems under practical application conditions. S is defined as:(7) S=Tc/Tc,MgB22+P2
+
+where Tc,MgB2 represents the superconducting transition temperature for MgB2, and P denotes the applied pressure. To place the superconducting performance of the three hydrides investigated in this work into a broader context, Figure 7 compares them with several representative quaternary superconducting hydrides reported in the literature. As shown in Figure 7, the S values of LiMgZr2H12, LiMgHf2H12, and LiMgZrHfH12 all exceed 2. Among them, LiMgZr2H12 shows the most prominent performance, with an S value of 2.24. Notably, the S values of these three structures are not only significantly higher than those of their parent structures, GaMgZr2H12 (S = 0.46) and GaMgHf2H12 (S = 0.27), but also superior to those of other reported Fm-3-type XYZ2H12 compounds [25]. In addition, compared with the previously reported ambient-pressure superconducting phase Pmmm-LiMgZr2H12 [26], the Fm-3-type LiMgZr2H12 predicted in this work exhibits a higher superconducting transition temperature Tc at ambient pressure. Figure 7 further shows the variation in the superconducting transition temperatures of the three compounds under applied pressure. At μ* = 0.10, the Tc values of LiMgZr2H12, LiMgHf2H12, and LiMgZrHfH12 at 20 GPa are 103.8 K, 95.1 K, and 93.5 K, respectively. These values are significantly higher than the corresponding ambient-pressure values, indicating that pressure can further increase the theoretical superconducting transition temperatures of these compounds. Overall, the three hydrides proposed in this work exhibit high superconducting figures of merit, suggesting their considerable potential for practical applications.
+
+4. Conclusions
+
+Based on first-principles calculations, this study systematically investigates the structural stability and superconducting properties of quaternary LiMgM2H12 hydrides (M denotes a transition metal) and the quinary LiMgZrHfH12 hydride at ambient pressure. The results show that LiMgZr2H12, LiMgHf2H12, and LiMgZrHfH12 are dynamically stable at ambient pressure but thermodynamically metastable with respect to their competing decomposition products. Electron–phonon coupling calculations indicate that LiMgZr2H12, LiMgHf2H12, and LiMgZrHfH12 exhibit Tc values of 87.4, 81.2, and 85.2 K at ambient pressure, respectively. These values are all above the liquid-nitrogen temperature, demonstrating excellent superconducting performance. Further analysis shows that strong electron–phonon coupling is the key factor responsible for their excellent superconducting performance. Compared with the Ga-based parent Fm-3-XYZ2H12 hydrides, Li substitution at the Ga site synergistically modulates the local structure of the compounds and the distribution of electronic states near the Fermi level. This substitution significantly increases the contribution of H atoms to the density of states near the Fermi level, thereby enhancing the electron–phonon coupling and favoring an increase in the superconducting transition temperature. This work extends the elemental substitution strategy from quaternary to quinary hydride systems, not only enriching the existing library of ambient-pressure superconducting hydrides but also providing theoretical guidance for the experimental investigation of multicomponent hydride superconductors.
+
+Acknowledgments
+
+All the authors thank the computing facilities at High Performance Computing Center of Xidian University.
+
+Supplementary Materials
+
+The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/ma19163465/s1, Figure S1: Phonon dispersion curves for (a) LiMgZr2H12, (b) LiMgHf2H12, and (c) LiMgZrHf2H12 at 20 GPa; Table S1: EPC constant λ, logarithmic average phonon frequency ωlog (in K), density of states at the Fermi level NF (in States/eV/f.u.), and Tc values (in K) estimated using the Allen-Dynes modified McMillan equation with μ* = 0.10–0.13 for LiMgZr2H12, LiMgHf2H12, and LiMgZrHf2H12 at selected pressures (in GPa); Table S2: The average charge value (e) and number of electrons transferred δ (e) for different atoms of LiMgZr2H12, LiMgHf2H12, and LiMgZrHfH12 at ambient pressure.
+
+Author Contributions
+
+Writing—original draft, X.W.; Investigation, X.W. and J.L.; Data curation, X.W. and J.L.; Writing—review & editing, Q.W. and M.Z.; Supervision, Q.W.; Project administration, Q.W.; Resources, M.Z.; Funding acquisition, M.Z. All authors have read and agreed to the published version of the manuscript.
+
+Institutional Review Board Statement
+
+Not applicable.
+
+Informed Consent Statement
+
+Not applicable.
+
+Data Availability Statement
+
+The original contributions presented in this study are included in the article/Supplementary Material. Further inquiries can be directed to the corresponding authors.
+
+Conflicts of Interest
+
+The authors declare no conflicts of interest.
+
+Figure 1 Crystal structure of (a) quaternary LiMgM2H12 and (b) quinary LiMgZrHfH12 hydrides. (c) The selected transition metal range for the M site.
+
+Figure 2 Calculated phonon dispersion curves, phonon density of states, Eliashberg phonon spectral function α2F(ω), and EPC parameter λ for (a) LiMgZr2H12, (b) LiMgHf2H12, and (c) LiMgZrHfH12.
+
+Figure 3 Relative enthalpies (ΔH) of (a) LiMgZr2H12, (b) LiMgHf2H12, and (c) LiMgZrHfH12 with respect to their corresponding decomposition products.
+
+Figure 4 Superconducting parameters of LiMgZr2H12, LiMgHf2H12, and LiMgZrHfH12 at ambient pressure, including the superconducting transition temperature (Tc) calculated using the Allen–Dynes modified McMillan equation (μ* = 0.1), the EPC parameter λ, the logarithmic average phonon frequency ωlog, the electronic density of states at the Fermi level N(EF), and the average charge obtained by each H atom (H_Charge).
+
+Figure 5 Electronic localization function (ELF) of (a) LiMgZr2H12, (b) LiMgHf2H12, and (c) LiMgZrHfH12.
+
+Figure 6 Calculated band structures and projected density of states (PDOS) of (a) LiMgZr2H12, (b) LiMgHf2H12, and (c) LiMgZrHfH12. The dashed line at zero denotes the Fermi energy.
+
+Figure 7 The superconducting transition temperature (Tc) of LiMgZr2H12, LiMgHf2H12, LiMgZrHfH12, and representative quaternary hydride superconductors reported in the literature [25,26], calculated using the Allen–Dynes-modified McMillan equation with μ* = 0.10 at various pressures. The background dotted lines represent the superconducting figure of merit S.
+
+materials-19-03465-t001_Table 1 Table 1 Optimized structural parameters and energies above the convex hull (Ehull in eV/atom) of LiMgZr2H12, LiMgHf2H12, and LiMgZrHfH12 at ambient pressure.
+
+Structures	Lattice Parameter (Å)	Wyckoff Position	E hull	
+Atoms	x	y	z	
+LiMgZr2H12	a = b = c = 7.5631
+α = β = γ = 90°	H (48h)	0.748	0.367	0.500	0.191	
+Mg (4b)	0.500	0.500	0.500	
+Li (4a)	0	0	0	
+Zr (8c)	0.750	0.750	0.250	
+LiMgHf2H12	a = b = c = 7.4929
+α = β = γ = 90°	H (48h)	0.749	0.368	0.500	0.181	
+Mg (4b)	0.500	0.500	0.500	
+Li (4a)	0	0	0	
+Hf (8c)	0.750	0.750	0.250	
+LiMgZrHfH12	a = b = c = 7.5280
+α = β = γ = 90°	H (48h)	0.249	0.867	0.498	0.192	
+Mg (4b)	0	0	0.500	
+Li (4a)	0	0	0	
+Zr (4c)	0.250	0.750	0.750	
+Hf (4d)	0.250	0.250	0.750	
+
+Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.
+
+
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+49. Bardeen J. Cooper L.N. Schrieffer J.R. Theory of Superconductivity Phys. Rev. 1957 108 1175 1204 10.1103/PhysRev.108.1175
+50. Pickard C.J. Errea I. Eremets M.I. Superconducting Hydrides under Pressure Annu. Rev. Condens. Matter Phys. 2020 11 57 76 10.1146/annurev-conmatphys-031218-013413
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+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Front Med (Lausanne)
+Journal ID: Front Med (Lausanne)
+NLM Journal ID: 101648047
+Journal ID: Front. Med.
+
+Frontiers in Medicine
+
+EISSN: 2296-858X
+Publisher: Frontiers Media SA
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC13350272
+PMID: 42433982
+DOI: 10.3389/fmed.2026.1870136
+Article version: 1
+Article version:
+Subjects: Original Research
+
+Incisura groove depth is associated with reduced rotational fibular displacement after syndesmotic injury: cadaveric validation of an automated three-dimensional incisura morphometric pipeline
+
+Omran Kareem 1 * Writing – review & editing Methodology Software Writing – original draft Visualization Data curation Resources Validation Investigation Formal analysis Conceptualization
+de Cesar Netto Cesar 2 Funding acquisition Resources Supervision Conceptualization Writing – review & editing
+Putnam Sara 1 Writing – review & editing Supervision Validation
+Sawatzke Alexander 1 Validation Writing – review & editing Supervision
+Dibbern Kevin 1 Validation Methodology Software Visualization Funding acquisition Conceptualization Writing – review & editing Supervision Resources Investigation Project administration
+1 Department of Orthopaedic Surgery and Rehabilitation, University of Nebraska Medical Center , Omaha , NE , United States
+2 Department of Orthopaedic Surgery and Rehabilitation, Duke University Hospital , Durham , NC , United States
+* Correspondence: Kareem Omran, komran@unmc.edu
+Electronic publication date: 2026 Jun 26
+Publication date: 2026
+Volume: 13
+Electronic Location ID: 1870136
+Received 2026 Apr 30; Revised 2026 Jun 13; Accepted 2026 Jun 15
+Copyright: Copyright © 2026 Omran, de Cesar Netto, Putnam, Sawatzke and Dibbern.
+Copyright year: 2026
+Copyright holder: Omran, de Cesar Netto, Putnam, Sawatzke and Dibbern
+License: This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Keywords: ankle, ankle joint, ankle sprain, incisura fibularis, orthopeadic trauma, syndesmosis, syndesmotic injuries, toolbox
+
+Funding: The author(s) declared that financial support was not received for this work and/or its publication.
+
+Figure count: 3
+Table count: 6
+Equation count: 0
+Reference count: 57
+Page count: 14
+
+section-at-acceptance: Precision Medicine
+
+Ÿ==============================Ÿ
+Background
+
+The tibial incisura provides the osseous constraint in which the fibula is seated at the distal tibiofibular syndesmosis. The morphology of this constraint varies substantially between individuals, making it plausible that incisura geometry modulates fibular displacement under a given injury pattern and the individual risk of injury under comparable mechanisms. Reproducible quantification of three-dimensional incisura morphometry is a prerequisite for testing these hypotheses. This study aimed to develop and validate an automated three-dimensional morphometric toolbox for the tibial incisura, and secondarily to test the resulting outputs in a controlled cadaveric model of syndesmotic injury.
+
+Methods
+
+An automated MATLAB toolbox was developed to compute eight three-dimensional morphometric parameters of the incisura from CT-derived data. The toolbox was evaluated on 34 cadaveric tibiae from 17 matched specimen pairs for reproducibility across repeat acquisitions and for bilateral reliability. Under a cadaveric protocol of repeat scanning before and after complete four-ligament syndesmotic sectioning, outputs were correlated with fibular displacement magnitude from paired six-degree-of-freedom kinematics.
+
+Results
+
+All eight toolbox outputs showed no significant difference between pre- and post-sectioning acquisitions of the same bone, demonstrating reproducibility across repeat CT acquisitions. Bilateral reliability was good for all eight outputs (ICC ≥ 0.75), with seven exceeding 0.80. Four of the six outputs tested against displacement were significantly negatively associated with the magnitude of external rotation: mean groove depth (r = −0.48, p = 0.004), maximum groove depth (r = −0.46, p = 0.006), the conventional single-level incisura floor depth (r = −0.44, p = 0.010), and total groove volume (r = −0.37, p = 0.030). The first principal component explained 85.4% of variance and was negatively associated with the magnitude of external rotation (r = −0.42, p = 0.015).
+
+Conclusion
+
+The incisura metrics toolbox provides reproducible, bilaterally reliable, and fully automated three-dimensional morphometric characterization of the tibial incisura fibularis from CT-derived surface meshes, supplying the methodological foundation required for prospective clinical study of incisura morphology. As a secondary exploratory finding, larger osseous constraint envelopes were associated with reduced rotational fibular displacement under controlled cadaveric sectioning, while morphology did not modulate translational displacement, supporting the construct validity of the pipeline and indicating that incisura morphometry is a candidate input to future diagnostic and predictive injury models.
+
+1 Introduction
+
+The distal tibiofibular syndesmosis is a fibrous articulation between the distal tibia and fibula stabilized by four ligaments and by the osseous geometry of the tibial incisura fibularis. It transmits load between the tibia and fibula during weight-bearing and constrains fibular motion during ankle rotation. Disruption of this articulation accounts for approximately 20 % of operatively treated ankle fractures and represents a common injury in athletic populations, particularly in contact and cutting sports (1–5). Operative management aims to restore the native fibular position within the incisura, and although reduction techniques have been described to guide this process, malreduction rates remain substantial across reported series (4, 6–9). Malreduction of the distal fibula within the tibial incisura has been repeatedly linked to chronic pain, post-traumatic arthritis, persistent disability, and an elevated risk of secondary surgery, making accurate reduction one of the principal determinants of long-term recovery (4, 10, 11).
+
+Reduction quality, in turn, partly depends on the bony anatomy of the distal tibia itself. Patients with shallow tibial incisurae have been shown to be overrepresented in ligamentous ankle injury cohorts and tend toward anterior fibular malreduction following surgical fixation, while deeper and more retroverted incisurae are associated with posterior malreduction (12–16). The convergence of these two observations, that morphology associates with both injury occurrence and the direction of post-surgical malreduction, suggests that the bony anatomy of the syndesmosis exerts a mechanical influence at multiple stages of injury and recovery. These patterns are reproducible across independent clinical series and raise the question of whether preoperative morphometric assessment could refine individualized surgical planning, and recent work has begun to identify discrete morphological phenotypes that influence stability after syndesmotic injury (14–19). The evidence is nonetheless almost exclusively observational, drawn from cohorts that differ in injury mechanism, sex, body mass, and loading history, and the contribution of incisura morphology itself has not been isolated under equivalent injury conditions (13).
+
+This evidence base also rests on a measurement convention with its own limitations. The standard quantification of the tibial incisura is taken from a single axial CT slice at a fixed level 10 millimeters above the tibial plafond, from which linear and angular parameters such as incisura depth, width, facet angle, and anterior and posterior tubercle length are extracted (17, 20, 21). The convention is reproducible, easy to teach, and amenable to existing clinical CT workflows, which together explain its persistence across decades of imaging and surgical literature. Anatomical work has nonetheless shown that the deepest point of the notch does not consistently sit at the conventional level (15) and that the optimal measurement plane differs by sex (16), which means a single fixed cross-section can sample a different anatomical location in different individuals (21–26). Three-dimensional reconstructions have been used to extract the same linear and angular parameters in a volumetric visualization environment and have replicated the association between shallow incisura morphology and ligamentous ankle injury (12, 27). These approaches still sample the incisura at a single cross-sectional level, however, rather than across the whole superoinferior height, and depend on manual landmark placement that limits scalability. Whether three-dimensional measurement of the incisura captures information beyond what the single-level convention provides is unknown.
+
+A reproducible, automated method for capturing the three-dimensional geometry of the incisura, in a way that integrates information across its full superoinferior extent rather than at any single fixed level, would address both the observational and methodological limitations described above and provide a quantitative morphometric foundation on which prospective study of incisura anatomy and its clinical correlates could be built. Accordingly, the primary aim of this study was to develop and validate an automated three-dimensional morphometric toolbox for the tibial incisura, evaluating its reproducibility across repeat acquisitions and its bilateral reliability between contralateral limbs. As a secondary, exploratory aim, the toolbox outputs were tested against fibular displacement in a controlled cadaveric model of syndesmotic injury, to demonstrate that the morphometric measurements behave in a biomechanically interpretable manner under standardized conditions.
+
+2 Materials and methods
+
+2.1 Study design and specimens
+
+This cadaveric experimental study used 34 thawed fresh-frozen through-the-knee lower extremity specimens drawn from 17 donors (17 matched pairs; Table 1). Specimens were screened and confirmed to have no radiographic or clinical evidence of prior ankle fracture, prior ankle surgery, acute fracture, or gross deformity. The proximal portion of each specimen was prepared by removal of surrounding soft tissue while preserving the proximal tibiofibular joint. The proximal tibia was potted in polymethylmethacrylate and fixed in a plantigrade position within a radiolucent external loading frame. A calibrated loading mechanism applied 356 N of axial compression through the proximal tibial cut surface to approximate single-limb stance-phase ground reaction force. Each specimen underwent paired imaging in the intact state and after standardized sequential sectioning of the four primary syndesmotic ligaments. All sectioning was performed through a direct lateral fibular approach by a single fellowship-trained orthopedic surgeon. Ten complete plantar flexion and dorsiflexion manual range-of-motion cycles were performed after sectioning to mobilize the ankle joint prior to post-sectioning imaging.
+
+Table 1 Anthropometric characteristics of the cadaveric cohort (17 donors, 34 limbs; 11 male and 6 female donors).
+
+Characteristic	Mean ± SD	Median [range]	
+Age at death (years)	74.2 ± 8.3	77 [55–85]	
+Stature (cm)	174.8 ± 9.7	177.8 [157.5–190.5]	
+Body mass (kg)	84.3 ± 24.8	81.6 [42.6–155.1]	
+Body mass index (kg/m2)	27.3 ± 6.3	27.9 [15.2–42.7]	
+Data are summarized as mean ± standard deviation and as median with bracketed range. Body mass index was computed as body mass divided by the square of stature in meters.
+
+2.2 Cadaveric imaging and segmentation
+
+Cadaveric specimens were imaged in a dedicated extremity cone-beam weight-bearing CT system (HiRise; CurveBeam, Hatfield, PA) at an isotropic voxel size of 0.37 millimeters, with a metal artifact reduction algorithm applied during reconstruction. Left and right limbs were imaged sequentially within each session under identical scanner geometry and loading parameters, and the loaded configuration was maintained throughout each acquisition to ensure that all measured positional relationships reflected the loaded state.
+
+Three-dimensional surface models of the tibia, fibula, and talus were generated from DICOM volumes using a semi-automated segmentation pipeline in Disior Bonelogic 2.0 (Paragon 28, Englewood, CO). The pipeline applied Hounsfield unit thresholding to isolate cortical and cancellous bone from surrounding soft tissue, followed by region-growing algorithms to produce closed volumetric bone masks for each structure. All segmentations then underwent review and manual refinement in 3D Slicer (version 5.6.2; Brigham and Women’s Hospital, Boston, MA) to correct any threshold-induced artifacts at bone boundaries. Quality control included visual inspection across orthogonal axial, coronal, and sagittal planes, confirmation of smooth surface topology free of stair-stepping artifact at the articular surfaces, and verification that the tibiofibular and tibiotalar joint spaces were resolved as distinct surfaces. Volumetric masks were then converted to triangulated surface meshes and exported in stereolithography file format for all downstream computational analyses. Right-sided tibiae were reflected across the sagittal plane prior to coordinate assignment to produce canonical left-sided configurations and to permit direct bilateral comparison in a single coordinate frame.
+
+2.3 Incisura metrics toolbox architecture
+
+The incisura metrics toolbox is implemented as a single MATLAB function (The MathWorks, Natick, MA) that launches an interactive graphical user interface with two processing modes. The Automatic mode executes a fully deterministic pipeline from mesh input to metric output without user intervention (Figure 1). The Manual mode provides interactive placement of the anterior and posterior boundary curves by the operator, after which all subsequent geometric computations proceed identically to the automatic pathway (Figure 2). Both modes output an identical metric set and support single-specimen and batch directory workflows. All analyses reported in the present work were produced using the Automatic mode, with manual verification of boundary curves confirming anatomically appropriate ridge trajectories in all 34 tibiae without requiring manual override. Boundary verification was performed by the lead author for each specimen. End-to-end processing time per specimen, from segmented mesh input to complete morphometric output, was approximately 10 to 20 s on a standard laptop workstation.
+
+Figure 1 Incisura metrics toolbox graphical user interface in automatic mode on a representative right tibia. Following input of the segmented tibial mesh, the toolbox executes a fully deterministic pipeline from coordinate normalization through morphometric output without further user intervention. The right-hand panel exposes the parameters governing each stage of the pipeline: directories, batch or single-specimen scope, superoinferior integration range, apex closure detection, and tubercle leveling, together with a real-time results log of completed batch outputs. The central viewer renders the processed tibia with optional overlays of the computed metrics, with the constraint volume integration shown here as a stacked green wireframe of the cross-sectional contours sampled across the constraint envelope. View buttons (Anterior, Posterior, Superior, Lateral, Medial, Oblique) and overlay toggles (Tubercles & FA, Max Depth) at the bottom of the viewer permit interactive inspection of any computed output.
+
+Screenshot of the Incisura Volume Toolbox in automatic mode showing a right tibia rendered in ivory at left. A stacked series of green wireframe contours fills the fibular notch region, representing cross-sectional slices sampled across the constraint envelope, with a red label marking the constraint end at Z equals 28.2 millimetres. View buttons and overlay toggles sit below the model. The right panel exposes pipeline parameters including directories, batch scope, superoinferior integration range, apex closure detection, and tubercle levelling, plus a green “COMPLETE - Run Again?” button above a results log of batch morphometric outputs.
+
+Figure 2 Interactive manual mode interface on the same right tibia, illustrating operator-controlled placement of the anterior and posterior boundary curves. Following user-specified curve placement on the rendered surface, all subsequent geometric computations, including coordinate normalization, cross-sectional area integration, and morphometric output extraction, proceed identically to the automatic mode pathway. The manual mode is intended for cases in which the operator elects to define ridge trajectories directly rather than rely on the template-guided automatic boundary detection.
+
+Screenshot of the Incisura Volume Toolbox in manual mode showing the same right tibia rendered in ivory at left. Two operator-placed boundary curves run vertically along the bone surface, a magenta curve marking the anterior ridge and a blue curve marking the posterior ridge of the fibular notch. The right panel contains processing mode controls, input directories, mesh loading, anterior and posterior curve definition tools showing thirteen and fourteen points, volume settings, a red “COMPUTE VOLUME” button, and a results log reporting depth, ratio, angle, and orientation measurements for the defined incisura.
+
+A dual-mesh architecture is maintained throughout processing. A Laplacian-smoothed detection mesh, produced by 30 smoothing iterations with a lambda coefficient of 0.4, is used exclusively for ridge identification and boundary curve extraction. All metric computations are performed on the unsmoothed native mesh to preserve the true osseous geometry of the individual specimen. This separation ensures that template-guided ridge detection is not confounded by surface noise while final metric outputs accurately reflect the anatomical dimensions of each bone.
+
+2.3.1 Coordinate system and scale normalization
+
+A standardized anatomical coordinate system was established prior to morphometric measurement. Initial gross orientation was provided by the Automatic Anatomical Foot and Ankle Coordinate Toolbox (AAFACT) framework described by Peterson and colleagues, which aligns the tibia to a population-derived mean-shape template and defines the primary superoinferior, mediolateral, and anteroposterior axes (28). Two further geometric refinements were applied within the AAFACT-initialized frame. The medial malleolus centroid, identified from surface vertices with Z coordinate below minus 5 millimeters, was used to correct the mediolateral axis toward the true anatomical medial direction. The longest edge of the tibial plafond convex hull on the lateral side was then used to align the incisura face parallel to the anteroposterior axis, and a corrective rotation about the X axis removed any residual anteroposterior plafond tilt. No translational adjustment was applied, preserving the AAFACT convention in which the tibiotalar joint center lies at the coordinate origin.
+
+Cross-sectional area–based scale normalization was then applied. The tibial cross-sectional area at 10 millimeters above the tibiotalar joint center was computed from the input mesh and compared against the corresponding area on the pre-computed mean-shape template. A scale factor was derived as the square root of the template-to-subject area ratio and applied uniformly to the specimen mesh before boundary detection. This template-scale alignment ensures that template-guided ridge detection performs consistently across the full range of tibial sizes present in the specimen cohort. All reported output metrics are expressed in true anatomical units by inverting the scale factor at the output stage, preserving dimensional fidelity in the final morphometric values.
+
+2.3.2 Anteroposterior midline and boundary curve extraction
+
+The anteroposterior midline (Ymid) of the incisura at each superoinferior level was computed dynamically using a two-pass linear regression of the Y coordinates of tibial surface vertices within a fibula-proximity region of interest. The region of interest was identified by a k-d tree nearest-neighbor search between the subject tibial mesh and the paired fibular mesh, retaining the closest 20 percent of tibial vertices as the fibula-proximity cloud. A first-pass linear Ymid fit was computed using a constant median Y value, boundary curves were constructed using this initial fit, and the Ymid line was then refit from the resulting curves to produce a final midline that accounts for the approximately 30-degree anteroposterior twist of the incisura from inferior to superior levels.
+
+Boundary curves defining the anterior ridge (corresponding to Chaput’s tubercle) and the posterior ridge (corresponding to Volkmann’s tubercle) were extracted through a two-stage process. In the first stage, pre-computed mean-shape template ridge curves were transferred to each specimen at corresponding Z levels and snapped to the nearest lateral mesh contour point within a 12-millimeter tolerance, filtered through a 5-millimeter corridor around the refined anterior and posterior detection planes to prevent snapping to anatomically implausible features. In the second stage, curvature-based vertex refinement relocated each snapped curve point to the local ridge maximum within a 3-millimeter search radius along the ordered mesh contour. Smoothed final curves were constructed from the refined points using cubic smoothing spline interpolation with 200 resampled curve points.
+
+2.3.3 Cross-sectional area and constraint envelope ceiling
+
+Cross-sectional area at each superoinferior level was computed from a closed polygon defined by the anterior and posterior ridge anchors together with the intervening groove arc. The opening chord between the anchors closed the polygon medially, and the enclosed area was computed using the shoelace formula. A medial floor clipping step using the Sutherland–Hodgman polygon clipping algorithm removed any artifactual medial extension of the groove arc into the tibial shaft, which would otherwise inflate cross-sectional area estimates at levels where the incisura transitions toward the flat medial tibial surface (29).
+
+The superoinferior integration range for volumetric computation was bounded inferiorly by the level at which the anterior and posterior boundary curves first converged and superiorly by a consensus closure ceiling. The closure ceiling was determined by four independent geometric criteria evaluated at each Z level. Method 1 flagged levels where the ratio of groove depth to chord width fell below 0.04, indicating the groove had flattened relative to its width. Method 2 flagged levels where the mean signed perpendicular distance from the chord to interior groove-arc points fell below 0.5 millimeters. Method 3 applied a cross-sectional area floor, flagging levels where the area fell below 25 percent of the cohort median area. Method 4 evaluated the concavity fraction of the groove contour, flagging levels where less than 50 percent of the interior arc was concave toward the groove axis. Each criterion produced a candidate closure Z, and the final ceiling was taken as the median of the candidate Z values when three or more criteria agreed, the minimum when exactly two agreed, and the single value when only one criterion fired. Constraint volume was computed by integrating cross-sectional area from the inferior boundary to the closure ceiling using the trapezoidal rule across 200 evenly spaced superoinferior levels.
+
+2.3.4 Primary morphometric outputs
+
+Eight scalar morphometric parameters were computed per specimen and specified prior to analysis to characterize the constraint envelope across four geometric dimensions, comprising volumetric constraint, groove depth, angular aperture, and anteroposterior tubercle geometry (Figure 3). The full set of parameter definitions is summarized in Table 2.
+
+Figure 3 Primary toolbox outputs visualized on the same right tibia in the lateral oblique view. Annotated outputs include the deepest point of the groove (green marker, “Deepest”), maximum groove depth (4.22 mm at Z = 14 mm above the tibiotalar joint center), anterior tubercle prominence (red marker, ATT = 4.1 mm), posterior tubercle prominence (blue marker, PTT = 4.4 mm), the facet angle (FA = 149.3°) at the conventional 10-millimeter level, and the superior limit of the constraint envelope (red, “Constraint ends” at Z = 28.2 mm).
+
+Screenshot of the Incisura Volume Toolbox showing the same right tibia in lateral oblique view with colour-coded morphometric annotations on the fibular notch. Labelled markers indicate the deepest groove point in green, maximum groove depth of 4.22 millimetres at Z equals 14 millimetres, anterior tubercle prominence of 4.1 millimetres in red, posterior tubercle prominence of 4.4 millimetres in blue, the facet angle of 149.3 degrees, and the constraint envelope upper limit in red at Z equals 28.2 millimetres. The right panel shows automatic mode parameters and a results log, with a green “COMPLETE - Run Again?” button.
+
+Table 2 Definitions of the eight morphometric parameters computed by the incisura metrics toolbox.
+
+Parameter	Units	Definition	
+Constraint volume (FNV₁₀)	mm3	Trapezoidal integral of groove cross-sectional area from 10 mm above the tibiotalar joint center to the closure ceiling, representing the three-dimensional osseous constraint envelope available to the fibula across its full superoinferior engagement height.	
+Incisura floor depth (IFD₁₀)	mm	Maximum perpendicular distance from the anteroposterior chord to the deepest point of the groove contour at 10 mm above the tibiotalar joint center, measured in the mediolateral plane.	
+Facet angle (FA₁₀)	degrees	Angle subtended at the deepest groove point by vectors directed toward the anterior and posterior ridge tips at 10 mm above the tibiotalar joint center. Larger values indicate a shallower, more open notch configuration.	
+Maximum groove depth	mm	Maximum perpendicular mediolateral distance from the anteroposterior chord to the deepest point of the groove contour across all superoinferior levels within the constraint zone.	
+Mean groove depth	mm	Mean perpendicular mediolateral distance from the anteroposterior chord to the groove contour averaged across all superoinferior levels within the constraint zone.	
+Total groove volume	mm3	Total three-dimensional volume of the incisura groove integrated across the full superoinferior extent of the constraint zone. Complements FNV₁₀ by capturing the complete groove volume without restriction to levels above the plafond apex.	
+Anterior tubercle prominence	mm	Lateral X distance from the anterior tibial tubercle (Chaput’s tubercle) anchor to the deepest groove point at 10 mm above the tibiotalar joint center.	
+Posterior tubercle prominence	mm	Lateral X distance from the posterior tibial tubercle (Volkmann’s tubercle) anchor to the deepest groove point at 10 mm above the tibiotalar joint center.	
+
+2.4 Syndesmotic sectioning and six-degree-of-freedom displacement
+
+Six-degree-of-freedom fibular displacement components were computed from bilateral CT registration of the intact and post-sectioning acquisitions using an ICP-based alignment framework with per-vertex correspondence weighting (30, 31). Three displacement components were selected for correlation with morphometric outputs on anatomical and biomechanical grounds. External rotation (Rz) was selected because it is the dominant displacement mode under physiological and injury loading conditions at the syndesmosis across cadaveric biomechanical studies (1, 3, 32), and because groove depth in the mediolateral plane defines the rotational arc available before osseous engagement. Anteroposterior translation (Ty) was selected because the anterior and posterior walls of the incisura directly bound the fibula in the anteroposterior plane, making this the anatomically anticipated outcome of constraint envelope morphometry. Lateral translation (Tx) was included as the displacement component targeted by conventional widening-based imaging criteria, despite the incisura providing no osseous barrier to mediolateral fibular escape, permitting direct testing of whether bony morphology modulates the component that clinical measurement currently relies upon.
+
+2.5 Statistical analysis
+
+Statistical analyses were performed in MATLAB R2025b (The MathWorks, Natick, MA). Two validation checks were performed prior to the primary correlation analysis. Pipeline and segmentation reproducibility was assessed by comparing morphometric outputs from intact and post-sectioning CT acquisitions of the same bone using paired Wilcoxon signed-rank testing of the eight toolbox outputs, on the assumption that syndesmotic ligament sectioning should not alter osseous geometry and that any pre- to post-sectioning difference would reflect combined CT acquisition and semi-automated segmentation variability rather than true anatomical change. Bilateral reliability across the 17 intact specimen pairs was quantified using two-way mixed-effects intraclass correlation coefficients with absolute agreement, interpreted according to the conventions of Koo and Li (33), under which values at or above 0.75 are considered to indicate good reliability. Systematic side-to-side bias was assessed using paired Wilcoxon signed-rank testing on left-versus-right values.
+
+Bivariate Spearman rank correlations were then computed between six toolbox outputs, comprising constraint volume, single-level incisura floor depth, facet angle, mean groove depth, maximum groove depth, and total groove volume, and the magnitude of three fibular displacement components from the kinematic analysis, comprising external rotation, mediolateral translation, and anteroposterior translation. The Spearman test was selected over Pearson to accommodate the non-normal distribution of displacement values without imposing distributional assumptions. Principal component analysis of the eight standardized toolbox outputs was conducted to characterize inter-parameter co-variation across the constraint geometry, and the first principal component score was tested as a single additional predictor against the magnitude of each displacement component.
+
+Multivariate modeling was not undertaken because the sample size of 34 limbs provides insufficient degrees of freedom relative to the number of candidate predictors, and because the morphometric parameters are geometrically related such that shared variance would produce unstable coefficient estimates. The analysis was treated as exploratory and hypothesis-generating, and formal correction for multiple comparisons was not applied; individual associations near the significance threshold are interpreted with appropriate caution. Statistical significance was accepted at p < 0.05 throughout.
+
+3 Results
+
+3.1 Descriptive morphometrics
+
+The eight toolbox outputs across the 34 intact control tibiae demonstrated substantial inter-specimen variability, consistent with broad morphological heterogeneity of the tibial incisura previously reported in anatomical and imaging series (Table 3). Constraint volume (FNV₁₀) ranged from 114.7 to 880.0 mm3 (mean 402.4 ± 178.9 mm3). Incisura floor depth at 10 millimeters above the plafond apex ranged from 1.94 to 6.45 mm (mean 3.99 ± 1.10 mm). Facet angle ranged from 117.6 to 157.8 degrees (mean 141.0 ± 9.6 degrees). Mean groove depth ranged from 1.24 to 3.31 mm (mean 2.23 ± 0.52 mm), and maximum groove depth from 1.93 to 6.07 mm (mean 3.96 ± 1.03 mm). Total groove volume ranged from 347.3 to 1771.5 mm3 (mean 940.8 ± 337.2 mm3). Anterior tubercle prominence ranged from 1.74 to 6.62 mm (mean 3.64 ± 1.18 mm), and posterior tubercle prominence from 2.13 to 7.29 mm (mean 4.27 ± 1.12 mm). The superoinferior level at which the deepest point of the groove occurred ranged from 4.31 to 16.15 mm above the tibiotalar joint center (mean 12.04 ± 2.07 mm, median 12.28 mm). The conventional 10-millimeter sampling plane fell within 1 millimeter of the deepest point in 17.6% of specimens, while 50.0% of specimens had their deepest point within 1 millimeter of the 12-millimeter level.
+
+Table 3 Descriptive statistics for the eight incisura metrics toolbox outputs across 34 intact control tibiae (17 matched specimen pairs).
+
+Parameter	Mean ± SD	Median [Q1, Q3]	Range	
+Constraint volume (mm3)	402.4 ± 178.9	369.8 [270.0, 512.7]	114.7–880.0	
+Incisura floor depth (mm)	3.99 ± 1.10	3.88 [3.05, 4.47]	1.94–6.45	
+Facet angle (°)	141.0 ± 9.6	140.5 [135.3, 149.4]	117.6–157.8	
+Maximum groove depth (mm)	3.96 ± 1.03	3.94 [3.23, 4.44]	1.93–6.07	
+Mean groove depth (mm)	2.23 ± 0.52	2.16 [1.93, 2.56]	1.24–3.31	
+Total groove volume (mm3)	940.8 ± 337.2	923.5 [660.8, 1149.3]	347.3–1771.5	
+Anterior tubercle prominence (mm)	3.64 ± 1.18	3.54 [2.84, 3.97]	1.74–6.62	
+Posterior tubercle prominence (mm)	4.27 ± 1.12	4.27 [3.42, 4.92]	2.13–7.29	
+Height from plafond center of deepest point (mm)	12.04 ± 2.07	12.28 [11.16, 13.05]	4.31–16.15	
+SD, standard deviation; Q1, first quartile; Q3, third quartile.
+
+3.2 Reproducibility across intact and post-sectioning acquisitions
+
+All eight toolbox outputs showed no statistically significant difference between intact and post-sectioning CT acquisitions of the same bone on Wilcoxon signed-rank testing (Table 4). Wilcoxon p-values ranged from 0.209 (total groove volume) to 0.885 (mean groove depth), with no parameter approaching the conventional significance threshold. The absence of measurable change across independent scan sessions of identical osseous geometry confirms that the combined pipeline, including cone-beam CT acquisition, semi-automated segmentation, coordinate assignment, boundary detection, and metric computation, produces reproducible morphometric outputs at the level of within-specimen variability expected from repeated acquisition and segmentation.
+
+Table 4 Reproducibility of the eight incisura metrics toolbox outputs across paired intact and post-sectioning CT acquisitions of the same specimens (n = 34 tibiae).
+
+Parameter	Intact median	Post-sectioning median	Wilcoxon p	
+Constraint volume (FNV₁₀, mm3)	369.8	417.8	0.249	
+Incisura floor depth (IFD₁₀, mm)	3.88	4.17	0.521	
+Facet angle (FA₁₀, °)	140.5	139.0	0.791	
+Maximum groove depth (mm)	3.94	4.16	0.417	
+Mean groove depth (mm)	2.16	2.12	0.885	
+Total groove volume (mm3)	923.5	967.6	0.209	
+Anterior tubercle prominence (mm)	3.54	3.77	0.871	
+Posterior tubercle prominence (mm)	4.27	4.36	0.317	
+Wilcoxon signed-rank test for paired intact and post-sectioning acquisitions of the same specimen. No parameter showed a statistically significant pre- to post-sectioning difference. The absence of measurable change confirms that combined CT acquisition, semi-automated segmentation, coordinate assignment, and metric computation produce reproducible morphometric outputs.
+
+3.3 Bilateral reliability
+
+All eight toolbox outputs demonstrated intraclass correlation coefficients at or above 0.75 across the 17 intact specimen pairs, with no significant bilateral side difference on paired Wilcoxon signed-rank testing (Table 5). Constraint volume (FNV₁₀) demonstrated an ICC of 0.845 (bilateral p = 0.554), maximum groove depth an ICC of 0.880 (p = 0.177), and incisura floor depth (IFD₁₀) an ICC of 0.874 (p = 0.309). Total groove volume demonstrated an ICC of 0.867 (p = 0.493), facet angle an ICC of 0.843 (p = 0.084), mean groove depth an ICC of 0.756 (p = 0.493), anterior tubercle prominence an ICC of 0.810 (p = 0.084), and posterior tubercle prominence an ICC of 0.866 (p = 0.831). By the conventions of Koo and Li, all eight parameters exceeded the lower threshold for good reliability, with seven of the eight exceeding 0.80. Mean groove depth recorded the lowest coefficient at 0.756, at the lower bound of the good range. No parameter showed systematic side-to-side bias. The Z-location of the deepest groove point demonstrated comparable bilateral reliability (ICC = 0.797, p = 0.136), confirming that the longitudinal positioning of the deepest geometry is preserved between contralateral limbs.
+
+Table 5 Bilateral reliability of the eight incisura metrics toolbox outputs across 17 intact specimen pairs.
+
+Parameter	ICC (2-way mixed, absolute agreement)	Bilateral p (Wilcoxon)	
+Constraint volume (FNV₁₀)	0.845	0.554	
+Incisura floor depth (IFD₁₀)	0.874	0.309	
+Facet angle (FA₁₀)	0.843	0.084	
+Maximum groove depth	0.880	0.177	
+Mean groove depth	0.756	0.493	
+Total groove volume	0.867	0.493	
+Anterior tubercle prominence	0.810	0.084	
+Posterior tubercle prominence	0.866	0.831	
+Z-location of deepest point	0.797	0.136	
+All eight parameters demonstrated intraclass correlation coefficients (ICC) at or above 0.75 with no significant bilateral side difference. ICC thresholds from Koo and Li (33): 0.75–0.9 good, above 0.9 excellent.
+
+3.4 Morphometric associations with the magnitude of fibular displacement
+
+Bivariate Spearman correlations between the six toolbox outputs and the magnitude of each of the three fibular displacement components are presented in Table 6. Four of the six toolbox outputs were significantly negatively associated with the magnitude of external rotation following complete syndesmotic sectioning. Mean groove depth showed the strongest association (r = −0.480, p = 0.004), followed by maximum groove depth (r = −0.462, p = 0.006), the conventional single-level incisura floor depth (r = −0.438, p = 0.010), and total groove volume (r = −0.374, p = 0.030). Constraint volume and facet angle were not significantly associated with the magnitude of external rotation in this cohort. No toolbox output was significantly associated with the magnitude of mediolateral or anteroposterior translation. As no formal correction for multiple comparisons was applied, all associations are reported as exploratory; the association closest to the conventional significance threshold (total groove volume, p = 0.030) should be interpreted with particular caution and treated as hypothesis-generating.
+
+Table 6 Bivariate spearman correlations between six incisura metrics toolbox outputs and the magnitude of three fibular displacement components from the kinematic analysis (n = 34 limbs).
+
+Parameter	External rotation	Lateral translation	Anteroposterior translation	
+r	p	r	p	r	p	
+Constraint volume (FNV₁₀)	−0.263	0.133	+0.128	0.470	−0.330	0.058	
+Incisura floor depth (IFD₁₀)	−0.438	0.010 *	+0.035	0.844	−0.213	0.226	
+Facet angle (FA₁₀)	+0.308	0.077	−0.048	0.789	+0.108	0.542	
+Maximum groove depth	−0.462	0.006 **	−0.009	0.959	−0.209	0.235	
+Mean groove depth	−0.480	0.004 **	+0.101	0.567	−0.267	0.127	
+Total groove volume	−0.374	0.030 *	+0.021	0.907	−0.327	0.059	
+First principal component (PC1)	−0.416	0.015 *	+0.064	0.720	−0.261	0.135	
+r denotes the Spearman rank correlation coefficient and p denotes the two-tailed significance value. The first principal component (PC1) was derived from a principal component analysis of the eight standardized incisura metrics toolbox outputs and explained 85.4% of variance across the parameter set; its loading was approximately equal across the eight contributing outputs. * p < 0.05; ** p < 0.01. Bold means p < 0.05.
+
+The first principal component of the eight standardized toolbox outputs explained 85.4% of variance across the eight parameters, with all eight outputs loading on the first component with comparable magnitude. The first principal component was significantly negatively associated with the magnitude of external rotation (r = −0.416, p = 0.015) but not with the magnitude of mediolateral or anteroposterior translation. The high proportion of variance explained by a single component, together with similar loadings across all eight outputs, indicates that the toolbox parameters reflect a common underlying construct of constraint envelope geometry rather than independent geometric features.
+
+4 Discussion
+
+The principal contribution of this study is the development and validation of an automated three-dimensional morphometric toolbox for the tibial incisura fibularis. As a secondary exploratory analysis, the toolbox outputs were tested against fibular displacement under a highly controlled cadaveric environment with complete four-ligament syndesmotic sectioning to confirm that the morphometric measurements behave in a biomechanically interpretable manner. Across 17 matched cadaveric specimen pairs, all eight toolbox outputs demonstrated reproducible behavior between independent CT acquisitions and bilateral reliability with intraclass correlation coefficients at or above 0.75, with no systematic side-to-side bias. Applied to the same specimens under standardized injury conditions, the four toolbox outputs that capture the depth and overall volume of the osseous constraint envelope were each significantly negatively associated with the magnitude of external rotation, with deeper grooves corresponding to less rotational fibular displacement. The first principal component of the eight outputs, which explained 85.4% of variance and represented the dominant axis of co-variation across the constraint geometry, was likewise associated with reduced rotational displacement. No morphometric parameter was significantly associated with the magnitude of mediolateral or anteroposterior translation. These findings provide the first direct evidence to the knowledge of the authors that incisura morphometry modulates the magnitude of rotational fibular displacement under controlled equivalent ligamentous disruption, with potentially significant diagnostic and operative implications for the management of syndesmotic injury.
+
+The descriptive morphometric distribution of the present cohort aligns closely with the published anatomical literature. The mean facet angle, mean incisura floor depth, and mean tubercle prominence values all fall within ranges previously reported in cadaveric CT, dry bone, and MRI cohorts (17–22). The observed anteroposterior asymmetry, with the posterior facet and posterior tubercle consistently longer and more prominent than their anterior counterparts, recapitulates a pattern documented across populations and specimen types (18–20, 23, 30). The descriptive distributions from the present cohort therefore provide no evidence of systematic bias relative to the established morphometric literature, and the toolbox outputs can be interpreted against existing reference ranges without adjustment. The bilateral reliability data provide convergent validation against prior studies of incisura symmetry. Lepojärvi and colleagues found no significant asymmetry between uninjured ankles in single subjects with good inter- and intraobserver reliabilities, and Park and Kim confirmed the absence of significant side-to-side differences in bilateral ankle CT of uninjured volunteers (24, 31). The consequence of native bilateral symmetry for clinical diagnostics has been emphasized most directly by Kubik and colleagues, who demonstrated that unilateral CT assessment frequently produces anterior–posterior distance differences exceeding the standard malreduction threshold in uninjured ankles, and that a substantial proportion of native uninjured syndesmoses would be classified as malreduced by current diagnostic standards when assessed on bilateral CT (33). The toolbox’s bilateral reliability across the matched specimen pairs supports the validity of bilateral morphometric comparison as a quantitative framework and establishes the pipeline as suitable for deployment in studies that compare injured and uninjured contralateral ankles.
+
+Against these validated morphometric results, the kinematic associations identified in the present analysis converge to a unified anatomical signal. All three depth parameters reached statistical significance against the magnitude of external rotation, with effect sizes in a comparable range. The three measurements quantify the same geometric relationship of perpendicular distance from the anteroposterior chord to the deepest groove point, differing only in whether the depth is sampled at one fixed superoinferior level or aggregated across the full superoinferior extent of the constraint zone. The convergence of the three measurements on a similar association with rotation suggests that under the morphometric range and sample size of this cadaveric cohort, the mechanical signal in the data is robust enough to be detected by either sampling strategy. In the present cohort, the deepest point of the groove sat a mean of 12.04 mm above the tibiotalar joint center on the plafond (SD 2.07, range 4.31 to 16.15) and the conventional 10-millimeter sampling plane fell within 1 millimeter of the true deepest point in only 17.6% of specimens, corroborating the documented offset between the conventional sampling level and the true geometric maximum of the groove. In larger or more morphologically heterogeneous cohorts, where this offset may translate into a greater fraction of mismeasured specimens, aggregation across the full constraint zone may capture mechanically meaningful geometry more consistently than a single fixed level.
+
+The directional specificity of these findings is reinforced by the corresponding null observation along the mediolateral axis. The absence of any significant association between osseous morphometric parameters and the magnitude of lateral translation serves as a construct-validity check on the pipeline. The incisura is open laterally by anatomical definition, with its walls running anteriorly and posteriorly and its floor lying medially, but none of these surfaces creates a mechanical barrier to mediolateral fibular escape. Lateral fibular separation is resisted by the combined action of the interosseous ligament, the anterior inferior tibiofibular ligament, and the posterior inferior tibiofibular ligament, with the interosseous ligament demonstrating the highest tensile failure load of the three (34). Massri-Pugin and colleagues confirmed arthroscopically in a cadaveric series that no significant coronal diastasis occurs until all three syndesmotic ligaments are sectioned (35). Physiological lateral translation is small under normal loading conditions (36). In the present analysis, even complete four-ligament sectioning produced relatively modest lateral translation compared with the substantial external rotation magnitudes observed, and none of the bony morphometric parameters modulated the degree of this lateral escape. Beumer and colleagues demonstrated consistent results, showing that in the neutral position the largest displacements of the fibula following syndesmotic sectioning consisted of external rotation rather than lateral diastasis (37). A tool measuring osseous constraint geometry should produce a null association for a displacement component that osseous geometry does not resist, and the present toolbox produces that, in a manner that is clinically and biomechanically coherent with the ligamentous architecture of the coronal-plane syndesmotic constraint.
+
+These results sit alongside a broader recent shift in syndesmotic assessment toward three-dimensional analysis. Three-dimensional volumetric approaches to syndesmotic assessment have emerged over the past decade and represent a substantial advance over single-slice measurement. Bhimani and colleagues demonstrated that three-dimensional tibiofibular joint space volume on weight-bearing CT discriminates syndesmotic instability more effectively than two-dimensional measurements (38). Ashkani-Esfahani and colleagues subsequently reported high sensitivity and specificity for subtle syndesmotic instability using volumetric assessment up to five centimeters above the plafond (32). De Cesar Netto and colleagues extended this work with a 3D distance mapping algorithm that detected significantly increased syndesmotic distances at all measured levels above the plafond following complete ligament sectioning under axial load, with diagnostic accuracy highest at the first one and three centimeters of the incisura (39). Furthermore, Peiffer and colleagues developed an automated pipeline using neural network segmentation and iterative closest point registration that produced bilateral 3D reference values with excellent manual-to-automated agreement (40). Each of these approaches, however, quantifies the position of the fibula relative to the tibia rather than the morphometry of the osseous groove itself. The joint-space volume captured by existing tools varies jointly with incisura geometry and fibular position and therefore conflates two distinct anatomical contributions to stability. The incisura metrics toolbox addresses this gap by providing volumetric characterization of the incisura as an osseous constraint envelope whose geometry reflects the passive resistance the bony articulation alone provides against fibular displacement, independent of the fibula’s instantaneous location.
+
+Alongside these volumetric approaches, statistical shape modeling has emerged as the principal computational approach for characterizing population-level skeletal variation in the foot and ankle, and several recent studies have applied it to the distal tibiofibular joint and the broader syndesmotic complex (41–43). Statistical shape modeling builds a mean-shape template from a registered cohort and decomposes inter-specimen variation into orthogonal principal modes that, by construction, capture independent dimensions of geometric variability. However, statistical shape modeling does not, on its own, attach explicit anatomical meaning to the modes it extracts. The principal modes are conventionally interpreted by visual inspection of the rendered shape extremes, and the lack of clinical interpretation of the resulting modes of variation has been recognized as a recurring limitation of the technique. The incisura metrics toolbox may have utility in bridging this gap. Applied to the shapes generated at each end of a statistical shape model’s principal modes, the toolbox can produce explicit anatomical descriptors of how the PCA modes, or their extremes differ.
+
+Clinically, these findings may carry implications for preoperative assessment and intraoperative reduction. The cadaveric design supports mechanistic inference about the constraint role of the bony incisura but cannot establish clinical risk; the implications outlined below are hence best interpreted as hypotheses for prospective study rather than as direct conclusions for current practice. Rotational fibular malreduction is invisible to conventional radiographic assessment, which detects coronal-plane lateral widening but not external rotation of the fibula within the incisura (44, 45). Existing operative imaging protocols rely heavily on the tibiofibular clear space and tibiofibular overlap on anteroposterior and mortise views to confirm reduction quality, and these measurements are insensitive to the rotational component of fibular position. Cadaveric work has demonstrated that the standard fluoroscopic indices remain within their normal range with up to 30 degrees of induced fibular external rotation and are unable to detect external rotational malreduction of this magnitude (44). Intraoperative reduction technique itself further influences fibular position within the incisura, with reduction clamp tine placement shown to systematically bias the resulting reduction direction, and the rotational component of the resulting fibular position is the most likely to escape conventional radiographic detection (46–48). Shallower incisurae and smaller constraint envelopes were associated in the present cohort with greater rotational fibular displacement under equivalent ligamentous disruption, identifying this morphometric phenotype as a candidate marker of heightened susceptibility to residual rotational malreduction following operative fixation. Bilateral CT assessment of the syndesmosis, using the contralateral uninjured ankle as a within-subject reference, has been advocated for several years to address the limitations of plain radiography, and morphometric stratification by preoperative incisura geometry could refine the indications for this advanced postoperative assessment (21, 49–51). Automated morphometric outputs of the kind produced by the toolbox take seconds to compute from a bilateral weight-bearing CT acquisition, and weight-bearing CT use in foot and ankle assessment has grown rapidly over the past decade, with multiple studies demonstrating superior diagnostic performance over conventional radiography and non-weight-bearing CT for syndesmotic instability detection (32, 52–54). Incorporating automated incisura morphometry into the same bilateral weight-bearing CT workflow may improve sensitivity for subtle syndesmotic injury where MRI is unavailable or has not yet been obtained.
+
+Morphometric quantification of incisura geometry could, if these associations are reproduced clinically, help explain several clinical observations that current imaging alone cannot resolve. Patients with apparently equivalent injury mechanisms can experience markedly different injury severity, some patients develop chronic ankle instability after an isolated lateral ligament sprain while others do not, and some appear predisposed to syndesmotic malreduction following operative fixation (15, 18, 55, 56). Definitive linkage of incisura morphology to injury susceptibility, postoperative reduction quality, and long-term rehabilitation trajectory will require prospective clinical studies correlating preoperative morphometric outputs with intraoperative reduction quality, postoperative bilateral CT assessment, and patient-reported outcome measures at minimum two-year follow-up. The present cadaveric associations provide a biomechanically grounded rationale for that investigation and effect-size estimates to inform powering.
+
+These findings however, should be interpreted in the context of several limitations. The sample of 34 limbs provides adequate power to detect moderate bivariate correlations but limits the ability to examine multivariate relationships among correlated morphometric parameters simultaneously; the eight toolbox outputs are geometrically related, with a single principal component explaining 85.4% of variance across them, and the independent contribution of any single parameter cannot be isolated in a bivariate framework where the underlying constraint envelope dimension dominates. The present analysis was designed as a validation of the toolbox and as exploratory identification of candidate morphometry–displacement associations to inform larger clinical studies powered for multivariate modeling, and the reported effect sizes provide preliminary estimates for such powering calculations. Statistical significance was accepted without formal correction for multiple comparisons; this is justified by the apriori specification of the displacement components and morphometric parameters on anatomical and biomechanical grounds rather than post hoc selection, but the possibility of inflated Type I error at borderline significance levels remains, and associations at the margins of conventional thresholds are interpreted with caution. The donor cohort consisted entirely of older decedents with no reported history of ankle injury, which may reflect a selection for protective morphological phenotypes; if individuals with shallower incisurae are at higher lifetime risk of ligamentous ankle injury as epidemiological data suggest (13), the present cohort may be skewed toward deeper and more constraining geometries relative to clinical populations in whom shallow morphology is overrepresented, potentially compressing the range of the predictor variables and attenuating observable correlation magnitudes. This is a generalizability limitation, as syndesmotic injury most commonly affects younger athletic populations rather than the older decedents from whom the present specimens were obtained, and the morphometric phenotypes most relevant to clinical injury may be underrepresented in this cohort. Future studies should address this directly by recruiting younger, more active, or injury-prone cohorts in whom the morphological distribution more closely reflects the clinical syndesmotic-injury population. Significant sex differences in incisura morphology have been documented in independent populations, but the present sample was insufficiently powered to stratify correlations by sex; the morphometry–displacement relationships may differ between male and female anatomy, and sex-stratified analysis in larger cohorts is warranted (24, 57). An anatomical limitation of the present scope is that constraint geometry at the syndesmosis is determined by both surfaces of the articulation, the tibial incisura and the apposed fibular notch, while the present toolbox characterizes only the tibial side. The fibular cross-sectional geometry, in particular the curvature and width of the fibular notch, modulates how the fibula engages the tibial groove and could plausibly explain residual displacement variance not accounted for by the tibial morphometry alone. Two specimens with identical tibial groove depth but different fibular geometry may experience different rotational constraint under equivalent injury. Extension of the toolbox to extract analogous morphometric parameters from the fibular surface, and to compute joint-level constraint metrics that combine both contributions, is a natural next step that we are actively pursuing. Finally, the cadaveric model does not replicate active neuromuscular stabilization or the time-dependent viscoelastic ligamentous behavior that modulates the in vivo response to syndesmotic injury, which necessarily limits the direct translation of the reported effect sizes to clinical loading. These limitations notwithstanding, the present work provides the first direct evidence to the knowledge of the authors that three-dimensional incisura morphometry is associated with the magnitude of fibular displacement under controlled equivalent ligamentous disruption, rather than serving as an epidemiological risk marker for injury occurrence at the population level.
+
+In conclusion, the incisura metrics toolbox provides reproducible, bilaterally reliable, and fully automated three-dimensional morphometric characterization of the tibial incisura fibularis from weight-bearing CT-derived surface meshes. Applied within a controlled cadaveric model of complete syndesmotic sectioning, it provides evidence that three-dimensional incisura morphometry is associated with the magnitude of fibular displacement under controlled equivalent ligamentous disruption. Deeper grooves and greater constraint volumes were associated with reduced rotational fibular displacement, and the absence of any association along the mediolateral and anteroposterior translational axes is consistent with the open lateral architecture of the incisura and supports the construct validity of the pipeline. Whether these cadaveric associations translate into clinically meaningful differences in reduction quality, postoperative malreduction risk, or functional recovery remains to be established by prospective clinical study. The toolbox provides the reliable and reproducible morphometric quantification that such investigations will require.
+
+Data availability statement
+
+The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.
+
+Author contributions
+
+KO: Writing – review & editing, Methodology, Software, Writing – original draft, Visualization, Data curation, Resources, Validation, Investigation, Formal analysis, Conceptualization. CC: Funding acquisition, Resources, Supervision, Conceptualization, Writing – review & editing. SP: Writing – review & editing, Supervision, Validation. AS: Validation, Writing – review & editing, Supervision. KD: Validation, Methodology, Software, Visualization, Funding acquisition, Conceptualization, Writing – review & editing, Supervision, Resources, Investigation, Project administration.
+
+Conflict of interest
+
+The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
+
+Generative AI statement
+
+The author(s) declared that Generative AI was not used in the creation of this manuscript.
+
+Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.
+
+Publisher’s note
+
+All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.
+
+Glossary
+
+AAFACT Automatic Anatomical Foot and Ankle Coordinate Toolbox
+
+AITFL anterior inferior tibiofibular ligament
+
+CT computed tomography
+
+DOF degrees of freedom
+
+FA₁₀ facet angle at 10 millimeters above the tibiotalar joint center
+
+FNV₁₀ fibular notch (constraint) volume from 10 millimeters above the tibiotalar joint center
+
+ICC intraclass correlation coefficient
+
+ICP iterative closest point
+
+IFD₁₀ incisura floor depth at 10 millimeters above the tibiotalar joint center
+
+IFL₁₀ incisura fibular length at 10 millimeters
+
+IMT Incisura Metrics Toolbox
+
+IOL interosseous ligament
+
+IOM interosseous membrane
+
+PITFL posterior inferior tibiofibular ligament
+
+PROM patient-reported outcome measure
+
+ROI region of interest
+
+Rz external rotation component
+
+STL stereolithography
+
+Tx lateral translation component
+
+Ty anteroposterior translation component
+
+WBCT weightbearing computed tomography
+
+Edited by: Longbin Zhang, Hunan University, China
+
+Reviewed by: Yingbai Hu, Hunan University, China
+
+Nurşen Zeybek, Istanbul Okan Universitesi, Türkiye
+
+
+References
+
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+26. Ostrum RF De Meo P Subramanian R . A critical analysis of the anterior-posterior radiographic anatomy of the ankle syndesmosis. Foot Ankle Int. (1995) 16:128–31.7599729 10.1177/107110079501600304
+27. Burssens A Vermue H Barg A Krähenbühl N Victor J Buedts K . Templating of syndesmotic ankle lesions by use of 3D analysis in Weightbearing and Nonweightbearing CT. Foot Ankle Int. (2018) 39:1487–96. doi: 10.1177/1071100718791834, 30122077
+28. Peterson AC Kruger KM Lenz AL . Automatic anatomical foot and ankle coordinate toolbox. Front Bioeng Biotechnol. (2023) 11:1255464. doi: 10.3389/fbioe.2023.1255464, 38026875 PMC10644787
+29. Sutherland IE Hodgman GW . Reentrant polygon clipping. Commun ACM. (1974) 17:32–42.
+30. Bartonícek J . Anatomy of the tibiofibular syndesmosis and its clinical relevance. Surg Radiol Anat. (2003) 25:379–86. doi: 10.1007/s00276-003-0156-4, 14504816
+31. Lepojärvi S Pakarinen H Savola O Haapea M Sequeiros RB Niinimäki J . Posterior translation of the fibula may indicate malreduction: CT study of normal variation in uninjured ankles. J Orthop Trauma. (2014) 28:205–9. doi: 10.1097/BOT.0b013e3182a59b3c, 23899768
+32. Ashkani Esfahani S Bhimani R Lubberts B Kerkhoffs GM Waryasz G DiGiovanni CW . Volume measurements on weightbearing computed tomography can detect subtle syndesmotic instability. J Orthop Res. (2022) 40:460–7. doi: 10.1002/jor.25049, 33830524 PMC8497639
+33. Kubik JF Rollick NC Bear J Diamond O Nguyen JT Kleeblad LJ . Assessment of malreduction standards for the syndesmosis in bilateral CT scans of uninjured ankles. Bone Joint J. (2021) 103-B:178–83. doi: 10.1302/0301-620X.103B1.BJJ-2020-0844.R1, 33380196
+34. Hoefnagels EM Waites MD Wing ID Belkoff SM Swierstra BA . Biomechanical comparison of the interosseous tibiofibular ligament and the anterior tibiofibular ligament. Foot Ankle Int. (2007) 28:602–4. doi: 10.3113/FAI.2007.0602, 17559768
+35. Massri-Pugin J Lubberts B Vopat BG Guss D Hosseini A DiGiovanni CW . Effect of sequential sectioning of ligaments on syndesmotic instability in the coronal plane evaluated arthroscopically. Foot Ankle Int. (2017) 38:1387–93. doi: 10.1177/1071100717729492, 28884593
+36. Souleiman F Heilemann M Hennings R Hepp P Gueorguiev B Richards G . Effect of weightbearing and foot positioning on 3D distal tibiofibular joint parameters. Sci Rep. (2022) 12:9357. doi: 10.1038/s41598-022-12963-2, 35672426 PMC9174190
+37. Beumer A Valstar ER Garling EH Niesing R Ginai AZ Ranstam J . Effects of ligament sectioning on the kinematics of the distal tibiofibular syndesmosis: a radiostereometric study of 10 cadaveric specimens based on presumed trauma mechanisms with suggestions for treatment. Acta Orthop. (2006) 77:531–40. doi: 10.1080/17453670610012557, 16819696
+38. Bhimani R Ashkani-Esfahani S Lubberts B Guss D Hagemeijer NC Waryasz G . Utility of volumetric measurement via weight-bearing computed tomography scan to diagnose syndesmotic instability. Foot Ankle Int. (2020) 41:859–65. doi: 10.1177/1071100720917682, 32419488
+39. de Cesar Netto C Barbachan Mansur NS Talaski G Behrens A Mendes de Carvalho KA Dibbern K . Cadaveric diagnostic study of subtle syndesmotic instability using a 3-dimensional weight-bearing CT distance mapping algorithm. J Bone Joint Surg Am. (2025) 107:397–407. doi: 10.2106/JBJS.24.00199, 39700305
+40. Peiffer M Van Den Borre I Segers T Ashkani-Esfahani S Guss D De Cesar Netto C . Implementing automated 3D measurements to quantify reference values and side-to-side differences in the ankle syndesmosis. Sci Rep. (2023) 13:13774. doi: 10.1038/s41598-023-40599-3, 37612321 PMC10447572
+41. Peiffer M Burssens A De Mits S Heintz T Van Waeyenberge M Buedts K . Statistical shape model-based tibiofibular assessment of syndesmotic ankle lesions using weight-bearing CT. J Orthop Res. (2022) 40:2873–84. doi: 10.1002/jor.25318, 35249244
+42. Lenz AL Krähenbühl N Peterson AC Lisonbee RJ Hintermann B Saltzman CL . Statistical shape modeling of the talocrural joint using a hybrid multi-articulation joint approach. Sci Rep. (2021) 11:7314. doi: 10.1038/s41598-021-86567-7, 33795729 PMC8016855
+43. Lapins ER Fendler A LaTulip S Nixon DC Lenz AL . Morphological similarities of chronic ankle instability and Cavus foot type using statistical shape modeling. J Orthop Res. (2026) 44:e70128. doi: 10.1002/jor.70128, 41473950 PMC12754693
+44. Marmor M Hansen E Han HK Buckley J Matityahu A . Limitations of standard fluoroscopy in detecting rotational malreduction of the syndesmosis in an ankle fracture model. Foot Ankle Int. (2011) 32:616–22. doi: 10.3113/FAI.2011.0616, 21733425
+45. Bai L Zhou W Cheng Z Liu J Liu P Zhang W . A radiological study for assessing syndesmosis Malreduction: its validity and limitation. J Foot Ankle Surg. (2020) 59:1181–5. doi: 10.1053/j.jfas.2020.04.014, 32893108
+46. Cosgrove CT Putnam SM Cherney SM Ricci WM Spraggs-Hughes A McAndrew CM . Medial clamp tine positioning affects ankle syndesmosis malreduction. J Orthop Trauma. (2017) 31:440–6. doi: 10.1097/bot.0000000000000882, 28471914 PMC5539925
+47. Phisitkul P Ebinger T Goetz J Vaseenon T Marsh JL . Forceps reduction of the syndesmosis in rotational ankle fractures: a cadaveric study. J Bone Joint Surg Am. (2012) 94:2256–61. doi: 10.2106/JBJS.K.01726, 23318616
+48. Goetz JE Szabo N Rudert MJ Karam MD Phisitkul P . Achilles tension mitigates fibular malalignment measured in cadaveric studies of syndesmotic clamping. Foot Ankle Int. (2019) 40:465–74. doi: 10.1177/1071100718816037, 30623692
+49. Hagemeijer NC Chang SH Abdelaziz ME Casey JC Waryasz GR Guss D . Range of Normal and abnormal syndesmotic measurements using Weightbearing CT. Foot Ankle Int. (2019) 40:1430–7. doi: 10.1177/1071100719866831, 31442094
+50. Palmanovich E Brin YS Kish B Nyska M Hetsroni I . Value of early postoperative computed tomography assessment in ankle fractures defining joint congruity and criticizing the need for early revision surgery. J Foot Ankle Surg. (2016) 55:465–9. doi: 10.1053/j.jfas.2016.01.013, 26968233
+51. Schon JM Brady AW Krob JJ Lockard CA Marchetti DC Dornan GJ . Defining the three most responsive and specific CT measurements of ankle syndesmotic malreduction. Knee Surg Sports Traumatol Arthrosc. (2019) 27:2863–76. doi: 10.1007/s00167-019-05457-8, 31020353
+52. Raheman FJ Rojoa DM Hallet C Yaghmour KM Jeyaparam S Ahluwalia RS . Can Weightbearing cone-beam CT reliably differentiate between stable and unstable syndesmotic ankle injuries? A systematic review and Meta-analysis. Clin Orthop Relat Res. (2022) 480:1547–62. doi: 10.1097/CORR.0000000000002171, 35275097 PMC9278899
+53. Karaismailoglu B Ashkani-Esfahani S DiGiovanni CW . Weight-bearing computed tomography volumetric analysis for diagnosis of syndesmotic instability: a new standard of care? Knee Surg Sports Traumatol Arthrosc. (2026) 34:1081–7. doi: 10.1002/ksa.70066 41531014
+54. Silva L Morimoto LR Watanabe GG Rhodes NG Cruz I Arruda PHC . Distal tibiofibular syndesmosis: anatomy, biomechanics, imaging approach, and postoperative evaluation. Radiographics. (2026) 46:e250065. doi: 10.1148/rg.250065 41610035
+55. Pacheco J Guerra-Pinto F Araújo L Flora M Alçada R Rocha T . Chronic ankle instability has no correlation with the number of ruptured ligaments in severe anterolateral sprain: a systematic review and meta-analysis. Knee Surg Sports Traumatol Arthrosc. (2021) 29:3512–24. doi: 10.1007/s00167-021-06610-y, 33993320
+56. Spindler FT Böcker W Polzer H Baumbach SF . A 3-ligament syndesmotic injury is at higher risk for Malreduction than a 2-ligament injury: a CT-based analysis. Foot Ankle Int. (2024) 45:812–21. doi: 10.1177/10711007241238227, 38817051 PMC11344963
+57. Yildirim H Mavi A Büyükbebeci O Gümüşburun E . Evaluation of the fibular incisura of the tibia with magnetic resonance imaging. Foot Ankle Int. (2003) 24:387–91. doi: 10.1177/107110070302400502, 12801193
diff --git a/corpus/psychology/text/54333afdb0b50795.txt b/corpus/psychology/text/54333afdb0b50795.txt
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+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Front Sports Act Living
+Journal ID: Front Sports Act Living
+NLM Journal ID: 101765780
+Journal ID: Front. Sports Act. Living
+
+Frontiers in Sports and Active Living
+
+EISSN: 2624-9367
+Publisher: Frontiers Media SA
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC13377498
+PMID: 42491492
+DOI: 10.3389/fspor.2026.1794029
+Article version: 1
+Article version:
+Subjects: Systematic Review
+
+Effects of post-exercise hot and cold-water immersion on performance recovery and physiological markers in athletes: a systematic review
+
+Bustos Carvajal Juan 1 Methodology Writing – original draft Investigation Writing – review & editing Conceptualization Visualization Formal analysis Validation
+Pérez Hurtado Elkin 1 Investigation Visualization Resources Writing – review & editing Validation Methodology Supervision Writing – original draft Conceptualization
+Bustos Carvajal Mónica 2 Supervision Conceptualization Resources Writing – review & editing Visualization Project administration Writing – original draft
+Celis Villamizar Diego Mauricio 1 Visualization Writing – original draft Writing – review & editing Supervision
+Arias Coronel Florencio 3 * Investigation Formal analysis Resources Writing – original draft Writing – review & editing Methodology Visualization Conceptualization
+1 Faculty of Education, University of Pamplona , Pamplona , Colombia
+2 Research Group in Parasitic, Tropical and Infectious Diseases (GIEPATI), University of Pamplona , Pamplona , Colombia
+3 Faculty of Health, Universidad Santiago de Cali , Cali , Colombia
+* Correspondence: Florencio Arias Coronel florencioarias00@usc.edu.co
+Electronic publication date: 2026 Jul 3
+Publication date: 2026
+Volume: 8
+Electronic Location ID: 1794029
+Received 2026 Jan 22; Revised 2026 May 15; Accepted 2026 Jun 9
+Copyright: © 2026 Bustos Carvajal, Pérez Hurtado, Bustos Carvajal, Celis Villamizar and Arias Coronel.
+Copyright year: 2026
+Copyright holder: Bustos Carvajal, Pérez Hurtado, Bustos Carvajal, Celis Villamizar and Arias Coronel
+License: This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Keywords: athletic performance, cold water immersion, exercise-induced muscle damage, hot water immersion, hydrotherapy, muscle fatigue, muscle recovery
+
+Funding: The author(s) declared that financial support was received for this work and/or its publication. This research has been funded by Dirección General de Investigaciones of Universidad Santiago de Cali under call No. 01-2026.
+
+Figure count: 1
+Table count: 9
+Equation count: 0
+Reference count: 26
+Page count: 16
+
+section-at-acceptance: Elite Sports and Performance Enhancement
+
+Ÿ==============================Ÿ
+Cold water immersion (CWI) and hot water immersion (HWI) are widely used recovery strategies in sports, yet their comparative efficacy remains unclear. This systematic review evaluates the effects of post-exercise CWI and HWI on performance recovery and physiological markers in athletes.
+
+Methods
+
+Following PRISMA guidelines, a systematic search of Scopus, Web of Science, PubMed, and other databases was conducted up to December 2024. Randomized controlled trials and crossover studies comparing CWI, HWI, and control conditions in athletes or physically active individuals were included. Outcomes included perceptual recovery (DOMS, fatigue), biochemical markers (CK, cytokines), hormonal responses, and performance metrics.
+
+Results
+
+Eight studies were included. Neither CWI nor HWI consistently reduced DOMS or improved perceived recovery compared to control. However, HWI significantly improved sleep quality and acute anaerobic power, while CWI impaired immediate power output. Biochemically, chronic HWI reduced CK and increased testosterone, whereas CWI elevated HSP-72. Hormonal and inflammatory responses were modest, with no significant changes in cortisol or testosterone to cortisol ratio.
+
+Conclusions
+
+The effects of water immersion are temperature and context dependent. HWI may benefit sleep and anaerobic performance, while CWI may hinder immediate power and induce cellular stress adaptations. Recovery strategy selection should align with specific athletic goals.
+
+Systematic Review Registration
+
+https://www.crd.york.ac.uk/prospero/display_record.php?ID=CRD420251156387, CRD420251156387.
+
+1 Introduction
+
+In the context of sports and exercise sciences, the optimization of athletic performance is a multifactorial goal that depends on a precise balance between the application of training stimuli and the implementation of appropriate recovery strategies. Effective recovery is a critical pillar not only for restoring physiological homeostasis and facilitating chronic adaptations to training, but also for minimizing the risk of injury, preventing overtraining, and ensuring long term adherence to exercise programs (1–3). When rest and recovery periods are insufficient, athletes may experience cumulative fatigue that compromises performance and increases susceptibility to injury (4).
+
+High-intensity physical exercise, particularly that which predominantly involves an eccentric component, induces a phenomenon known as exercise-induced muscle damage (EIMD) (5, 6). This process is characterized at the ultrastructural level by microtrauma within muscle fibers, including sarcomere disruption and alterations in sarcolemmal integrity (6, 7). Physiologically, such damage triggers an acute inflammatory response necessary for tissue repair and remodeling (5). The clinical manifestations of EIMD include a reduction in the muscle's functional capacity, such as loss of strength and power, and the onset of delayed-onset muscle soreness (DOMS)—a sensation of discomfort and stiffness that typically peaks between 24 and 72 h after exercise (7). At the systemic level, EIMD is evidenced by the release of intramuscular proteins into the bloodstream, such as creatine kinase (CK) and myoglobin, which are widely employed as indirect biochemical markers of the extent of muscle damage (8–10).
+
+To speed up the restoration process and mitigate the symptoms of EIMD, athletes and coaches turn to a variety of recovery strategies. Among the most widespread are active rest, massage therapy, the use of compression garments, nutritional interventions and, notably, therapies based on immersion in water (11, 12). The latter have gained remarkable popularity due to their relative ease of application and perceived benefits.
+
+Within hydrotherapies, cold water immersion (CWI) and hot water immersion (HWI) are two of the most researched modalities, although their physiological foundations are opposite. CWI, which involves immersion in water at temperatures generally below 20 °C, is postulated to exert its effects through cold induced vasoconstriction (13). This narrowing of blood vessels can reduce edema, attenuate the inflammatory response by limiting the migration of immune cells to the injured tissue, and decrease the perception of pain by reducing nerve conduction velocity (14, 15). In contrast, HWI relies on heat induced vasodilation, which increases muscle blood flow. Theoretically, this increase in perfusion could facilitate the elimination of metabolic byproducts generated during exercise and improve the supply of oxygen and nutrients necessary for tissue repair processes (16).
+
+Despite the existence of plausible mechanisms of action for both interventions, the current scientific literature presents conflicting results and a lack of consensus on their comparative efficacy. Some studies have suggested that CWI is superior for reducing DOMS and accelerating recovery of muscle function (11), while other research has found no significant differences between CWI, HWI, and passive recovery (25, 26). This inconsistency in the findings can be attributed, in part, to the large heterogeneity in the research protocols used (different temperatures, dive durations, and types of previous exercise).
+
+Therefore, the objective of this systematic review is to comprehensively evaluate the effectiveness of cold-water immersion compared to hot water immersion as a post-exercise recovery strategy. The research question addressed, formulated under the PICO framework, is: In athletes and physically active individuals (P), how does cold water immersion (I) compare to hot water immersion (C) in terms of functional recovery, muscle pain perception, and biochemical markers of damage (O)?
+
+2 Materials and methods
+
+This study was conducted following the recommendations of the Cochrane Collaboration and the PRISMA statement. The protocol was registered in the international prospective registry of systematic reviews (Prospero): CRD420251156387.
+
+The review focused on studies that met the following PICOS criteria: (P) Physically active adults or athletes undergoing exercise-induced fatigue or muscle damage. (I) Immersion in cold water (CWI) as a post-exercise recovery strategy. (C) Immersion in hot water (HWI) and/or a control condition (CON/Passive recovery). (O) Functional recovery (strength, power), biochemical markers (CK, IL-6), and perceptual recovery (DOMS, fatigue). (S): Randomized controlled trials (RCTs), randomized crossover trials, and quasi-experimental studies with a control group.
+
+2.1 Criteria
+
+2.1.1 Inclusion criteria
+
+Studies that meet the following criteria will be included in this review:
+
+Study Design (S): Inclusion was restricted to Randomized Controlled Trials (RCTs), randomized crossover trials, and quasi-experimental studies (pre-post designs with a control group) that investigated the acute or chronic effects of water immersion on recovery markers.
+
+Population: Athletes of any discipline and competitive level, or physically active individuals of young ages (who regularly participate in structured training programs and who have been subjected to an exercise protocol designed to induce fatigue or muscle damage.
+
+Intervention: The primary intervention should be the application of one or more forms of aquatic or thermal therapy for the purpose of facilitating post-exertional recovery. This includes, but is not limited to: hydrotherapy, cold water immersion (CWI), hot water immersion, contrast water therapy (CWT), cryotherapy (whole body or local), and heat therapy.
+
+Comparator: Studies should include a control group or a comparison condition, such as passive recovery (total rest), no intervention, or a placebo intervention.
+
+Results: The study must measure and report at least one of the following primary or secondary outcomes:
+
+Primary: Late onset muscle pain (DOMS), markers of exercise induced muscle damage (EIMD) (e.g., Creatine Kinase—CK), and perception of muscle fatigue.
+
+Secondary: Performance in subsequent exercise (e.g., jump, sprint, strength), inflammatory markers, and joint range of motion (ROM).
+
+Language: Articles published in Spanish or English.
+
+The ethical approval and adherence to the Declaration of Helsinki of all primary studies were verified during the selection process.
+
+2.1.2 Exclusion criteria
+
+Studies that meet one or more of the following conditions will be excluded from this review:
+
+Type of Study: Systematic reviews, meta-analyses, letters to the editor, editorials, conference abstracts, single case studies, books or book chapters.
+
+Population: Studies conducted exclusively in sedentary populations, patients with chronic non sport related pathologies (e.g., fibromyalgia, arthritis, circulatory diseases), or in animal models.
+
+Procedure: Studies in which aquatic or thermal therapies are applied chronically (as part of training) and not as an acute intervention for post-exercise recovery.
+
+Interventions that combine therapies of interest with other active treatments (e.g., massage, compression, supplementation) if the effects of aquatic/thermal therapy cannot be independently analyzed.
+
+Therapies applied before exercise in order to improve performance (warm-up), rather than after for recovery.
+
+Results: Studies that do not report any of the outcomes of interest defined in the inclusion criteria (e.g., studies that only measure body temperature or psychological variables such as mood without a measure of physical recovery or performance).
+
+Availability: Items from which the full text cannot be obtained after reasonable attempts.
+
+2.2 Factor to evaluate
+
+2.2.1 Primary result
+
+Sources of information: The bibliographic search was carried out in the databases: Scopus, Science Direct, WebofScience, Sportdiscuss and Sage Journal, controlled clinical trials, case-control studies, cohorts and cross-sectional studies were included from the beginning to December 2024, to ensure the saturation of the literature, references of relevant articles identified through references, congresses, thesis databases, Open Grey, Google Scholar and Clinicaltrials.gov were scanned.
+
+The search was performed using DeCS/Mesh terms and related words, the different combinations with the Boolean operators were used. No language or time restrictions were imposed. (Appendix A). Search strings were adapted to the specific syntax and Boolean operators of each database to ensure conceptual equivalence. Filters in Scopus (e.g., excluding “notes” or “reviews”) were applied to strictly align with the inclusion criteria established in the PICOS framework, ensuring that only primary research articles were retrieved across all platforms.
+
+2.2.2 Study selection and data collection process
+
+To ensure transparency and reproducibility, a reference management software (Zotero) was used to automatically remove duplicates. Two authors (EP-H and JSB-C) independently screened the titles and abstracts of all identified records using the Rayyan online tool. Subsequently, the full texts of potentially eligible studies were retrieved and assessed by the same two reviewers to confirm they met the PICOS inclusion criteria. Any discrepancies were resolved through discussion or, if necessary, by consulting a third senior reviewer (FA-C). The search was last updated in December 2024. Data extraction followed a standardized protocol and included the following: Bibliographic characteristics: study design, location, authors, and title. Methodological aspects: objectives, sample size. Outcome variables: definitions, reported results and measures of effect. When numerical data were not explicitly reported in tables or text, values were visually estimated from the original figures using digital calipers or scale projection. An inherent imprecision of approximately ±5% was assumed for these extracted data points.
+
+2.2.3 Risk of bias assessment (quality)
+
+The methodological quality of the studies and the risk of bias were assessed using specific instruments for clinical trials. First, the PEDro scale was applied, which assesses fundamental aspects such as randomization, blinding and the presentation of results. The included studies scored between 6 and 7 on this scale (Table 1). Additionally, the Cochrane tool for randomised trials (RoB 2) was used in order to examine in more detail the risk of bias in the studies analysed (Table 2).
+
+Table 1 PeDro scale.
+
+Estudio	1	2	3	4	5	6	7	8	9	10	11	PEDro score	
+1. Horgan et al. (17) acute Inflammatory, anthropometric, and perceptual (muscle soreness) effects of postresistance exercise water immersion in junior international and subelite male volleyball athletes	✔	✔	✘	✔	✘	✘	✘	✔	✔	✔	✔	6 de 10	
+2. Colomer et al. (18) monitoring jump performance and DOMS following resistance training and hydrotherapy	✔	✔	✘	✔	✘	✘	✘	✔	✔	✔	✔	6 de 10	
+3. Wellauer et al. (19) no acceleration of recovery from exercise-induced muscle damage after cold or hot water immersion in women	✔	✔	✔	✔	✘	✘	✘	✔	✔	✔	✔	7 de 10	
+4. Menzies et al. (20) post-exercise hot or cold-water immersion does not alter perception of effort or neuroendocrine responses	✔	✔	✘	✔	✘	✘	✘	✔	✔	✔	✔	6 de 10	
+5. Gustafsson et al. (21) cold- and hot-water immersion are not more effective than placebo in soccer players	✔	✔	✘	✔	✘	✘	✔	✔	✔	✔	✔	7 de 10	
+6. Horgan et al. (22) acute performance, daily well-being, and hormone responses to water immersion in volleyball athletes	✔	✔	✘	✔	✘	✘	✘	✔	✔	✔	✔	6 de 10	
+7. Coertjens et al. (23) energetic responses of head-out water immersion at different temperatures during post-exercise recovery	✔	✔	✘	✔	✘	✘	✘	✔	✔	✔	✔	6 de 10	
+8. Horgan et al. (24) effect of repeated post-resistance exercise cold or hot water immersion on inflammatory responses in rugby players	✔	✔	✘	✔	✘	✘	✘	✔	✔	✔	✔	6 de 10	
+PEDro scale criteria: (1) choice criteria were specified (*this item is not used to calculate the PEDro score). (2) Subjects were randomly assigned to groups (in a crossover study, subjects were randomly assigned in an order in which they received treatments). (3) Assignment was hidden. (4) Groups were similar at baseline with respect to the most important prognostic indicators. (5) There was blinding of all subjects. (6) There was blinding of all therapists who administered therapy. (7) There was blinding of all assessors who measured at least one key outcome. (8) Measures of at least one key outcome were obtained from more than 85% of subjects initially assigned to groups. (9) All subjects for whom outcome measures were available received the treatment or control condition as assigned or, when this was not the case, data on at least one key outcome were analyzed by “intention-to-treat.” (10) Results of statistical comparisons between groups are reported for at least one key outcome. (11) The study provides point measures and measures of variability for at least one key outcome.
+
+Table 2 Tool (RoB 2).
+
+Study	D1: randomization process	D2: Deviations from intended interventions	D3: missing outcome data	D4: measurement of the outcome	D5: Selection of the reported result	Overall risk of bias	
+Horgan et al. (22)							
+Colomer et al. (18)							
+Horgan et al., (22)							
+Coertjens et al. (23)							
+Horgan et al., (24)							
+Wellauer et al. (19)							
+Menzies et al. (20)							
+Gustafsson et al. (21)							
+, Low risk of bias; , some concerns; , high risk of bias.
+
+2.3 Data synthesis and assessment of heterogeneity
+
+A narrative synthesis approach was adopted for this review. A meta-analysis was not performed due to the high methodological heterogeneity identified among the included studies, including variations in water temperature (CWI: 8–15 °C; HWI: 38–42 °C), immersion duration (5–20 min), and the nature of the preceding exercise stimulus (e.g., resistance training vs. endurance sports). These discrepancies in protocols precluded a meaningful quantitative pooling of data.
+
+2.4 Definition of outcome variables
+
+To ensure a comprehensive evaluation of post-exercise recovery, the following primary and secondary variables were analyzed, categorized into three distinct physiological dimensions:
+
+Perceptual Recovery Markers: Delayed Onset Muscle Soreness (DOMS): Quantified using Visual Analogue Scales (VAS) to assess the subjective sensation of pain and stiffness that typically peaks 24–72 h post-exercise.
+
+Perceived Fatigue and Well-being: Evaluated through psychometric tools (e.g., ARSS or Likert scales) to reflect the athlete's subjective state of readiness and overall systemic tiredness.
+
+Sleep Quality: Assessed to determine the impact of thermal therapy on nocturnal restoration and central nervous system recovery.
+
+Biochemical and Hormonal Markers: Creatine Kinase (CK): Measured as the gold-standard indirect marker of sarcolemmal disruption and exercise-induced muscle damage (EIMD).
+
+Inflammatory Cytokines (IL-6, IL-1ra): Analyzed to evaluate the magnitude of the acute inflammatory response and the subsequent anti-inflammatory modulation.
+
+Testosterone and Cortisol: Assessed to determine the anabolic-to-catabolic balance (T:C ratio) and the neuroendocrine stress response to the training-recovery cycle.
+
+Heat Shock Proteins (HSP-72): Used as a cellular-level marker of thermal stress and proteostatic adaptation.
+
+Performance and Physiological Markers: Neuromuscular Function: Evaluated via Countermovement Jump (CMJ) height and Maximal Voluntary Isometric Contraction (MVIC) to track the recovery of explosive and absolute strength.
+
+Anaerobic Potency: Measured through the Wingate Test (WAnT) to assess the acute effects of water temperature on muscle enzyme kinetics and peak power output.
+
+Systemic Physiological Responses: Including heart rate (HR), core/skin temperature, and femoral blood flow, to elucidate the underlying thermoregulatory and cardiovascular mechanisms of hydrotherapy.
+
+3 Results
+
+A total of 1,058 records were initially identified through database searches. After removing 389 duplicates, 669 records were screened by title and abstract. Of these, 647 were excluded based on inclusion/exclusion criteria. From the 22 publications retrieved for full-text evaluation, 14 were unrecovered or did not meet eligibility, resulting in 8 studies that met the criteria and were included in this systematic review (Figure 1).
+
+Figure 1 Prism diagram.
+
+Flowchart outlining the identification and selection process for studies in a systematic review. Of 1,058 total records identified from six databases, 389 duplicates were removed, 669 were screened by title and abstract, 647 were excluded, and 22 were reviewed in full, with 14 unrecovered. Eight publications were assessed, none excluded for review or PEDro scale reasons, resulting in eight studies included in the final review.
+
+A total of eight studies were included for analysis. Methodologically, all the articles corresponded to randomized controlled clinical trials, with a notable predominance of the crossover design, used in six of the eight investigations. The geographical distribution of the evidence was mainly concentrated in Oceania, with four studies carried out in Australia, followed by Europe, with three studies (from Switzerland, Belgium, the United Kingdom and Sweden), and one study from the American continent (Brazil). All articles were published in English in a recent period, between 2017 and 2025 (Table 3).
+
+Table 3 Bibliographic characteristics.
+
+#	Authors	Qualification	Study type	Country	Language	Year	Aim	
+1	Horgan et al. (17)	18 international junior and sub-elite male volleyball athletes.	Randomized crossover clinical trial (RCT-crossover).	Australia	English	2022	Investigate the acute inflammatory, anthropometric, and perceptual effects of post-resistance exercise water immersion.	
+2	Colomer et al. (18)	19 male volleyball players at the sub-elite level. (24.1 ± 5.5 years)	ECA-crossover.	Australia	English	2017	To assess the acute effects of hydrotherapy on recovery of jump performance and delayed onset muscle soreness (DOMS) after resistance training.	
+3	Wellauer et al. (19)	30 healthy and recreationally active women. (23.3 ± 2.9 years)	Parallel group RCTs.	(Suiza-Bélgica).	English	2025	To compare the effects of cold water immersion (CWI) and hot water immersion (HWI) on muscle recovery after muscle damage exercise in women.	
+4	Menzies et al. (20)	14 trained endurance runners and triathletes (men and women). (28 ± 7 years)	ECA-crossover.	United Kingdom	English	2024	Investigate whether post-exercise water immersion (cold or hot) alters the perception of exertion and neuroendocrine responses in a subsequent exercise on the same day.	
+5	Gustafsson et al. (21)	40 national male footballers (15–19 years old).	RCT with CON group.	Sweden	English	2025	(1) Compare CWI, HWI and placebo at recovery. 2) Evaluate impact of repeated use over 15 weeks.	
+6	Horgan et al. (22)	18 international junior and sub-elite male volleyball athletes. (19.9 ± 3.4 years)	ECA-crossover.	Australia	English	2023	Investigate acute effects of 3 water immersion strategies on performance, well-being and hormonal responses after endurance exercise.	
+7	Coertjens et al. (23)	21 trained male cyclists. (26.9 ± 5.8 years)	ECA-crossover.	Brazil	English	2023	Investigate energy responses of immersion in water at different temperatures during post-exercise recovery and its effect on subsequent anaerobic potency.	
+8	Horgan et al. (24)	18 male academy rugby players (Super Rugby). (19.9 ± 1.5 years)	ECA-crossover (pre-post by blocks).	Australia	English	2024	Investigate the effects of repeated immersion (cold or hot) post-resistance exercise on seasonal inflammatory and hormonal responses.	
+
+3.1 Characteristics of excluded studies
+
+Excluded items showed no connection to the result of interest. In addition, letters to the editor, systematic/narrative reviews, medication intervention protocols were dispensed with.
+
+3.2 Methodological quality
+
+The average score on the PEDro scale for the studies analyzed, detailed in Table 2, was 5 points with methodological quality studies, observing that the most frequent omissions were observed in the blinding of all therapists who administered the therapy and in the blinding of all evaluators who measured at least one key outcome.
+
+3.3 Characteristics of the participants
+
+Samples ranged from 14 to 40 participants. Subjects’ age ranged from adolescent athletes (15–19 years) to young adults, with most research focusing on the 20–30 age range. Regarding the distribution by sex, a clear predominance of the male sex was observed, with six of the eight studies including exclusively men, one study carried out only with women and one with a mixed sample. The population studied was diverse in terms of sports discipline, including team sports (volleyball, football, rugby) and endurance sports (cycling, running); one study was conducted with recreationally active participants instead of competitive athletes. It is noteworthy that all studies with athletes focused on a high-level population, described as “trained”, “sub-elite”, “elite” or “academy”, which ensures the applicability of the findings to the field of sports performance (Table 4).
+
+Table 4 Results of perceptual and subjective measures (DOMS, fatigue, sleep quality, RPE, general recovery).
+
+Study	Cluster (group)	Extent (parameter)	Initial value	Final value	Difference/Tracking	p value	
+Colomer et al. (18)	CON	DOMS (mm shift)a	(Baseline)	∼ + 25 mm (Peak 24–48 h)	Significantly increase	Time effect: p < 0.03 Intervention: NSb	
+CWI (cold water)	DOMS (mm shift)a	(Baseline)	∼ + 28 mm (Peak 24–48 h)	Significantly increase	—	
+CWT (contrast)	DOMS (mm shift)a	(Baseline)	∼ + 30 mm (Peak 24–48 h)	Significantly increase	—	
+HWI (hot water)	DOMS (mm shift)a	(Baseline)	∼ + 30 mm (Peak 24–48 h)	Significantly increase	—	
+Wellauer et al. (19)	CON	DOMS (VAS 0–10 cm)	1.0 cm	∼ 6.5 cm (24 h Peak)	Significantly increase	Time effect: p < 0.001 Intervention: NSb (p = 0.752)	
+CWI (cold water)	DOMS (VAS 0–10 cm)	1.0 cm	∼ 6.5 cm (24 h Peak)	Significantly increase	—	
+HWI (hot water)	DOMS (VAS 0–10 cm)	1.0 cm	∼7.0 cm (24 h Peak)	Significantly increase	—	
+Menzies et al. (20)	CON	General recovery (ARSS)	4.0 ± 0.8	3.4 ± 0.7	−0.6	Time effect: p = 0.0003 Intervention: NSb (p = 0.31)	
+CWI (cold water)	General recovery (ARSS)	3.7 ± 0.6*	3.3 ± 0.6	−0.4	—	
+HWI (hot water)	General recovery (ARSS)	3.9 ± 0.6*	3.4 ± 0.6*	−0.5	—	
+CON	Perception of effort (RPE 6–20)	15.1 ± 2.2	15.2 ± 2.3	No change	Intervention: NSb (p = 0.68)	
+CWI (cold water)	Perception of effort (RPE 6–20)	14.9 ± 2.4	14.8 ± 2.6	No change	—	
+HWI (hot water)	Perception of effort (RPE 6–20)	15.0 ± 2.3	15.2 ± 2.4	No change	—	
+Gustafsson et al. (21)	CON	Perception of effort (RPE 1–10)	∼6.5	∼ 7.5 (Peak 21 h)	Significantly increase	Time effect: p < 0.05 Intervention: NSb (p = 0.45)	
+CWI (cold water)	Perception of effort (RPE 1–10)	∼6.5	∼ 7.5 (Peak 21 h)	Significantly increase	—	
+HWI (hot water)	Perception of effort (RPE 1–10)	∼6.5	∼7.6 (Peak 21 h)	Significantly increase	—	
+Horgan et al. (22)	HWI vs. CON	Sleep quality (VAS 0–100 mm)c	N/A	N/A	HWI significantly better than WITH	p < 0.001	
+HWI vs. CWI	Sleep quality (VAS 0–100 mm)c	N/A	N/A	HWI significantly better than WITH	p = 0.017	
+HWI vs. CWT	Fatigue (VAS 0–100 mm)c	N/A	N/A	HWI significantly less than CWT	p = 0.050	
+Coertjens et al. (23): The exclusion of this study in the table is maintained due to its qualitative evaluation of preference, which does not fit into the quantitative format. ARSS, Acute Recovery and Stress Scale; CON, control group; CWI, cold water immersion; CWT, contrast water therapy; DOMS, late onset muscle pain; HWI, hot water immersion; NS, not significant; RPE, effort perception scale; VAS, visual analogue scale.
+
+* Significant difference compared to the initial value (p < 0.05).
+
+a DOMS (mm change): Initial and final values are visual estimates extracted from the original study figures, as exact numerical data were not provided in text or tables. These estimates carry an inherent degree of imprecision (approx. ± 5% based on axis scale resolution).
+
+b NS (not significant): The p-value of the intervention indicates that there were no statistically significant differences between the groups. This is a key finding: although athletes felt worse after exercise (time effect), the recovery strategy did not significantly change that outcome compared to the others.
+
+c Direct Comparison: The study by Horgan et al. (22) does not report pre-post data for these variables, but direct comparisons of the effect of each treatment. The table reflects which group was higher and the p-value of that comparison. N/A (not applicable) is used because the table format does not fit this type of analysis.
+
+3.4 Most evaluated parameters
+
+The parameters evaluated in the included studies were grouped into three main categories: perceptual and subjective measures, blood biochemical markers, and objective neuromuscular performance. Perceptual measures, present in most investigations, included assessment of delayed onset muscle soreness (DOMS), fatigue, sleep quality, and overall perception of recovery, frequently quantified using visual analogue scales (VAS).
+
+In the biochemical realm, muscle damage was a key parameter, systematically assessed through serum Creatine Kinase (CK) concentration. Additionally, markers of the inflammatory response, such as various cytokines (e.g., IL-6, IL-1ra), and hormonal responses (testosterone and cortisol) were analyzed.
+
+Neuromuscular performance was quantified primarily through countermovement jump height (CMJ) and maximal voluntary isometric force (MVIC), representing objective measures of muscle function. More specific parameters of sports performance, such as sprint speed over short distances and anaerobic power (measured with the Wingate test), were evaluated less frequently. A subgroup of studies also investigated acute systemic physiological responses, such as body temperature, heart rate, blood flow, and oxygen consumption (VO2), in order to elucidate the underlying mechanisms of interventions.
+
+3.5 Results of the evaluated parameters
+
+Analysis of perceptual and subjective measures (Table 4) reveals a predominant and consistent finding in most studies: hydrotherapy interventions, regardless of temperature, were not shown to be superior to control or placebo conditions to improve athletes' perceived recovery.
+
+Specifically, with regard to late onset muscle pain (DOMS), the studies by Colomer et al. (18) and Wellauer et al. (19) showed that, although pain increased significantly in all groups as a response to exercise, neither cold water immersion (CWI) nor hot water immersion (HWI) managed to attenuate this response more effectively than the control group. Similarly, perceived exertion (RPE) and overall recovery followed an analogous trajectory; work by Menzies et al. (20) and Gustafsson et al. (21) concluded that hydrotherapy interventions did not reduce perceived exertion in a subsequent exercise session or improve feelings of recovery compared to control or a credible placebo.
+
+In contrast to this general trend, the study by Horgan et al. (22) identified specific and selective benefits. In this research, hot water immersion (HWI) was the only modality that demonstrated a statistically significant improvement in sleep quality (compared to CWI and control) and a reduction in fatigue (compared to contrast therapy). This discrepancy could be attributed to the type of previous exercise (resistance training in the Horgan study vs. endurance/team sports in the others), suggesting that the perceptual benefits of HWI could be more pronounced after strength stimuli.
+
+Taken together, these findings suggest that, for the mitigation of general muscle pain and the perception of exertion, the effects of hydrotherapy are, at best, equivalent to those of passive rest or placebo. However, hot water immersion could offer a specific and relevant benefit to optimize sleep quality and reduce fatigue, especially in strength training contexts.
+
+The analysis of blood markers (Table 5) presents a complex and sometimes contradictory picture, suggesting that the effects of hydrotherapy depend on both the specific marker and the chronicity of the intervention (acute vs. repeated).
+
+Table 5 Blood markers (muscle damage and inflammation) (creatine kinase—CK, cytokines).
+
+Study	Cluster (group)	Extent (parameter)	Initial value	Final value	Difference/Tracking	p value	
+Horgan et al. (22)a	CWI vs. WITH	Creatine kinase (CK)	N/A	N/A	Significant reduction of CK vs. CON	p = 0.007	
+CWT vs. WITH	Creatine kinase (CK)	N/A	N/A	Significant reduction of CK vs. CON	p = 0.006	
+HWI vs. CON	Creatine kinase (CK)	N/A	N/A	Significant reduction of CK vs. CON	p < 0.001	
+CWT vs. HWI	Interleukin-6 (IL-6)	N/A	N/A	Highest IL-6 after CWT (not significant, g = 0.56)	NSb	
+Wellauer et al. (19)a	CON	Creatine kinase (CK) (U/L)	119.8 ± 50.2	700 (24 h peak)	Significant post-exercise increase	Time: p < 0.001	
+CWI (cold water)	Creatine kinase (CK) (U/L)	111.0 ± 41.5	600 (24 h peak)	Significant increase, no diff. vs. CON	Interv.: NSb	
+HWI (hot water)	Creatine kinase (CK) (U/L)	214.3 ± 180.9	850 (24 h peak)	Significant increase, higher than AT 24H	vs. CON (24 h): p = 0.046	
+Menzies et al. (20)a	CON	Interleukin-6 (IL-6) (pg/mL)	5	∼2.0 (Post-EX peak)	Post-e.g., increase, no significant diff.	Interv.: NSb	
+CWI (cold water)	Interleukin-6 (IL-6) (pg/mL)	5	∼2.2 (Post-EX peak)	Post-e.g., increase, no significant diff.	NSb	
+HWI (hot water)	Interleukin-6 (IL-6) (pg/mL)	5	∼2.0 (Post-EX peak)	Post-e.g., increase, no significant diff.	NSb	
+Horgan et al. (24)c	CWI vs. WITH	Creatine kinase (CK)	N/A	N/A	Trivial but significant reduction after 4 weeks	p = 0.025	
+HWI vs. CON	Creatine kinase (CK)	N/A	N/A	Moderate and significant reduction after 4 weeks	p < 0.001	
+HWI vs. CON	Interleukin-1ra (IL-1ra) (Δ)	N/A	N/A	Moderate (anti-inflammatory) reduction after 4 weeks	p = 0.013	
+CWI vs. HWI	Heat shock protein (HSP-72) (Δ)	N/A	N/A	Small increase of HSP-72 in CWI after 4 weeks	p = 0.004	
+N/A (not applicable): used when studies present results as direct comparisons between groups (e.g., “group A was significantly larger than group B”) rather than reporting initial and final numerical values. Excluded studies: the studies of Colomer et al. (18), Gustafsson et al. (21) and Coertjens et al. (23) did not measure CK or inflammatory cytokines and are therefore not included in this table. CK, creatine kinase; CON, control group; CWI, cold water immersion; CWT, contrast water therapy; g, g Hedges (effect size); HWI, hot water immersion; HSP-72, heat shock protein 72; IL-1ra, interleukin-1 receptor antagonist; IL-6, interleukin-6; N/A, not applicable; NS, not significant; p, p-value; U/L, units per liter; Δ, change from baseline.
+
+a Acute studies: the results of Horgan et al. (22), Wellauer et al. (19), and Menzies et al. (20) reflect the response to a single session of exercise and intervention.
+
+b NS (not significant): indicates that there was no statistically significant difference between the intervention groups for that specific parameter, even though the parameter changed over time due to exercise. In the case of Horgan et al. (17), the p-value for IL-6 was not significant, but the effect size (g = 0.56) suggests a mean difference.
+
+c Chronic study: the results of Horgan et al. (24) reflect the cumulative effects of repeated interventions over 4 weeks. Therefore, the result is presented as a change (Δ) in baseline levels.
+
+As for the main indicator of muscle damage, Creatine Kinase (CK), the acute effects seem inconsistent. On the one hand, Horgan et al. (17) reported that all immersion modalities (CWI, CWT, and HWI) significantly reduced CK levels compared to passive control. In direct contrast, the study by Wellauer et al. (19) found no such benefit for CWI and indeed observed that HWI resulted in significantly higher CK levels than control at 24 h post-exercise. This discrepancy could be attributed to differences in the exercise protocol (force vs. jump-induced injury), the population studied (men vs. women), or the timing of the measurement. However, when assessing chronic effects, the evidence aligns: Horgan et al. (24) showed that both CWI (trivial reduction) and HWI (moderate reduction) attenuated CK levels after 4 weeks of repeated application, with HWI being more effective.
+
+The behavior of inflammatory cytokines was equally nuanced. Generally, exercise was the main stimulus for the increase of cytokines such as IL-6, without hydrotherapy interventions significantly modifying this acute response (20). However, specific effects were observed: Horgan et al. (17) found an increase in IL-6 after CWT compared to HWI. Most notably, the chronic study by Horgan et al. (24) revealed that repeated HWI decreased baseline levels of the anti-inflammatory cytokine IL-1ra, a finding that could be linked to the lower burden of chronic muscle damage.
+
+Finally, a relevant mechanistic finding came from the chronic study, where repeated CWI induced an increase in Heat Shock Protein (HSP-72). This suggests a cellular adaptive response to cold heat stress, which was not observed with hot immersion.
+
+Regarding specific high-intensity tasks (Table 6), it reveals that the effects of hydrotherapy are highly dependent on both the type of task evaluated (sprint vs. power) and the timing of the measurement (long-term recovery vs. immediate performance).
+
+Table 6 Performance on specific tasks (sprint, power) (speed, anaerobic power).
+
+Study	Cluster (group)	Extent (parameter)	Initial value	Final value	Difference/tracking	p value	
+Gustafsson et al. (21)	CON	Sprint speed (20 m) (s)a	Pre-match	Did not return to baseline (21–45 h post)	Sprint ↑ time (∼1.5% post-match), incomplete recovery	Time: p < 0.05 Interv.: NSb (p = 0.90)	
+CWI (cold water)	Sprint speed (20 m) (s)a	Pre-match	Did not return to baseline (21–45 h post)	Sprint ↑ time (∼1.5% post-match), incomplete recovery	NSb	
+HWI (hot water)	Sprint speed (20 m) (s)a	Pre-match	Did not return to baseline (21–45 h post)	Sprint ↑ time (∼1.5% post-match), incomplete recovery	NSb	
+Coertjens et al. (23)	CON	Anaerobic average power (WAnT)b	WAnT₁	WAnT2	No significant changes (baseline)	N/A	
+CWI (cold water)	Anaerobic average power (WAnT)b	WAnT₁	WAnT2	−2.4% (↓Yield)	vs. CON: p < 0.05 vs. HWI: p < 0.0001	
+HWI (hot water)	Anaerobic average power (WAnT)b	WAnT₁	WAnT2	+2.2% (↑Yield)	vs. CON: p < 0.05 vs. CWI: p < 0.0001	
+NS (not significant): indicates that there were no statistically significant differences between the intervention groups. Excluded studies: the other 6 studies did not include direct measurements of sprint speed or maximum anaerobic power, so they are not listed in this table. CON, control group; CWI, cold water immersion; HWI, hot water immersion; m, meters; N/A, not applicable; NS, not significant; p, p-value; s, seconds; WAnT, Wingate anaerobic test.
+
+a Sprint speed (s): measured in seconds (s), therefore an increase in numerical value means a decrease in performance (slower sprint).The study by Gustafsson et al. showed that exercise (simulated football match) worsened sprint performance, and none of the interventions (CWI, HWI or Placebo) accelerated the return to baseline values.
+
+b Mean anaerobic power (WAnT): the study by Coertjens et al. used the Wingate test (WAnT). The table compares performance on a second test (WAnT2) after the recovery intervention, relative to the first test (WAnT₁). The results are very clear: hot water improved the power, while cold water significantly worsened it.
+
+In the context of sprint speed recovery at 21–45 h post-match, the study by Gustafsson et al. (21) found no benefit. Sprint performance decreased in all groups as a result of exercise induced fatigue, and neither cold water immersion (CWI) nor hot water immersion (HWI) accelerated the return to baseline levels more effectively than the CON group. This finding suggests that, for recovery of speed in the days following competition, these hydrotherapy modalities do not offer an objective advantage.
+
+In stark contrast, the study by Coertjens et al. (23) which evaluated anaerobic potency in a test performed minutes after the intervention, showed acute, significant and diametrically opposite effects. Hot water immersion (HWI) resulted in a 2.2% improvement in mean power, an acute potentiating effect. In contrast, cold water immersion (CWI) resulted in a 2.4% detriment in yield.
+
+This divergence can be explained by the underlying physiological mechanisms. HWI, by increasing muscle temperature, probably optimized enzyme kinetics and contraction rate, improving power output. CWI, by reducing muscle temperature, would have slowed these processes, resulting in underperformance.
+
+Analysis of hormonal responses (Table 7) indicates that hydrotherapy interventions, in general, have a modest effect on the hormonal axis, although specific effects of hot water immersion (HWI) are identified that could be relevant for adaptation to training.
+
+Table 7 Hormonal responses (testosterone, cortisol).
+
+Study	Cluster (group)	Extent (parameter)	Initial value	Final value	Difference/Tracking	p value	
+Menzies et al. (20)b	CON	Cortisol (ng/mL)	∼121 (pre-race 1)	∼92 (pre-race 2)	↓ Cortisol in all groups, with no differences between interventions	Time: p = 0.008 Interv.: NSa	
+CWI (cold water)	Cortisol (ng/mL)	∼121 (pre-race 1)	∼92 (pre-race 2)	↓ Cortisol in all groups, with no differences between interventions	NSa	
+HWI (hot water)	Cortisol (ng/mL)	∼121 (pre-race 1)	∼92 (pre-race 2)	↓ Cortisol in all groups, with no differences between interventions	NSa	
+Horgan et al. (22)b	HWI vs. CWT	Testosterone	N/A	N/A	Significantly higher ↑ testosterone in HWI vs. CWT	p = 0.038	
+All the groups	Cortisol	N/A	N/A	No significant differences between interventions	INTERV.	
+All the groups	Testosterone:Cortisol Ratio	N/A	N/A	No significant differences between interventions	Interv.: NSa	
+Horgan et al. (24)c	HWI vs. CON	Testosterone	N/A	N/A	Baseline testosterone ↑ levels after 4 weeks in HWI vs. WITH	R2: p = 0.012	
+All the groups	Cortisol	N/A	N/A	No significant differences between interventions after 4 weeks	Interv.: NSa	
+All the groups	Testosterone:Cortisol Ratio	N/A	N/A	No significant differences between interventions after 4 weeks	INTERV.	
+N/A (not applicable): used when the studies present the results as direct comparisons of the treatment effect (“group A was greater than B”) instead of reporting initial and final numerical values that allow a difference to be calculated. Excluded studies: the other 5 studies did not include hormonal measurements of testosterone or cortisol and are therefore not listed in this table. CON, control group; CWI, cold water immersion; CWT, contrast water therapy; HWI, hot water immersion; N/A, not applicable; ng/mL, nanograms per milliliter; NS, not significant; p, p-value.
+
+a NS (not significant): indicates that there was no statistically significant difference between the intervention groups for that specific parameter. In the study by Menzies et al., the decrease in cortisol was attributed to the passage of time (circadian cycle and recovery), not to hydrotherapy.
+
+b Acute study: the results of Menzies et al. (20) and Horgan et al. (22) reflect the hormonal response to a single session of exercise and intervention.
+
+c Chronic study: the results of Horgan et al. (24) reflect the cumulative effects of repeated interventions over 4 weeks on resting baseline hormone levels.
+
+The behavior of cortisol, a marker of catabolic stress, was not significantly influenced by any of the hydrotherapy modalities in the studies that evaluated it. In both the acute (20, 22) and chronic (24) contexts, fluctuations in cortisol levels were primarily attributed to the natural circadian cycle and response to exercise, with water immersion interventions not significantly altering this dynamic compared to control.
+
+In contrast, testosterone, a key hormone for anabolic processes, was shown to be sensitive to the temperature of the dive. Acutely, Horgan et al. (22) reported that HWI induced a significantly greater increase in testosterone compared to contrast therapy (CWT). This finding was reinforced by the chronic effects observed in the study by Horgan et al. (24), where 4 weeks of repeated HWI resulted in significantly higher baseline testosterone levels compared to the control group. These results suggest that hot water immersion could promote a hormonal environment more conducive to muscle recovery and adaptation.
+
+Despite the modifications in testosterone, the Testosterone: Cortisol (T:C) ratio, often used as an indicator of the balance between anabolism and catabolism, showed no significant changes in any of the studies.
+
+In the context of systemic physiological responses (Table 8) reveals the most direct, pronounced and divergent effects of hydrotherapy interventions, confirming that water temperature is a potent modulator of body homeostasis. These findings explain many of the results observed in the other variables.
+
+Table 8 Systemic physiological responses (temperature, heart rate, VO2, blood flow).
+
+Study	Cluster (group)	Extent (parameter)	Initial value	Final value	Difference/Tracking	p valuea	
+Wellauer et al. (19)	CON	Core Temperature ( °C)	2.	∼37.1 (30 min post)	Lightweight	HWI > CWI (p = 0.001)	
+CWI (cold water)	Core Temperature ( °C)	2.	∼36.9 (30 min post)	↓ Significant vs. HWI & CON		
+HWI (hot water)	Core Temperature ( °C)	2.	∼38.5 (post-immersion)	Significant		
+CWI (cold water)	Skin Temperature ( °C)	$0.32	∼16.0 (post-immersion)	Drastic	vs. WITH & HWI: p < 0.001	
+Menzies et al. (20)	CON	Heart rate (bpm)	60	60	No change	Intervention: p < 0.0001	
+CWI (cold water)	Heart rate (bpm)	60	54	↓ Below baseline rest		
+HWI (hot water)	Heart rate (bpm)	60	∼80	↑ Sustained after immersion		
+CON	Femoral blood flow (mL/min)a	∼200	151	Recovery to Baseline	Intervention: p < 0.0001	
+CWI (cold water)	Femoral blood flow (mL/min)a	∼200	66	Flow ↓ drastic		
+HWI (hot water)	Femoral blood flow (mL/min)a	∼200	.203	↑ Sustained after immersion		
+Gustafsson et al. (21)	CON	Heart rate (bpm)	−170	∼165 (45 h post)	PROGRESSIVE	Time: p < 0.01 Interv.: NSc	
+CWI (cold water)	Heart rate (bpm)	−170	∼165 (45 h post)	PROGRESSIVE		
+HWI (hot water)	Heart rate (bpm)	−170	∼165 (45 h post)	PROGRESSIVE		
+Coertjens et al. (23)	CON	HR recovery (τHR, s)d	N/A	64.0 ± 3.8	Recovery Baseline	Intervention: p < 0.0001	
+CWI (cold water)	HR recovery (τHR, s)d	N/A	60.5 ± 3.8	Faster recovery (τ↓)		
+HWI (hot water)	HR recovery (τHR, s)d	N/A	94.3 ± 3.8	Slower recovery (τ↑)		
+CON	Post-exercise O2 consumption (EPOC) (L)	N/A	3.7 ± 0.2	Metabolic baseline	Intervention: p < 0.001	
+CWI (cold water)	Post-exercise O2 consumption (EPOC) (L)	N/A	4.7 ± 0.2	↑ Significant energy expenditure		
+HWI (hot water)	Post-exercise O2 consumption (EPOC) (L)	N/A	4.4 ± 0.2	↑ Significant energy expenditure		
+NS (not significant): Indicates that there were no statistically significant differences between the intervention groups. COPD (excessive post-exercise oxygen consumption): represents the “extra” energy expenditure the body uses to recover after exercise. A higher value means a higher metabolic cost during the recovery period. Excluded studies: the other studies did not measure these systemic physiological variables. Values preceded by (∼) were visually estimated from study graphs. These estimates carry an inherent degree of imprecision (approx. ± 5%). bpm, beats per minute; CON, control group; CWI, cold water immersion; EPOC, post-exercise excessive oxygen consumption; HWI, hot water immersion; L, liters; mL/min, milliliters per minute; NS, not significant; p, p-value; s, seconds; τHR, heart rate tau (recovery rate indicator); °C, degrees celsius.
+
+a Acute data (post-immersion): the values of Menzies et al. represent the physiological state immediately after the intervention, showing the acute and divergent effects of each temperature.
+
+c Long-term recovery data: Gustafsson et al. values are from a sub-maximal test 45 h later, showing that acute differences in heart rate are no longer evident.
+
+d τHR (heart rate tau): a measure of recovery kinetics. A lower Tau (τ) value indicates a faster recovery of the heart rate towards resting levels.
+
+Body temperature showed a predictable and significant response. The study by Wellauer et al. (19) clearly demonstrated that hot water immersion (HWI) raised core temperature, while cold water immersion (CWI) significantly decreased it. Even more drastic was the effect on skin temperature, where CWI caused an abrupt decline, confirming a powerful peripheral thermal stimulus.
+
+These thermal alterations triggered equally marked cardiovascular responses. Menzies et al. (20) reported that CWI reduced heart rate (HR) below resting levels, while HWI kept it elevated, indicating increased cardiovascular stress. These changes in HR were directly related to the modulation of peripheral blood flow: CWI induced severe vasoconstriction, drastically reducing flow in the femoral artery, while HWI caused vasodilation, maintaining high flow. The study by Coertjens et al. (23) corroborated this dynamic, showing that CWI accelerated the recovery kinetics of HR, while HWI slowed it down.
+
+Finally, in the metabolic realm, Coertjens et al. (23) provided a key finding: both CWI and HWI significantly increased post-exercise oxygen consumption (EPOC) compared to passive control. This indicates that both interventions pose an additional energy cost to the body during recovery. In the case of CWI, this increase is attributed to the processes of thermogenesis (heat production to combat cold), and in the case of HWI, to the general increase in heat-induced metabolism.
+
+4 Discussion
+
+The present systematic review aimed to evaluate the effectiveness of post-exercise water immersion, comparing different temperatures (cold, hot and contrast) on recovery in athletes, analyzing their effects on perceptual, biochemical, performance and physiological parameters. The main findings reveal a complex landscape that challenges the conception of hydrotherapy as a universal recovery strategy. Available evidence indicates that the effects are highly dependent on the water temperature and the specific recovery target. Overall, interventions were not shown to be superior to placebo or a control group in attenuating muscle pain or improving long-term sprint speed recovery. However, specific and divergent effects emerge: hot water immersion proved effective for acute potentiation of anaerobic performance and for improving sleep quality and anabolic hormonal profile, while cold water immersion, although referred to subjectively by athletes, showed a detrimental effect on immediate power performance and induced unique cellular adaptive responses at the chronic level.
+
+4.1 Comparison with previous literature
+
+A reiterated finding in the present review is the discrepancy between athletes' subjective perception and the absence of objective evidence demonstrating a superiority of hydrotherapy over placebo or passive control. In relation to late-onset muscle pain (DOMS) and the perception of effort (RPE), the available results are consistent: both the study by Colomer et al. (18) and that by Wellauer et al. (19) showed that the increase in DOMS was comparable in all the groups evaluated, without observing a significant mitigating effect of immersion in cold water (CWI) or hot water (HWI).This aligns with research such as Machado et al. (25), where the results show variable effects: some protocols reduce DOMS (depending on temperature/time), but methodological heterogeneity limits generalization. Similarly, inconsistent results, reported in the literature, as in the study by Moore et al. (26), conclude mixed results for performance and perceptual measures (DOMS, RPE) and highly variable evidence in biomarkers (CK).
+
+Furthermore, a significant finding of this review is the evidence of potential sex-specific responses to water immersion. The corpus of evidence is characterized by a clear male predominance, with 75% of the studies (n = 6) focusing exclusively on men. In this context, the study by Wellauer et al. (19) is pivotal, as it observed that HWI resulted in significantly higher CK levels compared to control in a female population—a result that diverges from findings in male cohorts. These differences may be attributed to biological dimorphism, including variations in subcutaneous fat distribution, which influences thermal insulation, and the protective role of estrogen against exercise-induced muscle damage (EIMD). These factors may fundamentally alter the kinetics of heat transfer and inflammatory modulation, suggesting that recovery protocols should be tailored to the biological sex of the athlete.
+
+However, it would be simplistic to dismiss all perceptual benefits. A specific and notable finding came from Horgan et al. (22), who identified that HWI significantly improved sleep quality and reduced fatigue compared to other modalities. This effect, which was not observed with CWI, suggests a distinct mechanism of action, possibly related to the effects of HWI on central thermoregulation, which is known to facilitate sleep onset. Thus, although hydrotherapy does not appear to be a superior tool for the overall management of post-exercise muscle pain, HWI emerges as a specific and promising strategy to optimize key aspects of athlete wellbeing, such as night rest.
+
+The role of the placebo effect remains a critical consideration in the interpretation of hydrotherapy benefits. The methodological inclusion of a credible placebo group in the study by Gustafsson et al. (21) provides a robust framework to distinguish physiological recovery from psychological expectations. Their findings, which showed no objective superiority of CWI or HWI over a placebo for performance return, suggest that the perceived benefits frequently reported by athletes may be largely driven by the “recovery ritual” or the psychological conviction of efficacy. This discrepancy between subjective perception and objective physiological markers underscores the need for future research to incorporate control conditions that account for the psychological influence of recovery interventions.
+
+Analysis of blood markers reveals that the effect of hydrotherapy transcends a simple suppression of inflammation, pointing towards a complex modulation of cellular signaling pathways that depends on the temperature and chronicity of the stimulus. Regarding acute muscle damage (CK), the evidence from this review is conflicting. While Horgan et al. (17) reported a reduction in CK with all immersion modalities, aligning with previous meta-analyses, Wellauer et al. (19), found no such benefit, and even observed an increase in CK with HWI in a female population. This discrepancy underscores the heterogeneity of the response, possibly influenced by the participant's sex or type of exercise. However, when examining chronic effects, Horgan et al. (24) found a clearer result: repeated use of both CWI and HWI reduced baseline CK levels, suggesting a protective or recovery enhancing effect in the long term.
+
+Beyond muscle damage, findings on cytokines and other signaling proteins challenge the paradigm that CWI is purely “anti-inflammatory.” In fact, the most significant finding from the chronic study by Horgan et al. (24) was that repeated CWI increased levels of Heat Shock Protein (HSP-72). This is an indicator of a cellular stress response, positioning CWI not only as a recovery modality, but also as an adaptive stimulus. This result aligns with the literature that warns that CWI can attenuate anabolic signals necessary for muscle hypertrophy, possibly through modulation of these stress pathways. In contrast, chronic HWI appeared to promote a more proadaptive environment, evidenced by reduced anti-inflammatory cytokine IL-1ra and increased growth factors.
+
+4.2 Strengths and limitations
+
+A major strength of this review is its currency, incorporating high-quality trials from 2024 to 2025 that challenge previous recovery paradigms. However, several limitations must be considered to contextualize these findings. First, the high methodological heterogeneity in water temperatures and immersion durations prevented a quantitative meta-analysis. Second, the clear predominance of male participants limits the generalizability of the results to elite female athletes, who may exhibit different thermoregulatory and inflammatory responses.
+
+Most importantly, it must be acknowledged that a substantial proportion of the evidence analyzed (50%; n = 4) originates from a single research group [Horgan et al.]. While these studies maintained high methodological standards, as evidenced by their PEDro scores (6–7), such a concentration of data may introduce a “laboratory-specific bias.” The consistency in their findings (particularly regarding sleep quality and anabolic hormonal profiles in volleyball and rugby players) might reflect specific laboratory protocols or the characteristics of their particular sub-population rather than a universal phenomenon. Therefore, independent replication by diverse research teams across different athletic disciplines is necessary to strengthen the external validity and global applicability of these conclusions.
+
+4.3 Practical applications
+
+Based on the synthesized evidence, practitioners and coaches should adopt a context-specific approach to hydrotherapy:
+
+Prioritize HWI (38–42 °C) when the primary goal is to improve sleep quality, reduce perceived fatigue, or provide an acute potentiating effect before anaerobic performance (e.g., between tournament rounds on the same day).
+
+Exercise caution with CWI (8–15 °C) if explosive power or vertical jump height is required immediately following the intervention, as it may cause an acute decrement in performance.
+
+“Align CWI use with cellular adaptation goals”: Repeated CWI may be used to induce cellular stress responses (HSP-72), but its potential to attenuate anabolic signaling should be considered during hypertrophy-focused training phases.
+
+4.4 Future research directions
+
+Future studies should prioritize “placebo-controlled” designs to further isolate the physiological effects of water immersion from psychological expectations. There is a critical need for research focused exclusively on elite female athletes to address the current biological sex gap in the literature. Additionally, longitudinal studies (exceeding 15 weeks) are required to determine how chronic use of HWI affects long-term training adaptations and hormonal health, moving beyond acute recovery metrics.
+
+5 Conclusions
+
+This systematic review strongly demonstrates that post-exercise hydrotherapy is not a monolithic or universally beneficial recovery strategy. Its effectiveness is highly dependent on the context, the water temperature, the time of application, and the desired physiological or performance outcome. The evidence analyzed challenges the widespread practice of using cold water immersion (CWI) as the primary method for accelerating objective recovery, as it does not demonstrate consistent superiority over placebo or passive control for attenuating muscle pain or improving performance in the days following exercise.
+
+Moreover, the findings reveal clearly divergent and specific action profiles for each temperature. Cold water immersion (CWI), although often subjectively preferred by athletes, evidences a detrimental acute effect on immediate anaerobic potency. Its main role at the chronic level seems to be that of a cellular stress stimulus, as evidenced by the increase in Heat Shock Protein (HSP-72), positioning it more as a possible adaptive modulation tool than as a simple recovery accelerator.
+
+In contrast, hot water immersion (HWI) emerges with a well-defined benefit profile: it is an effective strategy for acute enhancement of anaerobic performance, significantly improves perceived sleep quality, and promotes a more anabolic hormonal environment through increased testosterone levels. These effects position HWI not only as a recovery modality, but also as a possible adjuvant in training adaptation processes.
+
+The choice between CWI and HWI should not be arbitrary, but a strategic decision: HWI should be considered to enhance performance between short efforts or to improve rest, while CWI should be used with caution, especially if immediate power performance is a priority. Ultimately, the question for the clinician and trainer should not be “should we use hydrotherapy?”, but rather “what specific physiological response do we want to modulate and at what point in the training cycle?”, using water temperature as a precise tool to achieve this.
+
+Data availability statement
+
+The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.
+
+Author contributions
+
+JB: Methodology, Writing – original draft, Investigation, Writing – review & editing, Conceptualization, Visualization, Formal analysis, Validation. EP: Investigation, Visualization, Resources, Writing – review & editing, Validation, Methodology, Supervision, Writing – original draft, Conceptualization. MB: Supervision, Conceptualization, Resources, Writing – review & editing, Visualization, Project administration, Writing – original draft. DC: Visualization, Writing – original draft, Writing – review & editing, Supervision. FA: Investigation, Formal analysis, Resources, Writing – original draft, Writing – review & editing, Methodology, Visualization, Conceptualization.
+
+Conflict of interest
+
+The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
+
+Generative AI statement
+
+The author(s) declared that generative AI was not used in the creation of this manuscript.
+
+Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.
+
+Publisher's note
+
+All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.
+
+Appendix A
+
+Note on Search Strategy: The syntax of search strings varies across databases (Scopus, PubMed, WOS, etc.) due to differences in indexing systems and Boolean logic. We ensured that the search terms were conceptually identical across all platforms. In Scopus, specific document type filters (excluding “notes”, “editorials”, or “reviews”) were utilized to refine the results according to our primary research inclusion criteria, ensuring a high-quality retrieval process consistent with PRISMA guidelines.
+
+SCOPUS	Results	
+(TITLE-ABS-KEY (hydrotherap * OR “water immersion” OR “cold water immersion” OR “hot water immersion” OR “contrast water therapy *” OR “thermoneutral water immersion” OR “heat therapy *” OR “cold therapy *” OR cryotherap * OR “thermal therapy *” OR “aquatic therapy *”)) AND (TITLE-ABS-KEY (“muscle fatigue” OR “Exercise-induced Muscle Damage” OR “EIMD” OR exhaustion OR “Exercise Performance” OR “Delayed onset muscle soreness” OR “DOMS” OR “training stress” OR “muscle ache” OR “muscle soreness”)) AND pubyear > 2014 AND pubyear < 2026 AND (EXCLUDE (DOCTYPE, “re”) OR EXCLUDE (DOCTYPE, “no”) OR EXCLUDE (DOCTYPE, “cp”) OR EXCLUDE (DOCTYPE, “sh”) OR EXCLUDE (DOCTYPE, “ch”) OR EXCLUDE (DOCTYPE, “le”) OR EXCLUDE (DOCTYPE, “er”) OR EXCLUDE (DOCTYPE, “ed)”)	292	
+SPORTDISCUSS		
+(TI (hydrotherap * OR “water immersion” OR “cold water immersion” OR “hot water immersion” OR “contrast water therapy” OR “thermoneutral water immersion” OR “heat therapy *” OR “cold therapy” OR “cryotherap * OR” thermal therapy * “OR” aquatic therapy * “) OR AB (hydrotherap * OR” water immersion “OR” cold water immersion “OR” hot water immersion “OR” contrast water therapy * “OR” thermoneutral water immersion “OR” heat therapy * “OR” cold therapy * “OR” cryotherap * OR “thermal therapy *” OR “aquatic therapy *”)) AND (TI (“muscle fatigue” OR “Exercise-induced Muscle Damage” OR “EIMD” OR exhaustion OR “Exercise Performance” OR “Delayed onset muscle soreness” OR “DOMS” OR “stress training” OR “muscle ache” OR “muscle soreness”) OR AB (“muscle fatigue” OR “Exercise-induced Muscle Damage” OR “EIMD” OR exhaustion OR “Exercise Performance” OR “Delayed onset muscle soreness” OR “DOMS” stress training “OR” OR “muscle soreness”)	135	
+TAYLOR AND FRANCYS		
+(title: (hydrotherap * OR “water immersion” OR “cold water immersion” OR cryotherap *) OR abstract: (hydrotherap * OR “water immersion” OR “cold water immersion” OR “hot water immersion” OR “contrast water therapy *” OR “thermoneutral water immersion” OR “heat therapy *” OR “cold therapy *” OR cryotherap * OR “thermal therapy *” OR “aquatic therapy *”)) AND (title: (“muscle fatigue” OR “muscle soreness” OR “DOMS”) OR abstract: (“muscle fatigue” OR “Exercise-induced Muscle Damage” OR “EIMD” OR exhaustion OR “Exercise Performance” OR “Delayed onset muscle soreness” OR “DOMS” OR “training stress” OR “muscle ache” OR “muscle soreness”))	10	
+WOS		
+(TS = (hydrotherap * OR “water immersion” OR “cold water immersion” OR “hot water immersion” OR “contrast water therapy *” OR “thermoneutral water immersion” OR “heat therapy *” OR “cold therapy *” OR cryotherap * OR “thermal therapy *” OR “aquatic therapy *”)) AND (TS = (“muscle fatigue” OR “Exercise-induced Muscle Damage” OR “EIMD” OR exhaustion OR “Exercise Performance” OR “Delayed onset muscle soreness” OR “DOMS” OR “training stress” OR “muscle ache” OR “muscle soreness”))	353	
+ScienceDirect		
+(hydrotherap OR “contrast water” OR cryotherap) AND (“muscle fatigue” OR “DOMS” OR “muscle soreness” OR “muscle ache” OR “training stress”)	74	
+PubMed		
+(((“Hydrotherapy”[Mesh]) OR “Cryotherapy”[Mesh] OR “Hot Temperature”[Mesh] OR “Cold Temperature”[Mesh]) OR (hydrotherap *[tiab] OR “water immersion”[tiab] OR “cold water immersion”[tiab] OR “hot water immersion”[tiab] OR “contrast water therapy *”[tiab] OR “thermoneutral water immersion” [tiab] OR “heat therapy *” [tiab] OR “cold therapy *” “[tiab] OR cryotherap * [tiab] OR” thermal therapy * “‘ [tiab] OR’ aquatic therapy *’ [tiab]) AND (((“Muscle Fatigue”[Mesh]) OR “Myalgia”[Mesh] OR “Athletic Performance” [Mesh]) OR (“muscle fatigue” [tiab] OR “Exercise-induced Muscle Damage”[tiab] OR “EIMD” [tiab] OR exhaustion [tiab] OR “Exercise Performance” [tiab] OR “Delayed onset muscle soreness” [tiab] OR “DOMS”[tiab] OR “stress training” [tiab] OR “muscle acheab” [tiabeness]))	194	
+TOTAL	1,058	
+
+Edited by: Rodrigo Aquino, Confederacao Brasileira de Futebol, Brazil
+
+Reviewed by: Víctor Hernández-Beltrán, University of Extremadura, Spain
+
+Lamia Ben Ezzeddine, University of Manouba, Tunisia
+
+Abbreviations CON, control group; CWI, cold water immersion; CWT, contrast water therapy; HWI, hot water immersion assessment parameters; ARSS, acute recovery and stress scale; DOMS, delayed onset muscle soreness; RPE, rating of perceived exertion; VAS, visual analogue scale; CK, creatine kinase; HSP-72, heat shock protein 72; IL-1ra, interleukin-1 receptor antagonist; IL-6, Interleukin-6; T:C ratio, testosterone-to-cortisol ratio; CMJ, countermovement jump; EPOC, excess post-exercise oxygen consumption; HR/FC, heart rate; MVIC, maximal voluntary isometric contraction; τHR, heart rate tau (time constant indicating the rate of heart rate recovery); TTE, time to exhaustion; VO2, oxygen consumption; WAnT, Wingate anaerobic test units of measurement; bpm, beats per minute; cm, centimeters; L, liters; m, meters; mL/min, milliliters per minute; mm, millimeters; ng/mL, nanograms per milliliter; s, seconds; U/L, units per liter; °C, degrees celsius statistical and general terms Δ (Delta), symbol representing the change or difference from the initial value g, Hedges' g (standardized measure of effect size); N/A, not applicable; NS, not significant; p, p-value.
+
+
+References
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diff --git a/corpus/psychology/text/565b4e0ddd11a7ef.txt b/corpus/psychology/text/565b4e0ddd11a7ef.txt
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+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: BMC Psychol
+Journal ID: BMC Psychol
+NLM Journal ID: 101627676
+
+BMC Psychology
+
+EISSN: 2050-7283
+Publisher: BMC
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC10594677
+PMID: 37872571
+DOI: 10.1186/s40359-023-01394-x
+Article ID: 1394
+Article version: 1
+Subjects: Correction
+
+Correction: An empirical investigation of the associations between metacognition, mindfulness experiential avoidance, depression, and anxiety
+
+Ådnøy Torstein 1
+Solem Stian 1
+Hagen Roger 1 2 3
+Havnen Audun audun.havnen@ntnu.no
+1 4
+1 https://ror.org/05xg72x27 grid.5947.f 0000 0001 1516 2393 Department of Psychology, Norwegian University of Science and Technology, Trondheim, Norway
+2 https://ror.org/01xtthb56 grid.5510.1 0000 0004 1936 8921 Department of Psychology, University of Oslo, Oslo, Norway
+3 grid.5510.1 0000 0004 1936 8921 Research institute, Modum Bad, Vikersund, Norway
+4 https://ror.org/01a4hbq44 grid.52522.32 0000 0004 0627 3560 Division of Psychiatry, Nidaros Community Mental Health Centre, St. Olavs University Hospital, Trondheim, Norway
+Electronic publication date: 2023 Oct 23
+Publication date: 2023
+Volume: 11
+Electronic Location ID: 350
+Copyright: © The Author(s) 2023
+License: Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated in a credit line to the data.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Erratum for: An empirical investigation of the associations between metacognition, mindfulness experiential avoidance, depression, and anxiety 11 21 9 2023 281 BMC Psychology 10.1186/s40359-023-01336-7 PMC10514934 37735705
+issue-copyright-statement: © BioMed Central Ltd., part of Springer Nature 2023
+
+Ÿ==============================Ÿ
+BMC Psychology (2023) 11:281
+
+10.1186/s40359-023-01336-7
+
+Following publication of the original article [1], the authors flagged the following error in the Results section of the Abstract: where it now says ‘Metacognition, experiential avoidance, and the non-judging subscale of FFMQ-24 constituted’, ‘Mindfulness’ had erroneously been written in place of ‘Metacognition’. The published article has since been corrected. The authors thank you for reading this erratum and apologize for any inconvenience caused.
+
+The online version of the original article can be found at 10.1186/s40359-023-01336-7
+
+Publisher’s Note
+
+Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
+
diff --git a/corpus/psychology/text/572079fb8aaa3dd0.txt b/corpus/psychology/text/572079fb8aaa3dd0.txt
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@@ -0,0 +1,3 @@
+Altered States, Enhanced Potential: Psychedelics and Physical Performance
+
+Interest in psychedelics has expanded beyond clinical treatment contexts, yet little empirical work has examined how users describe psychedelic use in relation to sport and physical activity. This study conducted a qualitative content analysis of Reddit discussions involving psychedelics and physical performance. A Reddit search for “sports psychedelics” returned 253 threads. After screening, 39 threads and 290 comments met inclusion criteria. Analysis identified eight content categories: physical performance enhancement; flow state/automaticity; perceptual and cognitive enhancement; risks, limitations, and safety concerns; reduced fatigue/pain perception; microdosing as strategy; psychological and emotional benefits; and fairness, ethics, and governance. Psilocybin mushrooms and LSD were the most frequently mentioned substances. Across accounts, users most often described psychedelics as enhancing performance indirectly through altered attention, increased mind-body connection, flow-like absorption, and reduced pain or fatigue. Some users reported greater perceived strength, speed, endurance, coordination, or overall capability during activity, while others described effortless movement, reduced self-consciousness, sharper perception, and improved focus. Reports were predominantly positive or mixed, with concerns about overexertion, injury risk, impaired judgment, and fairness in competitive settings. These findings suggest that psychedelics may be understood less as traditional performance-enhancing drugs and more as potential-enhancing substances that alter the subjective conditions under which performance occurs. However, because all accounts were self-reported, it remains unclear whether perceived performance gains correspond to measurable physiological or behavioral improvement. Future controlled research using objective performance outcomes is needed to clarify the relationship between psychedelic use, subjective experience, and physical performance.
diff --git a/corpus/psychology/text/57a13ce2b7e248c8.txt b/corpus/psychology/text/57a13ce2b7e248c8.txt
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@@ -0,0 +1,3 @@
+Habit learning and expression as stable traits
+
+Individual differences in the capacity to learn and control habits are central to current models of psychopathology, which assume an overreliance on habit behavior in transdiagnostic compulsivity. However, whether these tendencies reflect stable, trait-like cognitive processes remains unclear. We examined the temporal stability of individual differences in habit learning and expression. Across two preregistered experiments, we assessed stimulus–response habits using the same stimuli after one day or different stimuli after four months. Evidence for stable individual differences in habit commissions was strong and comparable across experiments, indicating trait-like habit learning and expression. Improvements in response time across learning were stable and correlated with habits, suggesting an early trait-like index of habitualization. Stable processes of habit formation were reflected during both habit acquisition and expression.
diff --git a/corpus/psychology/text/5bf5049e9904d84d.txt b/corpus/psychology/text/5bf5049e9904d84d.txt
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+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Adv Sci (Weinh)
+Journal ID: Adv Sci (Weinh)
+NLM Journal ID: 101664569
+Journal ID: ADVS
+
+Advanced Science
+
+EISSN: 2198-3844
+Publisher: Wiley
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC13477256
+PMID: 42603306
+DOI: 10.1002/advs.77180
+Article ID: ADVS77180
+Article version: 1
+Subjects: Research Article, Research Article
+
+Magnetoelectric BaTiO3/CoFe2O4 Thin‐Film Meshes for Neuronal Differentiation
+
+Mirjolet Mathieu https://orcid.org/0000-0002-8471-3184 1
+Ye Hao https://orcid.org/0000-0003-3526-9627 1 haoyeh@ethz.ch
+
+Attalhaoui Abderrahim Lahlahi https://orcid.org/0009-0004-4380-8824 1 2
+Kim Donghoon 1
+Pustovalov Vitaly 1
+Zhang Elric https://orcid.org/0000-0003-1681-5573 1
+Tudela‐Pi Marc 3 4
+Gebauer Bastian https://orcid.org/0009-0003-0290-6199 1
+Castelló Juan Bautista Carda 2
+Guimerà‐Brunet Anton https://orcid.org/0000-0003-1768-3293 3 4
+Puigmartí‐Luis Josep https://orcid.org/0000-0002-7510-9815 5 6
+Chen Xiang‐Zhong https://orcid.org/0000-0002-2294-7487 7 8
+Kim Minsoo https://orcid.org/0000-0002-3478-1277 1 9 minkim@dgist.ac.kr
+
+Pané Salvador https://orcid.org/0000-0003-0147-8287 1 vidalp@ethz.ch
+
+1 Multi‐Scale Robotics Lab Institute of Robotics and Intelligent Systems ETH Zurich Zurich Switzerland
+2 Department of Inorganic and Organic Chemistry Universitat Jaume I Castellón de la Plana Spain
+3 Instituto de Microelectronica de Barcelona (IMB‐CNM, CSIC) Bellaterra Spain
+4 Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina (CIBER‐BBN) Madrid Spain
+5 Departament de Ciència de Materials i Química Física Institut De Química Teòrica i Computacional Universitat De Barcelona Barcelona Spain
+6 Institució Catalana de Recerca i Estudis Avançats (ICREA) Barcelona Spain
+7 International Institute for Intelligent Nanorobots and Nanosystems College of Intelligent Robotics and Advanced Manufacturing State Key Laboratory of Photovoltaic Science and Technology Shanghai Frontiers Science Research Base of Intelligent Optoelectronics and Perception, Institute of Optoelectronics Fudan University Shanghai People's Republic of China
+8 Zhejiang Key Laboratory of Extreme Environment Functional Materials Yiwu Research Institute of Fudan University Yiwu
+9 Department of Robotics and Mechatronics Engineering DGIST Daegu Republic of Korea
+Electronic publication date: 2026 Aug 15
+Electronic Location ID: e77180
+Revised 2026 Jul 21; Received 2026 Apr 30; Accepted 2026 Aug 7
+Copyright: © 2026 The Author(s). Advanced Science published by Wiley‐VCH GmbH
+License: This is an open access article under the terms of the http://creativecommons.org/licenses/by/4.0/ License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Keywords: cell differentiation, freestanding thin films, magnetoelectric, multiferroic, neural progenitor cells, pulsed laser deposition
+
+Funding: Swiss National Science Foundation 10.13039/501100001711 213113
+Figure count: 5
+Table count: 0
+Page count: 13
+
+source-schema-version-number: 2.0
+edited-state: corrected-proof
+details-of-publishers-convertor: Converter:WILEY_ML3GV2_TO_JATSPMC version:6.8.6 mode:remove_FC converted:15.08.2026
+
+Ÿ==============================Ÿ
+ABSTRACT
+
+Magnetoelectric composites offer a powerful route for remotely converting magnetic stimuli into local electrical cues, with promising biomedical applications in electrical stimulation. In strain‐mediated magnetoelectric heterostructures, however, efficient coupling depends strongly on crystallinity, interface quality, and mechanical boundary conditions. Epitaxial thin films provide excellent crystallinity and well‐defined interfaces, but substrate clamping suppresses strain transfer and limits magnetoelectric performance. Here, we report a freestanding magnetoelectric mesh based on an epitaxial BaTiO3/CoFe2O4 bilayer and demonstrate its use for magnetic‐field‐driven neural progenitor cell differentiation. By systematically relaxing the mechanical boundary condition from substrate‐clamped films to polydimethylsiloxane (PDMS)‐transferred structures and ultimately to freestanding meshes, we show a progressive enhancement in the magnetoelectric coupling coefficient. This enhancement is directly reflected in improved neural progenitor differentiation, establishing magnetoelectric transduction as a key driver of the observed cellular response. Our results show that engineering mechanical compliance in epitaxial magnetoelectric platforms can substantially improve biofunctional stimulation, providing a design strategy for next‐generation cell culture, differentiation, and wireless stimulation systems.
+
+We engineer an epitaxial BaTiO3/CoFe2O4 magnetoelectric mesh that overcomes boundary‐induced mechanical clamping. Progressively reducing the mechanical constraint, from substrate‐clamped to PDMS‐transferred and ultimately freestanding, enhances magnetic‐to‐electric transduction and strengthens magnetoelectric coupling. This tunable coupling, in turn, influences neural progenitor cell differentiation, providing a strategy for optimizing magnetoelectric biointerfaces.
+
+1 Introduction
+
+Functional oxide ceramics are generally associated with brittleness and limited deformability. Yet, when reduced to nanoscale dimensions and integrated into engineered bilayer architectures, they can display mechanical responses that differ markedly from those of their bulk counterparts. Recent studies on epitaxial BaTiO3/CoFe2O4 (BTO/CFO) bilayers have revealed an unusual combination of superelastic behavior, transferability to compliant supports, and retention of functional integrity [1, 2, 3]. These observations suggest that nanoscale ceramic bilayers may provide a promising platform for biointerfaces capable of operating under mechanically dynamic conditions, including those imposed by adherent cells. In such systems, mechanical adaptability is not merely a structural advantage, but a potentially important factor for maintaining functional performance in biological environments.
+
+In this context, BTO/CFO bilayers are particularly attractive, as the combination of a piezoelectric BTO layer and a magnetostrictive CFO layer gives rise to magnetoelectric (ME) coupling capable of converting external magnetic fields into localized electrical signals through strain‐mediated transduction [4, 5, 6, 7]. This wireless transduction capability makes ME composites broadly attractive for biomedical technologies where remote actuation without wired connections or implanted power sources is desirable. ME composites have therefore attracted growing interest for applications including cell differentiation [8, 9, 10, 11], neurostimulation [12, 13, 14, 15, 16, 17, 18, 19], drug delivery [20, 21, 22, 23, 24, 25], tissue regeneration [26, 27, 28], and physiological signal acquisition [29]. For these applications, however, the effectiveness of the material platform depends not only on the magnitude of the ME response, but also on its ability to interface mechanically with soft and dynamically active biological systems.
+
+Different composite architectures have been explored to meet these requirements. Core–shell magnetoelectric nanoparticles (MENPs), especially CFO‐BTO systems, have been widely investigated for biomedical use because of their minimal invasiveness and their ability to be magnetically guided to target sites [11, 12, 13, 15, 18, 19, 22, 23, 30, 31, 32]. They have shown promise in neural stimulation, cancer treatment, and spinal cord repair [12, 23, 27]. However, their practical implementation remains limited by imperfect core–shell interfaces, random particle orientation, reduced macroscopic coupling, and difficulties in localization or retrieval after treatment. Laminated ME composites can offer improved control over electric‐field orientation and may benefit from resonance‐enhanced responses [14, 28, 29, 33, 34], but they generally rely on mechanically bonded interfaces, which restrict strain transfer and can increase invasiveness and device complexity.
+
+Among ME composite platforms, thin‐film architectures offer a particularly attractive balance between reduced dimensions and strong interfacial coupling. In epitaxial magnetostrictive/piezoelectric bilayers, coherent interfaces can promote efficient strain transfer, making them promising for high‐performance ME transduction [35, 36, 37, 38, 39, 40, 41]. At the same time, the functional response of such systems is strongly influenced by mechanical boundary conditions. In conventional substrate‐clamped films, deformation of the magnetostrictive layer is constrained by the rigid support, suppressing strain transfer to the piezoelectric layer and thereby limiting the overall ME response [42]. Recent work on released and transferred epitaxial BTO/CFO heterostructures has pointed to the importance of mechanical constraint in governing coupling behavior, suggesting that the controlled release of substrate clamping could provide an effective route for enhancing ME functionality [1, 2, 3].
+
+Motivated by this opportunity, here we introduce epitaxial ME mesh structures that combine strong interfacial coupling with mechanical flexibility and tunable mechanical constraint. The mesh architecture was selected to provide high surface coverage while preserving structural robustness and enabling different degrees of mechanical release. By optimizing mesh geometry and processing conditions, we realized homogeneous BTO/CFO ME meshes in three boundary‐dependent configurations: substrate‐clamped, polydimethylsiloxane (PDMS)‐transferred, and fully freestanding. These structures preserve epitaxial quality while progressively relaxing substrate clamping, resulting in tunable strain transfer and ME coupling behavior. To evaluate this effect across length scales, the magnetoelectric coupling coefficient (MECC) was quantified locally by piezoresponse force microscopy and macroscopically through ME‐induced electrolyte conductance measurements. The ME response was found to depend strongly on the mechanical boundary conditions, with the fully freestanding meshes exhibiting the highest coupling, followed by the PDMS‐transferred and substrate‐clamped configurations. Finally, neural progenitor cells (NPCs) cultured on these ME meshes exhibited differentiation under alternating magnetic stimulation, and the biological response followed the same trend as the MECC. These results identify mechanical boundary conditions as a key design parameter linking ME coupling in epitaxial ceramic composites to bioelectrical stimulation and cell differentiation.
+
+2 Results
+
+Figure 1 illustrates the overall concept of ME thin‐film meshes that induce magnetoelectric stimulation to promote NPC differentiation. NPCs are cultured on the ME meshes (Figure 1a), where the application of an external magnetic field induces electric field modulation that stimulates the cells. The applied magnetic field deforms the magnetostrictive layer, and the resulting strain is transferred to the piezoelectric layer, leading to the generation of an electric field (Figure 1b).
+
+FIGURE 1 Magnetoelectric (ME) mesh for cell differentiation. (a) Schematic illustration of the configuration of the ME mesh and neural progenitor cells (NPCs). (b) Mechanism of the strain‐mediated ME effect. (c) Boundary condition‐dependent ME effect and corresponding cell differentiation performance. (d) Scanning electron microscopy (SEM) image of differentiated cells cultured on the PDMS‐transferred ME mesh (scale bar: 10 µm).
+
+This strain‐mediated ME effect is strongly influenced by the substrate, as substrate‐induced clamping compromises strain generation in the magnetostrictive layer. Building on our previous findings, we designed three ME mesh configurations with distinct mechanical boundary conditions: freestanding, PDMS‐transferred, and substrate‐clamped (Figure 1c). Among them, the freestanding mesh produced the most effective magnetoelectric stimulation, resulting in enhanced neural progenitor cell (NPC) differentiation. A representative result of ME‐induced NPC differentiation is shown in Figure 1d.
+
+2.1 Design and Fabrication of ME Thin‐Film Mesh
+
+Figure 2a shows the overall fabrication process for the substrate‐clamped, freestanding, and PDMS‐transferred meshes. First, BTO/CFO (15 nm/15 nm) bilayers were deposited onto 10 × 10 mm2 MgO substrates using pulsed laser deposition (PLD). The PLD process enabled epitaxial bilayers with a coherently strained interface (Figure 2b,c). Subsequently, photolithography and etching were employed to define the mesh patterns. A positive photoresist was applied and patterned using a photolithographic mask corresponding to the mesh design. After exposure and development, the unprotected regions of the film were physically etched by Ar ion milling. The remaining photoresist was subsequently removed, completing the preparation of substrate‐clamped mesh (Figure 2d,e). The substrate‐clamped mesh was then immersed in a sodium bicarbonate‐saturated solution, which selectively etched the MgO substrate to release the freestanding mesh (Figure 2f,g). Finally, the freestanding mesh was transferred onto a PDMS host substrate via a stamping process, resulting in a PDMS‐transferred mesh (Figure 2h,i). The scalability of this fabrication process was demonstrated by the successful preparation of large‐area meshes, as shown in the optical images of the freestanding (Figure 2j,k) and PDMS‐transferred (Figure 2l) configurations.
+
+FIGURE 2 Fabrication procedure of ME meshes. (a) Schematic illustration of the fabrication process. In each stage (after ion milling, wet etching, and stamping), the substrate‐clamped mesh, freestanding mesh, and PDMS‐transferred mesh are obtained, respectively. (b) Transmission electron microscopy (TEM) cross‐sectional image of the BTO/CFO bilayer of substrate‐clamped ME mesh (scale bar: 5 nm). (c) X‐ray diffraction (XRD) θ‐2θ spectra around the 002 MgO reflection for the substrate‐clamped, freestanding, and PDMS‐transferred meshes. (d) Optical image and (e) tilted SEM image of the substrate‐clamped mesh. (f) Optical image and (g) tilted SEM image of the freestanding mesh. (h) Optical image and (i) tilted SEM image of the PDMS‐transferred mesh. (j, k) Optical images of the freestanding mesh and (l) PDMS‐transferred mesh showing their scalable fabrication. Scale bars in (d–i) represent 5 µm, and those in (j–l) represent 100 µm.
+
+A regular mesh pattern was selected as the structural design for this study. Since wet etching of the MgO substrate is relatively slow, a pattern that allows the etchant to access the substrate surface efficiently was preferred to complete the process within a reasonable timescale. To achieve this, the mesh was designed with thin stripes oriented along the [100] and [010] crystallographic directions, enabling uniform and efficient substrate removal during etching. In addition, the regular mesh pattern provides a mechanically robust geometry that minimizes the influence of residual stress compared with more complex designs. Here, the mesh was further divided into several submeshes to prevent a single fracture from propagating and damaging the entire structure. As a result, this design and fabrication strategy allows the production of large‐scale freestanding meshes with minimal fracture, representing a clear advantage over continuous membrane structures.
+
+Mesh design parameters include stripe width, spacing, and submesh size. They are critical for increasing fabrication yield, mesh structure reliability, and NPC stimulation efficiency. For example, a smaller stripe width allows faster substrate etching and increases structural flexibility (Figure S1); however, it reduces the amount of active material per unit area, potentially limiting the efficiency of NPC stimulation. In the case of spacing, it influences both the mechanical stability of the mesh and overall stimulation efficiency. Last, a smaller submesh size minimizes the propagation of fractures but also decreases the available stimulation area due to the gap required for dividing the mesh into submeshes.
+
+Considering these factors, the mesh geometry was empirically optimized to achieve minimum fracture of meshes upon release from the MgO substrate while retaining as much ME material as possible. We found that larger stripes with smaller spacing increased the ME material coverage but were limited by manufacturability and structural stability issues, including significantly longer MgO etching times. Conversely, smaller stripes with wider spacing yielded a higher proportion of intact meshes but substantially reduced the amount of active ME material. Details of the optimization process are provided in Note S1 and Figures S2–S6. The optimized mesh parameters were determined to be a stripe width of 2–3 µm and a spacing of 5 to 9 µm, ensuring that approximately 60% of the ME material remained on the substrate. The entire sample surface was divided into 60 × 60 submeshes, each approximately 150 × 150 µm2, separated by 10 µm gaps that left the ME thin film clamped to the substrate. This design helps relieve stress accumulation and minimize the number of fractured meshes during release. Finally, using the optimal photolithographic mesh design (Figure S7), the clamped, freestanding, and PDMS‐transferred meshes were successfully implemented (Figure S8).
+
+To support the experimental optimization of mesh geometry, computational simulations were performed using COMSOL Multiphysics based on a bilayer BTO/CFO mesh design. The design parameters, including stripe width (1, 2, and 3 µm), spacing (4, 8, and 12 µm), and number of patterns (2 × 2, 4 × 4, and 6 × 6), were systematically varied to evaluate structural deformation and stress distribution. The primary factors of interest were the maximum deflection and the stress concentration at the corners. Simulation results revealed that increasing the stripe width led to higher stress but lower deflection. Increasing the spacing and the number of patterns resulted in slightly higher stress concentrations and greater deflection. Therefore, narrower stripe widths, smaller spacing, and fewer patterns (i.e., smaller submesh) are preferable for maintaining structural integrity. These findings highlight a trade‐off between mechanical stability and coverage (e.g., ME material covering area per total surface area), suggesting that stripe widths of 2–3 µm and spacing of 5–9 µm are acceptable parameters for achieving both structural reliability and cell stimulation efficiency.
+
+2.2 Boundary Condition‐Dependent Properties of ME Thin‐Film Mesh
+
+2.2.1 Microstructures
+
+X‐ray diffraction θ‐2θ scan in clamped BTO/CFO bilayer reveals that the bilayers show high crystallinity with 001 crystalline orientation (Figure 2c and Figure S13). The 002 reflection of CFO is a small shoulder located at 2θ ≈ 43.1°, accompanied by Laue fringes and corresponding to a c‐axis c CFO = 4.186 Å, as expected for a CFO strained layer onto an MgO (4.021 Å) substrate. On the other hand, the 002 BTO reflection is located at 2θ ≈ 45.4°. The corresponding c‐axis, c BTO = 3.996 Å, denotes the prevalence of a‐ and b‐domains. Long‐range θ‐2θ scan (Figure S13c) also confirms the highly crystalline nature of both layers.
+
+Atomic force microscopy images of the as‐deposited BTO/CFO bilayer (Figure S14) show a predominantly flat surface with a root‐mean‐square (RMS) roughness of 0.36 ± 0.02 nm, indicating mostly layer‐by‐layer growth. The smooth morphology suggests good epitaxial quality, although partial strain relaxation is expected in the BTO layer due to the lattice mismatch with CFO.
+
+To ensure that the integrity and high crystallinity of the BTO/CFO mesh were preserved during the fabrication process, we performed the θ‐2θ scans of clamped, freestanding, and PDMS‐transferred meshes (Figure 2c). The results show that all samples maintained high crystallinity. No discernible change in lattice parameters was detected between the clamped and freestanding meshes. In contrast, the mesh transferred onto PDMS clearly shows peak shifts, with c‐axis values of c CFO = 4.199 Å and c BTO = 4.009 Å. The elongation of these c‐axes indicates strain relaxation following complete release from the MgO‐induced tensile strain. The freestanding mesh does not go through the same relaxation, as it is still anchored to the MgO substrate at its edges.
+
+Surface morphology of the clamped and PDMS‐transferred meshes (Figures S15 and S16) confirms that the 2‐µm stripe width and 5‐µm spacing were well patterned. Cross‐sectional views of the transferred mesh show a BTO/CFO thickness of ≈30 nm, indicating preferential etching of the MgO substrate and preservation of film integrity throughout the process. The mesh is therefore cleanly transferred onto the PDMS substrate, demonstrating that the etching steps did not degrade the film. More details on the microstructure characterization can be found in Note S2.
+
+The high epitaxial quality of the BTO/CFO bilayer was confirmed by high‐angle annular dark‐field scanning transmission electron microscopy (HAADF‐STEM) throughout the boundary conditions. The TEM lamella image shows a uniform thickness across the bilayer structure (Figure S17a). Magnified TEM images show that the epitaxial BTO/CFO bilayer is well preserved in both the clamped configuration (Figure 2b and Figure S17b) and the freestanding configuration (Figure S17c). TEM images of the PDMS‐transferred configuration (Figure S18) also reveal a well‐preserved bilayer with crystallinity comparable to that of the freestanding and clamped configurations. No degradation in film crystallinity or thickness is observed, confirming that the fabrication process does not adversely affect film quality.
+
+2.2.2 Magnetoelectric Properties
+
+Using both piezoresponse force microscopy (PFM) and electrochemical measurements, we evaluated the magnetoelectric properties of meshes under different boundary conditions, namely clamped, PDMS‐transferred, and freestanding. Figure 3a,b shows the PFM amplitude and phase loops, respectively, for a freestanding mesh. Increasing the external magnetic field produces a horizontal shift in both amplitude and phase loops, enabling estimation of the MECC [43]. The MECC is calculated using Equation (1). (1) αME=ΔEΔH=ΔV/tΔH
+
+where ΔE is the measured out‐of‐plane electric field that can be estimated by the shift of the center of the hysteresis loop ΔV, t is the thickness of the ferroelectric layer (here 15 nm), and ΔH is the applied in‐plane magnetic field. In Figure 3b, the center of the phase loop shifts from +0.554 V to −0.348 and −0.695 V as the applied magnetic field increases from 0 Oe to 500 and 1000 Oe, respectively. This shift in the center of the phase loop was consistently observed across multiple cycles of magnetic field application (Figure S19). From the shift observed between 0 and 500 Oe (Figure 3b), and using Equation (1), we obtained a MECC of α ME ≈ 12 × 105 mV cm−1 Oe−1. Overall, an average MECC of α ME ≈ 10.5 × 105 mV cm−1 Oe−1 is observed for the freestanding meshes. The average MECC decreases to α ME ≈ 5.6 × 105 mV cm−1 Oe−1 in PDMS‐transferred meshes, and to α ME ≈ 1.3 × 105 mV cm−1 Oe−1 in substrate‐clamped meshes (illustrative measurements can be found in Figure S20). Figure 3c summarizes the MECC variation across the different boundary conditions. Freestanding, PDMS‐transferred, and substrate‐clamped meshes correspond to low, intermediate, and high clamping levels, respectively. The MECC exhibits a clear trend, displaying an inverse dependence on the degree of clamping. These values and trends are in close agreement with our previous findings [2].
+
+FIGURE 3 Boundary condition‐dependent ME properties. (a, b) Amplitude and phase loops of freestanding ME meshes under varying external magnetic field application, measured by piezoresponse force microscopy (PFM). (c) Comparison of the magnetoelectric coupling coefficient extracted from PFM measurements for meshes with different boundary conditions. (d) Comparison of the change in electrolyte conductance induced by the ME effect of meshes with different boundary conditions, measured using an electrochemical setup.
+
+To correlate this observation, we similarly compared the set of thin‐film meshes in an electrochemical conductance measurement setup. The setup consists of a small cuvette filled with a thin layer of saline solution with 4 electrodes arranged in a standard 4‐point probe setup. When the ME meshes are placed in solution, an applied magnetic field produces a high‐strength, localized electric field that interferes with the free‐ion mobility in solution, changing the conductance in a measurable fashion. As the strength of the electric field corresponds with the strength of the magnetoelectric effect, it is expected that the mesh with the lowest degree of clamping would correspond with the largest change in conductance, which was observed experimentally (Figure 3d). The conductance change appears to scale proportionally with the MECC, which matches the trend observed with PFM measurements.
+
+2.3 ME Mesh‐Based NPC Differentiation
+
+2.3.1 Biocompatibility
+
+We investigated whether ME meshes can drive cell differentiation, especially neural progenitor cell (NPC), and first verified their biocompatibility. We prepared six experimental groups, including (i) NPCs (control), (ii) NPCs + MgO substrate (G1), (iii) NPCs + MENPs dispersed on MgO substrate (G2), (iv) NPCs + substrate‐clamped ME mesh (G3), (v) NPCs + PDMS‐transferred ME mesh (G4), and (vi) NPCs + freestanding ME mesh (G5). Each experimental group was further divided into subgroups that were either exposed to or not exposed to an alternating magnetic field (AMF). The samples were placed at the center of a solenoid coil with an internal diameter of 5 cm, operating in a resonant tank configuration (Figure 4a). This solenoid coil generated an AMF with an amplitude of 20 mT and a frequency of 1.18 kHz. The AMF was applied for 2 h, twice daily, over two consecutive days. Figure 4b quantifies NPC viability in each group with and without AMF. Both the presence of the ME materials and AMF led to only modest decreases relative to control. Group G4 with the CFO layer facing the cells showed the lowest viability, consistent with the inherent cytotoxicity of CFO. All groups nevertheless remained above 80%, which exceeds the ISO 10993–5 2009 cytotoxicity threshold and indicates overall biocompatibility within the experimental timeframe.
+
+FIGURE 4 ME mesh‐based NPC differentiation. (a) Experimental setup for magnetoelectric stimulation of NPCs to evaluate biocompatibility and differentiation performance. (b) Evaluation of biocompatibility on ME meshes under varied boundary conditions, showing maintained cell viability. (c–e) Immunofluorescence analysis of ME meshes showing the expression of neuronal markers. Samples were stained for βIII‐tubulin and MAP2 to identify differentiated neurons. Quantitative assessment was performed through mean fluorescence intensity (MFI) across all samples (n = 3, means ± s.e.m.). **** p < 0.0001. Scale bar: 8 µm.
+
+2.3.2 Differentiation of NPCs Using ME Meshes
+
+To evaluate the differentiation potential of NPCs under ME stimulation, we employed the same AMF protocol as described in Section 2.3.1. The AMF exposure lasted for 2 h, twice daily, over two consecutive days to activate the ME effect and enhance NPC differentiation. For the control, the same mass of MENPs was dispersed onto the MgO substrate (G2) to compare the efficiency of ME meshes in promoting cell differentiation. Figure 4c shows immunofluorescence imaging conducted after AMF stimulation, revealing pronounced neuronal differentiation of NPCs cultured on ME meshes, evidenced by enhanced expression of βIII‐tubulin and microtubule‐associated protein 2 (MAP2). Quantitative analysis of mean fluorescence intensity (MFI) revealed significant increases in both neuronal markers compared to unstimulated controls (Figure 4d,e and Figure S22). Under the three respective boundary conditions, AMF application resulted in increases in MFI of 17.3‐, 21.0‐, and 48.0‐fold for βIII‐tubulin, and 17.4‐, 20.7‐, and 63.3‐fold for MAP2. Comparison of SEM images showing cell differentiation on the PDMS‐transferred mesh (Figure 1d and Figure S21a, with AMF; Figure S21b, without AMF) further confirms effective neural induction mediated by the ME mesh under AMF stimulation. Differences in neuronal marker expression were also observed among ME meshes with varied boundary conditions. An increasing trend was observed from substrate‐clamped to PDMS‐transferred to freestanding meshes, consistent with the trend in the ME coupling coefficient, indicating that the boundary state influences the efficiency of ME‐mediated neural induction. Notably, the ME meshes exhibited slightly enhanced differentiation outcomes compared to MENPs.
+
+3 Discussion
+
+This study demonstrates the significance of high‐quality, efficiently engineered multiferroic thin‐film meshes for biomedical applications, particularly for stimulating and promoting the differentiation of NPCs. In BTO/CFO heterostructures, the piezoelectric polarization of BTO is modulated through the magnetostrictive response of CFO under external magnetic fields, thereby tuning the out‐of‐plane polarization. This tunability alters the surface charge environment of the BTO layer and, consequently, influences local ionic behavior at the cell interface. Because NPC differentiation is closely linked to Ca2+ channel activity and ion migration, the ability of ME meshes to electrically modulate this ionic landscape provides a powerful pathway for controlling cellular behavior. To enable this functionality, we developed the multiferroic heterostructure, optimized the mesh geometry, and established robust fabrication processes. Boundary‐condition control clearly demonstrates the role of the ME effect in NPC differentiation, with freestanding meshes exhibiting the strongest response. Moreover, the PDMS‐transferred design offers a more stable and application‐ready device configuration.
+
+The enhanced NPC differentiation observed here may be related to local magnetoelectric charge modulation at the cell‐material interface, which could induce membrane depolarization, activate Ca2+‐permeable ion channels, promote Ca2+ influx, and subsequently trigger electrostimulation‐associated signaling pathways involved in neuronal differentiation. This proposed mechanism is consistent with previous work using the same induced pluripotent stem cell (iPSC)‐derived NPCs and CFO‐BTO magnetoelectric system, in which AMF stimulation was shown to enhance intracellular Ca2+ influx, while Ca2+ channel blockade markedly reduced the expression of neuronal and astrocytic markers [27]. In the present study, we primarily focus on the materials design and boundary‐condition‐dependent enhancement of magnetoelectric coupling in BTO/CFO meshes. However, further studies are needed to fully elucidate the biological mechanisms underlying the response observed in this mesh system.
+
+Optimizing the mesh design has been important for achieving magnetoelectrically induced NPC differentiation. While a stripe width of 2–3 µm has been finally selected to ensure a high packing ratio, mechanical stability could be further improved with narrower stripes in the 1–2 µm range. Specifically, a 1.5 µm stripe width reliably produced a fully preserved sample without any submesh fracture (Figure S1), indicating that thinner stripes combined with larger spacing promote high structural stability and robustness. This geometry, however, was not chosen because the remaining BTO/CFO material after patterning was relatively low (≈22%) compared with the final selected designs (≈60%). Moving forward, an application‐specific balance between mechanical reliability and ME material coverage will be important to optimize, depending on the targeted performance requirements of the mesh.
+
+Interestingly, for the optimal geometry, the fracture rate remains below 5%, and in multiple fabrication batches we achieve a 100% yield of fully freestanding submeshes. Several factors can increase the likelihood of submesh fracture, including intrinsic film defects (e.g., point defects, microcracks), imperfections introduced during patterning (such as dust particles, photoresist edge beads, or non‐uniform coating), and variations in the release steps, particularly the substrate etching rate and total etching time. Understanding and minimizing these factors are essential for improving fabrication reliability.
+
+The proposed fabrication method has proven to be a highly efficient and versatile approach for producing freestanding BTO/CFO structures. We demonstrate a broad range of mesh geometries with systematically varied parameters. In addition, our previous work has shown that this method can realize diverse architectures, from simple stripe patterns to complex kirigami designs, that exhibit enhanced mechanical properties (e.g., superelasticity and shape memory) and improved magnetoelectric performance due to reduced substrate clamping [1, 2, 3, 42]. This geometrical versatility allows for further variation in design, ranging from 2D to 3D, thereby enabling a wider range of functional applications (e.g., implantable cell‐stimulation devices adaptable to curved surfaces). Here, a simple 2D mesh design was selected for its high surface coverage and mechanical stability. However, the same methodology could be applied to membranes of other shapes that, for instance, could guide NPC growth in specific directions, ultimately producing a desired shape for the generated neuronal structure.
+
+In comparing the MECC under different boundary conditions, analyses of the PFM hysteresis loops (e.g., amplitude and phase) show an increasing trend of MECC, which is enhanced from substrate‐clamped samples to PDMS‐transferred and freestanding meshes. When the magnetic field is applied, the hysteresis loop generally shifts along the voltage axis as the magnetostrictive strain affects the built‐in electric field. For example, if the magnetostrictive strain favors polarization pointing up, the phase loop will shift so that switching to the disfavored direction requires a larger opposite voltage. Here, we observed that changes in the boundary conditions altered the degree of the PFM loop shift, likely due to the clamping effect restricting magnetostriction. These variations in MECC are consistent with the results from the electrochemical method, which quantifies ionic conductance, and ultimately lead to differences in magnetoelectric cell‐differentiation performance.
+
+Despite these achievements, several tasks remain before these multiferroic materials can be fully implemented in practical biological applications. While fully freestanding meshes exhibit strong ME coupling, they are impractical for biomedical use due to their fragility and handling challenges. Conversely, substrate‐clamped films provide mechanical stability, but display limited ME responses because of substrate‐induced constraints. The PDMS‐transferred mesh thus serves as a practical alternative, offering mechanical flexibility and biocompatibility while maintaining effective ME functionality suitable for bioelectronic applications.
+
+Freestanding ME meshes have exhibited superior NPC differentiation performance compared to MENPs, which may be attributed to the use of commercial CFO nanoparticles and sol–gel synthesis methods. That is, interface control and geometry optimization were not considered for enhancing the ME properties. With further refinement of the synthesis process, the ME properties of MENPs are expected to improve. Moreover, ME thin films and MENPs can be regarded as complementary platforms, each offering distinct advantages and addressing different application needs. The selection between the two should be guided by the specific requirements of the target application, such as spatial precision, stimulation strength, and fabrication scalability.
+
+While this study establishes a robust fabrication strategy and demonstrates the fundamental performance of freestanding BTO/CFO magnetoelectric meshes, several avenues remain open for future investigation. First, the influence of mesh geometry on magnetoelectric performance was not systematically explored. Whether specific shapes (e.g., geometries incorporating larger openings) could enhance magnetostriction and thereby increase the MECC, as suggested in previous work [42], remains an important question. Also, a deeper understanding of stress‐release mechanisms during etching and transfer, as well as microstructural evolution such as crack initiation and propagation, will be essential for improving mesh yield and long‐term reliability. Together, these findings establish the promise of multiferroic ME meshes as versatile, wireless bioelectronic interfaces and lay a solid foundation for their advancement toward neuromodulation and regenerative medicine applications.
+
+4 Experimental Section
+
+4.1 Thin Film Deposition
+
+BTO/CFO bilayers were deposited by PLD onto 10 × 10 mm2 (001) MgO substrates (Crystal GmbH) using a 248 nm KrF excimer laser. A Neocera PLD system was used, which provides improved thickness uniformity over a large substrate area due to its relatively large target‐to‐substrate distance (approximately 75 mm).
+
+Prior to deposition, substrates were ultrasonically cleaned in acetone and isopropanol, followed by a light ion‐milling step (with 250 mA of beam current and 600 V of voltage) for 1 min to remove contamination (from carbonates, hydroxides, hydrocarbons), shortly before introducing the substrate into the PLD chamber. The 15 nm CFO layer was then deposited at TS = 550°C and PO2 = 10 mTorr, using a laser fluence of 1.8 J cm−2 at 5 Hz; followed by the BTO layer deposition at TS = 750°C and PO2 = 200 mTorr, with laser fluence of 1.5 J cm−2 at 4 Hz.
+
+4.2 Mesh Patterning
+
+Mesh patterning was done by photolithography, using AZ1505 positive photoresist, followed by dry etching of the undesired parts by ion‐milling (Oxford IonFab 300 Plus). This dry etching was done in 15 short cycles of 20 s at 500 mA beam current (and 600 V beam voltage), with resting steps of 90 s between cycles to limit photoresist hardening. After physical etching, the resist was stripped by acetone and oxygen plasma at 600 W for 3 min. For freestanding meshes, the samples were placed in sodium bicarbonate‐saturated solution for about 48–72 h to etch the MgO substrate. After thorough rinsing with deionized (DI) water and isopropyl alcohol (IPA), the samples were dried using a critical point drier (from Tousimis). Samples were either left as such, to create freestanding meshes, or transferred to PDMS by stamping method.
+
+The mesh structure was designed by opening square regions in the continuous bilayer, resulting in grids of 90°‐intertwined stripes of 2–3 µm width whose centers are separated by 5–9 µm. It was designed in a way that only regions ≈150 × 150 µm2 are freestanding, to avoid excessive material loss in case of fracture, by leaving clamped wider stripes of ≈10 µm width in between the freestanding regions. All in all, the ME bilayer covers ≈60% of the total substrate surface (10 × 10 mm2).
+
+For the PDMS‐transferred meshes, the stamping was done by a dry‐transfer stamping process. A flat PDMS substrate was manually placed onto the freestanding mesh on the MgO substrate and subsequently peeled away in a single motion, transferring the mesh onto the PDMS.
+
+4.3 Nanoparticle Preparation
+
+The CFO‐BTO core–shell nanoparticles were synthesized using a sol–gel method. For the core material (CFO), commercial cobalt ferrite nanoparticles (CAS: 12052‐28‐7) were used. To deposit the BTO shell, two precursor solutions (A and B) were first prepared. Solution A was prepared by dissolving 1.736 g of barium acetate (CAS: 543‐80‐6) in 5 mL of acetic acid (CAS: 64‐19‐7), which was slightly heated to facilitate dissolution. The mixture was stirred for 1 h and then cooled to room temperature. Solution B was prepared by mixing 10 mL of 2‐methoxyethanol (CAS: 109‐86‐4) with 1 mL of acetylacetonate (CAS: 123‐54‐6) under vigorous stirring for 5 min, followed by the dropwise addition of 2.776 mL of titanium(IV) butoxide (CAS: 5593‐70‐4). Once Solution A had cooled, it was added dropwise to Solution B to form Solution C, which was stirred for an additional 30 min. A suspension of 250 mg of CFO dispersed in 1 mL of DI water was added to Solution C at a 1:10 v/v ratio and shaken for 1 h. The resulting mixture was then dried overnight on a hotplate at 100°C without stirring. The dried powder was subsequently annealed in an oven at 900°C for 2 h. All chemicals were obtained from Sigma–Aldrich and used as received.
+
+4.4 Structural Analysis
+
+The crystalline structure of the ME meshes was analyzed by X‐ray diffraction (XRD, Panalytical X'Pert MRD) employing Cu Kα1 radiation (λ = 1.5406 Å). Surface morphology and topographical features were examined by atomic force microscopy (AFM, Bruker Dimension FastScan) in semi‐contact mode. Optical microscopic images were captured using a Keyence VHX‐X1 digital microscope. For transmission electron microscopy (TEM) measurements, lamellae of the BTO/CFO meshes were prepared by focused ion beam (FIB) in situ lift‐out method with a Helios 5 UX system (Thermo Scientific, USA). For atomic structure analysis, the lamellae were examined using a double Cs‐corrected GrandARM microscope (JEOL, Japan), operated at 300 kV in scanning transmission electron microscopy (STEM) mode.
+
+4.5 Magnetoelectric Coupling Property Evaluation: Piezoresponse Force Microscopy
+
+Ferroelectric properties of BTO/CFO samples were investigated by piezoelectric force microscopy (PFM, NT‐MDT). Freestanding meshes were transferred onto Au‐coated Si substrates. PDMS‐transferred meshes were transferred to Au‐coated PDMS. Clamped meshes were deposited onto a MgO substrate first coated with a TiN or BLSO bottom electrode. For magnetoelectric coupling evaluation, PFM measurements were acquired at different dc magnetic fields ranging from 0 to 1000 Oe, and the MECC α ME was defined by Equation (1). Three independent samples were measured for each boundary condition.
+
+4.6 Magnetoelectric Coupling Property Evaluation: Electrochemical Setup
+
+ME coupling evaluated via conductance measurements was performed using a custom‐assembled cuvette with four electrodes arranged in a standard four‐point probe setup, similar to previously reported experiments [44]. After placement of the sample, the cuvette was filled with phosphate‐buffered saline (PBS), diluted 1:4 (v/v) with DI water, sufficient to fully cover the sample. After sufficient time to stabilize the conductance level, a 350‐mT magnetic field was applied to the sample, causing an immediate change in conductance. This shift was then compared against the baseline value to calculate the normalized change in conductance.
+
+4.7 Cell Culture
+
+Human iPSC‐derived neural progenitor cells (NPCs, Merck, SCC035) were expanded on Matrigel‐coated culture vessels. Matrigel was thawed on ice, diluted 1 to 50 in ice‐cold Dulbecco's Modified Eagle Medium, applied to flasks, and incubated overnight at 4°C. Immediately before seeding, the coating solution was aspirated, and vessels were equilibrated with prewarmed ENStem‐A Neural Expansion Medium (Merck, SCM004a). Cryopreserved NPCs were then rapidly thawed at 37°C, transferred to a sterile 15 mL conical tube, and gently diluted with prewarmed medium to minimize osmotic stress. Cells were pelleted by centrifugation, the supernatant was removed, and the pellet was resuspended in fresh expansion medium. Viability and cell number were determined, and cells were seeded onto the prepared Matrigel‐coated vessels. Cultures were maintained at 37°C in a humidified 5% CO2 atmosphere with expansion medium exchange every two days. At confluence, NPCs were dissociated with Accutase (Merck, SCR005), counted, and replated into freshly coated T75 flasks for continued expansion.
+
+4.8 Biocompatibility Test
+
+The biocompatibility was evaluated through cell viability assays using MTT over a 48‐h period. Each ME mesh was sterilized by UV irradiation overnight, followed by immersion in a 10% penicillin–streptomycin and Amphotericin B solution. The samples were then thoroughly rinsed with phosphate‐buffered saline (PBS) and placed individually into wells of a culture plate (e.g., ibidi, 81201) for NPC seeding. Before cell seeding, the chamber was coated with Matrigel using the same protocol and incubated overnight. NPCs were cultured at a defined cell density (5000 cells/well) for subsequent MTT [3‐(4,5‐dimethylthiazol‐2‐yl)‐2,5‐diphenyltetrazolium bromide] analysis. Six experimental groups were prepared: (i) NPCs (control), (ii) NPCs + MgO substrate (G1), (iii) NPCs + MENPs dispersed on MgO substrate (G2), (iv) NPCs + substrate‐clamped ME mesh (G3), (v) NPCs + PDMS‐transferred ME mesh (G4), and (vi) NPCs + freestanding ME mesh (G5). Each group was further divided into subgroups with or without exposure to an alternating magnetic field (AMF). Each subgroup contained 3 biologically independent samples (n = 3) prepared and analyzed under the same experimental conditions. Twenty‐four hours post‐seeding, following the previously established AMF stimulation protocol [27], samples were positioned within a solenoid coil (5 cm inner diameter) operating in a resonant tank configuration. An alternating magnetic field with an amplitude of 20 mT and a frequency of 1.18 kHz was applied for 2 h twice daily over two consecutive days. After treatment, cell viability was assessed via MTT assay using a tetrazolium salt concentration of 3 mg mL−1. Absorbance was measured at 570 nm with a reference wavelength of 630 nm using a Varioskan Flash multimode microplate reader. Mean absorbance values from triplicate wells were used to calculate cell viability according to: CellviabilityofNPC%=ODsample−ODblankODcontrol−ODblank×100
+
+where OD sample, OD blank, and OD control represent the optical densities of treated NPCs, blank medium (without cells), and untreated control NPCs (without ME mesh or AMF exposure), respectively.
+
+4.9 NPC Differentiation
+
+The neurostimulation capability of the ME meshes was evaluated using the same experimental groups described in Section 4.8 by assessing their ability to promote NPC differentiation. Following the AMF stimulation protocol detailed in Section 4.8, an AMF with an amplitude of 20 mT and a frequency of 1.18 kHz was applied for 2 h, twice daily, over two consecutive days. After stimulation, cells were fixed with 4% paraformaldehyde for 10 min at room temperature. Cells were permeabilized with 0.5% Triton X‐100 for 30 min at room temperature, then blocked with 2% bovine serum albumin for 30 min to reduce nonspecific binding. For neuronal marker detection, cells were incubated overnight at 4°C with primary antibodies against βIII‐tubulin (Sigma–Aldrich T2200) and MAP2 (Proteintech 67015‐1). Secondary antibodies were fluorescein isothiocyanate (FITC)‐conjugated goat anti‐rabbit IgG (Sigma–Aldrich AP132F) and tetramethylrhodamine isothiocyanate (TRITC)‐conjugated goat anti‐mouse IgG (Sigma–Aldrich AP503R), each applied for 1 h, followed by several washes and nuclear counterstaining. The images were captured on a Zeiss LSM 880 Airyscan confocal microscope.
+
+Author Contributions
+
+Xiang‐Zhong Chen: supervision, conceptualization, methodology, formal analysis, project administration, resources, funding acquisition, writing – original draft, writing – review and editing. Abderrahim Lahlahi Attalhaoui: data curation, validation, investigation, formal analysis. Hao Ye: methodology, validation, formal analysis, data curation, visualization, writing – review and editing. Juan Bautista Carda Castelló: supervision, writing – review and editing, funding acquisition, resources. Marc Tudela‐pi: investigation, methodology. Anton Guimerà‐brunet: methodology, investigation, funding acquisition, supervision, formal analysis. Mathieu Mirjolet: conceptualization, methodology, data curation, investigation, validation, formal analysis, supervision, writing – original draft, writing – review and editing. Josep Puigmartí‐luis: methodology, supervision, funding acquisition, investigation, formal analysis, project administration, resources. Elric Zhang: supervision, formal analysis, writing – review and editing. Donghoon Kim: conceptualization, methodology, supervision, writing – review and editing. Salvador Pané: conceptualization, methodology, supervision, funding acquisition, project administration, resources, writing – original draft, writing – review and editing. Minsoo Kim: conceptualization, methodology, data curation, investigation, formal analysis, supervision, writing – original draft, writing – review and editing, validation. Bastian Gebauer: validation, investigation, data curation, formal analysis, visualization, methodology. Vitaly Pustovalov: validation, data curation, investigation.
+
+Funding
+
+This work was funded by the Swiss National Science Foundation (Grant No. 213113).
+
+Conflicts of Interest
+
+The authors declare no conflicts of interest.
+
+Supporting information
+
+Supporting File: advs77180‐sup‐0001‐SuppMat.pdf.
+
+Acknowledgements
+
+This work received financial support from the Swiss National Science Foundation under project No. 213113. The authors would like to thank the Cleanroom Operations Team of the Binning and Rohrer Nanotechnology Center (BRNC), the Scientific Center for Optical and Electron Microscopy (ScopeM), and the FIRST laboratory at ETH for their technical support. The authors would also like to thank Dr. Thomas Weber and the Department of Materials at ETH Zurich for support with the X‐ray diffraction.
+
+Data Availability Statement
+
+The data that support the findings of this study are available from the corresponding author upon reasonable request.
+
+
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+44 M. Sadeqi‐Moqadam and J. Glaum , “Characterizing Piezoelectric Materials under Mechanical Stress in Liquid media: An Electrokinetic Approach,” Colloids and Surfaces A: Physicochemical and Engineering Aspects 688 (2024): 133569, 10.1016/j.colsurfa.2024.133569.
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+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Langmuir
+Journal ID: Langmuir
+NLM Journal ID: 9882736
+Journal ID: la
+
+Langmuir
+
+ISSN: 0743-7463
+EISSN: 1520-5827
+pubs.acs.org/Langmuir
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC12961929
+PMID: 41708294
+DOI: 10.1021/acs.langmuir.5c06135
+Article version: 1
+Subjects: Article
+
+Focused Liquid Pinching in Coaxial Drop Capsule Generation
+
+7978753 Taraki Nilofar
+6694231 https://orcid.org/0000-0002-4392-2983 Said Ismail A.
+School of Engineering and Materials Science , 4617 Queen Mary University of London , London E1 4NS , U.K.
+* Email: a.ismail@qmul.ac.uk.
+Electronic publication date: 2026 Feb 18
+Publication date: 2026 Mar 3
+Volume: 42
+Issue: 8
+First page: 6344
+Last page: 6353
+Received 2025 Nov 20; Accepted 2026 Feb 12; Revised 2026 Feb 12; 2026 Feb 18
+Copyright: © 2026 The Authors. Published by American Chemical Society
+Copyright year: 2026
+Copyright holder: The Authors
+
+License: This article is licensed under CC-BY 4.0
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Funding: Engineering and Physical Sciences Research Council 10.13039/501100000266 EP/V04382X/1
+document-id-old-9: la5c06135
+document-id-new-14: la5c06135
+production-flag-MathML-config-version: 3
+production-flag-journal-citation-display-style: acs-titles
+production-flag-journal-date-display-style: dates-used-rcd-rvd-acc
+document-id-alt-64: 99d365777a29bf7fc9b58d5194bb95a5124144ee029095f4e75b309b172fb749
+
+Ÿ==============================Ÿ
+The pinching dynamics of an inviscid inner drop in a coaxial pendant drop structure have been investigated here both experimentally and numerically. The thinning rate of the inner drop, when it pinches in an inertial regime in this configuration, is found to be faster than that of a single drop pinching in a liquid medium. This is attributed to a focusing of the flow between the inner and outer drop interfaces induced by the contraction of the outer drop during its own pinching process. Our results reveal that this focusing effect increases dramatically when the ratio of the inner to outer nozzle radii, R̃, in a coaxial nozzle configuration exceeds 0.67. Beyond this value, the thinning rate becomes dependent on the outer nozzle size. Furthermore, the difference between the minimum neck radii of the inner and outer drop, denoted as Δh min, serves as a reliable predictor of the inner drop’s thinning rate, even for different outer liquid viscosities, and helps identify the conditions under which the satellite droplets form. Satellite droplets are observed when the outer drop squeezes the inner filament above its minimum neck location, which occurs when Δh min ranges between 0.3% and 1% of the capillary length.
+
+Introduction
+
+A capsule, in which a drop is trapped inside another immiscible liquid drop, appears vital in many industries, such as biological applications, − drug administration, , pharmaceuticals, , food, and medical diagnosis. Scientists have been working on optimizing coaxial flow devices , to create more controlled capsules that allow for more precise usage in the aforementioned applications. A common process to create the capsule in these devices is the pinching of the coaxial flow structure into coaxial drops. Drop pinch-off has been carefully studied over the last decades, covering aspects such as the thinning of the formed liquid filament neck prior to its pinching, the length of the liquid filament, the pinching angle, the formation of satellite droplets during the pinching process and the more global geometrical effect, such as the nozzle size and angle.
+
+A set of mathematical models have been developed to predict the pinching dynamics of a single drop in different regimes, − namely the inertial, viscous, and inertial-viscous regimes. Within the inertial regime, the inertia is balanced with the capillary force, and the viscous force is considered to be negligible. The minimum necking radius, h min, in the inertial regime, decreases with time following the scaling h̅min=Aτ2/3 , where h̅min is the dimensionless minimum necking radius and A is the inertial prefactor, which reflects the thinning rate of the neck and exhibits a nonmonotonic variation over time. τ is the dimensionless time defined by the equation τ = (t b – t)/t c , where t b is the breakup time, t is the time step, and tc=(ρRn3/σ) is the capillary time. Here ρ is the fluid density, R n is the nozzle radius, and σ is the surface tension. The maximum value of A, or the peak, is thought to be around 0.7 for a single drop pinching in air; however, Deblais et al. found that A is not universal and can be significantly altered by changing the nozzle size from which the drop is suspended or by making small changes to the viscosity. For drop pinching in another liquid, another study found that A peak can vary between 0.4 and 0.7, based on the external liquid viscosity.
+
+The formation of satellite droplets after the pinching of the liquid drop filament has been drawing the attention of researchers. This is primarily because many industrial applications, such as inkjet printing and microfluidic flow systems, deem the presence of the droplets as being unwanted and compromising the device’s precision. Recent research, conducted by Li et al., provided theoretical proposals for suppressing the production of said satellite droplets by manipulating the influence that the slenderness of the liquid filament has upon the final destination of the satellite droplet. It was concluded that if the filament slenderness exceeded 1.81, the satellite droplet would be recollected or absorbed back into the upper mound of the fluid.
+
+All of the work discussed thus far focused only on the pinching dynamics of a single drop. In this article, the pinching dynamics of coaxial liquid drop structures are investigated experimentally and numerically by dripping coaxial pendant drops from a coaxial nozzle. We focus our work mainly on understanding how the inner drop pinches off when the thinning is happening in the inertial regime and aim to reveal the conditions in which satellite droplets are produced and potentially inhibited in such a structure.
+
+Experiments and Numerical Simulations
+
+The experimental setup shown in Figure a is built to generate, and eventually pinch, coaxial pendant drops emerging from a coaxial nozzle. As illustrated in Figure b, the coaxial device includes a junction connected to two plastic tubes: a plastic tube from the side, which carries the outer fluid, and a plastic tube on the top, which carries the inner fluid straight through. These tubes are in turn connected to two 10 mL syringes mounted on syringe pumps to independently control the flow rates of the inner and the outer fluids, denoted as Q i and Q o , respectively. Both fluids are injected at very low flow rates, less than 2 mL/min, to ensure that the drop pinches off under the effect of its weight only. In this study, two immiscible liquids, water, and oil, are injected through the outer and inner nozzles and then allowed to pinch-off in the air, as shown in Figure c. The pendant drop method is used to measure the surface tension of the oil and the interfacial tension of the water and oil. A high-speed camera (Photron Fastcam Mini AX200) is used to capture the pinch off process of the inner and outer filaments. Consistent lighting is maintained using an optical diffuser to ensure an accurate detection of the drop interface in all images.
+
+1 Diagrams showing (a) experimental setup, (b) zoom-in into the configuration of the coaxial nozzle, and (c) further zoom-in into the coaxial nozzle device’s exit showing the order of the fluids in this three-phase configuration.
+
+A series of experiments are conducted using the coaxial nozzle with an inner nozzle radius, R i , of 0.45 mm and an outer nozzle radius, R o , of 1.5 mm. Figure shows experimental images of the coaxial pinching process when oil is injected through the inner nozzle and water through the outer nozzle, with an inner-to-outer flow rate ratio, Q = 0.5, where Q = Q i /Q o . As the inner and outer drops expand, the inner drop eventually forms a neck, as shown in the images in Figure by the slender filaments that join the top and bottom of the drop. This neck thins progressively until it is pinched off, which is then followed by the thinning and eventual pinching of the outer drop. The images in Figure highlight certain optical limitations in the experiment. The external drop acts as a convex lens, which focuses the light at the center and makes it difficult to accurately detect the inner drop interface, especially when the inner and outer interfaces become closer at higher inner-to-outer nozzle ratio R.
+
+2 Experimental images showing the coaxial pinching sequence of sunflower oil (inner fluid) surrounded by water (outer fluid), pinching-off in air, where the inner nozzle radius, R i = 0.45 mm and the outer nozzle radius, R o = 1.5 mm.
+
+To tackle this limitation, a multiphase model is developed using open-source software Gerris. The model simulates the coaxial pinching process to accurately track the inner interface during the thinning, even at a high value of R. An axisymmetric computational domain is considered, and the fluids used are assumed to be incompressible and immiscible; thus, the simulation relies on solving the Navier–Stokes equation with surface tension and the continuity equation shown below, respectively. 3.1 ρ(∂_()tv+v·∇v)=−∇p+∇·(2μD)+σκδsn
+
+3.2 ∇·v=0
+
+where v and p represent the velocity field and pressure distribution, respectively, while ρ and μ represent the fluid density and the dynamic viscosity, respectively. The deformation tensor, D , is dictated by the equation D = (∇ v + ∇ v T )/2. The nature of the surface tension coefficient, σ, functioning along the interface is represented by the Dirac distribution function, δ s . κ and n denote the radius of curvature and perpendicular unit vector of the interface, respectively. To track the interface position of the inner and outer drop, volume fractions c i ( x , t) are calculated using the advection equation below. 3.3 ∂ci∂t+v·∇ci=0
+
+The subscript i = 1,2 with the numbers denotes the inner-to-outer drop fluid fraction and air-to-outer fluid fraction, respectively. This equation is solved using a piecewise-linear geometrical Volume-Of-Fluid (VOF) scheme. The volume fractions c 1 and c 2, which vary between 0 and 1, are then used to estimate the values of the local viscosity and density in the three-phase computational domain by using the following equations 3.4 μ(c1,c2)=c1μi+c2μa+(1−c1−c2)μo
+
+3.5 ρ(c1,c2)=c1ρi+c2ρa+(1−c1−c2)ρo
+
+where μ i , μ o , and μ a represent the dynamic viscosity of the inner fluid, outer fluid, and the surrounding air, respectively, while ρ i , ρ o , and ρ a represent the density of the inner fluid, outer fluid, and the surrounding air, respectively. The combination of variables in eqs and () allows for the correct fluid properties to run in their designated regions.
+
+Figure shows the computational domain that is used, with dimensions of 20 × 10 mm. The boundary conditions on the left side of the domain were divided into three parts, as shown in Figure : the inlet velocity for the first fluid and the inlet velocity for the second fluid, which together mimic a coaxial nozzle outlet flow. The remainder of the left side of the domain, along with the top side, consisted of a solid wall with no-slip boundary conditions, where the velocity components were set to 0. On the right-hand side, the outflow boundary condition is set, in which the pressure and the velocity gradient are set to zero.
+
+3 Schematic of the three-phase axisymmetric computational domain that was used to simulate the coaxial drop pinching.
+
+An adaptive mesh gradient is used to save computational costs and time while simulating at a high enough refinement to precisely capture the delicate necking filament. The reader is referred to Popinet’s paper about the used adaptive mesh technique for more details. A mesh convergence study is conducted to identify the appropriate refinement level that ensures consistency of the fluid interface across meshes. Since our main focus within this work is to study the thinning rate during the pinching while in the inertial regime, we examine the inertial prefactor, A, against varying levels of refinement. A was determined using the approach described by Li & Sprittles, by extracting the slope from the relationship (h min/R i )3/2 = A 3/2τ. This technique avoids the need to calculate the precise moment when h min = 0. From Figure it becomes clear that the temporal inertial prefactor converges above level 11 and the characteristic peak inertial prefactor, A peak, (indicated by the black cross in Figure ), becomes almost independent of the mesh size. Based on this analysis, we use level 12 mesh refinement throughout the breadth of our study to ensure accurate results while maintaining efficient computational costs. The mesh size Δ = 0.01/2Level. For level 12, this gives a mesh size of approximately 2.4 μm near the liquid interface.
+
+4 Comparison of the temporal inertial prefactor for different mesh refinement levels; the black markings shown by “x” represent the peak values of the inertial prefactor, A peak.
+
+In order to validate the computational model, a side-by-side comparison is performed between the experimental images of the coaxial drops and their corresponding computational simulations. The inner fluid used is silicone oil (100cSt), with a density of 960 kg/m3, and the outer fluid used is water. The values of the inner and outer radii were 0.45 mm and 1.5 mm, respectively, with Q = 1. The interfacial tension between the silicone oil­(100cSt) and water was measured experimentally to be 0.037 N/m using the pendant drop technique. The experimental and computational images show excellent agreement, as seen in Figure , which demonstrates that the model accurately predicts the temporal evolution and thinning behavior of coaxial drops.
+
+5 Computational images (bottom) and their experimental counterparts (top) of the pinching process. The breakup time used to calculate τ is the one for the inner drop.
+
+Results and Discussion
+
+Within the confines of this study, we primarily focused on the pinching of the inner drop in the coaxial structure. We fix both the inner and the outer flow rate to Q i = 1 mL/min and Q o = 0.2 mL/min, and we use water as the inner fluid and silicone oil­(10cSt) as the outer fluid. The density of the silicone-oil­(10cSt) used is 930 kg/m3, and the interfacial tension between the water and oil is 0.023 N/m, whereas the surface tension between the oil and air is 0.0185 N/m. To understand the dynamics of this pinching, we first run numerical simulations to compare the pinching of the water inner drop in a coaxial nozzle configuration with the pinching of a single water drop dripping from a single nozzle in a liquid pool of silicone oil (10 cSt) (see configurations in Figure , sub-picture). The values of the inner radius of the coaxial nozzle and the radius of the single nozzle are kept the same to ensure comparable results. In Figure , the temporal distribution of the inertial prefactor, for nozzles with three different sizes, shows that the value of A for the inner drop in the coaxial configuration is higher in all three cases than that of the single ones, reflecting a faster thinning rate.
+
+6 Thinning of the drop filament for single and coaxial droplet cases represented as A vs τ.
+
+To have a more quantitative comparison, we represent the peak inertial prefactor, A peak, for each configuration against their nozzle sizes. As shown in Figure a, for a single nozzle, A peak, and hence the thinning rate increases with the nozzle size as long as the nozzle radius <1 mm. Above 1 mm, the pinching mechanism behaves as a local phenomenon and becomes independent of the nozzle size. Moreover, the thinning rate, represented in the form of A peak, is higher in the coaxial configuration for all cases. Additionally, as R i increases in the coaxial configuration, the thinning rate increases slowly for R i < 1 mm and increases dramatically for R i > 1 mm, as it approaches R o in size. If one were to look at the coaxial configuration, shown by Figure b, we can see that the interface of the external drop is far away from the inner drop neck, and thus, it is expected that the thinning rate should not be influenced by the external interface. However, as seen in Figure b, there are points of contact between the two fluids along their interfaces. As the external drop grows bigger in size, its weight increases, which pulls the inner drop down, leading to a faster thinning rate in comparison to the single drop pinching. This observation can be verified by comparing the inner drop in the coaxial nozzle configuration with a single drop pinching in a single-nozzle configuration. Figure c demonstrates that the inner-drop thread in the former case is more elongated than that in the latter, which is attributed to the increased pull of gravitational force.
+
+7 (a) Peak inertial prefactor as a function of the nozzle size for both single and coaxial cases (R 0 for all the coaxial cases is the same at 1.5 mm), (b) coaxial drop pinching at the moment of A peak when R i = 0.25 mm and R o = 1.5 mm, and (c) inner drop in the coaxial nozzle (thick green line) compared with a drop in single nozzle (thin black line).
+
+To understand this nonlinear thinning behavior in the coaxial configuration, we run simulations of the coaxial pinching with different inner and outer nozzle radii. Figure shows the inner drop A peak versus the dimensionless inner nozzle radius R̃i=Ri/Lc for different dimensionless outer nozzle radii R̃o=Ro/Lc , where the capillary length Lc=σio/(ρi−ρo)g and σ io is the interfacial tension between the inner and outer liquids. The general trend is that A peak increases slowly with the inner nozzle for R̃i< 0.17. Above 0.17, A peak increases rapidly with a rate dependent on the outer nozzle before it saturates at A peak = 0.8.
+
+8 Peak inertial prefactor for the inner drop as a function of the inner nozzle size for different outer nozzle sizes.
+
+For R̃i< 0.17, A peak increases slowly with R̃i independently of R̃o . This increase in A peak is attributed to a focusing effect introduced when the external interface approaches the internal one, as it can be seen in Figure . This focusing effect is an increase in the flow between the inner and outer interfaces that happens to conserve the mass as the cross-sectional area between the two interfaces decreases with the outer drop contraction. Bigger nozzle causes the drop to grow bigger before it pinches, so when the inner nozzle increases, the overall drops weight increases allowing the outer drop to stretch downward under its weight leading to more contraction of the outer drop neck on the inner drop filament (see Figure a–c). This causes the focusing effect, which increases the inner drop thinning rate. The contraction increases also the stretching of the inner drop filament before the pinching, leading to longer filament length.
+
+9 Coaxial drop pinching configurations at R̃o= 0.25 for R̃i of (a) 0.04, (b) 0.1, and (c) 0.17. The snapshots were taken at the moment of A peak.
+
+The pressure and velocity contours shown in Figure reveal how the focusing effect, produced by the outer interface when its neck is contracting, accelerates the rate of thinning. As the outer interface approaches the inner interface, the pressure in the inner neck region increases. This leads to a higher-pressure difference in the axial direction that accelerates the flow out of the neck, causing a higher thinning rate. This is evident from the velocity contour, which shows a higher axial velocity when there is more outer drop neck contraction. For R̃i = 0.1, the contraction causes a maximum pressure at the inner neck of 414 Pa, while for R̃i = 0.17, we see more contraction leading to a higher maximum pressure of 868 Pa.
+
+10 Side-by-side pressure and axial velocity distribution at the inertial prefactor peak time for (a) R̃i = 0.1 and R̃o = 0.25 and (b) R̃i = 0.17 and R̃o = 0.25.
+
+Figure reveals that for nozzle ratio R̃=R̃i/R̃o between 0.37 and 0.67, the outer neck contraction rate becomes faster than the thinning of the inner neck. Once the outer neck reaches the inner filament, a squeezing happens at a contact point, leading to the formation of a bulb. The contours in Figure show how the contraction of the outer neck causes a localized high pressure at a certain location above the minimum inner neck. This leads to a flow out of this contact location, creating a new inner neck. The bulb is then formed between this contact point and the original inner neck. Figure indicates that this localized pressure increases as R̃ increases from 0.37 to 0.67. Moreover, the distance between the contact point and the original minimum inner neck decreases as R̃ increases, leading to the formation of smaller bulbs. After the pinching of the original inner neck, the other formed inner neck is also pinched, leading to the formation of a satellite droplet trapped inside the outer drop.
+
+11 Pressure contours during outer drop contraction for (a) R̃ = 0.37, (b) R̃ = 0.57, and (c) R̃ = 0.67.
+
+Figure illustrates that, for R∼i>0.17 , the thinning rate increases very rapidly before it reaches a maximum A peak of 0.8. In this region, the contraction of the outer neck happens very close to the inner minimum neck (see Figure b), which accelerates the thinning in comparison with lower R̃i (Figure a). Figure also shows that A peak becomes dependent on R̃o when R̃i>0.17 . The thinning rate increases as R̃o decreases, mainly because the outer interface becomes closer to the inner interface during the inner pinching (see Figure c,d). For R̃ > 0.67, A peak ranges between 0.5 and 0.8, which for higher R̃ (>0.7) can surpass A peak values found in literature for single-drop pinching, such as pinching in another liquid 0.6623 and pinching in air 0.6, including the theorized value of 0.7. This reflects the significance of the coaxial nozzle configuration to enhance and increase the thinning rate. Once the maximum A peak of 0.8 is reached, at higher R̃, a resemblance between the interfaces (see Figure e,f) results in an identical thinning rate regardless of any higher R̃.
+
+12 Zooming of the coaxial drop pinching configurations for (a) R̃ = 0.67, (b) R̃ = 0.75, (c) R̃i= 1.2 and R̃o= 1.75, (d) R̃i= 1.2 and R̃o= 1.5, and (e) R̃ = 0.85 and (f) R̃ = 0.91, at the moment of A peak.
+
+Another aspect to explore is the temporal thinning nonlinear behavior. Figure shows that as the nozzle ratio increases, the temporal inertial prefactor and hence the thinning rate distribution become more complex. For R̃ < 0.4, the thinning rate increases to a peak point before it declines as the time approaches the pinching moment. This is similar to the inertial prefactor distribution in the pinching of a single drop case. However, for R̃ > 0.4, a second peak of the thinning rate starts to appear (Figure a). This second peak reflects the focusing effect from the outer drop contraction when the outer drop neck starts to approach the inner drop filament, which leads to an increase in the inner drop thinning rate again. For R̃ > 0.67, the increase in the second peak becomes significant (see Figure b) as the contraction of the external interface happens close to the minimum inner drop neck, as shown in Figure c,d.
+
+13 Temporal distribution of A for the inner drop when R̃ is between (a) 0.1 and 0.65 and (b) 0.67 and 0.93.
+
+In the coaxial configuration, we found that the thinning rate is affected not only by the nozzle radii but also by the viscosity of the outer liquid. Figure represents the peak inertial prefactor as a function of the Ohnesorge number Oh o of the outer liquid for different nozzle ratios, where Oho=μ/(ρoσLc) . Here, we used the capillary length as the characteristic length to consider viscous effects independent of the external geometry. The results in Figure show that the thinning rate of the inner drop decreases by increasing the outer liquid viscosity, in agreement with a previous study for single drop pinching in other liquids, as viscous force resists the flow, reducing the thinning rate. This viscous effect becomes less important at higher nozzle ratios, as the focusing effect of the outer interface on the inner neck becomes more dominant on the pinching process. This leads to a fast thinning with A peak around 0.8. Figure b,c reveals a linkage between the inhibiting effect of the viscosity and the proximity between the inner and outer interfaces of the coaxial drops. As the viscosity increases, the interfaces are more distanced. This means less contraction on the inner neck and hence a lower thinning rate, in agreement with the pattern found in Figure a.
+
+14 (a) Maximum inertial prefactor A peak represented for liquids with different viscosities and nozzle radii and the zooming of the coaxial drop pinching configurations for (b) Oh o = 0.006 and (c) Oh o = 0.059.
+
+From the previous discussions, we can conclude that the inner drop thinning rate is mainly affected by the proximity between the inner and the outer drop’s neck. Therefore, to reflect this, we define a characteristic parameter Δhmin=hmin⁡outer−hmin⁡inner (see Figure a), which is the difference between the inner and outer minimum neck radii. We can then use this parameter to explain the complexity of the temporal thinning behavior for the different cases. For R̃< 0.4, Δh min increases as the time to the pinching progresses (see Figure b). This means that the inner drop neck moves away from the outer drop neck, and there is no outer contraction effect on the inner thinning rate. As a result, we get the same single-peak behavior as if the inner drop is thinning in a single-nozzle configuration. However, we need to emphasize that A peak is still higher than the single case because the outer drop weight pulls the inner drop downward. For R̃ > 0.4, Δh min decreases with time as the outer drop thinning rate becomes faster (see Figure c). When Δh min becomes small enough, a focusing effect led by the outer drop neck contraction starts to appear. This causes the inner thinning rate to increase again, creating a second inertial prefactor peak. Because the inner thinning rate is now faster, Δh min starts to increase, as shown in Figure c. In cases where a bulb is formed in the inner drop filament (Figure ), multiple inertial prefactor peaks might appear, as shown in Figure d. In this case, Δh min declines with a high rate, causing the appearance of a second peak. During this second peak, the inner minimum neck thinning becomes faster. However, hmin_outer still declines causing a squeezing of the inner filament at the contact point. As a result, Δh min keeps decreasing, but at a slower rate. Once Δh min is small enough, a second focusing effect causes another inertial prefactor peak to appear. This is then followed by an increase in Δh min because the inner drop thinning becomes much faster. For R̃ > 0.77, when the outer drop neck thins next to the inner drop neck, Δh min keeps declining, causing a second peak of the inertial prefactor with a significant increase (see Figure e).
+
+15 (a) Schematic showing the temporal inertial prefactor of the inner drop and its corresponding Δh min for R̃ of (b) 0.1, (c) 0.65, (d) 0.67, and (e) 0.91.
+
+Finally, we represent A peak against its corresponding Δh̃min=Δhmin/Lc for all our data, which consider the effect of nozzle size and outer liquid viscosity. Figure shows a nice collapse of all data in a monotonic relation. In general, the thinning rate represented in A peak increases as Δh̃min decreases. This increase of A peak is slow for Δh̃min > 0.01 and rapid for 0.0002 < Δh̃min < 0.01 because the outer drop’s neck approaches the inner drop’s filament close enough to squeeze it and rapidly increase the rate of thinning. Lastly, when Δh min→ 0 (Δh̃min < 0.0002), the thinning rate becomes independent of Δh min, as shown in Figure , subgraph. The highlighted area in Figure , where 0.003 < Δh̃min < 0.01, indicates the region where satellite droplet formation occurs for a coaxial configuration. In this region, the outer drop neck squeezes the inner drop filament above the inner neck, causing the formation of a bulb that eventually pinches from both ends into a satellite droplet inside the outer drop. For very small Δh̃min below 0.003, the contraction of the outer drop neck happens very close to the inner drop neck. This does not allow for an inner drop double pinching, inhibiting the formation of a satellite droplet.
+
+16 Variation of A peak as a function of the corresponding Δh̃min for the inner drop. The section in green highlights the values of Δh̃min where encapsulated satellite droplets are produced within the outer drop after the pinching.
+
+Conclusions
+
+In conclusion, our results demonstrate that the thinning rate of the inner drop in a coaxial dripping structure is faster than that of a single drop dripping into a liquid pool. Given that we consider in this study an inner drop with low viscosity, our results are more focused on the pinching in the inertial regime. As the outer drop begins to contract, the thinning rate of the inner drop increases gradually with the inner nozzle R̃i , due to a focusing effect that increases the pressure at the neck of the inner drop, thereby accelerating fluid outflow. For R̃ > 0.67, the necking of both the inner and outer drops occurs simultaneously, and the difference between inner and outer minimum neck radii Δh min continues to decrease. This results in a rapid increase in the thinning rate with increasing R̃. Also, for R̃ > 0.67, the thinning rate decreases with the outer nozzle size before it reaches a constant A peak of 0.8. In the region of constant A peak, the interfaces of the inner and outer drops remain matched with their minimum necks located at the same axial position from the nozzle. Consequently, the thinning rate becomes independent of R̃. Outer liquid drop viscosity is found to reduce the thinning rate at low R̃. As R̃ increases, the viscosity becomes less effective, and the focusing effect from the outer drop contraction dominates, causing a thinning rate with A peak ∼ 0.8. The temporal thinning behavior is found to be governed by Δh min. For R̃<0.4, Δh min increases over time, producing a single peak in the temporal distribution of the thinning rate A. In contrast, for R̃ > 0.4, Δh min decreases with time, leading to a squeezing of the inner drop filament and the emergence of multiple peaks in the temporal profile of A. Finally, the peak thinning rate of the inner drop, denoted as A peak, is expressed as a function of Δh̃min . For 0.003<Δh̃min<0.01 , the outer drop compresses the inner filament above its minimum neck, resulting in the formation of a satellite droplet encapsulated within the outer drop. This satellite regime also corresponds to a nozzle ratio R̃ between 0.37 and 0.67. These findings provide valuable insights into the dynamics of coaxial liquid pinching and offer strategies for better controlling the process, including the prevention of satellite droplet formation during capsule generation. This has significant implications for applications in drug delivery, cosmetics, agriculture, and biomedical engineering.
+
+This work was supported by the Engineering and Physical Sciences Research Council (United Kingdom) under Grant No. EP/V04382X/1.
+
+The authors declare no competing financial interest.
+
+
+Wen N. Zhao Z. Fan B. Chen D. Men D. Wang J. Chen J. Development of Droplet Microfluidics Enabling High-Throughput Single-Cell Analysis Molecules 2016 21 7 881 10.3390/molecules21070881 27399651 PMC6272933
+Lisowski P. Zarzycki P. Microfluidic Paper-Based Analytical Devices (μPADs) and Micro Total Analysis Systems (μTAS): Development, Applications and Future Trends Chromatographia 2013 76 19–20 1201 1214 10.1007/s10337-013-2413-y 24078738 PMC3779795
+Sjostrom S. L. Bai Y. Huang M. Liu Z. Nielsen J. Joensson H. N. Andersson Svahn H. High-Throughput Screening for Industrial Enzyme Production Hosts by Droplet Microfluidics Lab Chip 2014 14 4 806 813 10.1039/c3lc51202a 24366236
+Erni P. Dardelle G. Sillick M. Wong K. Beaussoubre P. Fieber W. Turning Coacervates into Biohybrid Glass: Core/Shell Capsules Formed by Silica Precipitation in Protein/Polysaccharide Scaffolds Angew. Chem. 2013 125 39 10524 10528 10.1002/ange.201303489 23881535
+Ma Q. Cao J. Gao Y. Han S. Liang Y. Zhang T. Wang X. Sun Y. Microfluidic-Mediated Nano-Drug Delivery Systems: From Fundamentals to Fabrication for Advanced Therapeutic Applications Nanoscale 2020 12 29 15512 15527 10.1039/D0NR02397C 32441718
+Riahi R. Tamayol A. Shaegh S. Ghaemmaghami A. Dokmeci M. Khademhosseini A. Microfluidics for Advanced Drug Delivery Systems Curr. Opin. Chem. Eng. 2015 7 101 112 10.1016/j.coche.2014.12.001 31692947 PMC6830738
+Li X. Jiang X. Microfluidics for Producing Poly­(lactic-co-glycolic acid)-Based Pharmaceutical Nanoparticles Adv. Drug Delivery Rev. 2018 128 101 114 10.1016/j.addr.2017.12.015 29277543
+Aliseda A. Hopfinger E. Lasheras J. Kremer D. Berchielli A. Connolly E. Atomization of Viscous and Non-Newtonian Liquids by a Coaxial, High-Speed Gas Jet: Experiments and Droplet Size Modelling Int. J. Multiphase Flow 2008 34 2 161 175 10.1016/j.ijmultiphaseflow.2007.09.003
+Yeo Y. Bellas E. Firestone W. Langer R. Kohane D. Complex Coacervates for Thermally Sensitive Controlled Release of Flavor Compounds J. Agric. Food Chem. 2005 53 19 7518 7525 10.1021/jf0507947 16159181
+Ismail A. S. Goodwin G. R. Castrejon-Pita J. R. Noyce A. J. Azevedo H. S. A Novel Capsule-Based Smell Test Fabricated via Coaxial Dripping J. R. Soc. Interface 2021 18 20210039 10.1098/rsif.2021.0039 33906383 PMC8086910
+Wang X. Zhu J. Shao T. Luo X. Zhang L. Production of Highly Monodisperse Millimeter-Sized Double-Emulsion Droplets in a Coaxial Capillary Device Chem. Eng. Technol. 2019 42 6 1330 1340 10.1002/ceat.201800040
+Berkland C. Kim K. Pack D. W. Fabrication of PLG Microspheres with Precisely Controlled and Monodisperse Size Distributions J. Controlled Release 2001 73 59 10.1016/S0168-3659(01)00289-9 11337060
+Castrejón-Pita J. Castrejón-Pita A. Thete S. Sambath K. Hutchings I. Hinch J. Lister J. Basaran O. Plethora of Transitions during Breakup of Liquid Filaments Proc. Natl. Acad. Sci. U. S. A. 2015 112 15 4582 4587 10.1073/pnas.1418541112 25825761 PMC4403208
+Castrejón-Pita A. A. Castrejón-Pita J. R. Hutchings I. M. Breakup of Liquid Filaments Phys. Rev. Lett. 2012 108 074506 10.1103/PhysRevLett.108.074506 22401212
+Castrejón-Pita J. R. Castrejón-Pita A. A. Hinch E. J. Lister J. R. Hutchings I. M. Self-Similar Breakup of Near-Inviscid Liquids Phys. Rev. E:Stat., Nonlinear, Soft Matter Phys. 2012 86 1 015301 10.1103/physreve.86.015301 23005482
+Zhang Y. Hu G. Liu Y. Wang J. Yang G. Li D. Suppression and Utilization of Satellite Droplets for Inkjet Printing: A Review Processes 2022 10 5 932 10.3390/pr10050932
+Taraki N. Ismail A. S. The role of geometry on controlled cavity collapse and top jet drop Phys. Fluids 2022 34 7 072103 10.1063/5.0097090
+Kovalchuk N. M. Jenkinson H. Miller R. Simmons M. J. H. Effect of Soluble Surfactants on Pinch-Off of Moderately Viscous Drops and Satellite Size J. Colloid Interface Sci. 2018 516 182 10.1016/j.jcis.2018.01.039 29408104
+Lagarde A. Josserand C. Protière S. Oscillating Path between Self-Similarities in Liquid Pinch-Off Proc. Natl. Acad. Sci. U. S. A. 2018 115 12371 10.1073/pnas.1814242115 30455302 PMC6298122
+Papageorgiou D. T. On the Breakup of Viscous Liquid Threads Phys. Fluids 1995 7 1529 10.1063/1.868540
+Eggers J. Villermaux E. Physics of Liquid Jets Rep. Prog. Phys. 2008 71 036601 10.1088/0034-4885/71/3/036601
+Deblais A. Herrada M. A. Hauner I. Velikov K. P. van Roon T. Kellay H. Eggers J. Bonn D. Viscous Effects on Inertial Drop Formation Phys. Rev. Lett. 2018 121 254501 10.1103/PhysRevLett.121.254501 30608844
+Ismail A. S. Taraki N. Liquid Pinching Dynamics in an Inertial Transitioning Regime Phys. Rev. Res. 2024 6 043131 10.1103/PhysRevResearch.6.043131
+Li D. Cao Y. Huang B. Wu X. Hu G. Wang X. Liu Y. Zhang Y. Fragmentation of Inviscid Liquid and Destination of Satellite Droplets Phys. Fluids 2022 34 8 084105 10.1063/5.0102220
+Popinet S. An Accurate Adaptive Solver for Surface-Tension-Driven Interfacial Flows J. Comput. Phys. 2009 228 16 5838 5866 10.1016/j.jcp.2009.04.042
+Popinet S. Gerris a tree-based adaptive solver for the incompressible Euler equations in complex geometries J. Comput. Phys. 2003 190 572 600 10.1016/S0021-9991(03)00298-5
+Li Y. Sprittles J. E. Capillary Breakup of a Liquid Bridge: Identifying Regimes and Transitions J. Fluid Mech. 2016 797 29 10.1017/jfm.2016.276
+Majumder A. Ghosh D. Kumar Das P. Dynamics of Drop Formation, Growth and Pinching Phenomena from a Submerged Nozzle Chem. Eng. Sci. 2021 245 116808 10.1016/j.ces.2021.116808
diff --git a/corpus/psychology/text/6a7ebe8e689c1a72.txt b/corpus/psychology/text/6a7ebe8e689c1a72.txt
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@@ -0,0 +1,3 @@
+The Impact of Social Perception on Message Perception
+
+Language processing research shows that listeners integrate linguistic content with contextual information early in interpretation. This context includes both world knowledge and beliefs about the speaker, which work together to jointly shape meaning resolution. Using a noisy-channel model of sentence processing, the current study examines how speaker information and language ideologies might affect listeners’ interpretations of anomalous sentences.  Specifically, this study compares interpretations of implausible sentences produced in Mainstream American English (MAE) and African American English (AAE), asking whether speaker voice socially shapes the expectations listeners bring to meaning resolution. Results showed that the MAE speaker was interpreted literally more often than the AAE speaker, which was most pronounced among White listeners. These findings suggest that social information and language ideologies shape both expectations about speakers and expectations about possible meanings, supporting further study of pragmatic inference as a sociolinguistic variable.
diff --git a/corpus/psychology/text/6c16a685660c8680.txt b/corpus/psychology/text/6c16a685660c8680.txt
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--- /dev/null
+++ b/corpus/psychology/text/6c16a685660c8680.txt
@@ -0,0 +1,61 @@
+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Occup Ther Int
+Journal ID: Occup Ther Int
+NLM Journal ID: 9433361
+Journal ID: OTI
+
+Occupational Therapy International
+
+ISSN: 0966-7903
+EISSN: 1557-0703
+Publisher: Wiley
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC10447129
+PMID: 37621370
+DOI: 10.1155/2023/9862036
+Article version: 1
+Subjects: Retraction
+
+Retracted: Animation Narrative on Stress Relief and Psychological Cognitive Development in Adolescents
+
+International Occupational Therapy oti@hindawi.com
+
+Publication date: 2023
+Electronic publication date: 2023 Aug 16
+Volume: 2023
+Electronic Location ID: 9862036
+Received 2023 Aug 15; Accepted 2023 Aug 15
+Copyright: Copyright © 2023 Occupational Therapy International.
+Copyright year: 2023
+License: This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Retraction of: Animation Narrative on Stress Relief and Psychological Cognitive Development in Adolescents 2022 2 9 2022 1111488 Occupational Therapy International 10.1155/2022/1111488 PMC9463020 36101670
+
+Ÿ==============================Ÿ
+This article has been retracted by Hindawi following an investigation undertaken by the publisher [1]. This investigation has uncovered evidence of one or more of the following indicators of systematic manipulation of the publication process: Discrepancies in scope
+
+Discrepancies in the description of the research reported
+
+Discrepancies between the availability of data and the research described
+
+Inappropriate citations
+
+Incoherent, meaningless and/or irrelevant content included in the article
+
+Peer-review manipulation
+
+The presence of these indicators undermines our confidence in the integrity of the article's content and we cannot, therefore, vouch for its reliability. Please note that this notice is intended solely to alert readers that the content of this article is unreliable. We have not investigated whether authors were aware of or involved in the systematic manipulation of the publication process.
+
+Wiley and Hindawi regrets that the usual quality checks did not identify these issues before publication and have since put additional measures in place to safeguard research integrity.
+
+We wish to credit our own Research Integrity and Research Publishing teams and anonymous and named external researchers and research integrity experts for contributing to this investigation.
+
+The corresponding author, as the representative of all authors, has been given the opportunity to register their agreement or disagreement to this retraction. We have kept a record of any response received.
+
+
+1 Jiang Q. Ma L. Yue M. Animation Narrative on Stress Relief and Psychological Cognitive Development in Adolescents Occupational Therapy International 2022 2022 10 10.1155/2022/1111488 1111488 36101670 PMC9463020
diff --git a/corpus/psychology/text/7181be53d01b0cb2.txt b/corpus/psychology/text/7181be53d01b0cb2.txt
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index 0000000000000000000000000000000000000000..c27fa43794805f8b72995d242f0ec50afd977752
--- /dev/null
+++ b/corpus/psychology/text/7181be53d01b0cb2.txt
@@ -0,0 +1,370 @@
+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Fluids Barriers CNS
+Journal ID: Fluids Barriers CNS
+NLM Journal ID: 101553157
+
+Fluids and Barriers of the CNS
+
+EISSN: 2045-8118
+Publisher: BMC
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC13525656
+PMID: 42665818
+DOI: 10.1186/s12987-026-00865-8
+Article ID: 865
+Article version: 1
+Subjects: Research
+
+Brain parenchyma deformation and strain in patients with spontaneous intracranial hypotension
+
+http://orcid.org/0000-0002-8250-5883 El Rahal Amir 1 2
+http://orcid.org/0000-0002-7687-6098 Beck Jürgen j.beck@uniklinik-freiburg.de
+1 2
+http://orcid.org/0000-0003-1468-3634 Wolf Katharina 1 2
+http://orcid.org/0000-0001-7274-519X Volz Florian 1 2
+http://orcid.org/0009-0007-0076-3170 Overstijns Manou 1 2
+http://orcid.org/0000-0003-0555-7863 Lützen Niklas 2 3
+http://orcid.org/0009-0009-5797-6825 Zander Charlotte 2 4
+http://orcid.org/0000-0001-7264-4807 Urbach Horst 2 3
+http://orcid.org/0000-0002-6596-456X Scheffler Pierre 1 2
+1 https://ror.org/0245cg223 grid.5963.9 0000 0004 0491 7203 Department of Neurosurgery, Medical Center–University of Freiburg, Breisacher-Str. 64, 79106 Freiburg im Breisgau, Germany
+2 https://ror.org/0245cg223 grid.5963.9 0000 0004 0491 7203 German CSF Center, Medical Center–University of Freiburg, Freiburg, Germany
+3 https://ror.org/0245cg223 grid.5963.9 0000 0004 0491 7203 Department of Diagnostic and Interventional Neuroradiology, Medical Center–University of Freiburg, Freiburg, Germany
+4 https://ror.org/0245cg223 grid.5963.9 0000 0004 0491 7203 Department of Diagnostic and Interventional Radiology, Medical Center–University of Freiburg, Freiburg, Germany
+Electronic publication date: 2026 Aug 27
+Publication date: 2026
+Volume: 23
+Electronic Location ID: 105
+Received 2026 Jun 1; Accepted 2026 Aug 17
+Copyright: © The Author(s) 2026
+Copyright year: 2026
+License: Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Keywords: Spontaneous intracranial hypotension, SIH, Brain sagging, Brain shift, AI, Convolutional neural network, Surgical closure, CSF Leak, CSF-venous fistula, Neurosurgery
+
+Funding: Universitätsklinikum Freiburg (8975) Open Access funding enabled and organized by Projekt DEAL.
+
+issue-copyright-statement: © BioMed Central Ltd., part of Springer Nature 2026
+
+Ÿ==============================Ÿ
+Background
+
+Spontaneous intracranial hypotension (SIH) is mainly associated with orthostatic headache but can also cause cognitive impairment, with symptoms mimicking behavioral-type frontotemporal dementia in severe cases. SIH is caused by a spinal cerebrospinal fluid (CSF) leak and can lead to brain sagging. The specific brain regions affected by this motion, their deformation, and the magnitude of the associated mechanical strain have not been quantitatively characterized. We investigated whether brain MRI in patients with SIH shows quantifiable strain, expansion, and compression of brain structures by comparing images before and after surgical occlusion of a spinal leak.
+
+Methods
+
+We performed a retrospective analysis of 96 patients with SIH who underwent surgical closure of a spinal CSF leak. We performed AI-assisted diffeomorphic registration of pre- and postoperative MRI. From the resulting displacement maps, we calculated the Jacobian determinant as an indicator of expansion and contraction, and the von Mises equivalent deviatoric strain as an indicator of distortion and shearing in brain regions. Results were compared with 61 healthy adults scanned twice over a comparable interval, and correlated with perioperative headache, quality-of-life and cognitive scores.
+
+Results
+
+Ventricles and transverse sinuses showed relevant perioperative expansion and contraction, respectively. Beyond these expected volumetric changes, significant deviatoric strain was observed in temporomesial and frontal structures, including the temporal poles (right/ left: 8.6/ 8.7%), hippocampus (9.0/ 9.8%), and basal forebrain (9.9/ 9.8%) (p < 0.001 for all), despite only moderate volumetric change in these regions. Deformation substantially exceeded that of healthy controls. Whole-brain strain showed a modest positive association with perioperative improvement in headache burden, whereas analyses of cognitive outcome were underpowered.
+
+Conclusion
+
+SIH is associated with quantifiable regional brain deformation resulting in region-specific mechanical strain. Elevated strain in fronto-limbic and temporomesial regions, implicated in behavioral and cognitive regulation, suggests a network-level mechanical effect that may contribute to the clinical presentation observed in severe SIH.
+
+Supplementary Information
+
+The online version contains supplementary material available at https://doi.org/10.1186/s12987-026-00865-8.
+
+Background
+
+Spontaneous intracranial hypotension (SIH) is an underdiagnosed condition caused by a cerebrospinal fluid (CSF) leak along the spine [1]. While orthostatic headache is the hallmark symptom, SIH can produce a wide spectrum of manifestations, including tinnitus, diplopia, and cognitive or behavioral changes. In severe and prolonged cases, patients may develop neuropsychiatric symptoms that closely mimic the behavioral variant of frontotemporal dementia (bvFTD) [2–5]. This overlap is increasingly recognized and has given rise to the concept of “spinal dementia” [6–8].
+
+Magnetic resonance imaging (MRI) is central to the diagnosis and follow-up of SIH. Spinal CSF leaks are associated with characteristic qualitative brain MRI findings, commonly termed “brain sagging” [9]. Some of these imaging features have been aggregated into an SIH-specific scoring system, including reduced CSF cistern size, venous engorgement, pachymeningeal enhancement, and subdural effusions [10]. However, these changes remain mainly descriptive, and importantly, brain sagging represents not only simple, uniform downward displacement of intracranial structures as a whole, but also deformation of the brain parenchyma and surrounding structures. Such deformation may include both volumetric redistribution and distortional strain, reflecting mechanical stress that may vary between anatomical regions. To date, it remains unknown which specific regions bear the greatest mechanical burden and whether that burden is distributed uniformly or concentrates in functionally eloquent networks. Advances in artificial intelligence now enable automated, reproducible quantitative analysis of structural MRI, allowing for objective, voxel-wise measurement of brain deformation. A quantitative assessment of strain across functionally connected brain areas could help explain the diversity of clinical manifestations in SIH, including the cognitive and behavioral changes related to CSF leaks, and enable development of quantitative deformation biomarkers.
+
+In this study, we aimed to investigate and characterize regional patterns of mechanical deformation and strain in specific brain regions in SIH patients before and after surgical closure of a spinal leak.
+
+Methods
+
+Ethics approval
+
+Our study protocol was approved by the local ethics committee (IDs: 22-1512-S1-retro/ 24-1296-S1-retro); the study was conducted in accordance with good clinical practice.
+
+Participants
+
+For this single-center study from a tertiary referral center, we used a local MRI dataset of patients who met the ICHD-3 criteria for SIH and underwent surgery for a spinal CSF leak between April 2018 and December 2024 at our center, and who had adequate pre- and postoperative MRI imaging [11]. Patients were required to have pre- and postoperative brain MRI scans with isotropic contrast-enhanced T1-weighted sequences at least 1 mm in resolution. Preoperative imaging had to be acquired within 12 months prior to surgery; postoperative imaging was required within 1–12 months after surgery, preferably at the 3-month follow-up. If multiple scans were available, the most recent preoperative and the postoperative scan closest to follow-up were selected. MRI images were also screened to exclude those showing subdural effusions or significant metal artifacts.
+
+As a control group, we used the Beijing Normal University 2 (BNU 2) dataset, a publicly available dataset published by the Consortium for Reliability and Reproducibility (CoRR) [12]. The dataset includes 61 healthy adults between 19 and 23 years old who underwent two T1 MRI scans at least three months apart (103–189 days).
+
+Image processing
+
+Image processing was automated with Python scripts. MRI data were converted from DICOM to NIfTI format. Automated segmentation of 155 brain regions and CSF spaces, as described by the Desikan-Killiany-Tourville protocol, was performed using AssemblyNet, followed by visual verification of all segmentations by two authors (PS, AER) [13, 14]. Diffeomorphic registration between pre- and postoperative scans was performed with SynthMorph to generate a voxel-wise displacement field \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\left(\mathbf{u}\right)$$\end{document} [15]. The displacement field was then used to calculate the Jacobian determinant and the von Mises equivalent strain; the interpretation of these values is illustrated in Fig. 1.
+
+Fig. 1 Illustration showing interpretations of the values generated for the study; the black spheres represent individual voxels within a grid. The displacement map is generated through diffeomorphic registration of pre- and postoperative images and shows voxel-wise translation movements in three-dimensional space. The displacement map is used to calculate the Jacobian determinant, for which values below 1 indicate local compression and values above 1 indicate local expansion. The von Mises equivalent strain indicates any deviatoric strain irrespective of expansion or compression
+
+Quantification of expansion and compression
+
+Local changes in tissue volume were quantified using the Jacobian determinant ( J), a standard measure of local volume change in tensor-based morphometry [16, 17]. We first defined the deformation gradient tensor as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\mathbf{F}=\mathbf{I}+\:\nabla\:\mathbf{u}$$\end{document} where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\mathbf{I}$$\end{document} is the identity matrix and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\nabla\:\mathbf{u}$$\end{document} is the gradient of the displacement field. The determinant of this matrix was calculated at each voxel:\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:J\:=\mathrm{d}\mathrm{e}\mathrm{t}\left(\mathbf{F}\right)$$\end{document}
+
+A value of  J>1 indicates local volumetric expansion, while  J < 1 indicates local compression. For example,  J=1.1 would indicate a 10% local volume expansion.
+
+Quantification of deviatoric strain
+
+The Jacobian determinant captures changes in volume but not changes in shape. To quantify the shape-distorting deformation, we first calculated the Green-Lagrange strain tensor \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\mathbf{E}$$\end{document}. This measure ensures rotational invariance, meaning that global head tilting does not introduce artificial strain values:\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\mathbf{E}=\frac{1}{2}({\mathbf{F}}^{\mathrm{T}}\mathbf{F}-\mathbf{I})$$\end{document}
+
+At each voxel, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\mathbf{E}\:$$\end{document} is a symmetric 3 × 3 tensor that carries the volumetric component in the sum of its diagonal (the trace, denoted \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\mathrm{t}\mathrm{r}$$\end{document}). We then isolate shape change by taking the deviatoric strain \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\mathrm{e}$$\end{document}:\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\mathrm{e}=\mathbf{E}-\frac{1}{3}\mathrm{t}\mathrm{r}\left(\mathbf{E}\right)\mathbf{I}$$\end{document}
+
+Consequently, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\mathrm{e}$$\end{document} carries no information about expansion or compression, only about shape change. We summarized \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\mathrm{e}$$\end{document} into a single per-voxel distortion value using the von Mises equivalent strain \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\epsilon\:}_{vm}$$\end{document}, which we defined in direct analogy to the von Mises stress [18, 19]:\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\epsilon\:}_{vm}=\:\sqrt{\frac{2}{3}\mathrm{e}:\mathrm{e}}$$\end{document}
+
+Here, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\mathrm{e}:\mathrm{e}$$\end{document} denotes double tensor contraction and the factor \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:\frac{2}{3}$$\end{document} normalizes \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\epsilon\:}_{vm}$$\end{document} to equal the axial strain under volume-preserving uniaxial deformation; as a result, for example, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\epsilon\:}_{vm}=0.1$$\end{document} would indicate local shape change comparable to a 10% stretch in one direction at constant volume.
+
+ J and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\epsilon\:}_{vm}$$\end{document} were used to generate color-coded heatmaps on 3D brain reconstructions to identify regions of maximum mechanical distortion. Regional values were extracted by overlaying the maps with the segmented brain structures.
+
+Clinical correlation
+
+Electronic medical records of all included patients were checked for pre- and postoperative clinical evaluations and scores, including Headache Impact Test (HIT-6), which measures the impact of headaches, EuroQol five dimension five-level (EQ-5D-5 L) including the visual analogue scale-based evaluation (EQ-VAS), which measures health-related quality of life, and Montreal Cognitive Assessment (MoCA), to screen for cognitive deficits [20–22]. Clinical scores were correlated with whole-brain von Mises equivalent strain and per-region Jacobian determinant and von Mises equivalent strain in all patients in which perioperative scores were available.
+
+Statistics
+
+For each brain region, voxel-wise Jacobian determinant and von Mises equivalent strain values were averaged across patients.
+
+For the Jacobian determinant, deviations from unity were assessed using two-tailed one-sample t-tests. As the von Mises equivalent strain is represented by a non-negative number, testing regional means against zero is uninformative. We therefore employed a within-patient normalization approach: for each patient, we calculated the mean and standard deviation of the average strains of all regions. We then calculated the within-patient z-score for each region by subtracting the mean and dividing by the standard deviation (SD) of all regions. To identify regions with significant distortional strain, the resulting z-scores were tested for positive deviation from zero using one-tailed one-sample t-tests. Because within-patient z-scores use a dispersion estimate that extreme regions can inflate, the regional analysis was repeated under robust median/scaled median absolute deviation (MAD) normalization with a one-tailed t-test, with mean/SD normalization and a Wilcoxon signed-rank test, and with median/MAD normalization and a Wilcoxon signed-rank test. The per-region statistical comparisons between SIH group and control group were performed with Welch’s t-test. For the clinical correlation, we calculated the Spearman rank correlation coefficient (rs) adjusted for age, sex and the corresponding preoperative baseline score, and reported it with 95% confidence intervals (CI).
+
+To control for multiple comparisons across regions, p-values were adjusted using the Benjamini–Hochberg false discovery rate (FDR) procedure. P-values < 0.05 were considered statistically significant.
+
+Results
+
+Patient characteristics
+
+A total of 96 patients with adequate MRIs were included in the deformation and strain analysis. Patients were on average 43.4 ± 11.5 years old, with 62.5% female. Median time between preoperative MRI and surgery was 6 days (interquartile range/IQR: 4–16); median time between surgery and postoperative MRI was 98 days (IQR: 78–123), and median time between pre- and postoperative MRI was 112 days (IQR: 94–147).
+
+Global deformation patterns of the Jacobian determinant
+
+The spatial distribution of volumetric changes derived from the Jacobian determinants across patients is illustrated in Fig. 2, with selected representative coronal and axial planes shown and compared to the control group in Fig. 3. The most pronounced expansion was seen around the lateral ventricles and to a lesser degree in apical and lateral frontobasal cortical regions. Conversely, the most prominent compression was found along the transverse and straight venous sinuses. Compared to the SIH group, the control group showed no relevant tissue expansion or contraction.
+
+Fig. 2 Illustration of the Jacobian determinant from different perspectives. The mode of all included volumetric brain models is represented as a grey, transparent wire mesh. Regions with a Jacobian determinant > 1 (representing expansion) are colored in red; regions with a Jacobian determinant < 1 (representing compression) are colored in blue. For illustrative purposes, only values above the 99th percentile (deviation from unity) are shown, and less extreme values are rendered with increasing transparency
+
+Fig. 3 Illustration of the Jacobian determinant in the SIH and control groups in selected representative planes: a coronal view of the average of all included SIH brain models with a section of the lateral and third ventricles, and an axial view at the level of the transverse sinuses. Expanding areas are colored red, compressed areas are colored blue. Orientation is indicated by letters: anterior (A), posterior (P), right (R) and left (L)
+
+Distribution of distortional strain
+
+A visual representation of the average distortional strain and its spatial distribution is shown in Fig. 4, with selected representative coronal and axial planes shown and compared to the control group in Fig. 5. The highest distortion was observed in the ventricular regions, mostly along the lateral ventricular walls. Here, high distortional strain coincided with pronounced volumetric expansion. This co-occurrence is mechanically expected at a fluid-filled cavity where the deformation field at the ventricular margin necessarily combines volume change with shape change. Relevant distortion was also observed along the transverse and superior sagittal sinuses, where it likewise accompanies the volumetric compression described above. Distortional strain was further increased in the frontobasal and temporomesial brain regions, in particular in the ventromedial prefrontal cortex, orbitofrontal cortex, temporal poles, hippocampal and parahippocampal regions, and the amygdala. In contrast to the ventricles and venous sinuses, these regions exhibited substantial distortional strain despite only moderate volumetric changes (Jacobian determinant = 1.021–1.067), indicating that mechanical deformation of the brain parenchyma is not limited to areas of maximal volumetric expansion. Compared to the SIH group, the control group showed no relevant distortional strain.
+
+Fig. 4 Illustration of the von Mises equivalent strain from different perspectives. The mode of all included volumetric brain models is represented as a grey, transparent wire mesh. Regions with relevant strain are colored with intensity based on the viridis color scale. For illustrative purposes, only values above the 95th percentile (deviation from zero) are shown, and lower values are rendered with increasing transparency
+
+Fig. 5 Illustration of the von Mises equivalent strain in the SIH and control groups in selected representative planes: a coronal view of the average of all included SIH brain models with a section of the lateral and third ventricles, and an axial view at the level of the transverse sinuses. Regions with relevant strain are colored with intensity based on the viridis color scale. Orientation is indicated by letters: anterior (A), posterior (P), right (R) and left (L)
+
+Regional patterns of volumetric change and mechanical strain
+
+Regional averages of the Jacobian determinant and distortional strain for major brain regions are summarized in Tables 1 and 2 respectively, with the complete set of segmented regions provided in Supplement 1 and Supplement 2, respectively. Consistent with the global maps, most regions demonstrated statistically significant volumetric expansion following surgical leak closure. The largest Jacobian determinant changes were observed in ventricular regions (right lateral ventricle: 1.174, left lateral ventricle: 1.176), with smaller changes toward the cortical surface. Distortional strain was very high around the lateral (right: 0.127, left: 0.130) and third (0.126) ventricles; on average, none of the major lobes showed significantly elevated strain. In direct comparison with the control group, except for the brainstem, all regions showed statistically significant expansion or compression.
+
+Table 1 Overview of results for the Jacobian determinant for all major brain regions, with means and standard deviations (SD)
+
+Region	 J- Mean	 J- SD	P-Value	Significant	
+Brainstem	1.001	0.037	0.696	No	
+Right cerebellum	1.026	0.060	5.86 * 10− 5	Yes	
+Left cerebellum	1.021	0.053	2.24 * 10− 4	Yes	
+Right frontal lobe	1.035	0.050	8.15 * 10− 10	Yes	
+Left frontal lobe	1.032	0.049	7.42 * 10− 9	Yes	
+Right temporal lobe	1.024	0.040	5.09 * 10− 8	Yes	
+Left temporal lobe	1.026	0.042	1.62 * 10− 8	Yes	
+Right parietal lobe	1.041	0.053	2.75 * 10− 11	Yes	
+Left parietal lobe	1.037	0.052	2.96 * 10− 10	Yes	
+Right occipital lobe	1.026	0.045	1.57 * 10− 7	Yes	
+Left occipital lobe	1.025	0.044	1.96 * 10− 7	Yes	
+3rd ventricle	1.120	0.164	1.57 * 10− 10	Yes	
+4th ventricle	1.070	0.121	1.81 * 10− 7	Yes	
+Right lateral ventricle	1.174	0.276	1.75 * 10− 8	Yes	
+Left lateral ventricle	1.176	0.262	2.35 * 10− 9	Yes	
+P-values are unadjusted; significance is determined after FDR correction
+
+Table 2 Overview of results for the von Mises equivalent strain for all major brain regions, with means and standard deviations (SD)
+
+Region	\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\epsilon\:}_{vm}$$\end{document}- Mean	\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\:{\epsilon\:}_{vm}$$\end{document}- SD	P-Value	Significant	
+Brainstem	0.069	0.031	> 0.999	No	
+Right cerebellum	0.078	0.033	0.992	No	
+Left cerebellum	0.076	0.032	> 0.999	No	
+Right frontal lobe	0.074	0.027	> 0.999	No	
+Left frontal lobe	0.074	0.027	> 0.999	No	
+Right temporal lobe	0.072	0.023	> 0.999	No	
+Left temporal lobe	0.072	0.024	> 0.999	No	
+Right parietal lobe	0.071	0.028	> 0.999	No	
+Left parietal lobe	0.070	0.027	> 0.999	No	
+Right occipital lobe	0.078	0.030	0.989	No	
+Left occipital lobe	0.077	0.029	0.999	No	
+3rd ventricle	0.126	0.085	4.39 * 10− 14	Yes	
+4th ventricle	0.081	0.038	0.818	No	
+Right lateral ventricle	0.127	0.102	4.91 * 10− 9	Yes	
+Left lateral ventricle	0.130	0.100	1.41 * 10− 10	Yes	
+P-values are unadjusted; significance is determined after FDR correction
+
+Significantly elevated distortional strain was consistently observed across fronto-limbic and temporo-mesial structures (Fig. 6). These included the subcallosal area (mean strain = 0.095/ 0.094 on the right/ left), basal forebrain (0.099/ 0.098), hippocampus (0.090/ 0.098), parahippocampal region (0.090/ 0.091), amygdala (0.089/ 0.090), and temporal pole (0.086/ 0.087) (all p < 0.001). Similar values were also observed in the ventromedial prefrontal cortex and orbitofrontal cortex (0.073–0.090). All regions significant in the primary analysis remained significant under robust normalization, and compared to the healthy control group, all regions showed elevated strain; additional statistical testing is detailed in Supplement 2.
+
+Fig. 6 Bar plot showing the von Mises equivalent strain for fronto-limbic and temporo-mesial structures on the left and right. Asterisks indicate regions with significantly elevated strain after correction for multiple testing
+
+Clinical correlation
+
+Clinical correlation between whole-brain von Mises equivalent strain and clinical scores are shown in Fig. 7; a summary of clinical score distribution and detailed per-region correlation analysis can be found in Supplement 3. We found a modest association between whole-brain strain and improvement in HIT-6 scores (rs =0.25; CI: 0.00–0.47; p = 0.046); other clinical scores showed comparable effect sizes, but with markedly wider confidence intervals for the MoCA score correlation. In the per-region analysis, after FDR correction, none of the brain regions showed a statistically significant correlation with any clinical score. The highest correlation between strain and perioperative MoCA improvement was found in the left temporal pole (rs =0.40; CI: 0.12–0.65; p = 0.037), but the correlation was not significant after correction for multiple testing.
+
+Fig. 7 Whole-brain von Mises equivalent strain across the perioperative interval versus clinical improvement. Annotated coefficients (rs) are partial Spearman rank correlations adjusted for age, sex and the corresponding baseline score, with 95% confidence intervals. Regression lines are unadjusted Theil–Sen fits shown for visualisation only
+
+Discussion
+
+This study provides a quantitative assessment of brain tissue deformation in spontaneous intracranial hypotension (SIH). We demonstrate that SIH is not only associated with “brain sagging” and measurable volumetric changes, but also with significant mechanical strain. Hot spots with elevated mechanical strain turned out to be in the frontobasal and temporomesial brain regions, independent of volumetric redistribution. Whether these intriguing findings offer a mechanistic explanation for the clinical manifestations of patients with SIH needs further study.
+
+The strain analysis revealed a spatial organization with pronounced strain in the ventromedial prefrontal cortex and mesial temporal lobes. When visualized across the brain, these regions form a spatially coherent pattern extending from the temporomesial structures toward the ventromedial prefrontal and orbitofrontal cortices. This distribution corresponds to the anatomical organization of fronto-limbic networks that connect the hippocampus, amygdala, basal forebrain, and medial prefrontal cortex [23–25].
+
+These structures constitute the core of fronto-limbic circuits supporting behavioral and executive control, emotional regulation, cognition, memory, and affective processing. They are central to the pathophysiology of bvFTD and related syndromes [26–28]. Previous reports of “brain sagging dementia” or “spinal dementia” have been descriptive, highlighting symptomatic similarities and radiological signs of downward brain displacement. Our results extend these observations by providing quantitative data hinting that mechanical stress and SIH-related symptoms like cognitive and behavioral changes may relate to region-specific mechanical distortion within cognition-relevant networks. Emerging hypotheses, e.g., that chronic, region-specific strain may contribute to potential axonal injury, synaptic dysfunction, and possible structural neurodegeneration, require further investigation. The prompt improvement in some patients after closure of a spinal leak would favor the view that the observed deformation pattern constitutes a mechanically induced network dysfunction rather than irreversible tissue loss. Distortional strain may transiently alter the efficiency of connectivity within fronto-limbic networks and is consistent with the reversibility of cognitive symptoms after leak closure [3]. On the other hand, it might be worthwhile to analyze whether residual symptoms could be related to more permanent mechanically induced tissue dysfunction or damage.
+
+Similar concepts have been proposed in other neurological disorders where mechanical forces play a role, such as traumatic brain injury and chronic traumatic encephalopathy, supporting the plausibility of a strain-mediated pathogenic mechanism [29–31].
+
+Our analysis based on the Jacobian determinant demonstrated structured expansion and compression patterns following surgical leak closure (e.g., ependymal and parenchymal re-expansion adjacent to the ventricles and compression of brain parenchyma along venous sinuses). Analogous volumetric changes have already been demonstrated by Zander et al. and Mehan et al. using manual measurements and align with the re-expansion of CSF spaces and the normalization of venous engorgement seen on brain MRIs [32, 33].
+
+Our Jacobian determinant maps extend these observations from compartment-level volume measurements to a voxel-wise spatial distribution, showing where within the brain expansion and compression occur. A comparable regional distinction has been described using magnetic resonance elastography in normal-pressure hydrocephalus, where periventricular stiffness changes partly normalize after shunting [34, 35], indicating that tissue immediately around the ventricles responds to volume change differently from the rest of the parenchyma — the same regional contrast we observed in our strain maps.
+
+Functional imaging studies point in the same direction. Perfusion imaging in SIH is limited to case observations, in which SPECT showed reduced cerebral perfusion in the sagging brain that improved after epidural patching, in parallel with cognitive recovery [36]. Functional MRI is more informative: imaging before and one month after leak closure, Amemiya et al. found abnormal activity in the bilateral orbitofrontal and medial frontal cortices with altered default-mode network activity, normalizing as working memory recovered [37]. This independently derived abnormality involves the same orbitofrontal and ventromedial prefrontal territory in which we measured disproportionate strain, suggesting a mechanical substrate for a reversible functional deficit. Multimodal imaging in frontotemporal brain sagging syndrome likewise implicates altered frontal connectivity rather than atrophy [38].
+
+Although direct comparisons are limited, earlier imaging studies of SIH have emphasized global brain sagging and secondary signs such as venous engorgement, subdural collections, and reduced cisternal spaces – all visible with the naked eye. Dobrocky et al. introduced an MRI-based SIH score that captured these features but did not quantify local deformation [10]. Our results may provide a missing link by showing that deformation is not uniformly distributed but concentrated in regions implicated in higher cognitive and behavioral control.
+
+Concerning the correlation with clinical symptoms, we found a modest association between perioperative headache improvement as measured by the HIT-6 score and increased whole-brain von Mises equivalent strain. The correlation is only weak, and is confounded by postoperative rebound hypertension and residual symptoms, as was described in previous publications [39, 40]. Comparing perioperative whole-brain strain with improvements in quality-of-life scores such as EQ-5D-5 L and cognitive assessment tools such as MoCA showed positive correlations that were similar in magnitude to HIT-6, but with markedly wider confidence intervals, especially for MoCA. The cognitive analysis should be regarded as underpowered rather than negative: Out of the 96 subjects included in this study, only 30 had both pre- and post-operative MoCA scores. In addition, only a minority of subjects showed cognitive impairment, with a median preoperative MoCA score of 28. The low proportion of cognitively impaired patients in our population is aggravated by our study design: Exclusion of patients with subdural hygroma or hematoma, whose effusions generate deformation far exceeding that of sagging alone, further removes the subgroup with the most severe symptoms and the largest shifts. Establishing or refuting a link between strain and cognition will require a larger cohort with protocol-driven neurocognitive testing.
+
+Several other limitations should be acknowledged. First, the retrospective, single-center design may introduce selection bias, and the study was restricted to patients with sufficient pre- and postoperative imaging, potentially introducing bias. Second, although diffeomorphic registration and AI-based segmentation provide robust tools for quantifying deformation, registration errors and segmentation inaccuracies cannot be fully excluded, despite verification by the authors. The healthy control group provides an empirical estimate of this residual noise floor: applying the identical pipeline to subjects without brain sagging yielded almost no measurable expansion, compression or distortional strain, whereas the deformation measured in patients was severalfold larger. The control cohort was, however, younger than our patients (19–23 years versus 43.4 ± 11.5 years) and was imaged without contrast agent on different scanners. These differences would, if anything, be expected to increase rather than decrease apparent deformation in the control group, so we regard the comparison as conservative, but it is not perfectly matched. Third, FDR correction assumes independence among tests; neighbouring regions are spatially and physiologically positively correlated, so the effective number of independent tests is smaller than the nominal one, which renders our regional testing conservative. Finally, the observed association between mechanical strain and symptomatic improvement is correlational; causal inference is not possible from these data, and prospective studies with systematic clinical and especially neurocognitive testing will be required.
+
+Conclusions
+
+Our model shows that spinal leaks in patients with spontaneous intracranial hypotension (SIH) are associated with quantifiable region-specific mechanical strain on the brain. The overlap between deformation hotspots and fronto-limbic and temporomesial regions may provide an intriguing explanation for the clinical phenotype observed in some patients.
+
+Supplementary Information
+
+Below is the link to the electronic supplementary material.
+
+Supplementary Material 1
+
+Supplementary Material 2
+
+Supplementary Material 3
+
+Acknowledgements
+
+Not applicable.
+
+Author contributions
+
+Study design: AER, PS, JB. Data acquisition: PS, AER, FV, KW; Provision of infrastructure: HU, JB. Data analysis: PS, AER, JB, FV, KW. Manuscript writing: contributions from all authors.
+
+Funding
+
+Open Access funding enabled and organized by Projekt DEAL. This study has not received any external funding.
+
+Data availability
+
+Parts of the dataset containing data from patients who agreed to share it with other researchers will be made available upon reasonable request to the corresponding author.
+
+Declarations
+
+Ethics approval and consent to participate
+
+Our study protocol was approved by the local ethics committee (Ethik-Kommission der Albert-Ludwigs-Universität Freiburg; IDs: 22-1512-S1-retro/ 24-1296-S1-retro) and was conducted in accordance with good clinical practice and the Declaration of Helsinki; all patients or their caretakers gave their informed consent.
+
+Consent for publication
+
+Not applicable.
+
+Competing interests
+
+The authors declare no competing interests.
+
+Abbreviations
+
+AI Artificial intelligence
+
+bvFTD Behavioral variant frontotemporal dementia
+
+CSF Cerebrospinal fluid
+
+FDR False discovery rate
+
+MRI Magnetic resonance imaging
+
+SIH Spontaneous intracranial hypotension
+
+Publisher’s note
+
+Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
+
+
+References
+
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+Mehan WA, Poyiadji N, Paul AB, Buch K. Volumetric Changes in the Choroid Plexus Associated with Spontaneous Intracranial Hypotension in Patients with Spinal CSF Leak. Am J Neuroradiol. 2024;45(8):1162–5. 10.3174/ajnr.A8291.39025635 PMC11383421
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+Zander C, Lützen N, Rau A, Wolf K, Arnold P, Mast H, et al. Volumetric response after closure of a spinal CSF leak in patients with spontaneous intracranial hypotension: a multicompartmental longitudinal study. J NeuroInterventional Surg. 2026;18(1):241–7. 10.1136/jnis-2024-022712 . PubMed PMID: 39870517.PMC12772593 39870517
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+Perry A, Graffeo CS, Fattahi N, ElSheikh MM, Cray N, Arani A, et al. Clinical Correlation of Abnormal Findings on Magnetic Resonance Elastography in Idiopathic Normal Pressure Hydrocephalus. World Neurosurg. 2017;99:695–e7001. 10.1016/j.wneu.2016.12.121.28063896 PMC5357459
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+Aunan-Diop JS, Pedersen CB, Halle B, Jensen U, Munthe S, Harbo F, et al. Magnetic resonance elastography in normal pressure hydrocephalus—a scoping review. Neurosurg Rev. 2022;45(2):1157–69. 10.1007/s10143-021-01669-0.34687356
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+Vetrugno R, Vella A, Mascalchi M, Della Nave R, Ginestroni A, Gallassi R, et al. Patching improves perfusion of the sagged brain in intracranial hypotension. J Neurol. 2011;258(1):146–8. 10.1007/s00415-010-5681-6 . PubMed PMID: 20680323.20680323
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+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: BMC Med Educ
+Journal ID: BMC Med Educ
+NLM Journal ID: 101088679
+
+BMC Medical Education
+
+EISSN: 1472-6920
+Publisher: BMC
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC13032610
+PMID: 41723442
+DOI: 10.1186/s12909-026-08859-8
+Article ID: 8859
+Article version: 1
+Subjects: Research
+
+A systematic search for evaluated interventions to increase nursing students’ participation in international scientific conferences: an empty review and implementation implications
+
+Kubota Kazumi kkubota@m.u-tokyo.ac.jp
+1 2
+Samura Shiho 3
+1 https://ror.org/01fyk0v41 grid.444795.f 0000 0000 9832 2884 Research Organization, Shimonoseki City University, 2-1-1 Daigaku-Cho, Shimonoseki, Yamaguchi, 751-8510 Japan
+2 https://ror.org/022cvpj02 grid.412708.8 0000 0004 1764 7572 Department of Healthcare Information Management, The University of Tokyo Hospital, Tokyo, Japan
+3 Former Japan International Nursing Student Association, Tokyo, Japan
+Electronic publication date: 2026 Feb 21
+Publication date: 2026
+Volume: 26
+Electronic Location ID: 505
+Received 2025 Oct 15; Accepted 2026 Feb 16
+Copyright: © The Author(s) 2026
+Copyright year: 2026
+License: Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Keywords: Nursing students, International scientific conferences, Systematic review, Empty review, Implementation science, Diffusion of innovations, Theory of planned behavior, Peer mentorship, Language anxiety
+issue-copyright-statement: © BioMed Central Ltd., part of Springer Nature 2026
+
+Ÿ==============================Ÿ
+Background
+
+International scientific conferences expose nursing students to current evidence, professional identity formation, and global networks, yet participation remains low. We aimed to identify evaluated interventions designed to increase nursing students’ participation in international scientific conferences.
+
+Methods
+
+Following PRISMA 2020, we searched PubMed, CINAHL, Scopus, and Web of Science for English/Japanese records from January 2005 to 31 May 2025. We also examined three International Council of Nurses (ICN) Congress proceedings items authored by the research team as contextual sources. Two reviewers independently screened titles/abstracts. Eligible studies targeted pre-licensure undergraduate nursing students and evaluated strategies intended to increase participation, reporting objective participation outcomes (e.g., abstract submission, registration, attendance, presentation).
+
+Results
+
+Database searches identified 173 records. After removing 58 duplicates, 115 records were screened by title and abstract. All 115 records were excluded at the title/abstract stage; therefore, no eligible evaluative studies were identified (n = 0).
+
+Conclusions
+
+No evaluated interventions were identified. This empty review highlights an actionable evaluation gap. Informed by implementation and behavior-change theory and adjacent evidence, we outline implementation implications that can be adopted and monitored using routine indicators (key performance indicators) and iterative improvement cycles (Plan–Do–Study–Act).
+
+Supplementary Information
+
+The online version contains supplementary material available at 10.1186/s12909-026-08859-8.
+
+Introduction
+
+International scientific conferences, including the International Council of Nurses (ICN) Congress, give nursing students the chance to encounter up‑to‑date scholarship, develop professional identity, and build global networks [1]. Preparing a resilient and internationally engaged nursing workforce is a strategic priority [2]. Yet participation remains low. Across settings, reports point to recurring barriers: late or fragmented information, English language anxiety and presentation apprehension, limited structured peer mentorship, and financial constraints [3–5]. As contextual information, three conference proceeding items authored by the research team (ICN Congress; 2019, 2021, 2023) echo these themes and help contextualize the problem space, but they do not evaluate solutions [6–8].
+
+Closing the gap between interest and action needs attention to both individual decision processes and the organizational conditions that enable sustainable practice. Diffusion theory describes a progression from awareness through interest, evaluation, trial, and adoption, and underlines the role of social systems in sustaining change [9]. In digital environments, information‑seeking and sharing can amplify diffusion after initial awareness (e.g., AISAS: Attention-Interest-Search-Action-Share) [10]. The theory of planned behavior explains how perceived behavioral control and social norms shape intention and behavior [11]. To embed change under real‑world constraints, implementation frameworks such as the Consolidated Framework for Implementation Research (CFIR), RE‑AIM, and Plan-Do-Study-Act (PDSA) provide practical guidance for introduction, evaluation, and maintenance [12–14]. Work on foreign language anxiety shows that avoidance often reflects anxiety rather than ability—a salient point for students considering international scholarly engagement [15]. Sustainable internationalization of curricula also favors integration within existing courses and assessments over ad hoc activities [16].
+
+This study had two objectives. First, we conducted a systematic review to determine whether evaluated interventions exist to increase undergraduate nursing students’ participation in international scientific conferences; no eligible evaluative studies were identified. Second, we propose a minimal set of low‑cost, curriculum‑embedded, student‑led measures that institutions can put in place and steadily improve, with pragmatic metrics for monitoring impact.
+
+Materials and methods
+
+We conducted a systematic review in line with the PRISMA 2020 Statement [17]. Eligibility criteria, information sources, search strategies, and selection procedures were prespecified. The review protocol was not prospectively registered. To support transparency and reproducibility, we provide the full search strategies, screening forms, and decision rules in the Supplementary Materials. Ethics approval was not required.
+
+Eligibility criteria
+
+We included studies that: (i) targeted pre‑licensure undergraduate nursing students; (ii) evaluated educational, organizational, financial, or digital strategies intended to increase participation in international scientific conferences; and (iii) reported objective participation outcomes (abstract submission, registration, attendance, presentation). Any comparator was acceptable, including single‑group pre–post designs. We excluded studies focused solely on study abroad, exchanges, or clinical placements without linkage to conferences; studies limited to practicing nurses; and studies reporting only attitudes/intentions without measurable participation endpoints. Conference abstracts and proceedings were treated as contextual (non-eligible) sources where relevant; in practice, we examined three ICN Congress proceedings items authored by the research team as contextual sources [6–8]. Records in English or Japanese from January 2005 through 31 May 2025 were eligible.
+
+Information sources and search strategy
+
+We searched PubMed, CINAHL, Scopus, and Web of Science Core Collection. In addition, we examined three contextual conference items authored by the research team (ICN Congress proceedings; 2019, 2021, 2023) to describe commonly reported barriers; these items were treated as contextual sources and were not considered eligible evaluation studies. The PubMed strategy was: (("Students, Nursing"[MeSH] OR nursing student*[tiab]) AND (("Congresses as Topic"[MeSH] OR congress*[tiab] OR conference*[tiab] OR "International Council of Nurses"[tiab] OR "Scientific Societies"[MeSH]) AND ("Career Mobility"[MeSH] OR "Career Choice"[MeSH] OR "Education, Nursing"[MeSH] OR "Professional Practice"[MeSH] OR "Professional Competence"[MeSH] OR career*[tiab] OR "professional development"[tiab] OR employ*[tiab])) AND (attend*[tiab] OR participat*[tiab] OR present*[tiab])).
+
+Across all databases, the searches were finalized on 11 October 2025 and were rerun on 29 January 2026 during peer review to support reproducibility; the prespecified end-date limit (31 May 2025) was retained. We applied the end-date limit as 31 May 2025 based on the earliest online publication date (e.g., Epub/online ahead of print) where applicable; records with online publication dates after 31 May 2025 were excluded.
+
+We adapted strategies to each database’s syntax and controlled vocabulary. Full database-specific search strategies are provided in Supplementary File S1.
+
+Selection process and planned synthesis
+
+Two reviewers independently screened titles and abstracts against the eligibility criteria, resolving disagreements by discussion. Full texts would have been retrieved and assessed for eligibility if potentially eligible records had been identified at screening. Had eligible studies been found, we planned independent data extraction and risk‑of‑bias assessment using ROBINS‑I for nonrandomized designs and appropriate tools for qualitative studies, with tabular/graphical synthesis and, where feasible, meta‑analysis. Given the empty yield, evidence synthesis and risk‑of‑bias assessment were not applicable; we report screening outcomes narratively. Duplicate records were removed using DOI as the primary identifier and PMID as the secondary identifier. Records without DOI/PMID were not deduplicated based on title similarity alone.
+
+Results
+
+Database searches identified 173 records (PubMed, n = 32; Web of Science, n = 22; CINAHL, n = 52; Scopus, n = 67). After removing 58 duplicate records before screening, 115 records were screened by title and abstract. All 115 records were excluded at the title/abstract stage because none evaluated an intervention aimed at increasing participation in international scientific conferences, as prespecified; therefore, no studies were included in the review.
+
+Frequent reasons for exclusion at screening were ineligible populations (e.g., practicing nurses or mixed professional samples without extractable student data), a focus on study abroad, exchanges, or clinical placements rather than scientific conferences, and outcomes limited to attitudes/intentions without measurable participation endpoints. As contextual information, three ICN Congress proceeding items authored by the research team (2019, 2021, 2023) described recurring barriers, including late or fragmented information, English language anxiety, limited peer support, and financial burden [6–8].
+
+Discussion
+
+This empty review suggests that evaluated interventions to increase undergraduate nursing students’ participation in international conferences have not been reported. The absence of evidence is not evidence of absence, but it does highlight an actionable gap. Institutions already have plausible levers and infrastructure to start making progress while building practice‑based evidence.
+
+To support practical prioritization under routine constraints, we focus on components that can be implemented with minimal additional resources and iteratively refined in routine practice. Drawing on diffusion and behavior theory, implementation science, and work on language anxiety and peer support, we outline a minimal package designed for routine implementation and maintenance.
+
+Operational feasibility and maintenance
+
+A typical setup assigns one academic lead (or program coordinator) to keep timelines and quality on track—about 1–2 h per week during peak periods (before deadlines) and under an hour otherwise. Automated bilingual announcements can be templated and scheduled in the LMS using a rolling annual calendar; updating dates and links takes ~ 30 min per cycle. Micro–English‑for‑conference workshops fit within first‑year orientation or skills courses as five 60–90‑minute sessions led by an ESP instructor or trained faculty; materials can be reused each year. Student‑led peer mentorship can run as monthly 30‑minute huddles with light faculty oversight.
+
+A consolidated micro‑grants/fee‑waiver webpage can be maintained by administrative staff with a quick quarterly refresh. These choices spread workload and support maintainability despite turnover and budget constraints.
+
+Equity‑focused implementation and monitoring
+
+To reduce opportunity gaps tied to information access, English anxiety, peer support, and financial burden, announcements and micro‑workshops should sit within required first‑year courses and be repeated at varied times, with hybrid options for commuters and working students. Routine indicators can track: (i) timely awareness before deadlines (overall and by year/commuting/working status); (ii) abstract submission, registration, and presentation rates by household financial hardship and self‑reported English anxiety; (iii) mentee retention/progression, including first‑generation students; and (iv) median out‑of‑pocket costs pre/post micro‑grants/fee waivers. Programs can set simple targets to narrow gaps over time and use PDSA to adjust messaging, workshop sequencing, or funding criteria when disparities persist. RE‑AIM helps capture reach, adoption, fidelity/cost, and maintenance across cohorts [13, 14].
+
+Strengths and limitations
+
+Strengths include comprehensive searches across four databases over two decades, prespecified and transparent eligibility criteria, and dual independent screening. The main limitation is that no evaluative studies were found; empty yield may reflect unindexed or internal evaluations not publicly available. Still, the empty result is informative: it points to a neglected evaluation space where pragmatic, low‑risk steps can proceed while cumulative evidence is built through routine monitoring and iterative refinement. Future work should test components individually and as a bundle, with mixed‑methods process evaluations to understand mechanisms (anxiety reduction, navigational know‑how, social reinforcement). Agreement on a core outcome set—timely awareness, submission/registration rates, attendance/presentation, changes in English anxiety and self‑efficacy, and cost per participating student—would improve comparability.
+
+Conclusions
+
+We found no eligible evaluative studies of interventions designed to increase undergraduate nursing students’ participation in international scientific conferences. However, commonly reported barriers appear consistent and potentially modifiable.　A minimal package—early automated bilingual announcements, short micro–English‑for‑conference workshops, structured student‑led mentorship, and a consolidated micro‑grants/fee‑waivers page—can be implemented now using existing infrastructure, with simple indicators to track reach and impact. Iterating through PDSA cycles can progressively strengthen effectiveness and maintainability. As institutions put it into practice and iterate, routine monitoring can help build the practice‑based evidence that has been missing in this area.
+
+Supplementary Information
+
+Supplementary Material 1.
+
+Supplementary Material 2.
+
+Acknowledgements
+
+The inspiration for this study grew out of the first author’s participation in the Japanese Nursing Student's Association (JNSA), founded by nursing students who attended the 2001 ICN Copenhagen Congress. The experience at ICN was formative. We thank all JNSA members of that era-especially the first president, Ms. Mari Imafuku-Miyahara, and the second president, Ms. Yuka Kakinuma. We also wish to acknowledge Ms. Fusae Kurihara and Mr. Junpei Yuhara for their pivotal role in establishing JNSA. Since 2015, the Japanese International Nursing Students Association (JINSA) has supported nursing students and early career nurses interested in ICN. Both the first and second authors have contributed as supporters. We thank JINSA’s co-founders, Ms. Mana Kojima and Ms. Kihea Lee, and the current representative, Ms. Ami Ienaga, for their ongoing dedication.
+
+Authors’ contributions
+
+KK conceived the study, developed the search strategy and eligibility criteria, conducted screening, and drafted the manuscript; SS conducted screening and critically revised the manuscript. Both authors approved the final manuscript.
+
+Funding
+
+No external funding was received.
+
+Data availability
+
+Data availability No primary datasets were generated or analyzed. Search strategies, the screening log, and the PRISMA source file are available in the Supplementary Materials.
+
+Declarations
+
+Ethics approval and consent to participate
+
+Not applicable. This study involved a systematic search of the literature and did not involve the recruitment of human participants or the collection of identifiable personal data.
+
+Consent for publication
+
+Not applicable.
+
+Competing interests
+
+The authors declare no competing interests.
+
+Publisher’s Note
+
+Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
+
+
+References
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+Rogers EM. Diffusion of Innovations. 5th ed. New York: Free Press; 2003.
+10. Huang Z Li H Huang J Chinese consumers’ psychology and behavior of the foods with nutrition claims based on AISAS model Front Nutr 2024 11 1309478 10.3389/fnut.2024.1309478 38496793 PMC10941286
+Huang Z, Li H, Huang J. Chinese consumers’ psychology and behavior of the foods with nutrition claims based on AISAS model. Front Nutr. 2024;11:1309478. 10.3389/fnut.2024.1309478.38496793 10.3389/fnut.2024.1309478 PMC10941286
+11. Ajzen I The theory of planned behavior Organ Behav Hum Decis Process 1991 50 179 211 10.1016/0749-5978(91)90020-T
+Ajzen I. The theory of planned behavior. Organ Behav Hum Decis Process. 1991;50:179–211. 10.1016/0749-5978(91)90020-T.
+12. Damschroder LJ Aron DC Keith RE Kirsh SR Alexander JA Lowery JC Fostering implementation of health services research findings into practice: a consolidated framework for advancing implementation science Implement Sci 2009 4 50 10.1186/1748-5908-4-50 19664226 PMC2736161
+Damschroder LJ, Aron DC, Keith RE, Kirsh SR, Alexander JA, Lowery JC. Fostering implementation of health services research findings into practice: a consolidated framework for advancing implementation science. Implement Sci. 2009;4:50. 10.1186/1748-5908-4-50.19664226 10.1186/1748-5908-4-50 PMC2736161
+13. Glasgow RE Vogt TM Boles SM Evaluating the public health impact of health promotion interventions: the RE‑AIM framework Am J Public Health 1999 89 1322 1327 10.2105/ajph.89.9.1322 10474547 PMC1508772
+Glasgow RE, Vogt TM, Boles SM. Evaluating the public health impact of health promotion interventions: the RE‑AIM framework. Am J Public Health. 1999;89:1322–7. 10.2105/ajph.89.9.1322.10474547 10.2105/ajph.89.9.1322 PMC1508772
+14. Taylor MJ McNicholas C Nicolay C Darzi A Bell D Reed JE Systematic review of the application of the plan–do–study–act method to improve quality in healthcare BMJ Qual Saf 2014 23 290 298 10.1136/bmjqs-2013-001873 PMC3963536 24025320
+Taylor MJ, McNicholas C, Nicolay C, Darzi A, Bell D, Reed JE. Systematic review of the application of the plan–do–study–act method to improve quality in healthcare. BMJ Qual Saf. 2014;23:290–8. 10.1136/bmjqs-2013-001873.10.1136/bmjqs-2013-001862 PMC3963536 24025320
+15. Horwitz EK Horwitz MB Cope J Foreign language classroom anxiety Mod Lang J 1986 70 125 132 10.1111/j.1540-4781.1986.tb05256.x
+Horwitz EK, Horwitz MB, Cope J. Foreign language classroom anxiety. Mod Lang J. 1986;70:125–32. 10.1111/j.1540-4781.1986.tb05256.x.
+16. Leask B Internationalizing the curriculum 2015 New York Routledge
+Leask B. Internationalizing the curriculum. New York: Routledge; 2015.
+17. Page MJ McKenzie JE Bossuyt PM Boutron I Hoffmann TC Mulrow CD The PRISMA 2020 statement: an updated guideline for reporting systematic reviews BMJ 2021 372 n71 10.1136/bmj.n71 33782057 PMC8005924
+Page MJ, McKenzie JE, Bossuyt PM, Boutron I, Hoffmann TC, Mulrow CD, et al. The PRISMA 2020 statement: an updated guideline for reporting systematic reviews. BMJ. 2021;372:n71. 10.1136/bmj.n71.33782057 10.1136/bmj.n71 PMC8005924
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+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: J Funct Biomater
+Journal ID: J Funct Biomater
+NLM Journal ID: 101570734
+Journal ID: jfb
+
+Journal of Functional Biomaterials
+
+EISSN: 2079-4983
+Publisher: Multidisciplinary Digital Publishing Institute (MDPI)
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC13514323
+PMID: 42646207
+DOI: 10.3390/jfb17080404
+Article ID: jfb-17-00404
+Article version: 1
+Subjects: Article
+
+Finite Element Analysis of Stress Distribution in Healthy and Restored Mandibular Molars with Zirconia and Lithium Disilicate Crowns Under Vertical and Oblique Loading
+
+https://orcid.org/0000-0002-4486-5140 Hernández-Vázquez Rosa Alicia Conceptualization Methodology Validation Formal analysis Resources Writing – original draft Writing – review & editing Supervision Project administration 1 2
+https://orcid.org/0000-0002-8261-2427 Marquet-Rivera Rodrigo Arturo Conceptualization Methodology Validation Formal analysis Resources Writing – original draft Writing – review & editing Supervision Project administration 3 4 *
+Mastache-Miranda Octavio Alejandro Methodology Investigation Resources Visualization 5 6
+Madrigal-Carrillo Karina Gabriela Validation Investigation Data curation 4 7
+https://orcid.org/0000-0002-7528-1236 Rivera-Díaz Rosa Adriana 3
+Kim Hyun-Jung Academic Editor
+1 División de Mecatrónica, Universidad Politécnica del Valle de México, Avenida Mexiquense sin Número Esquina Avenida Universidad Politécnica, Colonia Villa Esmeralda, Tultitlán 54910, Mexico; alicia.hernandez@upvm.edu.mx
+2 Posgrado, Facultad de Odontología, Universidad Latinoamericana Campus Norte, Cumbres de Acultzingo 3, Fraccionamiento Los Pirules, Tlalnepantla de Baz 54040, Mexico
+3 Escuela Superior de Comercio y Administración Unidad Tepepan, Instituto Politécnico Nacional, Anillo Periférico Sur Manuel Gómez Morín 4863, Colonia Ampliación Tepepan, Alcaldía Coyoacán, Ciudad de México 16020, Mexico
+4 Escuela Superior de Ingeniería Mecánica y Eléctrica Unidad Culhuacán, Instituto Politécnico Nacional, Avenida Santa Ana 1000, San Francisco Culhuacán, Colonia Culhuacán CTM V, Alcaldía Coyoacán, Ciudad de México 04440, Mexico
+5 Unidad Profesional Interdisciplinaria de Energía y Movilidad, Instituto Politécnico Nacional, Avenida Wilfrido Massieu sin Número, Unidad Profesional Adolfo López Mateos, Nueva Industrial Vallejo, Gustavo A. Madero, Ciudad de México 07738, Mexico
+6 MARMAS Soluciones en Ingeniería e Investigación, Matagalpa 1021A, Residencial Zacatenco, Gustavo A. Madero, Ciudad de México 07369, Mexico
+7 Departamento de Física y Química Teórica, Facultad de Química, Universidad Nacional Autónoma de México, Circuito Escolar sin Número, Ciudad Universitaria, Alcaldía Coyoacán, Ciudad de México 04510, Mexico
+* Correspondence: rmarquetr@ipn.mx
+Electronic publication date: 2026 Aug 14
+Publication date: 2026 Aug
+Volume: 17
+Issue: 8
+Electronic Location ID: 404
+Received 2026 Jun 20; Revised 2026 Aug 11; Accepted 2026 Aug 13
+Copyright: © 2026 by the authors.
+Copyright year: 2026
+License: Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Keywords: finite element analysis, dental biomechanics, zirconia Y-TZP, lithium disilicate, stress distribution, full-coverage crown, mandibular molar, stress shielding
+
+Funding: Instituto Politécnico Nacional https://ror.org/059sp8j34 Secretaría de Ciencia, Humanidades, Tecnología e Innovación https://ror.org/059ex5q34 This research was supported by the Instituto Politécnico Nacional (IPN, México) and the Secretaría de Ciencia, Humanidades, Tecnología e Innovación (SECIHTI, México).
+
+Ÿ==============================Ÿ
+The mechanical compatibility between dental restorative materials and the natural tooth structure is a relevant factor for long-term clinical performance. Although zirconia (yttria-stabilized tetragonal zirconia polycrystal, Y-TZP) and lithium disilicate are widely used for full-coverage crowns, their biomechanical interaction with the underlying dentin and pulp under functional loading remains insufficiently characterized. This study reports a comparative finite element analysis (FEA) of a mandibular first molar under vertical (200 N, axial) and oblique (200 N, 30°) loading, evaluating three configurations: an intact healthy tooth, a zirconia Y-TZP full-coverage crown, and a lithium disilicate full-coverage crown. The three-dimensional geometry was obtained from a cone-beam computed tomography (CBCT) study of a caries-free mandibular first molar, previously described and verified by the present group, and was analyzed in ANSYS Workbench (Static Structural). Von Mises equivalent stress, maximum principal stress and total deformation were obtained for enamel or restoration, dentin, and pulp in each configuration. Zirconia produced the highest stress concentrations in the coronal restoration (88.4 MPa vertical; 174.5 MPa oblique), exceeding the healthy enamel baseline by 57.6% and 89.7%, respectively. Both restorative materials reduced dentin stress relative to the healthy tooth, consistent with the stress-shielding effect driven by elastic-modulus mismatch. Under oblique loading, the maximum principal stress in healthy enamel reached 61.7 MPa, approaching or exceeding the upper bound of the reported tensile strength range (~10–40 MPa) and identifying oblique loading as the more demanding of the two conditions analyzed. Within the limitations of the present finite element model, lithium disilicate demonstrated a more favorable stress distribution, with dentin stress values closer to the intact-tooth baseline. The model does not include a luting cement layer, a periodontal ligament, the dentin–enamel junction, anisotropic tissue behavior or cyclic loading, and no experimental validation was performed; the results are therefore presented as a controlled numerical comparison between three configurations under the specific conditions simulated, and not as direct clinical selection criteria.
+
+1. Introduction
+
+The selection of restorative materials for dental crowns involves a complex interplay between aesthetic requirements, mechanical resistance, and biomechanical compatibility with the remaining tooth structure. Zirconia (yttria-stabilized tetragonal zirconia polycrystal, Y-TZP) and lithium disilicate glass-ceramics have become the dominant materials for full-coverage restorations because of their favorable aesthetic outcomes and high flexural strength values of 900–1200 MPa and 360–500 MPa, respectively [1,2]. However, the clinical assumption that greater material hardness translates into improved restoration performance overlooks a fundamental biomechanical principle: elastic-modulus compatibility between the restorative material and the natural tooth tissues that it replaces.
+
+Natural enamel has an elastic modulus of approximately 70 GPa, whereas dentin exhibits a substantially lower value of approximately 18 GPa [3]. Zirconia, with a modulus of 200 GPa, is nearly three times stiffer than enamel, and lithium disilicate, at 95–105 GPa, also exceeds the natural tissue values. This mismatch has direct implications for how occlusal forces are transmitted through the restored tooth to the underlying dentin and periodontal structures. Stiffer restorations concentrate stress within the coronal material while shielding the underlying dentin—a phenomenon known as stress shielding—which may alter the physiological stress environment of dental tissues and ultimately affect long-term tissue remodeling and clinical longevity [4].
+
+Finite element analysis (FEA) has become a well-established tool for evaluating stress distributions in dental structures under functional loading. Previous studies have examined individual materials or specific loading scenarios, but systematic comparisons that include a healthy-tooth baseline under both axial and oblique loading remain scarce. Oblique loading is of particular clinical relevance, since functional masticatory movements generate lateral force components that have been identified as the primary mechanism of cusp fracture and restoration failure [5,6].
+
+Recent finite element studies have addressed the biomechanical behavior of zirconia and lithium disilicate restorations from several complementary perspectives. Dal Piva et al. [7] compared monolithic full-crown restorations fabricated from materials of differing stiffness and related the resulting stress fields to the elastic modulus of the crown material. Lin et al. [8] evaluated crown design and material in endodontically treated molars, and Abtahi et al. [9] analyzed endocrown cavity designs in CAD-CAM materials under static vertical load, both reporting that the material–design combination modified the resulting stress concentration. Epifania et al. [10] demonstrated in an implant-supported configuration that stiffer crowns retain a greater proportion of the stress within their own structure while reducing the demand on the supporting components, and Campaner et al. [11] reported an analogous dependence on core stiffness in posterior fixed partial dentures. Nokar et al. [12] extended this observation to implant components and peri-implant bone, and Karn et al. [13] compared lithium disilicate and monolithic zirconia endocrowns on a mandibular molar, showing that the material–design combination modifies the location and not only the magnitude of the peak stress. Sichi et al. [14] reported the same stiffness-driven behavior for zirconia crowns on endodontically treated teeth, and Shrestha et al. [15] showed, using an experimentally validated viscoelastic model, that material compatibility also governs the residual stress state generated during processing.
+
+Despite this body of evidence, three gaps persist. First, most comparative analyses evaluate restorative materials against each other but omit an intact, unrestored tooth as a common reference, so the magnitude of the departure from physiological stress transmission cannot be quantified. Second, a large proportion of these studies apply axial loading only, or report oblique loading without a paired axial condition on the same geometry, which prevents the direct attribution of the observed differences to load direction. Third, the simultaneous reporting of Von Mises equivalent stress, maximum principal stress and total deformation for enamel or restoration, dentin and pulp within a single controlled comparison is uncommon, although these three descriptors are jointly required in order to separate global mechanical demand from tensile fracture risk and from structural compliance. The present study addresses these three points within a single geometry, so that the only parameter modified between models is the coronal material.
+
+The purpose of the present study was to develop and compare three-dimensional FEA models of a mandibular first molar in its healthy state and restored with zirconia Y-TZP and lithium disilicate full-coverage crowns, subjecting them to vertical and oblique (30°) loading in order to quantify stress distributions across enamel or restoration, dentin, and pulp. The null hypothesis of the study was that no difference would be found in the stress behavior between the intact tooth and the two restored configurations under the conditions of the study; the alternative hypothesis was that the elastic-modulus mismatch between restorative materials and natural tooth structure would govern the biomechanical response of the models, with lithium disilicate producing a stress distribution closer to that of the intact tooth than zirconia. The study is conceived as a controlled numerical comparison; accordingly, its outcomes describe the relative biomechanical behavior of the three configurations under the specific conditions simulated and are not intended as direct clinical recommendations.
+
+2. Materials and Methods
+
+2.1. Geometric Model
+
+The three-dimensional geometric model of a mandibular first molar was obtained from a cone-beam computed tomography (CBCT) study of a caries-free, unrestored mandibular first molar. The image acquisition parameters, the segmentation protocol, the surface reconstruction procedure and the biofidelity verification of this biomodel have been described in detail in a previous methodological publication by the present research group [16]; the same verified geometry is used here in order to ensure continuity and reproducibility between studies. The model reproduces the anatomical regions of enamel, dentin and pulp chamber, including the cuspal anatomy relevant to occlusal contact distribution. Three configurations were analyzed: (a) intact healthy tooth with all natural tissues; (b) zirconia Y-TZP full-coverage crown replacing the entire enamel volume; and (c) lithium disilicate full-coverage crown replacing the entire enamel volume (Figure 1). In the restored models the enamel volume was replaced by the corresponding restorative material, while the dentin and pulp geometry remained unchanged. This configuration corresponds to a full-coverage crown restoration, in which the enamel is clinically removed and the crown seats directly on the dentin core; the substitution therefore represents the material condition of a complete crown preparation. What this convention does not reproduce is the additional reduction in the dentin core, the change in stump geometry and the finish line created during clinical tooth preparation, nor the difference in wall thickness between restorative materials, points addressed in Section 2.6 and examined in Section 4.5. It also fixes the external geometry, the occlusal contact area and the total volume of the three models to be strictly identical, so that the only parameter modified between models is the elastic modulus of the coronal material. All models were processed and meshed in ANSYS Workbench 2025 R2 (ANSYS Inc., Canonsburg, PA, USA).
+
+2.2. Material Properties
+
+All materials were modeled as linear-elastic, homogeneous and isotropic, in agreement with the majority of comparative FEA studies in dental biomechanics [3,17]. This assumption is the prevailing convention in studies with a primary objective to compare restorative materials, as it isolates the effect of the material variable and enables direct comparison with the existing body of FEA literature [18]. The natural tissues nevertheless depart from this idealization in three respects that are relevant to the interpretation of the results. Enamel is orthotropic, with mechanical properties that depend on prism orientation; Munari et al. [19] compared anisotropic and isotropic enamel in a premolar model under axial and oblique loading and reported that the isotropic assumption preserved the location of the stress concentrations while overestimating the tensile stress magnitudes. Dentin exhibits an anisotropy of the order of 7–35% depending on tubule orientation and depth, and its orthotropic modeling reduces displacement and strain magnitudes without reversing the relative stress trends between configurations [20]. The dental pulp is a soft connective tissue that has been represented as a low-modulus elastic solid in finite element studies of the pulp chamber [21], although its actual behavior is viscoelastic and its time-dependent response is not captured by a linear-elastic formulation; because the pulp stresses obtained in all configurations were three to four orders of magnitude below those of the mineralized tissues, this simplification is not expected to influence the coronal comparison, although it precludes any inference regarding pulpal fluid dynamics or proprioceptive response. The isotropic formulation adopted here is therefore expected to affect the absolute values more than the relative ordering between configurations, and this expectation is examined further in Section 4.5. The mechanical properties assigned to each tissue and restorative material are summarized in Table 1. The elastic modulus of dental pulp was set to 0.002 GPa (2 MPa), consistent with its nature as a soft connective tissue, as reported in the literature [22]. Properties of the restorative materials were taken from peer-reviewed primary sources reporting experimentally determined values for zirconia Y-TZP [1,23] and lithium disilicate [2,24].
+
+2.3. Finite Element Mesh
+
+All models were discretized using 10-node quadratic tetrahedral elements (SOLID187), with local mesh refinement in the regions of highest stress concentration, namely the occlusal surface, the cervical margin, and the dentin–enamel (or dentin–restoration) interface. The discretization of the reference model comprised 129,005 nodes and 74,907 elements. A mesh-convergence study was performed by progressively refining the element size and comparing the peak Von Mises stress between successive meshes; convergence was defined as a variation below 5% between consecutive refinements. The peak Von Mises stress varied by less than 3% between the final two mesh densities, confirming that the reported discretization (129,005 nodes; 74,907 elements) provided a converged solution (Figure 2). The resulting stress magnitudes for the healthy-tooth model were consistent with the ranges reported in previous finite element studies of intact molars under comparable occlusal loading [5,6]. This agreement constitutes a qualitative consistency check against published magnitudes and not a validation of the model; the scope and limits of this comparison are addressed in Section 4.6.
+
+2.4. Boundary Conditions and Loading
+
+A fixed support was applied to the entire root surface, constraining all translational and rotational degrees of freedom at the root boundary. This approach is consistent with previous FEA dental studies focusing on coronal stress distribution, in which the periodontal ligament (PDL) is not explicitly modeled [5,25]. Constraining the root directly increases the overall rigidity of the assembly and modifies the strains transmitted to the supporting structures; Özcan et al. [26] showed that the degree of anatomical complexity represented in a dental finite element model, including the way the supporting structures are described, changes the computed magnitudes without necessarily altering the ordering between configurations. The influence of this boundary condition is greatest on root, cervical and alveolar stress and on tooth mobility, and comparatively smaller on the coronal stress fields evaluated here under static loading. Because the identical constraint was applied to the three models, the comparison between them is not affected by this boundary condition, whereas the absolute values obtained in the cervical and radicular regions are model-specific and should not be interpreted as physiological. This limitation is addressed further in Section 2.6 and Section 4.5.
+
+Two loading conditions were applied as uniformly distributed pressure over the occlusal contact area (49.73 mm2), representing the functional contact region (Figure 3):
+
+Vertical loading: A compressive pressure of 4.02 MPa (equivalent to 200 N distributed over the contact area) was applied along the longitudinal axis of the tooth (Z-axis).
+
+Oblique loading (30°): A resultant force of 200 N was decomposed into axial (Z) and horizontal (Y) pressure components, PZ = 3.48 MPa (173 N/49.73 mm2) and PY = 2.01 MPa (100 N/49.73 mm2), simulating lateral excursive movements during mastication.
+
+2.5. Contact Conditions and Analysis Type
+
+All interfaces between adjacent structures (enamel–dentin, restoration–dentin, and dentin–pulp) were defined as bonded contacts, assuming perfect adhesion with no sliding or separation. A linear static-structural analysis was performed in ANSYS Workbench 2025 R2 (ANSYS Inc., Canonsburg, PA, USA). Two output variables were extracted for each tissue in each model: (i) the Von Mises equivalent stress (σVM), used as a global indicator of mechanical demand, and (ii) the maximum principal stress (σ1), used to assess tensile risk in brittle materials and tissues.
+
+2.6. Model Simplifications and Their Rationale
+
+The present model incorporates four simplifications that are common in comparative dental FEA but that condition the interpretation of the results. They are stated explicitly here, and their expected influence on the reported magnitudes is examined in Section 4.5.
+
+(i) Absence of a luting cement layer: Clinical crowns are always cemented, and the luting interface, typically 30–100 μm thick, modifies the transmission of stress between the restoration and the underlying dentin. Guler et al. [27] showed that in a crowned molar, the choice of luting agent alone changes the peak Von Mises stress by more than a factor of two. A cement layer was not included here because its thickness and properties would have to be assumed rather than measured for the present configuration, and because the introduction of a third material with an independent elastic modulus would confound the single variable under study. The three models are therefore compared under identical, idealized interfacial conditions.
+
+(ii) Absence of the periodontal ligament: A fixed support was applied at the root surface instead of an explicit PDL, as described in Section 2.4. This choice keeps the boundary condition identical across the three models but removes the shock-absorbing function of the ligament and increases the overall rigidity of the assembly.
+
+(iii) Substitution of the entire enamel volume by the restoration: The configuration corresponds to a full-coverage crown preparation, in which the enamel is removed and the crown seats on the dentin core. What it does not reproduce is the additional geometric reduction in the stump, the finish line, and the difference in preparation depth between materials: zirconia permits thinner walls and therefore a more conservative reduction in tooth structure than lithium disilicate, an advantage that the present fixed-envelope geometry does not represent.
+
+(iv) Absence of the dentin–enamel junction and linear-elastic, homogeneous, isotropic material behavior: The dentin–enamel junction is a graded, multilevel interface with a mechanical function to arrest cracks propagating between the two mineralized tissues [28]; it is represented here as a bonded contact of zero thickness. The consequences of the isotropic and linear-elastic assumptions for enamel, dentin and pulp are described in Section 2.2.
+
+3. Results
+
+3.1. Von Mises Stress Distribution Under Vertical Loading
+
+Under vertical loading (200 N axial), the maximum Von Mises stress in all models was located at the enamel or restoration surface (Table 2). Zirconia produced the highest coronal stress at 88.4 MPa (Figure 4b), representing a 57.6% increase over the healthy enamel baseline of 56.1 MPa (Figure 4a). Lithium disilicate yielded an intermediate value of 67.1 MPa (Figure 4c), corresponding to a 19.6% increase relative to the healthy tooth. Conversely, in the dentin layer, both restorative materials exhibited lower stress than the healthy tooth (zirconia: 24.0 MPa; lithium disilicate: 27.7 MPa; healthy: 29.2 MPa), demonstrating a stress-shielding effect. Pulp stress values were negligible in all configurations (<0.001 MPa), in line with its low elastic modulus and protected anatomical location.
+
+3.2. Maximum Principal Stress Under Vertical Loading
+
+Maximum principal (tensile) stress values under vertical loading remained below the lower bound of the flexural strength reported for each restorative material, and, in the healthy-tooth model, within the reported tensile strength range of enamel (~10–40 MPa). Healthy enamel reached 17.6 MPa (Figure 5a), while the zirconia and lithium disilicate restorations exhibited values of 28.4 MPa (Figure 5b) and 23.3 MPa (Figure 5c), respectively. Dentin tensile stresses remained well below the reported tensile strength of dentin (~52 MPa) in all configurations.
+
+3.3. Total Deformation Under Vertical Loading
+
+Maximum total deformation under vertical loading was highest in the healthy tooth (1.037 × 10−3 mm at the enamel surface; Figure 6a), followed by lithium disilicate (8.158 × 10−4 mm; Figure 6c) and zirconia (5.438 × 10−4 mm; Figure 6b). The inverse relationship between elastic modulus and deformation is consistent with theoretical predictions: the stiffest material (zirconia) deformed the least, while the natural tooth—with its lower-modulus enamel layer—exhibited the largest displacement.
+
+3.4. Von Mises Stress Distribution Under Oblique Loading
+
+Oblique loading (30°, 200 N) produced substantially higher stress magnitudes across all models and tissues compared with vertical loading (Table 3). Zirconia exhibited the highest coronal stress at 174.5 MPa (Figure 7b), an 89.7% increase over the healthy baseline of 92.0 MPa (Figure 7a). Lithium disilicate reached 122.8 MPa (Figure 7c), which is a 33.5% increase. The stress-shielding pattern in dentin was preserved under oblique conditions: zirconia (46.1 MPa) and lithium disilicate (54.7 MPa) both remained below the healthy dentin value (58.8 MPa). The difference between vertical and oblique loading was most pronounced in zirconia, in which the coronal stress nearly doubled (+97%), highlighting the sensitivity of high-modulus restorations to load direction.
+
+3.5. Maximum Principal Stress Under Oblique Loading
+
+Under oblique loading, the maximum principal stress in healthy enamel rose to 61.7 MPa (Figure 8a), approaching or exceeding the upper bound of the reported enamel tensile strength range (~10–40 MPa). The corresponding values at the restoration surface were 79.6 MPa for zirconia (Figure 8b) and 68.7 MPa for lithium disilicate (Figure 8c) (Table 4); these are referred to the flexural strength of each ceramic in Section 4.4. Within the limitations of the present model, and given that the isotropic formulation overestimates tensile magnitudes (Section 4.5), these values should be read as upper-bound estimates rather than as fracture predictions. Dentin tensile stresses remained well below the reported tensile strength of dentin (~52 MPa) in all scenarios.
+
+3.6. Total Deformation Under Oblique Loading
+
+Under oblique loading, deformation magnitudes increased approximately 2.5-fold relative to vertical loading in all models. The healthy tooth showed the greatest displacement (2.614 × 10−3 mm; Figure 9a), followed by lithium disilicate (2.04 × 10−3 mm; Figure 9c) and zirconia (1.37 × 10−3 mm; Figure 9b). The relative ordering of deformation magnitudes was preserved under both loading conditions, reflecting the dominant role of the elastic modulus of the coronal material.
+
+4. Discussion
+
+4.1. Elastic-Modulus Mismatch as the Primary Biomechanical Determinant
+
+The present results indicate that, within the conditions simulated, the elastic modulus of the coronal material rather than its flexural strength was the variable that governed the stress distribution across the three configurations. Zirconia, with an elastic modulus of 200 GPa, nearly three times that of natural enamel, concentrated substantially greater stress at the coronal surface while reducing dentin stress through stress shielding. This behavior agrees with the fundamental mechanics of composite structures, in which stiffer components attract a greater proportion of the load under displacement-controlled conditions [18], and with the stiffness dependence reported in comparable dental models [7,10,11,12]. It should be emphasized that this observation derives from a comparison in which the elastic modulus was the only parameter modified between models. The model was not designed to isolate the contribution of mechanical resistance, since no failure criterion or fracture-mechanics formulation was included; the present data therefore support the influence of stiffness within this controlled comparison, and do not establish a general hierarchy between stiffness and strength as determinants of clinical performance.
+
+A restoration that concentrates stress at its own surface while shielding the dentin may therefore behave differently from the intact tooth in ways that are not evident from strength data alone. Should the restoration eventually debond, or should microcracks initiate at the restoration–dentin interface, the previously shielded dentin would be exposed to the full occlusal stress [29]. This sequence is a mechanistic hypothesis consistent with the stress fields obtained here, and not an outcome demonstrated by a static linear-elastic analysis; its verification would require fatigue testing and clinical follow-up.
+
+4.2. Comparison with Previous Finite Element Studies
+
+The trends obtained here are consistent with those reported in comparable models. Dal Piva et al. [7], analyzing monolithic full crowns fabricated from materials of differing stiffness under axial load, related the stress transmitted to the substrate to the elastic modulus of the crown; the direction of that relationship corresponds to the 57.6% coronal increase and the 17.8% dentin reduction obtained here for zirconia under vertical loading. Karn et al. [13], comparing lithium disilicate and monolithic zirconia endocrowns on a mandibular molar, reported that the combination of restorative material and margin design modified the resulting stress concentration, which is consistent with the interfacial concentration described in Section 3. Epifania et al. [10] reported for implant-supported crowns that a stiffer crown retains a greater share of the load within its own structure while unloading the underlying components; this reflects the same load-partitioning principle that produces the dentin stress shielding quantified here, although in that study the underlying substrate is titanium and bone rather than dentin, so the parallel is mechanical and not biological. Campaner et al. [11] and Nokar et al. [12] observed an equivalent dependence on core and crown stiffness in fixed partial dentures and in implant components, respectively. The consistency of this ordering across different geometries and substrates suggests that the effect reported here is driven by the elastic-modulus contrast and is unlikely to be an artifact of the present geometry.
+
+The comparison is considerably less direct for the absolute values, and this is informative in itself. Guler et al. [27] reported peak Von Mises stresses of 478.09 MPa and 214.62 MPa in a crowned primary molar under 330 N vertical and oblique load with an explicit 30 μm cement layer. Scaling by the load ratio alone does not reconcile those values with the 88.4 MPa and 174.5 MPa obtained here; the difference is attributable to the combination of a different tooth and crown material, a different occlusal contact area, and above all to the presence of the cement interface, which introduces a compliant interlayer and an additional stress concentrator at the crown margin. This contrast quantifies the sensitivity of absolute stress magnitudes to the modeling assumptions declared in Section 2.6 and supports the restriction of the present conclusions to the comparison between the three configurations analyzed under identical conditions.
+
+With respect to load direction, Munari et al. [19] reported for a premolar model that non-axial loading raises tensile stress in the cervical region, and Özcan et al. [26] showed that model complexity, in particular the representation of the supporting structures and of mandibular kinematics, modifies absolute values without reversing the ordering between configurations. The 64–97% increase in coronal Von Mises stress obtained here on passing from axial to 30° oblique loading is consistent in direction with those reports and supports the identification of oblique loading as the more demanding condition. The magnitude of the increase is not directly comparable across studies, since it depends on the tooth analyzed, the load magnitude and inclination, and the representation of the supporting structures.
+
+4.3. Stress Shielding: Interpretation and Scope
+
+The paradoxical reduction in dentin stress observed with both restorative materials (zirconia: −17.8% vertical, −21.6% oblique; lithium disilicate: −5.1% vertical, −7.0% oblique) requires careful clinical interpretation. Although a reduction in dentin stress may appear favorable, prolonged stress shielding has been associated with atrophic changes in biological tissues, analogously to peri-implant bone loss observed under fully osseointegrated implants with high-modulus stems [30]. Although the remodeling capacity of dentin is more limited than that of bone, the alteration of its physiological stress environment warrants consideration in long-term outcome studies.
+
+From this perspective, lithium disilicate produced dentin stress values closer to the healthy baseline (−5.1% versus −17.8% for zirconia under vertical loading). Within the limitations of the present finite element model, lithium disilicate therefore demonstrated a more favorable stress distribution with respect to the intact tooth. Whether this numerical proximity translates into a clinical advantage cannot be established from a static linear-elastic analysis, and the analogy with peri-implant bone remodeling should be read as a mechanistic parallel rather than as evidence of an equivalent biological response in dentin, the remodeling capacity of which is considerably more limited. The clinical preference for lithium disilicate in posterior restorations reported in the prosthodontic literature [2] is therefore consistent with, but not demonstrated by, the present numerical comparison.
+
+4.4. Oblique Loading as the More Demanding Loading Condition
+
+The substantial increase in stress magnitudes under oblique loading (a 64–97% rise in coronal Von Mises stress depending on the model) emphasizes the importance of including non-axial loading conditions in FEA dental studies. The maximum principal stress in healthy enamel under oblique loading (61.7 MPa) approaches or exceeds the upper bound of the reported enamel tensile strength range (~10–40 MPa), providing a mechanistic explanation for the clinical observation that dental fractures occur predominantly during lateral excursive movements rather than during maximal intercuspation [31].
+
+For zirconia restorations, the coronal stress under oblique loading (174.5 MPa) represents about 19% of the lower-bound flexural strength (900 MPa); nevertheless, flexural strength values obtained from three-point bending tests do not translate directly to in situ multiaxial stress states and may therefore misrepresent the actual fracture risk. The restoration–dentin interface concentrated stress under oblique loading in both restored models and is accordingly identified as the region of highest mechanical demand within the model. In the present analysis, this interface is a bonded contact of zero thickness, whereas the corresponding clinical interface comprises a luting cement layer and a hybrid layer that degrades over time as a documented failure mechanism [27,29,32]. The present analysis therefore identifies the location of the concentration but cannot predict the failure mode, since neither the cement layer nor a fracture-mechanics criterion was included.
+
+4.5. Influence of the Model Simplifications on the Results
+
+The four simplifications declared in Section 2.6 do not affect the present results equally. Their expected influence is examined here in order to delimit which of the reported quantities may be regarded as robust and which are model-specific.
+
+The omission of the luting cement is the simplification with the largest effect on absolute magnitudes. A cement layer with an elastic modulus of the order of 4–8 GPa interposed between a 95–200 GPa restoration and 18 GPa dentin introduces a compliant interlayer that redistributes the load, generates its own stress concentration at the crown margin and alters the gradient across the restoration–dentin interface. The comparison with Guler et al. [27] in Section 4.2 illustrates the magnitude involved. The consequence for the present study is that the interfacial values reported in Section 3 correspond to an idealized, perfectly bonded interface and represent a best case; the introduction of a cement layer would be expected to raise the local stress at the margin and to reduce the degree of dentin stress shielding, because part of the modulus mismatch would be accommodated within the cement rather than transferred directly to the dentin.
+
+The omission of the periodontal ligament increases the overall rigidity of the model. Its effect is concentrated in the root and in the cervical third, where the fixed support imposes a boundary condition that does not exist physiologically; the coronal stress fields evaluated here under static occlusal load are considerably less sensitive to this boundary. Because the three models share the identical constraint and the comparison between them is unaffected, the cervical and radicular values should not be interpreted as physiological, and the model cannot be used to evaluate tooth mobility, load damping or stress transfer to the alveolar bone.
+
+The substitution of the entire enamel volume by the restoration corresponds to the material condition of a full-coverage crown, but does not reproduce three aspects of a clinical preparation: the additional reduction in the dentin core, its change in geometry toward a tapered stump with a defined finish line, and the difference in wall thickness that a clinician would give to zirconia versus lithium disilicate. This last point has a direction: a thinner zirconia crown over a larger residual dentin volume would be expected to reduce the degree of dentin shielding reported here. The present values for the zirconia model therefore likely overestimate the modulus effect relative to a clinically optimized preparation, and the comparison should be read as an evaluation of the material variable under a fixed geometry, and not as a comparison between clinical restorative protocols.
+
+The absence of the dentin–enamel junction and the isotropic, linear-elastic formulation affect chiefly the tensile field and the crack-related interpretation. The dentin–enamel junction is the structure that, in the intact tooth, arrests cracks travelling from enamel into dentin [28]; representing it as a bonded contact of zero thickness removes this toughening mechanism, so the healthy-tooth model does not reproduce the crack-arresting behavior of the natural interface, and the comparison of the healthy configuration against the restored ones is, in this specific respect, conservative. The isotropic assumption, following Munari et al. [19], preserves the location of the concentrations while overestimating tensile magnitudes; consequently, the comparison of the maximum principal stress against the reported tensile strength of enamel in Section 3.5 should be treated as an upper-bound estimate rather than as a fracture prediction.
+
+4.6. Validation and Predictive Capability
+
+The numerical behavior of the model was verified through a mesh-convergence study, as described in Section 2.3, and its outputs were compared with magnitudes reported in the FEA literature, as set out in Section 4.2. No experimental validation was performed: neither strain-gauge measurement, nor digital image correlation, nor in vitro fracture testing of the same geometry was available for the three configurations analyzed. The absolute stress values reported here have therefore not been shown to reproduce experimental measurements, and the predictive capability of the model with respect to fracture load or clinical survival is unverified.
+
+What the model does support is the comparison between the three configurations. All of them share the same geometry, the same mesh strategy and element type, the same boundary conditions, the same contact definitions, and the same applied load, so that the differences reported are attributable to the coronal material alone. Experimental validation against strain measurements on extracted molars, and subsequently against fatigue and fracture testing, is the necessary next step before any of these observations can be transferred to clinical decision-making. This constitutes the principal direction of the ongoing work of the present group.
+
+4.7. Limitations
+
+Several limitations should be acknowledged, in addition to the four simplifications declared in Section 2.6 and examined in Section 4.5. First, all materials were modeled as linear-elastic, homogeneous and isotropic, which does not capture the anisotropic behavior of enamel and dentin or the viscoelastic behavior of the pulp; future work should incorporate orthotropic material definitions in order to evaluate the extent to which these assumptions modify the tensile field. Second, the periodontal ligament was not explicitly modeled and a fixed support at the root surface was applied instead, which increases the rigidity of the assembly and removes the damping function of the ligament. Third, a single load magnitude of 200 N was applied in only two directions. This value lies within the reported range of maximum bite force in the molar region and was selected in order to permit comparison with published FEA studies that use magnitudes of the same order; because the analysis is linear-elastic, stress scales proportionally with the applied load, so the relative differences between configurations are independent of the magnitude chosen, whereas any threshold-based interpretation, such as the comparison against the tensile strength of enamel, is specific to 200 N. Clinical mastication involves cyclic loading of variable magnitude applied at multiple, migrating contact points, none of which is reproduced by two static load cases. Fourth, a single crown geometry derived from one CBCT study was analyzed; anatomical variation between patients and variation in preparation design may influence the stress distribution, and the present results should not be extrapolated to other tooth types or preparation geometries. Fifth, bond integrity was assumed to be perfect at all interfaces through bonded contacts, whereas in clinical practice adhesive and luting layers possess their own mechanical properties and degrade over time. Sixth, the analysis was performed under static loading conditions, whereas mastication is a cyclic, dynamic process; fatigue behavior was not modeled because the stress–life (S–N) curves required for the restorative materials under the present configuration were not available. Finally, no experimental validation of the model was performed, as discussed in Section 4.6. The evaluation of cyclic fatigue, of the explicit luting interface and of long-term durability, together with experimental validation, therefore, remain the principal directions for future work.
+
+5. Conclusions
+
+The present finite element analysis of a mandibular first molar under vertical and oblique loading, comparing a healthy tooth with full-coverage zirconia Y-TZP and lithium disilicate restorations, supports the following observations. All of them apply within the limitations of the model declared in Section 2.6 and examined in Section 4.5 and Section 4.6, and refer strictly to the comparison between the three configurations under the conditions simulated:Within this model, elastic-modulus mismatch was the dominant variable governing the biomechanical response: zirconia, with the highest modulus (200 GPa), generated the greatest coronal stress concentrations, 57.6% and 89.7% above the healthy baseline, under vertical and oblique loading, respectively. The analysis did not include a failure criterion and therefore does not establish a general hierarchy between elastic modulus and mechanical resistance.
+
+Oblique loading was the more demanding of the two conditions analyzed: under 30° lateral loading, the maximum principal stress in enamel or restoration approached or exceeded the reported tensile strength range of enamel in all models. This identifies lateral loading as the critical condition within the simulation and is consistent with, although it does not by itself demonstrate, the clinical predominance of fracture during excursive movements.
+
+Lithium disilicate demonstrated a more favorable stress distribution within the limitations of the present finite element model, producing dentin stress values closer to those of the intact tooth than zirconia under both loading conditions.
+
+These results quantify the influence of elastic-modulus compatibility on the stress distribution of a restored mandibular molar under two static load cases. They constitute a controlled numerical comparison between three configurations and do not, on their own, establish clinical material-selection criteria; their translation into clinical recommendations requires experimental validation and clinical evidence. Future work should incorporate an explicit cement layer, the periodontal ligament, orthotropic material definitions, a graded representation of the dentin–enamel junction, variable and cyclic loading, and fracture-mechanics criteria, together with experimental validation of the resulting model.
+
+Acknowledgments
+
+The authors thank the Instituto Politécnico Nacional and the Secretaría de Ciencia, Humanidades, Tecnología e Innovación for the institutional support provided throughout the development of this research.
+
+Author Contributions
+
+Conceptualization, R.A.M.-R. and R.A.H.-V.; methodology, R.A.M.-R., R.A.H.-V. and O.A.M.-M.; software, R.A.M.-R.; validation, R.A.M.-R., R.A.H.-V. and K.G.M.-C.; formal analysis, R.A.M.-R. and R.A.H.-V.; investigation, O.A.M.-M., K.G.M.-C. and R.A.R.-D.; resources, R.A.H.-V., O.A.M.-M. and R.A.R.-D.; data curation, R.A.M.-R. and K.G.M.-C.; writing—original draft preparation, R.A.M.-R. and R.A.H.-V.; writing—review and editing, R.A.M.-R., R.A.H.-V., O.A.M.-M. and R.A.R.-D.; visualization, R.A.M.-R. and O.A.M.-M.; supervision, R.A.H.-V. and R.A.M.-R.; project administration, R.A.M.-R. and R.A.H.-V. All authors have read and agreed to the published version of the manuscript.
+
+Institutional Review Board Statement
+
+The three-dimensional geometry analyzed in this study was obtained from a cone-beam computed tomography (CBCT) dataset previously acquired and published by the present research group [16]. The dataset corresponds to one of the authors of that study, who consented to its acquisition and to its use for research purposes. No patients or external human subjects were recruited, and no new human data were acquired for the present work, which consisted exclusively of numerical simulation performed on that previously published biomodel.
+
+Informed Consent Statement
+
+Not applicable.
+
+Data Availability Statement
+
+The data supporting the findings of this study are available from the corresponding author upon reasonable request.
+
+Conflicts of Interest
+
+Author O.A. Mastache-Miranda was employed by the company MARMAS Soluciones en Ingeniería e Investigación. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as potential conflicts of interest.
+
+Figure 1 Three-dimensional geometric models of the mandibular first molar showing the exploded view of tissue components and restorative configurations: enamel/restoration layer (top), dentin body (center), and pulp chamber (right): (a) healthy enamel; (b) zirconia Y-TZP full-coverage crown; and (c) lithium disilicate full-coverage crown. Y-TZP, yttria-stabilized tetragonal zirconia polycrystal.
+
+Figure 2 Finite element mesh of the healthy tooth model showing the element density distribution across enamel, dentin, and pulp regions.
+
+Figure 3 Schematic representation of the loading conditions: (a) vertical loading at 200 N along the tooth axis; (b) oblique loading at 30° with decomposed axial and horizontal pressure components.
+
+Figure 4 Von Mises equivalent stress distribution under vertical loading (200 N) in (a) the healthy molar, (b) the zirconia Y-TZP full-coverage crown configuration, and (c) the lithium disilicate full-coverage crown configuration. Each column shows, from top to bottom, the external molar view, the occlusal cross-section, the isolated dentin body, and the isolated pulp chamber. Each panel retains its own colour scale; peak values are reported in Table 2.
+
+Figure 5 Maximum principal stress distribution under vertical loading (200 N) in (a) the healthy molar, (b) the zirconia Y-TZP full-coverage crown configuration, and (c) the lithium disilicate full-coverage crown configuration. Each column shows, from top to bottom, the external molar view, the occlusal cross-section, the isolated dentin body, and the isolated pulp chamber. Each panel retains its own colour scale; peak values are reported in Section 3.2.
+
+Figure 6 Total deformation distribution under vertical loading (200 N) in (a) the healthy molar, (b) the zirconia Y-TZP full-coverage crown configuration, and (c) the lithium disilicate full-coverage crown configuration. Each column shows, from top to bottom, the external molar view, the occlusal cross-section, the isolated dentin body, and the isolated pulp chamber. Each panel retains its own colour scale; peak values are reported in Section 3.3.
+
+Figure 7 Von Mises equivalent stress distribution under oblique loading (200 N, 30°) in (a) the healthy molar, (b) the zirconia Y-TZP full-coverage crown configuration, and (c) the lithium disilicate full-coverage crown configuration. Each column shows, from top to bottom, the external molar view, the occlusal cross-section, the isolated dentin body, and the isolated pulp chamber. Each panel retains its own colour scale; peak values are reported in Table 3.
+
+Figure 8 Maximum principal stress distribution under oblique loading (200 N, 30°) in (a) the healthy molar, (b) the zirconia Y-TZP full-coverage crown configuration, and (c) the lithium disilicate full-coverage crown configuration. Each column shows, from top to bottom, the external molar view, the occlusal cross-section, the isolated dentin body, and the isolated pulp chamber. Each panel retains its own colour scale; peak values are reported in Table 4.
+
+Figure 9 Total deformation distribution under oblique loading (200 N, 30°) in (a) the healthy molar, (b) the zirconia Y-TZP full-coverage crown configuration, and (c) the lithium disilicate full-coverage crown configuration. Each column shows, from top to bottom, the external molar view, the occlusal cross-section, the isolated dentin body, and the isolated pulp chamber. Each panel retains its own colour scale; peak values are reported in Section 3.6.
+
+jfb-17-00404-t001_Table 1 Table 1 Mechanical properties of tissues and restorative materials.
+
+Material/Tissue	E (GPa)	ν	ρ (g/cm3)	Reference	
+Enamel	70.0	0.30	2.80	[3]	
+Dentin	18.3	0.30	2.00	[3]	
+Pulp	0.002	0.45	1.00	[3]	
+Zirconia (Y-TZP)	200.0	0.30	6.08	[1,23]	
+Lithium disilicate	105.0	0.23	2.50	[2,24]	
+Abbreviations: E (elastic modulus); ν (Poisson’s ratio); ρ (density); Y-TZP (yttria-stabilized tetragonal zirconia polycrystal).
+
+jfb-17-00404-t002_Table 2 Table 2 Maximum Von Mises stress by tissue under vertical loading (200 N).
+
+Tissue	Healthy (MPa)	Zirconia (MPa)	Li-Disilicate (MPa)	Δ vs. Healthy	
+Enamel/Restoration	56.1	88.4	67.1	+57.6/+19.6%	
+Dentin	29.2	24.0	27.7	−17.8/−5.1%	
+Pulp	0.0008	0.0004	0.0006	—	
+
+jfb-17-00404-t003_Table 3 Table 3 Maximum Von Mises stress by tissue under oblique loading (200 N, 30°).
+
+Tissue	Healthy (MPa)	Zirconia (MPa)	Li-Disilicate (MPa)	Δ vs. Healthy	
+Enamel/Restoration	92.0	174.5	122.8	+89.7/+33.5%	
+Dentin	58.8	46.1	54.7	−21.6/−7.0%	
+Pulp	0.0015	0.0008	0.0012	—	
+
+jfb-17-00404-t004_Table 4 Table 4 Maximum principal (tensile) stress by tissue and loading condition (MPa).
+
+Condition/Tissue	Healthy	Zirconia	Li-Disilicate	Tensile Strength *	
+Vertical, Enamel/Rest.	17.6	28.4	23.3	~10–40 (enamel) †	
+Vertical, Dentin	8.0	9.9	9.4	~52 (dentin)	
+Oblique, Enamel/Rest.	61.7	79.6	68.7	~10–40 (enamel) †	
+Oblique, Dentin	14.7	15.6	14.4	~52 (dentin)	
+* Reference tensile strength values from the literature: enamel ~10–40 MPa; dentin ~52 MPa. † The enamel tensile strength range applies to the healthy-tooth model only. The zirconia and lithium disilicate values are referred to the flexural strength reported for each ceramic (900–1200 MPa and 360–500 MPa, respectively [1,2]), as discussed in Section 4.4.
+
+Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.
+
+
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+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: GeroScience
+Journal ID: Geroscience
+NLM Journal ID: 101686284
+
+GeroScience
+
+ISSN: 2509-2715
+EISSN: 2509-2723
+Publisher: Springer
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC13356228
+PMID: 41872401
+DOI: 10.1007/s11357-026-02105-1
+Article ID: 2105
+Article version: 1
+Subjects: Publisher Correction
+
+Correction to: The effect of anthocyanins and anthocyanin‑rich foods on cognitive function: a meta‑analysis of randomized controlled trials
+
+Micek Agnieszka 1
+Godos Justyna 2
+Giampieri Francesca 3 4 5 6
+Battino Maurizio 3 4 5 7
+Quiles José L. 8
+Del Rio Daniele 9
+Mena Pedro 9
+http://orcid.org/0000-0003-1571-5327 Caruso Giuseppe giuseppe.caruso@unicamillus.org
+10 11
+Frias‑Toral Evelyn 12 13
+Azpíroz Irma Domínguez 6 14 15
+Xiao Jianbo 16
+Veronese Nicola 10
+Siervo Mario 17 18 19 20
+Vauzour David 21
+Ungvari Zoltan 22 23 24 25 26
+Galvano Fabio 2
+Grosso Giuseppe on behalf of the International Network for Evidence on Phytochemicals and Biotics for Human Health 2
+1 https://ror.org/03bqmcz70 grid.5522.0 0000 0001 2337 4740 Statistical Laboratory, Faculty of Health Sciences, Jagiellonian University Medical College, Cracow, Poland
+2 https://ror.org/03a64bh57 grid.8158.4 0000 0004 1757 1969 Department of Biomedical and Biotechnological Sciences, University of Catania, Catania, Italy
+3 https://ror.org/00x69rs40 grid.7010.6 0000 0001 1017 3210 Department of Clinical Sciences, Universita Politecnica Delle Marche, Ancona, Italy
+4 https://ror.org/00x69rs40 grid.7010.6 0000 0001 1017 3210 Joint Laboratory On Food Science, Nutrition and Intelligent Processing of Foods, Polytechnic University of Marche, Ancona, Italy
+5 https://ror.org/03jc41j30 grid.440785.a 0000 0001 0743 511X Universidad Europea del Atlantico, Spain and Jiangsu University, China at Polytechnic University of Marche, Ancona, Italy
+6 https://ror.org/048tesw25 grid.512306.3 0000 0004 4681 9396 Research Group On Food, Nutritional Biochemistry and Health, Universidad Europea del Atlantico, Santander, Spain
+7 https://ror.org/03jc41j30 grid.440785.a 0000 0001 0743 511X International Joint Research Laboratory of Intelligent Agriculture and Agri‑Products Processing, Jiangsu University, Zhenjiang, China
+8 https://ror.org/04njjy449 grid.4489.1 0000 0004 1937 0263 Department of Physiology, Institute of Nutrition and Food Technology “Jose Mataix Verdu”, Biomedical Research Centre, University of Granada, Armilla, Spain
+9 https://ror.org/02k7wn190 grid.10383.39 0000 0004 1758 0937 Human Nutrition Unit, Department of Food and Drug, University of Parma, Parma, Italy
+10 https://ror.org/00qvkm315 grid.512346.7 Departmental Faculty of Medicine, UniCamillus-Saint Camillus International University of Health and Medical Sciences, Rome, Italy
+11 https://ror.org/03njebb69 grid.492797.6 0000 0004 1805 3485 IRCCS San Camillo Hospital, Venice, Italy
+12 https://ror.org/00b210x50 grid.442156.0 0000 0000 9557 7590 School of Medicine, Universidad Espiritu Santo, Samborondon, Ecuador
+13 https://ror.org/05h9q1g27 grid.264772.2 0000 0001 0682 245X Division of Research, Texas State University, San Marcos, TX USA
+14 https://ror.org/04t45q150 0000 0004 9335 6881 Universidade Internacional Do Cuanza, Cuito, Angola
+15 https://ror.org/051sm7d31 Universidad de La Romana, La Romana, Dominican Republic
+16 https://ror.org/05rdf8595 grid.6312.6 0000 0001 2097 6738 Department of Analytical Chemistry and Food Science, Faculty of Food Science and Technology, University of Vigo, Ourense, Spain
+17 https://ror.org/02n415q13 grid.1032.0 0000 0004 0375 4078 Curtin‑Chulalongkorn Collaborative Centre for Nutrition and Food Research and Education, Curtin University, Perth, WA Australia
+18 https://ror.org/02n415q13 grid.1032.0 0000 0004 0375 4078 Faculty of Health Sciences, School of Population Health, Curtin University, Perth, WA Australia
+19 https://ror.org/02n415q13 grid.1032.0 0000 0004 0375 4078 Curtin Dementia Centre of Excellence, Enable Institute, Curtin University, Perth, WA Australia
+20 https://ror.org/02n415q13 grid.1032.0 0000 0004 0375 4078 Curtin Medical Research Institute (CMRI), Curtin University, Perth, WA Australia
+21 https://ror.org/026k5mg93 grid.8273.e 0000 0001 1092 7967 Norwich Medical School, Faculty of Medicine and Health Sciences, University of East Anglia, Norwich, UK
+22 https://ror.org/0457zbj98 grid.266902.9 0000 0001 2179 3618 Vascular Cognitive Impairment, Neurodegeneration and Healthy Brain Aging Program, Department of Neurosurgery, University of Oklahoma Health Sciences Center, Oklahoma City, OK USA
+23 https://ror.org/02aqsxs83 grid.266900.b 0000 0004 0447 0018 Stephenson Cancer Center, University of Oklahoma, Oklahoma City, OK USA
+24 https://ror.org/0457zbj98 grid.266902.9 0000 0001 2179 3618 Oklahoma Center for Geroscience and Healthy Brain Aging, University of Oklahoma Health Sciences Center, Oklahoma City, OK USA
+25 https://ror.org/0457zbj98 grid.266902.9 0000 0001 2179 3618 Department of Health Promotion Sciences, College of Public Health, University of Oklahoma Health Sciences Center, Oklahoma City, OK USA
+26 https://ror.org/01g9ty582 grid.11804.3c 0000 0001 0942 9821 International Training Program in Geroscience, Doctoral College/Institute of Preventive Medicine and Public Health, Semmelweis University, Budapest, Hungary
+Electronic publication date: 2026 Mar 24
+Publication date: 2026 Jun
+Volume: 48
+Issue: 3
+First page: 5107
+Last page: 5108
+Copyright: © The Author(s) 2026
+Copyright year: 2026
+License: Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Erratum for: The effect of anthocyanins and anthocyanin-rich foods on cognitive function: a meta-analysis of randomized controlled trials. 6 12 2025 Geroscience 10.1007/s11357-025-02008-7 41351717
+issue-copyright-statement: © American Aging Association 2026
+
+Ÿ==============================Ÿ
+Correction to: GeroScience
+
+10.1007/s11357-025-02008-7
+
+In this article, the consortium details in the author group were incorrectly given as “International Network for Evidence on Phytochemicals, Biotics for Human Health” but should have been “International Network for Evidence on Phytochemicals and Biotics for Human Health”.
+
+The original article has been corrected.
+
+The publisher sincerely apologizes for this error and any inconvenience caused to the authors and readers of the journal.
+
+Publisher's Note
+
+Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
+
diff --git a/corpus/psychology/text/7a8342359baa17c9.txt b/corpus/psychology/text/7a8342359baa17c9.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ceca0768f772dfcc0dad6c83274809afb7113d6c
--- /dev/null
+++ b/corpus/psychology/text/7a8342359baa17c9.txt
@@ -0,0 +1,15 @@
+Beyond Seeing and Knowing: The Development of an Intuitive Theory of Attention
+
+Where someone looks, and for how long, is a remarkably rich signal about their mind. It reveals
+what they find interesting, what they like, and what is new to them. These inferences are
+possible because as adults, we understand that people don’t just encode whatever is visible to
+them. This is instead modulated by what they choose to attend to, and for how long. Across
+four experiments (N = 220), we asked whether children understand these nuances. We found
+that unlike adults, children showed only partial expectations about what draws attention,
+expecting longer looking for larger sets by age six, but not for more complex or more varied
+objects (Exp. 1). However, children as young as five understood that an agent who looked
+longer formed a more accurate representation of what they saw (Exp. 2), and that they are more
+likely to look longer at things they find desirable (Exp. 3). Finally, six-year-olds, but not five-
+year-olds, inferred that agents who already know about a toy are less likely to look for an
+extended duration (Exp. 4). Together, these results suggest that an intuitive theory of attention
+is partly in place by age five and continues to develop past age six.
diff --git a/corpus/psychology/text/7b1bc80a605f1e81.txt b/corpus/psychology/text/7b1bc80a605f1e81.txt
new file mode 100644
index 0000000000000000000000000000000000000000..d6d1159df108161f6bbb890f36ed9f4ce4162d83
--- /dev/null
+++ b/corpus/psychology/text/7b1bc80a605f1e81.txt
@@ -0,0 +1,63 @@
+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Front Psychol
+Journal ID: Front Psychol
+NLM Journal ID: 101550902
+Journal ID: Front. Psychol.
+
+Frontiers in Psychology
+
+EISSN: 1664-1078
+Publisher: Frontiers Media SA
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC13141301
+PMID: 42094316
+DOI: 10.3389/fpsyg.2026.1852604
+Article version: 1
+Article version:
+Subjects: Correction
+
+Correction: Cognitive control: modeling the impact on mental health
+
+Alker Leon *
+Department of Psychology, Philipps University Marburg , Marburg , Germany
+* Correspondence: Leon Alker, leonalkersci@gmail.com
+Electronic publication date: 2026 Apr 21
+Publication date: 2026
+Volume: 17
+Electronic Location ID: 1852604
+Received 2026 Apr 10; Accepted 2026 Apr 13
+Copyright: Copyright © 2026 Alker.
+Copyright year: 2026
+Copyright holder: Alker
+License: This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Erratum for: Cognitive control: modeling the impact on mental health 16 21 2 2025 1452714 Frontiers in Psychology 10.3389/fpsyg.2025.1452714 PMC11885272 40062198
+Keywords: cognitive control, mental health, affective neuroscience, computational modeling, clinical neuropsychology, mind control
+Figure count: 0
+Table count: 0
+Equation count: 0
+Reference count: 0
+Page count: 1
+
+section-at-acceptance: Cognitive Science
+
+Ÿ==============================Ÿ
+In the published article, the acronyms SONA and SoSci were incorrectly defined in Section 8.1 (Participants).
+
+The following correction has been made:
+
+“This study was carried out in accordance with relevant guidelines and regulations and was approved by the ethics committee of Philipps-University Marburg, Germany. Informed consent was obtained from all 122 participants. Ninety-five participants were students, 27 of whom were employees of a university hospital. Students were recruited via the SONA first-year practicum and were then forwarded to the online survey platform SoSci Survey for study participation. SONA is an online participant management system used to recruit and schedule student participants, typically in exchange for course credit. SoSci Survey is an online survey platform used to administer questionnaires and collect data.”
+
+The original version of this article has been updated.
+
+Publisher's note
+
+All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.
+
+Approved by: Frontiers Editorial Office, Frontiers Media SA, Switzerland
+
diff --git a/corpus/psychology/text/7b810bb96d2a7f83.txt b/corpus/psychology/text/7b810bb96d2a7f83.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0a4bf004ff272d4ca06aacc485b8fe2b90edf627
--- /dev/null
+++ b/corpus/psychology/text/7b810bb96d2a7f83.txt
@@ -0,0 +1,3 @@
+Frequency-dependent selection in the English spelling system across 1000 years of history
+
+English orthography has largely been left to evolve freely across its thousand-year history with little top-down design or reform. Yet modern English spelling has become standardized, even if its standardized spellings are sometimes internally inconsistent. The relative freedom with which English orthography has been allowed to evolve makes it an interesting test-case for exploring whether spelling standardization might arise through a process of positive frequency-dependent selection. To maximize the chance of being understood, it pays for a writer to adopt spelling variants that occur with higher frequency, leading to those forms becoming increasingly entrenched. To evaluate this possibility, we assembled a diachronic dataset of English spelling variation, SpellEng, which we make freely available. SpellEng reports on the frequency of 112,080 spelling variants (across 32,264 lemmata) over the entire history of written English. We use this dataset along with a model of frequency-dependent selection to estimate the extent to which English standardization can be explained by such a process. Our findings suggest that the past 1000 years of English spelling have been characterized by both positive and negative frequency-dependent selection. We discuss how linguistic dynamics and external events have shaped these periods of stability and change.
diff --git a/corpus/psychology/text/7d0bb1ab754442d3.txt b/corpus/psychology/text/7d0bb1ab754442d3.txt
new file mode 100644
index 0000000000000000000000000000000000000000..f3a5fc7a4adcee2ca58297593f227826a64a3813
--- /dev/null
+++ b/corpus/psychology/text/7d0bb1ab754442d3.txt
@@ -0,0 +1,318 @@
+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: J Neuroendocrinol
+Journal ID: J Neuroendocrinol
+NLM Journal ID: 8913461
+Journal ID: JNE
+
+Journal of Neuroendocrinology
+
+ISSN: 0953-8194
+EISSN: 1365-2826
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC12989916
+PMID: 41834699
+DOI: 10.1111/jne.70153
+Article ID: JNE70153
+Article version: 1
+Subjects: Original Article, Original Article
+
+Acute and persistent neuroendocrine and behavioral alterations after social fear conditioning in adolescent male mice
+
+Bludau et al.
+
+Bludau Anna 1
+Kabas Melanie 1
+Menon Rohit https://orcid.org/0000-0002-9370-3818 1
+Neumann Inga D. 1 inga.neumann@ur.de
+
+1 Department of Behavioral and Molecular Neurobiology University of Regensburg Regensburg Germany
+* Correspondence
+Inga D. Neumann, Department of Behavioral and Molecular Neurobiology, University of Regensburg, Universitaetsstrasse 31, 93053 Regensburg, Germany.
+Email: inga.neumann@ur.de
+
+Electronic publication date: 2026 Mar 16
+Print publication date: 2026 Mar
+Volume: 38
+Issue: 3
+Electronic Location ID: e70153
+Revised 2026 Jan 15; Received 2025 Apr 29; Accepted 2026 Feb 16
+Copyright: © 2026 The Author(s). Journal of Neuroendocrinology published by John Wiley & Sons Ltd on behalf of British Society for Neuroendocrinology.
+License: This is an open access article under the terms of the http://creativecommons.org/licenses/by/4.0/ License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Keywords: corticosterone, oxytocin, social anxiety disorder, social avoidance
+
+Funding: Deutsche Forschungsgemeinschaft 10.13039/501100001659 Ne465/31 GRK‐2174
+Figure count: 4
+Table count: 2
+Page count: 12
+
+source-schema-version-number: 2.0
+cover-date: March 2026
+details-of-publishers-convertor: Converter:WILEY_ML3GV2_TO_JATSPMC version:6.7.1 mode:remove_FC converted:16.03.2026
+
+Bludau A , Kabas M , Menon R , Neumann ID . Acute and persistent neuroendocrine and behavioral alterations after social fear conditioning in adolescent male mice. J Neuroendocrinol. 2026;38(3):e70153. doi:10.1111/jne.70153 41834699 PMC12989916
+
+Anna Bludau and Melanie Kabas shared first authorship.
+
+Ÿ==============================Ÿ
+Abstract
+
+Adolescence is a critical developmental period with heightened stress susceptibility. Traumatic experiences during this phase are highly predictive of future affective disorders, such as social anxiety disorder (SAD), which may manifest during early adolescence. Social avoidance, a major symptom of SAD, can be robustly generated in adult male and female mice using the social fear conditioning (SFC) paradigm. Using the SFC paradigm in adolescent mice, we analyze behavioral and neuroendocrine responses after adolescent social trauma. Here, we demonstrate that social fear elicited by SFC in early adolescent (EA) male mice (SFC + EA/29d) persists until adulthood (SFC + EA/57d). We further compared neuroendocrine responses to a heterotypic (elevated platform) or homotypic (exposure to a conspecific) stressor after SFC performed either in EA (SFC + EA/29d, SFC + EA/57d) or adulthood (SFC + AD). While in non‐conditioned SFC − EA/29d mice plasma corticosterone concentrations remained unchanged after social exposure in adolescence, SFC + EA/29d resulted in a hyper‐response of the HPA axis to the social, but not heterotypic stressor, with a negative correlation of plasma corticosterone concentrations and social investigation times. This effect of SFC + EA/29d on plasma corticosterone response was absent in SFC + EA/57d and SFC + AD mice indicating a higher sensitivity to social trauma in EA. We further revealed a rise in plasma oxytocin (OXT) levels in adult SFC − mice in response to the social challenge, whereas the OXT system of SFC − EA/29d mice still seems to be unresponsive to the social stimulus. Importantly, after SFC + either in EA or AD, the OXT response to social exposure found in SFC −AD controls was completely abolished, whereas in SFC − EA/57d mice OXT levels positively correlated with social investigation times, indicating social trauma‐induced acute and long‐lasting dysfunctions of the OXT system. In summary, we show that exposure to social trauma (SFC+) in early adolescence exerts both short‐term as well as long‐term effects on social behavior. We further reveal that SFC+EA/29d prevents the corticosterone hypo‐response to social stimuli characteristic for early adolescence. Moreover, SFC+/AD and SFC+EA/57d impair the plasma OXT response to a social, but not heterotypic, stressor.
+
+1 INTRODUCTION
+
+Adolescence is a critical developmental period characterized by profound neuroanatomical plasticity, elevated stress sensitivity, and dynamic adaptations in socio‐emotional behavior. Adolescent rodents display increased social activity, 1 risk‐taking, 2 and impulsivity 3 as opposed to other age groups. Traumatic experiences during adolescence are highly predictive of the development of various affective disorders, 4 such as social anxiety disorder (SAD). Major symptoms of SAD include intense fear and avoidance of social situations. With a lifetime prevalence of 8%–15%, 5 SAD is deemed a major health concern. The onset of SAD typically occurs in early adolescence (EA) and tends to persist unless treated effectively. Acute or repeated exposure to severe traumatic events, such as social trauma, or stress during adolescence, a period of heightened brain plasticity, has a severe impact on behavioral and neuroendocrine development. 6 For example, exposure of rats and mice to chronic non‐social or social stressors during or around adolescence exerts long‐lasting effects on social, emotional, and cognitive behaviors. Some of these consequences have been linked to reduced hippocampal neurogenesis and neuroplasticity, 7 and to alterations of hypothalamic–pituitary–adrenal (HPA) axis functions, including increased cellular activity within the paraventricular nucleus (PVN) of the hypothalamus. 8 , 9
+
+Stress hormones, such as corticosterone (CORT), secreted in response to threatening stimuli and traumatic experiences, are known to promote fear generalization 10 and the retention of contextual fear. 11 CORT was also shown to improve the extinction of fear memory in adult rodents. 12 During adolescence, however, a high variability in the stress response of the HPA axis of rodents has generally been observed, with increased, 13 decreased, 14 or unaltered 15 plasma CORT responses dependent on the characteristics and severity of the applied chronic non‐social stress.
+
+The neuropeptide oxytocin (OXT), which essentially promotes various social behaviors, also exerts stress‐protective effects mostly studied in adulthood. 16 , 17 , 18 The distribution and quantity of OXT receptor‐expressing cells within distinct brain regions are dynamically shifted during development, with adolescence being a critical remodeling period. 19 , 20 , 21 These developmental changes in the OXT system are suggested to contribute to age‐specific adaptations in socio‐emotional behavior. 6 , 16 , 22 , 23 Interestingly, intranasal application of synthetic OXT has been suggested to mitigate isolation‐induced SAD in adolescent patients. 24 However, the neurobiological mechanisms underlying the etiology of SAD in adolescent subjects remain elusive.
+
+Social fear conditioning (SFC) is an established mouse model of SAD that has been shown to robustly evoke social avoidance in adolescent 22 and adult male 25 and female 26 mice by application of a mild foot shock when in direct contact with a conspecific. Subsequently, mice are repeatedly exposed to social stimuli during SFC extinction training, thereby shifting their behavior from social avoidance to social approach and investigation. However, it remains elusive whether social avoidance elicited by SFC during EA persists until adulthood (AD). Also, to what extent SFC exposure in EA (SFC+EA) or in AD (SFC+AD) differentially affects HPA axis and OXT responses to either a heterotypic or homotypic stressor is unknown.
+
+Here, we studied whether SFC+EA is capable of eliciting robust social fear, which may even persist until AD. We further compared the HPA axis and OXT responses to an acute 5‐min exposure to either a heterotypic (elevated platform; EPF) or homotypic (unknown conspecific) stressor in SFC+EA and SFC+AD male mice.
+
+2 MATERIALS AND METHODS
+
+2.1 Animals and husbandry
+
+Male CD1 mice (EA: 27–29 days, AD: 55–57 days at the start of experiment; Charles River Laboratories, Germany) were maintained under standard laboratory conditions (12/12 h light/dark cycle; lights on at 07:00 am, 21–23°C, 55%–60% humidity) with food and water available ad libitum. Initially, after arrival from the supplier, mice were group‐housed in groups of four for 3 days and single‐housed in observation cages (30 cm × 25 cm × 35 cm) for 2 days prior to acquisition of social fear until the end of the experiment. Weight‐, age‐, and sex‐matched conspecifics were used as social stimuli. All experiments were conducted between 08:00 am and 12:00 pm in accordance with the Guide for the Care and Use of Laboratory Animals by the National Institutes of Health, Bethesda, USA, approved by the government of Unterfranken and performed according to international guidelines on the ethical use of animals and ARRIVE guidelines. 27
+
+2.2 Social fear conditioning (SFC)
+
+The SFC paradigm was performed with a computerized fear conditioning system (TSE System GmbH, Germany) as previously described. 22 , 25 , 26 , 28 Briefly, during acquisition of social fear (Figure 1A), mice were habituated to the chamber for 30 s and subsequently exposed to a non‐social stimulus (small empty wire‐mesh cage) followed by a social stimulus (age and weight‐matched conspecific placed in a wire‐mesh cage; conditioned stimulus: CS). Unconditioned mice (SFC−) were allowed to freely explore the social stimulus, whereas conditioned mice (SFC+) received a mild foot shock (0.7 mA, approx. 1 s; unconditioned stimulus: US) when in direct contact with the social stimulus.
+
+FIGURE 1 Schematic representation of the experimental protocol. (A) During acquisition of social fear, early adolescent (EA, 28d of age) or adult (AD, 56d of age) mice were habituated to the chamber for 30 s and subsequently exposed to a non‐social stimulus (empty wire‐mesh cage) for 3 min followed by a social stimulus (conspecific in wire‐mesh cage). Social fear‐conditioned (SFC+) mice received a mild foot shock when investigating and sniffing an unknown same‐sex, same‐age conspecific, whereas unconditioned (SFC−) mice were allowed to freely investigate the social stimulus. (B) To analyze acute (29d old; 1 day after acquisition) and persistent (57d old; 28 days after acquisition) social avoidance elicited by SFC in EA, SFC+ and SFC− mice were consecutively exposed to 3 non‐social stimuli (wire‐mesh cages) and 6 different social stimuli (wire‐mesh cages containing an unknown conspecific) for 3 min each with a 3‐min inter‐stimulus interval during social fear extinction training. On the subsequent day during recall, mice were exposed to 6 unknown social stimuli. Hence, the following groups were analyzed: SFC−EA/29d, SFC+EA/29d, SFC−EA/57d, and SFC+EA/57d. (C) A separate cohort of mice was exposed to a 5‐min heterotypic (elevated platform; EPF) or homotypic (social stimulus) stressor or remained undisturbed in the home cage (basal) 1 day (SFC+/−EA/29d; adulthood SFC+/‐AD) or 28 days (SFC+/−EA/57d) after acquisition of social fear either in EA or AD. Plasma hormone levels for corticosterone (CORT), and oxytocin (OXT), OXT+ brain cells, as well as relative organ weights (thymus, adrenals, spleen) were analyzed, and splenocytes were quantified 10 or 30 min after termination of the stressor. Here, the stressor response of the following groups was analyzed: SFC−EA/29d, SFC+EA/29d, SFC−EA/57d, SFC+EA/57d, SFC−AD and SFC+AD. Created with BioRender (www.BioRender.com).
+
+To evaluate the persistence of social avoidance after SFC in EA, mice were exposed to 3 non‐social and 6 social stimuli either on the subsequent day (EA/29d) or 28 days later (EA/57d) during social fear extinction training (Figure 1B). During extinction recall on the following day (either 30d or 58d), mice were exposed to 6 social stimuli. The following groups were analyzed: SFC−EA/29d, SFC+EA/29d, SFC−EA/57d, and SFC+EA/57d.
+
+Social investigation behavior was manually scored by an observer blind to treatment and is shown as percentage of time spent in close interaction with and sniffing at the respective stimulus.
+
+As the behavioral effects of SFC in adult male mice are well known, 22 , 25 , 26 , 28 we included separate groups of adult mice (SFC−AD, SFC+AD) only after SFC acquisition to assess subsequent CORT and OXT responses to stressor exposure (Figure 1C).
+
+2.3 Stressor exposure
+
+To compare HPA and OXT responses to either a heterotypic or homotypic stressor after SFC in EA or in AD, mice were exposed to either the EPF or a social stressor (conspecific) for 5 min or were left undisturbed (basal; Figure 1C) either 1 day (EA: 29d; AD: 57d) or 4 weeks (EA: 57d) after acquisition of social fear (Figure 1A). The following groups were analyzed: SFC+EA/29d, SFC−EA/29d, SFC+EA/57d, SFC−EA/57d, SFC+AD, and SFC−AD.
+
+2.3.1 EPF (heterotypic stressor)
+
+Mice were individually placed on the EPF (diameter 18 cm; elevation 75 cm; 160 lux) for 5 min without behavioral monitoring and were returned to their home cage thereafter. 29
+
+2.3.2 Social (homotypic stressor)
+
+Mice were exposed to a novel social stimulus (within a small wire‐mesh cage) placed into their home cage for 5 min. Their behavior was videotaped. The social investigation behavior was manually scored by an observer blind to treatment and is shown as percentage of time spent in direct social contact.
+
+2.4 Trunk blood sampling
+
+Mice were sacrificed by decapitation under CO2 anesthesia either 10 min or 30 min after termination of acute stressor exposure. Trunk blood was collected in EDTA‐coated tubes (Sarstedt, Germany) on ice within 2 min after removal from their home cage, and centrifuged at 4°C (5000 rpm, 10 min). Plasma was stored at −20°C until assayed.
+
+2.5 Quantification of OXT + cells
+
+To quantify OXT‐producing (OXT+) neurons in the hypothalamic PVN and supraoptic nuclei SON of SFC−/+EA/29d and SFC−/+EA/57d male mice, animals were deeply anaesthetized with an intraperitoneal injection of ketamine (10%; 1 mL/kg; WDT, Garbsen, Germany) and xylazine (2%; 0.5 mL/kg; Serumwerk Bernburg AG, Bernburg, Germany) 90 min after 5‐min social stressor exposure. Subsequently, animals were transcardially perfused using 0.01 M PBS (pH 7.4) followed by a 4% paraformaldehyde solution (PFA; pH 7.4; in 0.01 M PBS). Brains were extracted, post‐fixed overnight in 4% PFA, cryo‐protected in 30% sucrose in 0.01 M PBS for 2–3 days at 4°C and finally snap‐frozen in N‐methylbuthane (Sigma Aldrich, Deisenhofen, Germany) on dry ice. Thirty or 40‐μm coronal brain sections were cryo‐cut (Cryostat CM 3050S; Leica, Wetzlar, Germany) and stained for OXT using immunofluorescent methods. Briefly, non‐specific binding was blocked using 0.1% triton X‐100 and 2% normal goat serum (NGS; Vector Laboratories, Burlingame, USA) in 0.01 M PBS for 1 h. Brain sections were incubated overnight at 4°C with the primary antibody mouse anti‐OXT‐neurophysin1 (PS‐38, 1:1000 in 0.01 M PBS, 0.1% Triton X‐100 and 2% NGS; kindly provided by Dr. Harold Gainer, NIH, Bethesda, USA) and subsequently incubated for 2 h at room temperature with the secondary antibody (1:1000; goat anti‐mouse Alexa Fluor™ 488, A11001, Thermo Fisher Scientific, Waltham, USA) in 2% NGS/0.01 M PBS. Slices were mounted onto SuperFrost object slides using ROTI®Mount FluorCare mounting medium with DAPI (Carl Roth GmbH & Co KG, Karlsruhe, Germany). Tissue images of the PVN and SON were acquired using a Leica Thunder Tissue Imager microscope with 20× objective lens (z‐stack with 1 μm steps), OXT (GFP: ex: 450–490, dc: 495, em: 500–550; exposure: 120 ms, illumination: 30%) and DAPI (DAPI: ex: 325–375, dc: 400, em: 435–485; exposure: 140 ms, illumination: 30%). Thunder automated computational clearance (large volume; medium: vectashield) was performed. Exported z‐stack pictures (lossless compression; .tiff) were compiled to 2D (>z‐projection > maximum intensity for OXT); (>z‐projection > average intensity for DAPI) and the OXT channel was edited (>subtract background > rolling ball radius 75 pixels and > enhance contrast > saturated pixels 0.15%) using ImageJ. The selection of the regions of interest (PVN or SON) as well as quantification of OXT+ cells were performed manually using ImageJ. DAPI channel images were further edited in Cellprofiler using the method EnhanceOrSupressFeatures (suppress; 14) and DAPI+ cells were counted automatically within the annotated regions using the StarDist model (dsb2018_heavy_augment.pb; normalizePercentiles (1, 99); threshold (0.3); pixelSize (0.6); cellExpansion (4)) in QuPath. For each animal, the mean value of OXT+/DAPI+ cells of 2–3 images from PVN and 4–6 images from SON were evaluated.
+
+2.6 Determination of organ weights and splenocyte number
+
+After decapitation, the left and right adrenal glands, thymus, and spleen were removed, pruned from fat, and weighed separately. Splenocytes were isolated and counted as previously described. 30
+
+2.7 Plasma hormone analysis
+
+Plasma CORT concentrations were analyzed using a commercially available ELISA (analytical sensitivity <1.631 nmol/L, intra‐assay and inter‐assay coefficients of variation ≤6.35%; IBL International, Germany). Plasma OXT was analyzed after an extraction procedure by radioimmunoassay (Riagnosis, Germany) as described. 31
+
+2.8 Statistical analysis
+
+For statistical analysis (SPSS 29; IBM) data were tested for normal distribution using the Kolmogorov–Smirnov test. Mixed model ANOVA followed by Bonferroni post hoc (ns1‐ns3 and s1‐s6 separately) was used to analyze extinction and recall of social fear: factor conditioning × stimulus. Geisser–Greenhouse correction was applied when sphericity was violated (tested by Mauchly test). Parametric two‐way analysis of variance (ANOVA; factor conditioning × stressor) followed by Bonferroni post hoc was performed to analyze plasma hormone levels within the three age groups (EA/29d, EA/57d, and AD). Parametric student's t‐test was performed to analyze social investigation during social exposure and as indicated in Table S1. Pearson's correlation was used to analyze relations between plasma hormone levels and social investigation. Statistical significance was accepted at p < .05. Statistical outliers were calculated by “mean ± 2 × standard deviation” and have been removed from analysis. Detailed reports for significant statistical analysis and group sizes are available in Tables S1 and S2. Graphs were plotted using Prism 10 (GraphPad).
+
+3 RESULTS
+
+A summary of all behavioral and endocrine data can be found in Table 1.
+
+TABLE 1 Summary of the found behavioral and endocrine effects.
+
+	Behavior	Plasma CORT	Plasma OXT	
+	SFC	Effect of conditioning	Effect of stressor	Effect of conditioning	Effect of stressor	
+SFC+/−EA/29d	SFC+: social avoidance and successful extinction	BAS	N/C	SFC−EA/29d	EPF > BAS	BAS	N/C	SFC−EA/29d	N/C	
+EPF	SFC+ < SFC−	N/C	EPF	N/C	N/C	
+SOC	SFC+ > SFC−	EPF > SOC	SOC	N/C	N/C	
+		SFC+EA/29d	EPF > BAS			SFC+EA/29d	N/C	
+		SOC > BAS			N/C	
+		EPF > SOC			N/C	
+SFC+/−EA/57d	SFC+: social avoidance and successful extinction	BAS	N/C	SFC−EA/57d	EPF > BAS	BAS	N/C	SFC−EA/57d	N/C	
+EPF	N/C	SOC > BAS	EPF	N/C	SOC > BAS	
+SOC	N/C	N/C	SOC	SFC+ < SFC−	EPF < SOC	
+		SFC+EA/57d	EPF > BAS			SFC+EA/57d	N/C	
+		SOC > BAS			N/C	
+		N/C			N/C	
+SFC+/‐AD	25 : SFC+: social avoidance and successful extinction	BAS	N/C	SFC−AD	EPF > BAS	BAS	N/C	SFC−AD	N/C	
+EPF	N/C	SOC > BAS	EPF	N/C	SOC > BAS	
+SOC	N/C	EPF > SOC	SOC	SFC+ < SFC−	EPF < SOC	
+		SFC+AD	EPF > BAS			SFC+AD	N/C	
+		N/C			N/C	
+		EPF > SOC			N/C	
+Abbreviations: AD, adult; BAS, basal; EA, early adolescence; EPF, elevated platform; N/C, no change; SFC, social fear conditioning; SFC−, unconditioned; SFC+, conditioned; SOC, social exposure.
+
+Note: The shading was included to highlight the significant effects.
+
+3.1 Social fear conditioning during early adolescence results in acute and persistent social avoidance
+
+To analyze whether SFC during EA, i.e., at the age of 28d, results not only in acute, but also in a persistent expression of social fear, SFC+EA and SFC−EA mice were subjected to extinction training either on the next day (SFC+/−EA/29d) or 4 weeks later (SFC+/−EA/57d) (Figure 1A,B). SFC+EA/29d and SFC+EA/57d mice received a similar number of CS‐US pairings during acquisition of social fear (SFC+EA/29d: 1.85 ± 0.19; SFC+EA/57d: 1.87 ± 0.13). During social fear extinction training, SFC+EA/29d and SFC+EA/57d mice showed lower investigation times especially of the first social stimuli (both SFC+EA/29d and SFC+EA/57d: s1–s3 p < .04 vs. SFC−EA/29d and SFC−EA/57d, respectively; Figure 2B,E and Table S1 for detailed statistics), representing social fear. Reflecting the successful extinction of social fear, both SFC+EA/29d and SFC+EA/57d mice showed a gradual increase in social investigation time of the six presented social stimuli. Independent of the period between acquisition and extinction, the success of social fear extinction was also reflected by overall high social investigation times of SFC+EA/29d and SFC+EA/57d mice on the subsequent day during recall (Figure 2C,F). The investigation times of the three non‐social stimuli presented prior to extinction training did not differ between SFC+ and SFC− groups (Figure 2B,E), which illustrates the absence of general fear after SFC. In summary, SFC in adolescence results in robust social fear, which persists until adulthood.
+
+FIGURE 2 Social fear conditioning (SFC) in early adolescence (EA) leads to acute and persistent social avoidance in male mice. (A) Schematic representation of acute effects of SFC in EA (age 28d on day of acquisition). EA mice were conditioned (SFC+) or remained unconditioned (SFC−) during social fear acquisition and underwent extinction (age 29d) and recall (age 30d) on the subsequent days (groups SFC+/−EA/29d). Investigation time of the 3 presented non‐social and 6 presented social stimuli during (B) social fear extinction training, and (C) recall in SFC+/−EA/29d mice. (D) Schematic representation of persistent effects of SFC in EA (SFC+/−EA/57d; age 28d on day of acquisition). Mice underwent extinction (age 57d) and recall (age 58d) in adulthood. Investigation time during (E) social fear extinction training and (F) recall in SFC+/−EA/57d mice. *p < .05 SFC+ vs. SFC−. Data represents mean ± SEM; n = 7‐13/group.
+
+3.2 Social trauma prevents CORT hypo‐response to social stress exposure in early adolescence
+
+To test whether acquisition of social fear, either during early adolescence or in adulthood, alters HPA axis responses to a heterotypic (EPF) or homotypic (social) stressor, plasma CORT levels were analyzed 10 min (and 30 min, see Figure S2) after 5‐min stressor exposure, either 1 day (SFC+EA/29d, SFC−EA/29d) or 28 days (SFC+EA/57d, SFC−EA/57d) after acquisition during early adolescence, or 1 day after acquisition in adulthood (SFC+AD, SFC−AD) (Figure 3A). In confirmation of the previous experiments (Figure 2), 25 all SFC+ mice (i.e., SFC+EA/29d, SFC+EA/57d, and SFC+AD) spent a lower percentage of time investigating the social stimulus compared to their respective SFC− controls (all age groups p < .003; Figure 3B), reflecting social fear during the 5‐min social exposure time.
+
+FIGURE 3 Social investigation during 5‐min exposure to a social stimulus, and plasma corticosterone (CORT) concentrations after 5‐min exposure to a non‐social or social stimulus in adolescent (EA) and adult (AD) social fear‐conditioned (SFC+) and unconditioned (SFC−) mice. (A) Male mice underwent social fear acquisition in EA (age 28d) or AD (age 56). On the subsequent day (EA/29d and AD) or 4 weeks later (EA/57d) they were either exposed to a 5‐min heterotypic (elevated platform; EPF) or homotypic (a single conspecific; SOC) stressor or remained undisturbed (BAS). Plasma CORT levels were obtained 10 min post stressor exposure. (B) Percent of social investigation time of SFC+/−EA/29d, SFC+/−EA/57d, and SFC+/‐AD mice during 5‐min exposure to a single SOC stressor. (C) Plasma CORT under BAS conditions and 10 min after exposure to the EPF or SOC stressor in SFC+/−EA/29d, SFC+/−EA/57d, and SFC+/‐AD mice. (D) Correlation of investigation time of the social stimulus and plasma CORT levels in SFC+/−EA/29d mice. *p < .05, **p < .01 SFC+ vs. SFC−, # p < .05, ## p < .01 stress vs. respective basal; ++ p < .01 SOC vs. respective EPF. Data represents mean + SEM; n = 6–8/group.
+
+Independent of SFC, increased plasma CORT concentrations were observed after exposure to the EPF compared to respective basal values in all age groups (for all comparisons p < .005, see Table S1 for detailed statistics; Figure 3C). However, an increased HPA axis response to a social stimulus was only found in adult mice, which acquired social fear during adolescence, independent of SFC, in SFC+EA/57d (p < .001) and SFC−EA/57d (p = .019), and upon adult SFC in SFC−AD (p = .001) when compared to basal values. In contrast, in EA, a rise in plasma CORT in response to the social stimulus was only found in SFC+EA/29d (p = .023), but not in SFC−EA/29d mice, indicating a physiological HPA axis hypo‐response to social stressors in EA, which becomes dysregulated after acquisition of social fear. In support, comparison of stress‐induced plasma CORT concentrations between SFC+ and SFC− mice revealed increased levels in response to the social stimulus in SFC+EA/29d mice (p = .034 vs. SFC−EA/29d), whereas exposure to the EPF resulted in lower levels in SFC+EA/29d mice (p = .001 vs. SFC−EA/29d), indicating a stressor‐specific shift in HPA responsiveness after SFC+EA.
+
+An SFC+‐induced shift in HPA axis responses was not found in adult mice (EA/57d or AD). Importantly, only plasma CORT concentrations of EA/29d, but not of EA/57d or AD mice, negatively correlated with social investigation times (R 2 = 0.482; p = .012; Figure 3D), confirming higher plasma CORT and social fear in SFC+EA/29d mice compared to SFC−EA/29d mice. Thus, the presence of a conspecific seems to be highly stressful in socially traumatized EA mice, which normalizes by adulthood. Independent of SFC, comparison of HPA axis responses to EPF versus social exposure revealed generally lower CORT responses to the social stimulus in EA mice (SFC+EA/29d and SFC−EA/29d both p < .001 vs. EPF) and in AD mice (SFC+AD p = .006, SFC−AD p = .001). However, in SFC+/−EA/57d mice we did not reveal such lower plasma CORT response to a social stressor compared to the EPF.
+
+Similar SFC+‐induced alterations in social investigation and in the patterns of stress‐induced CORT concentrations were found in the 30 min post‐stressor EA/29d, EA/57d, and AD groups (Figure S2B,D).
+
+In summary, social trauma in EA induced a CORT hyper‐response to a social, but not heterotypic, stressor seen in early adolescence, which becomes normalized until adulthood.
+
+3.3 Social trauma in early adolescence impairs OXT response to social stress in adult mice
+
+We further analyzed plasma OXT concentrations 10 min (and 30 min, see Figure S2) after exposure to either a heterotypic or homotypic stressor in SFC+ and SFC− mice of the EA/29d, EA/57d, and AD groups (Figure 3A).
+
+Independent of conditioning, exposure to the EPF did not alter plasma OXT levels compared to basal levels in all groups. However, plasma OXT levels rose in response to the social challenge, but only in unconditioned adult mice (SFC−EA/57d and SFC−AD p < .001 vs. respective basal; Figure 4A). In contrast, in adolescent mice, the OXT system seems still unresponsive to a social challenge, with unchanged OXT concentrations seen in SFC−EA/29d mice. Importantly, the increased OXT response to a social challenge found in adult SFC− controls was completely prevented by social fear acquisition, that is, in SFC+EA/57d and SFC+AD mice, with lower OXT levels found in comparison to respective SFC−EA/57d and SFC−AD groups (both p < .001). Further, a positive correlation of plasma OXT levels and social investigation time was only found in EA/57d (R 2 = 0.783; p < .001; Figure 4B), but not in EA/29d or AD mice.
+
+FIGURE 4 Plasma oxytocin (OXT) concentrations of adolescent (EA) and adult (AD) social fear‐conditioned (SFC+) and unconditioned (SFC−) mice after 5‐min stressor exposure. Male mice underwent SFC in EA or AD and were either exposed to a 5‐min heterotypic (elevated platform; EPF) or homotypic (conspecific; SOC) stressor or remained undisturbed (BAS) on the subsequent day (EA/29d and AD) or 4 weeks later (EA/57d). Plasma OXT levels were obtained 10 min post stressor exposure. (A) Plasma OXT under BAS conditions or 10 min after exposure to the EPF or SOC stressor in SFC+/−EA/29d, SFC+/−EA/57d, and SFC+/‐AD mice. **p < .01 SFC+ vs. SFC−; ## p < .01 stress vs. respective basal; ++ p < .01 SOC vs. respective EPF. (B) Correlation of plasma OXT levels and social investigation time of SFC+/−EA/57d mice. (C) Percentage of OXT+/DAPI+ cells within the paraventricular (PVN) and supraoptic (SON) nuclei of the hypothalamus of SFC+/−EA/29d and SFC+/−EA/57d mice. (D) Representative immunofluorescent image of OXT+/DAPI+ cells within the PVN and SON of SFC+/−EA/29d and SFC+/−EA/57d mice. Scale bar: 100 μm. **p < .01 EA57d vs. EA29d. Data represents mean + SEM; n = 5–9/group.
+
+In support of the specific OXT hypo‐response to the social stimulus after SFC+, higher OXT levels were only found in SFC−EA/57d and SFC−AD (both p < .001 vs. EPF), but not in SFC+EA/57d and SFC+AD mice after social versus non‐social exposure (EPF). Similar SFC‐induced alterations in social investigation and in the patterns of stress‐induced OXT concentrations with a positive correlation of plasma OXT and social investigation time only in EA/57d mice were found in the 30 min post‐stressor EA/29d, EA/57d, and AD groups (Figure S2B,D).
+
+Further analysis of OXT+ cells revealed a lower percentage of OXT+/DAPI+ cells within the PVN, but not SON, in EA/57d mice compared to EA/29d animals irrespective of the conditioning status of the animal (p = .008), illustrating an age‐dependent difference in the quantity of OXT+ cells (Figure 4C,D).
+
+Taken together, social trauma either in early adolescence or in adulthood prevented peripheral OXT release in response to a social challenge in adulthood. Moreover, we revealed a blunted plasma OXT response to social exposure in early adolescent mice independent of SFC.
+
+3.4 No effects of SFC and acute stressor exposure on organ weights
+
+We further assessed the relative adrenal and spleen weight of SFC+ and SFC− mice of the EA/29d, EA/57d, and AD groups 10 min (Figure S1A,B) and relative thymus weight and splenocyte quantity 30 min (Figure S2F–H) after EPF or social stressor exposure and of their respective unstressed controls. Neither SFC nor acute stressor exposure altered these parameters in all groups of mice. However, independent of SFC, adult mice (EA/57d, AD) showed lower relative thymus und spleen weights compared to EA/29d mice, confirming known physiological adaptations of lymphatic organs in AD (Figure S2I).
+
+4 DISCUSSION
+
+In this study, we show that SFC successfully induces social avoidance in male EA mice, which can be long‐lasting, i.e., persists for at least 4 weeks, and can be extinguished by repeated social exposure during extinction training performed either on the next day during EA or in AD. Furthermore, we describe developmental differences in the responsiveness of the HPA axis and the OXT system between unconditioned (SFC−) EA and AD mice. Specifically, we found a CORT hyper‐response to a non‐social stressor (EPF), but a CORT hypo‐response to a social challenge in EA, in comparison to AD mice. Exposure to social trauma in EA (SFC+EA) resulted in a CORT hyper‐response specifically to a social stimulus 1 day later, that is, in SFC+EA/29d mice, an effect which disappeared in SFC+AD mice. Regarding the responsiveness of the OXT system, we found elevated plasma OXT concentrations in SFC−AD, but not SFC−EA mice in response to a social challenge. This robust rise in plasma OXT of adult SFC− mice was found to be completely abolished by social fear acquisition performed either in EA or AD, that is, in SFC+EA/57d and in SFC+AD mice. Thus, our data provide a comprehensive view of the neuroendocrine (CORT and OXT) responses to social and non‐social stressors across different stages of development, which are severely affected by social trauma.
+
+4.1 SFC induces social avoidance in EA and AD mice
+
+In our study, exposure to the SFC paradigm during early adolescence induced robust acute and persistent social fear in mice. Social fear extinction training performed either 1 day or 28 days after acquisition successfully reversed SFC‐induced social fear (Figure 2). These results extend our previous study performed in adolescent mice of two strains differing in stress susceptibility. 22
+
+Studies assessing neurobiological mechanisms underlying associative learning in juvenile and adolescent rodents have mostly focused on non‐social forms of conditioned fear and described dramatic developmental changes in fear learning. Specifically, in juvenile rodents, contextual fear expression and extinction recruit only the amygdala, making juveniles unable to develop fear associations, whereas engagement of the hippocampus in addition to the amygdala in adults enables them to generate robust fear memories. 32 , 33 During adolescence, the hippocampus and medial prefrontal cortex (mPFC) are additionally recruited, leading to an age‐specific expression and extinction of fear. 32 Similarly, human studies also revealed blunted fear extinction learning in adolescent compared to adult individuals, 33 which has been suggested to originate in a shift in the amygdala‐PFC connectivity. 34 However, EA appears to be a unique developmental period, wherein expression and extinction of contextual fear are temporarily impaired before recovering in AD. 32 In contrast, we find intact expression and extinction of social fear in EA/29d male mice (Figure 2B,C), with fear expression persisting until adulthood as shown in EA/57d mice (Figure 2D,E).
+
+Social trauma experienced either in adolescence or adulthood has been associated with SAD and exerts long‐lasting effects. 35 In this context, adolescent humans have been shown to exhibit a heightened sensitivity toward social trauma compared to adults. 36 Here we show that SFC during EA resulted in social avoidance behavior that persists until adulthood, confirming the long‐lasting effects of social trauma during puberty. In rodents, social isolation in early life or adulthood is known to increase social avoidance in a novel environment, increase anxiety‐related behavior, and alter stress responses. 37 , 38 Interestingly, the 4‐week social isolation in SFC+/−EA/57d mice did neither intensify social avoidance behavior nor facilitate extinction of social fear compared to EA/29d and adult mice (Figure 2). 22 , 25 , 28 , 39 This suggests the interference of unknown mechanisms that prevent avoidance, exacerbating increased social motivation effects of social isolation on long‐lasting SFC‐induced social fear.
+
+Different neuronal circuits and molecular mechanisms are involved in the processing of social vs. non‐social fear. In this context, the amygdala is the principal brain region shaping fear responses of any kind, and across all age groups. 40 In contrast, age‐dependent morphological and neurochemical adaptations have been observed within social fear‐related brain regions, such as the lateral septum (LS) and ventromedial hypothalamus. 26 , 41 This indicates a differential modulatory capacity of these regions to acquire, express, and extinguish conditioned social fear compared to contextual or cued fear across age. Thus, the observed social avoidance behavior after SFC in EA/29d and EA/57d male mice might be based on the age‐specific development of underlying neurocircuits within the limbic system, known to be significantly remodeled in adolescence. 42
+
+4.2 SFC induces differential HPA axis stress responses in EA and AD mice
+
+In our study, the inclusion of SFC− control mice allowed the analysis of HPA axis responses to exposure to either a non‐social (EPF) or social stressor across development, that is, in EA and AD mice. Both EA/29d and AD mice showed lower plasma CORT levels after social stressor compared to EPF exposure, which might be explained by the comparatively low severity of the social stressor. In our experimental design, the stimulus mouse was restrained within a small wire‐mesh cage and presented within the home cage of the experimental mouse. However, after 4 weeks of social isolation, that is, in EA/57d mice, the differences between CORT responses to the social compared to EPF exposure disappeared. Post‐weaning social isolation of male mice was shown to persistently increase not only anxiety‐related behavior, but also neuroendocrine functions, especially the corticotropin‐releasing factor activity, which is a major regulator of the HPA axis. 43 In contrast, exposure to the non‐social stressor (EPF) led to increased plasma CORT levels in all age and SFC groups, which is in line with numerous previous studies. 44 , 45
+
+The adolescent rodent is suggested to be more susceptible to stressors aresulting ito high glucocorticoid levels compared to the adult brain, which ultimately leads to short‐ and long‐term behavioral alterations, such as anxiety‐related behavior, exploratory behavior, and avoidance learning. 46 Moreover, in adolescent humans, acute stress results in a CORT hyper‐response and poor recovery compared to basal levels. 47 As most studies are based on chronic stress in adolescent rodents or humans, knowledge on the HPA axis regulation after acute adolescent stress remains sparse.
+
+In EA, the low plasma CORT response to a social challenge found in SFC−EA/29d mice, turned hyper‐responsive after social trauma exposure, i.e, in SFC+ EA/29d mice (Figure 3C). The high CORT response in SFC+EA mice was found despite the fact that SFC+EA mice did not or only very little investigate the social stimulus. Thus, a negative correlation between social investigation time and plasma CORT levels in EA/29d mice was revealed indicating that the pure presence of the social stimulus in their home cage is highly stressful 1 day after social fear conditioning (Figure 3D).
+
+However, the high responsiveness of the HPA axis to the social stimulus was absent in SFC+EA/57d and SFC+AD mice. The observed SFC‐induced dysregulation of the HPA axis, reflected by reduced plasma CORT, is found in adolescents in response to social interaction 48 , 49 and is suggested to increase the vulnerability for SAD by altering a limbic 5‐HT receptor in humans. 50
+
+4.3 Effects of SFC on plasma OXT responses to social vs. non‐social stressors in EA and AD
+
+To the best of our knowledge, this is the first study showing an age‐dependent release pattern of OXT after a singular social encounter. Thus, exposure to a social stimulus only increased plasma OXT in all adult control mice, that is, in SFC−EA/57d and SFC−AD mice, but not in adolescent mice (SFC−EA/29d; Figure 4A). The non‐responsiveness of the OXT system to a social stimulus in EA/29d further supports a dynamic developmental profile of this system, as age‐dependent distribution patterns of the OXT receptor in the brain have been described, which may at least partly underly the age‐specific socio‐emotional behavior. 19 , 22 Interestingly, irrespective of the conditioning status, the percentage of OXT+ cells within the PVN, but not SON, decreased subtly with age (Figure 4C,D). Thus, our results indicate that the increased plasma OXT release in SFC−EA/57d in contrast to their SFC+ counterparts, and the absence of this conditioning effect in EA/29d mice is not reflected by differences in OXT cell number.
+
+OXT is capable of non‐specifically binding to arginine vasopressin (AVP) receptors, which are also dynamically expressed through development. 19 Both neuropeptides, OXT and AVP, are expressed in the developing brain. However, in rodents, AVP emerges prenatally, whereas OXT is only detectable postnatally. 19 The high level of social contact observed in SFC−EA/29d mice might be at least partly mediated by AVP or other factors, such as testosterone. As one of the major sex hormones, testosterone significantly rises during male puberty, thus affecting socio‐emotional behaviors in rodents and humans. 51 The OXT and testosterone systems exert partly opposite effects on multiple social behaviors in adulthood. 52 , 53 However, we did not analyze plasma testosterone levels in this study.
+
+Although we have only monitored peripheral OXT release, brain OXT plays an important role in regulating social behavior, especially the reversal of social fear and the promotion of social interactions. In general, exposure to socio‐emotional stress activates both intracerebral and peripheral OXT release, although in a stressor and region‐dependent manner. 16 , 54 , 55 For example, in male rats, exposure to social defeat results in OXT release within the hypothalamic PVN, accompanied by OXT secretion into blood. 55 Here, we show for the first time that also a mild social stimulus, that is, 5‐min exposure to a conspecific, results in elevated plasma OXT concentrations in adult mice. Similarly, social investigation during repeated exposure to social stimuli stimulates the release of OXT within the mouse LS as revealed by microdialysis, 39 suggesting a simultaneous peripheral and central OXT release in response to social interactions. OXT signaling in the LS has been repeatedly shown to be essential for social approach and the reversal of social fear. 26 , 28 , 39 However, OXT is also released within the LS in adult female rats when encountering an intruder and during the display of aggression. 56 Thus, it remains to be shown, to which extend the exposure to a social stimulus might be perceived as a threat or whether social motivation leads to the observed rise in plasma OXT in adult SFC− controls in our experiment.
+
+Interestingly, social trauma either in EA or AD completely prevented the rise in plasma OXT in response to social exposure in adult mice. This is in line with a previous study revealing an abolished OXT release within the LS in adult SFC+ mice in response to repeated social contact during social fear extinction training. 39 This indicates that SFC is effective in altering the functionality of the OXT system, thus affecting both peripheral secretion as well as release within distinct brain regions. However, plasma OXT levels positively correlated with the investigation time in EA/57d mice during exposure to a social stimulus (Figure 4B), which may indicate that the lack of social interaction and social contact is causal for the lack of OXT secretion in adult SFC+ mice. Interestingly, in humans, the experience of social trauma during childhood has been correlated with lower basal plasma OXT levels in adulthood, 57 which we did not confirm in our study.
+
+In conclusion, the SFC paradigm is a suitable animal model to generate acute and persistent social avoidance in EA mice, hence increasing its translational value with regard to the development of novel treatment options in adolescent patients. Moreover, we revealed age‐dependent responses of the HPA axis activity and the OXT system to a social, but not non‐social stressor. Experience of a social trauma in EA significantly interfered with the neuroendocrine development suggesting plasma CORT and/or OXT levels as biomarkers of trauma in puberty.
+
+AUTHOR CONTRIBUTIONS
+
+Conceptualization: Anna Bludau and Inga D. Neumann. Methodology: Anna Bludau, Melanie Kabas, Rohit Menon, and Inga D. Neumann. Formal analysis: Anna Bludau and Melanie Kabas. Software: Anna Bludau. Investigation: Anna Bludau and Melanie Kabas. Writing—original draft: Anna Bludau, Rohit Menon, and Inga D. Neumann. Writing—review and editing: Anna Bludau, Melanie Kabas, Rohit Menon, and Inga D. Neumann. Visualization: Anna Bludau. Funding acquisition: Inga D. Neumann. Supervision: Inga D. Neumann.
+
+CONFLICT OF INTEREST STATEMENT
+
+The authors declare no conflicts of interest.
+
+Supporting information
+
+Figure S1. Relative spleen and adrenal weight of adolescent (EA) and adult (AD) social fear‐conditioned (SFC+) and unconditioned (SFC−) mice after 5‐min stressor exposure. Male mice underwent SFC in EA or AD and were either exposed to a 5‐min heterotypic (elevated platform; EPF) or homotypic (conspecific; SOC) stressor or remained undisturbed (BAS) on the subsequent day (EA/29d and AD) or 4 weeks later (EA/57d). (A) Relative spleen weight (in mg/g), and (B) relative adrenal weight (in mg/g) under BAS conditions or 10 min after exposure to a EPF or SOC stressor in SFC+/−EA/29d, SFC+/−EA/57d, and SFC+/‐AD mice. Data represents mean + SEM; n = 4–8/group.
+
+Figure S2. Plasma hormone levels, social investigation time, as well as relative organ weights of adolescent (EA) and adult (AD) social fear‐conditioned (SFC+) and unconditioned (SFC−) mice after 5‐min stressor exposure. (A) Male mice underwent SFC in EA or AD and were either exposed to a 5‐min heterotypic (elevated platform; EPF) or homotypic (conspecific; SOC) stressor or remained undisturbed (BAS) on the subsequent day (EA/29d and AD) or 4 weeks later (EA/57d). Hormone plasma levels were obtained 30 min post stressor exposure. The given days represent the animal's age. (B) Plasma corticosterone (CORT, in ng/ml), (C) plasma oxytocin (OXT, in pg/ml), (D) social investigation time, (E) correlation of plasma OXT and social investigation time (in %) during SOC exposure, (F) relative thymus weight (in mg/g), (G) relative adrenal weights (in mg/g), (H) relative spleen weights (in mg/g), and (I) relative splenocyte number (in cells/mg) under BAS conditions or 30 min after exposure to the EPF or SOC either in SFC+/−EA/29d, SFC+/−EA/57d, and SFC+/‐AD mice. *p < .05, **p < .01 SFC+ vs. SFC−, # p < .05, ## p < .01 stress vs. respective basal; + p < .05 vs. respective EPF. Data represents mean + SEM; n = 6–8/group.
+
+Table S1. Statistical details corresponding to all figures.
+
+Table S2. Group sizes corresponding to all figures.
+
+ACKNOWLEDGMENTS
+
+The authors thank Korbinian Mitter, Lucas Lettner, and Andrea Havasi (University of Regensburg, Germany) for excellent technical assistance. This work was supported by grants of the German Research Foundation (DFG) to Inga D. Neumann (Ne465/31) and by the DFG‐funded Graduate School (GRK‐2174; Inga D. Neumann). Open Access funding enabled and organized by Projekt DEAL.
+
+DATA AVAILABILITY STATEMENT
+
+The data that supports the findings of this study are available in the Supporting Information of this article.
+
+
+REFERENCES
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+Seven Guiding Questions for Reproducible AI-Assisted Research in the Social and Behavioral Sciences
+
+Artificial Intelligence (AI) is increasingly used in social and behavioral research for tasks including literature search, stimulus generation, response annotation, code generation, and writing. These uses challenge conventional understandings of reproducibility because AI-assisted procedures may shape not only the final analysis but also the empirical materials, data-processing steps, and analytical inputs on which reported findings depend. In this opinion article, we propose seven guiding questions for deciding when, what, and how to document AI-assisted research to support reproducibility. We distinguish between two poles of a continuum: AI as a research partner, where transparent disclosure may often be sufficient, and AI as a methodological instrument, where AI outputs enter the evidential chain and therefore require more detailed documentation. The questions are structured across three stages: (a) clarifying the level of reproducibility required for AI use, (b) determining what needs to be reproducible, and (c) deciding how AI assistance should be documented in manuscripts and supplementary materials. Examples from AI-assisted research demonstrate how these questions guide documentation decisions across different reproducibility requirements. Overall, our proposal shifts the focus from generic AI disclosure to role-based documentation that makes AI-assisted workflows understandable, auditable, and, where necessary, reproducible. It also underscores that reproducibility should not be reduced to reporting prompts and AI model settings alone, but requires attention to output variability, changes introduced through human oversight, and the infrastructures through which AI systems are accessed, versioned, and preserved.
diff --git a/corpus/psychology/text/8a95470ab326d3e9.txt b/corpus/psychology/text/8a95470ab326d3e9.txt
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@@ -0,0 +1,3 @@
+Does Looking Like Meat Help? Visual Similarity and Consumer Evaluations of Plant-Based Steaks
+
+Plant-based meat alternatives (PBMAs) are often developed to be as similar to animal meat as possible, yet the extent to which such similarity benefits consumer preference remains unclear. Across two online studies (total N = 809), we examined how visual similarity to meat, as a central cue guiding consumers’ decision making at point-of-purchase, shapes evaluations of plant-based steaks using a comparative judgment paradigm. In both studies, plant-based steaks that were perceived as more similar to meat steaks were generally liked more. However, this relationship was not uniform across consumers. Vegans and vegetarians, as well as frequent PBMA consumers preferred lower levels of visual similarity, with evidence for diminishing returns at very high levels of similarity. Omnivores preferred visual similarity to be as high possible, whereas flexitarians fell in between. In sum, our findings suggest that visual similarity is generally beneficial, but the strength and shape of this relationship shifts depending on consumer segment and characteristics. These findings have implications for sustainable product design and marketing.
diff --git a/corpus/psychology/text/8e689772cdcdadc7.txt b/corpus/psychology/text/8e689772cdcdadc7.txt
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+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Psychol Med
+Journal ID: Psychol Med
+NLM Journal ID: 1254142
+Journal ID: PSM
+
+Psychological Medicine
+
+ISSN: 0033-2917
+EISSN: 1469-8978
+Publisher: Cambridge University Press
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC13125926
+PMID: 42037509
+DOI: 10.1017/S003329172610422X
+Article ID: S003329172610422X
+Article version: 1
+Subjects: Corrigendum
+
+A common symptom geometry of mood improvement under sertraline and placebo associated with distinct neural patterns – CORRIGENDUM
+
+https://orcid.org/0000-0001-5098-7921 Berkovitch Lucie
+Lee Kangjoo
+Ji Jie
+Helmer Markus
+Rahmati Masih
+Demsar Jure
+Kraljic Aleksij
+Matkovic Andraz
+Tamayo Zailyn
+Murray John
+Repovs Grega
+Krystal John
+Martin William
+Fonteneau Clara
+Anticevic Alan
+Corresponding authors: Lucie Berkovitch and Clara Fonteneau; Emails: lucie.berkovitch@yale.edu; fonteneau.clara@gmail.com
+Publication date: 2026
+Electronic publication date: 2026 Apr 27
+Volume: 56
+Electronic Location ID: e118
+Copyright: © The Author(s) 2026
+Copyright year: 2026
+Copyright holder: The Author(s)
+License: This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Erratum for: A common symptom geometry of mood improvement under sertraline and placebo associated with distinct neural patterns 55 4 7 2025 e185 Psychological Medicine 10.1017/S0033291725100962 PMC12270277 40611472
+Figure count: 1
+Reference count: 1
+Page count: 3
+tdm-reservation: 1
+tdm-policy: https://www.cambridge.org/tdm/tdmrep-policy.json
+
+Ÿ==============================Ÿ
+The author would like to apologise for the missing legends and arrows from Figure 4. The correct version of Figure 4 is provided below.Figure 4. Brain–behavior mapping of mood improvement during Stage 1. (A) Top: Correlation between the parcellated resting-state GBC and the PC1 scores in the sertraline (left) and the placebo (middle) groups during Stage 1, and interaction between the two treatment groups (right). Bottom: Correlation between the parcellated resting-state GBC and the CGI response status in the sertraline (left) and the placebo (middle) groups, and interaction between the two treatment groups (right). Correlation maps are visually different between the sertraline and the placebo groups, suggesting that the baseline cerebral predictors of clinical improvement differ according to the pharmacological intervention. Exploratory analyses showed a lower correlation between GBC–PC1 brain-behavior mapping and GBC–CGI response brain-behavior map in the sertraline group compared to the placebo group, suggesting that CGI response has the same brain predictive factors as PC1 for placebo but not for sertraline. The interaction between GBC, PC1, and treatment on the one hand, and GBC, CGI response, and treatment on the other hand, displayed in the right panel, shows how each parcel contributes to the pharmacological response (as opposed to the placebo effect). (B) Network parcellation. (C) Correlation between the parcellated resting-state GBC regrouped by networks and the PC1 scores in the sertraline (left) and the placebo (right) groups. Each dot represents a parcel, and each horizontal bar represents the mean of correlation r-values for a given network across subjects. (D) Correlation between the parcellated resting-state GBC regrouped by subcortical regions and the PC1 scores in the sertraline (left) and the placebo (right) groups. Each dot represents a parcel, and each horizontal bar represents the mean of correlation r-values for a given subcortical region across subjects. (E) Brain average GBC correlation with PC1 in the two treatment groups during Stage 1 (red: sertraline and blue: placebo). Each dot represents a subject, lines represent the linear regressions, and the shaded areas represent the 95% confidence interval. PC1 scores and GBC were significantly correlated in the sertraline group (F 1,86 = 11.42, p = 0.0011), but not in the placebo group (F 1,92 = 0.59, p = 0.44), indicating that baseline GBC is a predictive factor of pharmacologically-induced clinical improvement.
+
+
+Reference
+
+Berkovitch, L., Lee, K., Ji, J., et al. (2025). A common symptom geometry of mood improvement under sertraline and placebo associated with distinct neural patterns. Psychological Medicine, 55:e185. 10.1017/S0033291725100962 40611472 PMC12270277
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+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: eLife
+Journal ID: Elife
+NLM Journal ID: 101579614
+Journal ID: eLife
+
+eLife
+
+EISSN: 2050-084X
+Publisher: eLife Sciences Publications, Ltd
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC12677895
+PMID: 41342686
+DOI: 10.7554/eLife.93554
+Article ID: 93554
+Article version: 1
+Article version: version of record
+Subjects: Research Article, Neuroscience, Physics of Living Systems
+
+Sub-surface deformation of individual fingerprint ridges during tactile interactions
+
+Corniani Giulia https://orcid.org/0000-0003-2800-3329 gcorniani@mgh.harvard.edu 1 2 †
+Lee Zing S 3
+Carré Matt J https://orcid.org/0000-0003-3622-990X 3
+Lewis Roger 3
+Delhaye Benoit P https://orcid.org/0000-0003-3974-7921 benoit.delhaye@uclouvain.be 4 5
+Saal Hannes P https://orcid.org/0000-0002-7544-0196 h.saal@sheffield.ac.uk 1 2
+1 https://ror.org/05krs5044 Active Touch Laboratory, School of Psychology, University of Sheffield Sheffield United Kingdom
+2 https://ror.org/05krs5044 Insigneo Institute for in silico Medicine, University of Sheffield Sheffield United Kingdom
+3 https://ror.org/05krs5044 Human Interaction Group, School of Mechanical, Aerospace and Civil Engineering, University of Sheffield Sheffield United Kingdom
+4 https://ror.org/02495e989 Institute of Information and Communication Technologies, Electronics and Applied Mathematics, Université Catholique de Louvain Louvain-la-Neuve Belgium
+5 https://ror.org/02495e989 Institute of Neuroscience, Université Catholique de Louvain Louvain-la-Neuve Belgium
+Pruszynski J Andrew Reviewing Editor https://ror.org/02grkyz14 Western University London Canada
+
+Cardona Albert Senior Editor https://ror.org/013meh722 University of Cambridge Cambridge United Kingdom
+
+† Harvard Medical School at Spaulding Rehabilitation Hospital, Boston, United States.
+
+Electronic publication date: 2025 Dec 4
+Publication date: 2025
+Volume: 13
+Electronic Location ID: RP93554
+2023 Nov 3
+Copyright: © 2024, Corniani et al
+Copyright year: 2024
+Copyright holder: Corniani et al
+
+License: This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+10.1101/2023.07.02.547395
+10.7554/eLife.93554.1
+10.7554/eLife.93554.2
+Keywords: skin mechanics, tactile sensing, fingerprint
+Keywords: Human
+
+Funding: https://ror.org/00k4n6c32 Horizon 2020 Framework Programme 10.3030/813713 Corniani Giulia Saal Hannes P https://ror.org/0439y7842 Engineering and Physical Sciences Research Council EP/R001766/1 Lee Zing S Carré Matt J Lewis Roger https://ror.org/03q83t159 Fonds De La Recherche Scientifique - FNRS Delhaye Benoit P The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.
+
+Author impact statement: Sub-surface imaging demonstrates that vertical shear beneath fingertip ridges enables high mechanical spatial resolution to support tactile sensing.
+publishing-route: prc
+
+Ÿ==============================Ÿ
+The human fingertip can detect small tactile features with a spatial acuity roughly the width of a fingerprint ridge. However, how individual ridges deform under contact to support accurate and high-precision tactile feedback is currently unknown. The complex mechanical structure of the glabrous skin, composed of multiple layers and intricate morphology within which mechanoreceptors are embedded, makes this question challenging. Here, we used optical coherence tomography to image and track sub-surface deformations of hundreds of individual fingerprint ridges across ten participants and four individual contact events at high spatial resolution in vivo. We calculated strain patterns in both the stratum corneum and viable epidermis in response to a variety of passively applied tactile stimuli, including static indentation, stick-to-slip events, sliding of a flat surface in different directions, and interaction with small tactile features, such as edges and grooves. We found that ridges could stretch, compress, and undergo considerable shearing orthogonal to the skin surface, but there was limited horizontal shear. Therefore, it appears that the primary components of ridge deformation and, potentially, neural responses are deformations of the ridge flanks and their relative movement, rather than overall bending of the ridges themselves. We conclude that the local distribution of mechanoreceptors across the ridges might be ideally suited to extract the resulting strain gradients and that the fingertip skin may possess a higher mechanical spatial resolution than that of a single ridge.
+
+Introduction
+
+The human fingertip is a highly effective tactile sensing structure housing thousands of mechanoreceptors (Corniani and Saal, 2020) that convert skin deformations into neural responses (Handler and Ginty, 2021), which underlie our capacity for fine tactile discrimination and object manipulation (Lieber and Bensmaia, 2022; Johansson and Flanagan, 2009; Witney et al., 2004). The ridged structure of the volar skin of the fingertip gives rise to fingerprints, which are thought to determine the spatial resolution at which we can resolve small tactile features. Ridge spacing correlates with perceptual spatial acuity (Peters et al., 2009), and the size of receptive sub-fields of type-1 tactile afferents has been estimated in the sub-millimeter range, roughly matching the width of a single ridge (Jarocka et al., 2021; Sukumar et al., 2022).
+
+However, understanding how the mechanical properties of individual fingerprint ridges support high-precision tactile feedback presents significant challenges: any force applied to a papillary ridge on the skin’s surface causes deformations within multiple skin layers with distinct mechanical properties and complex morphology (Dahiya and Gori, 2010), before being transduced into neural activity by mechanoreceptors situated at the epidermis-dermis border, which are situated at specific landmarks relative to the limiting and intermediate ridge structures of the viable epidermis (see illustration in Figure 1A).
+
+Figure 1. Experimental setup.
+
+(A) Two major mechanically relevant skin layers constitute the epidermis on the human fingertip: the stratum corneum (blue shading) and the viable epidermis (orange). The papillary ridges making up the fingerprints at the skin surface extend to deeper layers, where morphological complexity increases. Interactions with surfaces (gray shading) take place at the outer boundary of the stratum corneum, while mechanoreceptors are located at the border between the epidermis and the dermis (red shading), at distinct landmarks associated with the ridge structure (dark red and blue circles). Identification of morphological landmarks related to the ridge structure allows the creation of a fine-grained mesh covering most of the sub-surface structure of a single papillary ridge (blue and orange overlaid meshes). (B) Potential deformations of the tracked ridge structure, including the stratum corneum and the bulk of the viable epidermis, during tactile interactions, with arrows indicating the directions of relative deformation. (i) Reference mesh (undeformed); (ii) Tension or compression of the whole structure along or orthogonal to the surface axis of the skin; (iii) horizontal (surface) shear, where the ridge structure tilts sideways; (iv) vertical shear, where the ridge structure tilts along the axis orthogonal to the surface of the skin. These deformations might affect different parts separately, e.g., via shearing in different directions across both ridge flanks as shown on the far right (see darker shading to highlight a single ridge flank). (C) Detail view of a single Optical Coherence Tomography (OCT) frame showing ridged skin structure and clear boundary between the stratum corneum and viable epidermis. A mesh covering the stratum corneum and the upper part of the viable epidermis (without the intermediate ridge) is overlaid spanning a single papillary ridge. The border between the viable epidermis and dermis is less clearly delineated, but some deeper features are resolved less well. (D) Ridge widths (n=153) across all participants. Each dot corresponds to a unique ridge with the participant mean indicated by the horizontal line. (E) Thickness of stratum corneum (blue) and viable epidermis (yellow). Markers, as in D. (F) The experimental apparatus consisted of a finger holder to which the left middle finger of the participant was secured. A horizontal plate with a smaller inlaid transparent surface could be moved to indent the fingertip. A motorized linear stage moved the plate in the distal/proximal direction across the fingertip. An OCT scanner recorded images through the transparent surface, while forces were recorded using a 3-axis force sensor. (G) Illustration of the three transparent polymethyl methacrylate (PMMA) surfaces: a flat surface, one embossed with a rounded edge, and a grooved one. (H) Individual images recorded by the OCT scanner using the three surfaces shown in panel G.
+
+Figure 1—video 1. Recordings of sub-surface skin deformations.
+
+Example recordings demonstrating stick-to-slip with the flat plate and interactions with a groove and an edge, respectively. Each sequence shows first the raw data, and then the processed sequence with a single tracked ridge overlaid.
+
+While numerous studies have investigated ridge deformations (Cauna, 1954; Gerling and Thomas, 2005; Gerling and Thomas, 2008; Willemet et al., 2021; Delhaye et al., 2016) and the mechanical properties of different skin layers (Pereira et al., 1991; Leyva-Mendivil et al., 2017; Leyva-Mendivil et al., 2015), most of this work has focused on ex-vivo specimens, surface measurements, or computer simulations. Consequently, the mechanical response of the skin below its immediate surface remains largely unknown, leading to conflicting interpretations in the literature. For instance, it has been proposed that the papillary ridges are stiffer than the neighbouring grooves (Swensson et al., 1998), which might imply that normal loading of the skin might not affect the ridges’ profile appreciably. Conversely, other observations have suggested that the grooves are relatively stiff, allowing the papillary ridges to deform considerably (Cauna, 1954; Johansson and LaMotte, 1983). However, the sub-surface consequences of this putative pliability during object contact or stick-to-slip transitions (see e.g. Delhaye et al., 2016) are unclear: the whole ridge structure might bend as proposed in Cauna’s lever mechanism (Cauna, 1954), but this view has proved controversial (see e.g. Gerling and Thomas, 2008), with direct empirical evidence lacking.
+
+From a mechanical standpoint, these conflicting interpretations raise the question of how the outermost two skin layers typically deform at the resolution of single papillary ridges, whether by tension, compression, or shear (see examples in Figure 1B). Additionally, such deformations might apply to individual papillary ridges and all their sub-surface structures equally, for example, horizontal shearing that bends the papillary ridge in a certain direction, while levering its sub-surface aspects in the opposite direction. Conversely, individual parts of the ridge structure might deform differently. For example, the viable epidermis might deform to a different extent or in a different direction due to its lower stiffness and different morphology. Additionally, if there are indeed mechanical differences between papillary ridges and their neighbouring grooves at the level of the stratum corneum, this might result in differential movements of the two sides of each papillary ridge, here referred to as ridge flanks (see Figure 1B-iv, right, for a potential example).
+
+To empirically address these questions, we employed Optical Coherence Tomography (OCT) to precisely measure the sub-surface deformation of individual fingerprint ridges in response to a variety of mechanical events. Specifically, we focused on the stratum corneum and the bulk of the viable epidermis (excluding intermediate ridges), which could be robustly resolved and tracked by our setup. OCT has been used previously to investigate sub-surface skin properties, however, its application has been limited to static characterization of the skin morphology, such as measuring tissues’ thickness and roughness (Maiti et al., 2020; Ding et al., 2021; Adabi et al., 2017; Czekalla et al., 2019; Lin et al., 2021). In the present study, we aimed to investigate the ways in which ridges are able to deform during dynamic contact events as well as the role played by different skin layers in order to better understand how the ridged structure of fingertip skin supports tactile sensing.
+
+Results
+
+Measuring skin deformation on a sub-ridge scale
+
+We developed a setup for tactile stimulation of the fingertip, which involved lowering a custom-made transparent thin plate onto the participant’s fixed fingertip at a set normal load and smoothly sliding the plate in both distal and proximal directions at a set speed (Figure 1F and G). Concurrently, we used an OCT scanner to capture images of the skin’s surface and sub-surface morphology. The scanner obtained 4 mm wide slices with 4.5 µm lateral and 5 µm axial resolution at a sampling frequency of 10 Hz. The images were taken by scanning through the transparent plate along the proximal-distal axis of the finger. Both the stratum corneum and viable epidermis were clearly distinguishable from each other (Figure 1C and H).
+
+After acquiring and pre-processing the OCT images, we used semi-automatic methods to track sub-surface landmarks associated with individual ridges across different video frames (see Methods, Figure 1—video 1). The resulting triangular mesh consisted of eight facets per ridge, distributed between the stratum corneum and viable epidermis, as well as the two flanks of the ridge (Figure 1B). Importantly, the mesh was fine-grained enough to identify canonical sub-surface ridge deformation patterns in response to various tactile events. The mesh also extended to and partially covered the dermis-epidermis border, where low-threshold mechanoreceptors are located (Figure 1A). We measured an average ridge width of 0.47 mm across participants (Figure 1D), consistent with previous studies (Moore, 1989; Ohler and Cummins, 1942). Average skin layer thickness was 0.38 mm for the stratum corneum and 0.12 mm for the viable epidermis across our dataset (Figure 1E), again in agreement with previous studies using both in vivo imaging and ex vivo histology (Fruhstorfer et al., 2000; Lintzeri et al., 2022; Maiti et al., 2020). We gathered a large and varied dataset to be able to make robust claims: across four protocols and ten participants, we identified a total of 393 unique ridge slices, which were tracked for 34 s on average and more than a minute in some cases, supported by hundreds of thousands of individually tracked landmarks.
+
+Static normal load
+
+To investigate the response of individual ridges to static normal loads, we applied a flat stimulus to the fingertip, incrementally increasing the load from initial contact in steps of 0.5 N until reaching a maximum of 3.5 N (see examples in Figure 2A and B). Deformation was measured relative to the unloaded ridge’s stereotypical configuration, and the principal tensile and compressive components of the strain experienced by each mesh facet were obtained (see Methods).
+
+Figure 2. Ridge deformation under normal load.
+
+(A) Example frames showing a single ridge unloaded (0 N; left) and maximally loaded (3.5 N; right). (B) Examples of ridge deformation under static normal load for different load conditions. Shown is the unloaded ridge outline (gray shaded regions) with the deformed ridge mesh superimposed (blue and orange), under 1 N, 2 N, and 3.5 N loading. (C) Examples of ridge deformation under static normal load for different participants. Shown is the unloaded ridge outline (gray shaded regions) with the ridge mesh under 3.5 N loading superimposed. Arrows indicate the principal compressive axis for each facet, with colors indicating different orientations relative to vertical. In the lower panels, the magnitude of principal tensile (e1, D) and compressive (e2, E) strains as well as area change (ea, F) as a function of normal load. Thin lines denote individual participants, and thick lines show the average. Data from five participants with seven individual ridges tracked each.
+
+Under load, the central part of individual ridges depressed, while the flanks stayed in place (vertical shear), which led to a flattening of the ridge structure and which was consistently observed across participants (see examples in Figure 2C). Ridges could also display horizontal shear and bend proximally or distally depending on their unloaded configuration and sometimes stretch horizontally along the axis of the skin surface. Both tensile and compressive strains increased monotonically with normal load, with rapid changes and, therefore, larger deformations at initial contact followed by slower and mostly linear changes from 0.5 N onwards (Figure 2D and E). Across all facets in a given layer, tensile strains reached around 15% in the stratum corneum and 10% in the viable epidermis, while compressive strains were above 20% in the viable epidermis and steadily increased with the load but remained below 10% in the stratum corneum. We noted a small increase in the area of the stratum corneum, which was possibly an artifact due to the imperfect fit of the mesh to the ridge’s curvature (but see Discussion for an alternative explanation). In contrast, we found a notable decrease in the area of the viable epidermis (Figure 2F). Our results, therefore, indicate that both the stratum corneum and the viable epidermis undergo deformation under static load, manifested predominantly as a flattening of the papillary ridge and its sub-surface structure, but that compression is higher in the viable epidermis.
+
+Lateral sliding and stick-to-slip
+
+After characterizing the deformation resulting from a static normal load, we investigated sliding interactions between the fingertip and the flat surface. The flat surface was first lowered onto the fingertip until stable contact was established (with a normal load below 0.5 N), then displaced at a constant speed of 0.8 mm/s by 7.6 mm in the distal or proximal direction for a total of 8 movements. In accordance with previous findings, we observed two distinct phases of relative movement between the skin and the plate: stick, where the ridges adhered to the plate and were dragged along with it, and slip, where the ridges stopped moving, and the plate slipped over them. The clear distinction between the stick and slip phases allowed us to classify each phase based on the average horizontal velocity over all tracked features (see Figure 3A for an example from a single participant).
+
+Figure 3. Ridge deformations during sliding.
+
+(A) Measurements during repeated movements of the flat plate along the distal-proximal axis for a single participant. Top: Tangential (purple) and normal (red) load as a function of time. The normal load was set at 0.5 N at the start of the trial by adjusting the indentation and then was not further controlled. Tangential load alternates between positive and negative values depending on the movement direction of the plate. Middle: Horizontal velocity of the plate (dash-dotted gray line) and average velocity of each tracked fingerprint ridge (thin black lines) during all eight transitions of the flat plate. Two phases are evident: when the ridge is moving along with the plate (stick, indicated by green shading) and when the ridge is stationary, but the plate is moving (slip: indicated by pink shading). Bottom: Vertical velocity of all tracked ridges along the normal axis, which is close to zero. (B) Example frames showing a single-tracked ridge for the stick and slip phases of the two movement directions. White arrows point to presumed collagen fiber bundles anchoring the skin to the bone. (C) Average ridge meshes (black lines) during each of the four phases calculated over all tracked ridges and all time points assigned to each phase for the same participant as in A, B. Colored lines indicate individual sample meshes (n=3773; blue: stratum corneum, yellow: viable epidermis). (D) Examples showing ridge deformation across the four phases for three participants. Shown are the ridge outline for the previous phase (gray shaded regions) with the ridge mesh for the current mesh superimposed. Arrows indicate the principal compressive axis for each facet, with colors indicating different orientations relative to vertical. (E) Average magnitude of maximal shear strains as a proxy for overall deformation in the stick-to-slip transition compared to the movement reversal. Thin lines denote individual participants (averaged over facets and movement directions), and thick lines show the grand average. Asterisks denote statistically significant differences (paired Wilcoxon tests). Strains are about a third higher during stick-to-slip transitions than during movement reversals. (F) Histograms of average principal strain angles for all mesh facets and participants in stick-to-slip transitions (left) and movement reversals (right). White bars denote angles that are within 22.5 degrees of the coordinate axes (horizontal or vertical) and, therefore, denote tension or compression without considerable shear. Gray bars denote angles within 22.5 degrees of the diagonal and, therefore, denote horizontal shear. Positive angles denote shear acting in the same direction as the plate movement, while negative angles denote shear in the direction opposite to the plate movement. (G) Change in principal strain angles when transitioning to slip (top) or stick (bottom) phases, separated by ridge flank (light and dark gray). Movement reversals cause a 90 degree shift in the strain angle, while stick-to-slip transitions cause little change, with no differences between ridge flanks evident.
+
+Figure 3—figure supplement 1. Ridge deformations for all participants during sliding of the flat plate.
+
+Previous studies have shown that stick-to-slip events elicit strain waves on the surface of the fingertip skin (Delhaye et al., 2021; Willemet et al., 2022; du Bois de Dunilac et al., 2023), but their effects on the sub-surface structure are unclear. Additionally, reversing the plate’s movement direction changes the tangential force applied to the skin and induces shear deformations within the tissue, but it is unclear whether these are absorbed in surface skin layers or in deeper tissues. To quantify the deformation that occurred between the transitions from stick to slip and between different movement directions of the plate, respectively, we calculated a stereotypical mesh covering a single papillary ridge by averaging the meshes of all tracked ridges (n=140 in total) across image frames within the same phase for each participant (Figure 3B and C, see Methods). We then calculated the principal tensile and compressive strain components experienced by each mesh facet on the transition from one phase to the next.
+
+Examining the ridge deformation changes between movement phases revealed large variability across participants, both in the magnitude and the orientation of the deformations (see individual examples in Figure 3D and all participants in Figure 3—figure supplement 1). This variability is likely explained by the fact that, during stick-to-slip transitions, some parts of the fingertip experience tension, while others experience compression (Delhaye et al., 2016), and, therefore, measurements depend on the precise location. Additionally, the mechanical properties of each individual fingertip influence its own mechanical response, and crucially, the timing of the stick-to-slip transition during plate transit (see Methods), leading to varied mechanical environments. Nonetheless, several consistent findings emerged from the data.
+
+First, we found that, across participants, strain magnitudes (quantified as maximal shear strain, see Methods) were consistently larger by about a third during the stick-to-slip transitions compared to the plate reversal transition (Figure 3E) for both the stratum corneum (p<0.01, paired Wilcoxon signed-rank test across all facets, movement directions, and participants) and viable epidermis (p<0.01). This was also true for individual participants, with strain largest during stick-to-slip transitions for eight out of nine participants. Thus, ridge deformations are most pronounced during stick-to-slip transitions rather than in response to different movement directions of the surface.
+
+Second, while the orientation of the principal strain axes varied between participants, they were relatively consistent within participants in individual phases: the average angular standard deviation was 26 degrees when considering all facets of the ridge within a given phase and, subsequently, averaging over phases and participants. Consequently, strains tended to act in a consistent direction along the entire extent of the ridge (see also examples in Figure 3D). Notably, the principal strain directions exhibited a greater alignment with the cardinal axes (0 and ±90 degrees) rather than diagonal axes (±45 degrees) for the majority of participants across most phases (averaging 60% overall, see Figure 3F). This alignment implies a predominance of tension and compression in the ridge rather than horizontal shear. When shear did manifest, it was more pronounced during stick-to-slip transitions compared to direction changes, and generally aligned with the direction of plate movement, although this alignment was not always observed. We did not find any significant differences in the distribution of principal angles between the stratum corneum and the viable epidermis for either stick-to-slip transitions or movement reversals (p>0.37 for both based on two-sample Kolmogorov-Smirnov tests across all facets, directions, and participants).
+
+The low amount of shear was surprising, as during stick phases, the skin was typically dragged along with the surface for several millimeters (mean: 3.4 mm, range: 0.9–6.3 mm). Assuming no motion of the bone and a distance of 5–10 mm between the lightly loaded skin surface and the bone (Birznieks et al., 2001) yields large expected shear strains of 45% on average (range: 9–126%), clearly much in excess of what we observed. Thus, it is possible that shearing is sustained by deeper tissues, an effect that could be tested in future studies by directly tracking the angle and orientation of collagen fiber bundles anchoring the epidermis to deeper tissues (see highlighted examples in Figure 3B).
+
+Finally, when switching movement direction, which caused the skin to stick to the surface again, we observed a 90 degree rotation of the principal axis of deformation (see Figure 3G, bottom panel). In contrast, there was relatively little change in the angle when transitioning to slip (Figure 3G, top panel). Thus, changing direction caused a reversal in the tension and compression axes but relatively little deformation in itself; this deformation then occurred during the transition to slip. The observed changes in orientation occurred consistently for both ridge flanks and, therefore, applied uniformly to the whole ridge.
+
+In summary, our findings indicate that the primary deformations occurring during contact with a flat plate predominantly involves tension and compression of individual ridges along the skin’s surface. Horizontal shear is only occasionally present and does not consistently align with the direction of movement. When shear is observed, it is more prominent during stick-to-slip transitions rather than during reversals of the plate movement.
+
+Ridge interactions with small tactile features
+
+Finally, we investigated ridge deformation during contact with small tactile features that were close in size to that of a single ridge itself (1 mm in width and 0.3 mm in height/depth). For this experiment, we used the plates with the edge and groove, respectively, keeping all other stimulation parameters the same. We identified five consecutive phases for each tracked ridge based on its position relative to the edge or groove: (1) sliding under the flat part of the surface, (2) approach of the feature, (3) located centrally under the feature, (4) withdrawal from the feature, and (5) sliding under the flat part of the surface (see illustrations in top rows of Figure 4A and D). We again quantified the deformation of the average ridge during all these phases (see Methods), with the strains calculated relative to the initial mesh before contact with the feature was made (phase 1).
+
+Figure 4. Ridge deformations and skin strains during transit of small tactile features.
+
+(A) Top row: Illustration of identified movement phases with the edge feature in different locations relative to the tracked fingerprint ridge. Bottom row: Average ridge deformation and associated principal compressive strain orientation for a single participant. Note that all strains are calculated with respect to the mesh shown in the left-most column, which represents the ridge during full slip before the interaction with the tactile feature. (B) Histograms of principal strain orientations across all ridge facets and participants for the approach (2), central (3), and withdrawal (4) phases. Red bars denote distal ridge flanks, and blue bars denote proximal ones. Darker shading denotes orientations close to diagonal, indicating shear, while lighter shadings denote angles aligned vertically or horizontally and, therefore, denote no shear. (C) Average magnitude of principal tensile (e1, left panel) and compressive (e2, middle panel) strains as well as area change (right panel) relative to the stereotypical ridge under full sliding (phase 1). Thin lines denote individual participants (n=9), and thick lines show the average. Asterisks denote statistically significant differences between the stratum corneum and the viable epidermis (Bonferroni corrected paired Wilcoxon tests). Ridges are most deformed when directly under the edge feature when strains are higher in the viable epidermis than the stratum corneum. While the stratum corneum is incompressible, the area of the viable epidermis expands when directly under the ridge. (D–F) Same as in A–C, but for a small groove transitioning over the ridge. Note that the findings broadly reflect those obtained with the edge feature, but with the direction of compressive and tensile strains reversed.
+
+Figure 4—figure supplement 1. Ridge deformations for all participants during transit of the edge feature.
+
+Figure 4—figure supplement 2. Ridge deformations for all participants during transit of the grooved feature.
+
+Ridge deformations were remarkably similar across participants but differed clearly across movement phases (see ridge deformations for a single participant in Figure 4A and D bottom rows and all participants in Figure 4—figure supplements 1 and 2). There was minimal evidence supporting the notion of a rigid ridge maintaining its shape, and instead, the central part of the ridge deformed considerably. Horizontal shear was relatively modest, with generally little bending of the ridge observed. Instead, our findings highlighted that the primary mechanism through which the ridge conformed to the shape of a feature involved vertical shearing of the whole ridge or the two ridge flanks against each other, as the skin moved vertically to conform to the feature. Consequently, during the transit of the edge, the full ridge initially sheared orthogonally to the skin’s surface with both the strain orientations of both flanks aligned (Figure 4B, left panel). When the edge was directly above the ridge, both flanks sheared against each other, leading to opposite strain orientations across the two flanks (Figure 4B, middle panel) before the ridge returned to its original configuration during the withdrawal of the edge (Figure 4B, right panel). This pattern was mirrored, but with strain orientations reversed, during the transit of the groove (Figure 4E).
+
+Strains increased and reached their maximum with respect to the initial configuration when the ridge was located directly under the feature and then decreased again as the ridge reverted to its original shape. For the edge, both strain components differed between the viable epidermis compared to the stratum corneum when the ridge was located directly below the feature (p<0.01 in Bonferroni corrected paired Wilcoxon tests across all facets and participants), resulting in an expansion of the area of the viable epidermis, as it was stretched around the edge feature, while the mostly incompressible stratum corneum retained its area (Figure 4C). Conversely, while interacting with the groove, a ridge experienced high compressive strains, which again were larger in the viable epidermis compared to the stratum corneum, and as a result, the area covered by the viable epidermis contracted, while the stratum corneum retained its area (Figure 4F).
+
+Discussion
+
+This study measured the sub-surface deformation of individual papillary ridges in the fingertip skin during tactile interactions in vivo. The dataset included hundreds of individual ridges, whose deformations were tracked using high-resolution meshes during static normal load, lateral stick, and slip using a flat surface, as well as during contact with small tactile features. We found that individual ridges tended to flatten considerably at relatively low forces of 0.5 N, with higher forces increasing deformations only moderately. Lateral sliding elicited strong tension and compression, often aligned with the surface orientation of the skin, which was especially strong during stick-to-slip transitions. Contact with edges and grooves yielded strong vertical shear, with ridge flanks moving relative to each other. We observed horizontal shear during static contact and sometimes when sliding the flat surface, however, it was limited in magnitude and was present only for some participants.
+
+Canonical ridge deformations during tactile interactions
+
+One of the main objectives of our study was to investigate the primary deformation patterns exhibited by individual ridges during tactile interactions. Previous studies combining mechanical measurements at the ridge surface and histology (Cauna, 1954) or analyzing the spatial keratin expression patterns within single ridges (Swensson et al., 1998) have suggested the presence of alternating softer and stiffer regions within the ridges. These findings implied a mechanically constrained set of canonical deformations, yet the specific nature of these deformations has been a subject of debate, lacking direct empirical evidence.
+
+In the present study, we have provided conclusive evidence that ridge peaks are not rigid and, instead, individual ridges undergo considerable flattening during contact. This finding challenges previous speculation that the grooves between the papillary ridges act as ‘hinges’ (Swensson et al., 1998). Instead, our results suggest that the fingerprint predominantly conforms to an external object through vertical shearing. Therefore, we propose that the primary mechanism through which a ridge conforms to an object might involve the relative movement and shearing of the ridge flanks, rather than relying on the grooves as articulated joints.
+
+In contrast to the prominent vertical shearing observed, our study revealed minimal and inconsistent horizontal shear. We propose that the flattening of the ridges during contact may prevent further bending of the ridges, thus limiting the occurrence of horizontal shear. The absence of horizontal shear during the stick phase of lateral sliding on the flat surface was particularly unexpected. During these periods, the skin re-adhered to the plate and was subsequently dragged along, often over a distance of several millimeters. It is possible that the majority of the surface movement of the skin was absorbed by deeper tissues rather than the surface layers of the skin imaged in the present study. If that is the case, recent modeling work has suggested that tissue deformations are highly dependent on the orientation of collagen fibers in these tissues (Duprez et al., 2024), which might be amenable to tracking in future OCT work to test this idea directly. Additionally, previous work investigating tactile afferent responses to tangential skin movements has reported strong activation of SA-2 receptors, thought to measure skin stretch mainly in deeper tissues (Saal et al., 2025), providing further indirect evidence.
+
+Implications for neural coding of touch
+
+Ridge deformations are ultimately transduced into neural activity by mechanoreceptors, and our findings provide new insights into this process.
+
+First, the magnitude of sub-surface deformation measured in our study correlated with neural response strengths observed in other studies. In trials with the flat surface, we measured larger deformations during stick-to-slip transitions than during reversals of the plate’s movement direction. Analogously, a previous study recorded neural responses during sliding stimulation of the fingertip and reported that rapidly adapting type I afferents (RA-I) showed little to no response during the onset and offset of the tangential load but strongly encoded the stick-to-slip transition (Delhaye et al., 2021), suggesting that mechanoreceptors directly encode the local amount of deformation. Our findings also extend these prior results by demonstrating that the large surface strains measured during the transition from stick to slip are mirrored in tissues below the surface and specifically at the depth at which type-1 mechanoreceptors are located. Altogether, these results provide a physiological explanation for the widely observed human capacity of fine-tuned grasping with quick adjustments of the grip force to friction changes (Johansson and Westling, 1984; Cadoret and Smith, 1996; Delhaye et al., 2024).
+
+Second, our finding that contact with small tactile features elicits shearing of both ridge flanks against each other suggests that the mechanical resolution of the fingerprint skin is on the order of half the width of an individual papillary ridge. In principle, such fine-grained and local differences in strain might be detectable by mechanoreceptors. Indeed, Meissner corpuscles innervate each flank of a fingerprint’s ridge, and prior work has shown that separate fibers can innervate the two flanks of the same ridge (Nolano et al., 2003). Previous psychophysical work also appears to support this idea because it has estimated the spatial resolution of static touch at around 200 m, thus approximately half the width of a single ridge of the fingerprint (Hollins and Risner, 2000; Bensmaia and Hollins, 2003). However, it should be pointed out that such estimates are notoriously difficult to obtain reliably as they depend on both the precise stimulus and the mode of contact and that this limit has traditionally been associated with the responses of Merkel cells rather than Meissner corpuscles. Previous neural recordings measured the spatial acuity of the receptive sub-fields of RA1 and SA1 afferents, which were estimated to lie in the submillimeter range, roughly matching the width of a single ridge (Jarocka et al., 2021; Sukumar et al., 2022). Our results also suggest that complementary features (edges and grooves, respectively) generate symmetrical deformation. Recording responses from the same tactile afferent to such complementary features might help to disentangle what aspects of shearing the afferent is sensitive to. Therefore, further electrophysiological and psychophysical work is needed to determine whether the sub-ridge mechanical resolution of the fingerprint skin does indeed translate into corresponding neural and perceptual acuity.
+
+Limitations and future work
+
+While our study was based on a large dataset, which contained a variety of tactile interactions, there are a number of limitations. First, while we could confidently track landmarks associated with the stratum corneum, we could not reliably identify intermediate ridges in the viable epidermis, though they were visible in some of the frames, limiting the depth of the fitted mesh. We hypothesize that the additional depth of these ridges, combined with their slender morphology, might have degraded the signal. 3D OCT imaging (see below) might help to resolve these features in future work and settle open questions regarding their precise morphology. Intermediate ridges are of importance because Merkel cell clusters are located at their tip, and they are, therefore, likely important for mechanotransduction. Indeed, intermediate ridges feature in the so-called ’lever hypothesis’ of tactile transduction (Cauna, 1954), which has been called into question (Gerling and Thomas, 2005; Gerling and Thomas, 2008), though direct empirical evidence is currently lacking. Ideally, future studies would improve imaging resolution and clarity to visualize morphological structures in more detail and at greater depth. We employed a state-of-the-art, clinical OCT scanner, routinely used in dermatological clinical assessments. Data from a recently developed experimental scanner demonstrated the possibility of resolving smaller structures in the tissues, even as small as Meissner corpuscles, by applying a technique called speckle-modulating OCT (Liba et al., 2017). Coupling such advanced imaging techniques with our experimental setup and analysis pipeline would further advance the understanding of sub-surface skin properties and deformation mechanisms and allow more direct investigation of neural mechanisms. Such advanced imaging could also be combined with electrophysiological recordings from afferent fibers using microneurography (see Delhaye et al., 2021, for an example).
+
+Second, while the edges and grooves of our feature plates were only marginally larger than a single papillary ridge and mimic those employed in other studies (Jarocka et al., 2021), even smaller stimuli would be capable of delivering much more localized forces (Johansson and LaMotte, 1983; Kao et al., 2022). In the present study, we were limited by the resolution of the 3D printing technique employed to manufacture the transparent plates. Additionally, sharp corners elicit optical artifacts in the obtained images, which can occlude landmarks.
+
+Third, we obtained two-dimensional slices oriented orthogonal to the orientation of the fingerprints, but the skin is a three-dimensional structure. Some of our tactile interactions might have caused skin deformations out of plane that were thus not measurable. For example, the slight increase in thickness of the stratum corneum under normal load might be explained as a measurement artifact due to the coarse nature of the mesh fitted, but could alternatively reflect tissue from out-of-plane regions pushing into the imaged space. Indeed, recent surface measurements of the skin’s behaviour during initial object contact have reported compression of the skin in the plane parallel to its surface (Doumont et al., 2025), which would result in increasing thickness, assuming that the stratum corneum is incompressible. Future studies could consider creating three-dimensional reconstructions of the fingerprint structure to study such effects.
+
+Fourth, in the present study, we focused on young, healthy participants, who were tested in a temperature and humidity-controlled environment. However, several studies have shown that morphological and mechanical skin properties can greatly vary with physiological and physical factors such as age (Jobanputra et al., 2020; Püllen et al., 2021; Skedung et al., 2018), sex (Luebberding et al., 2014; Diridollou et al., 2000), skin hydration (Tomlinson et al., 2011), moisturization (Dione et al., 2023), as well as ambient temperature and humidity levels (Klaassen et al., 2016). All these factors might, therefore, also influence how individual ridges deform and present opportunities for future studies.
+
+Finally, while we focused on the fingertip only, many other skin regions present interesting mechanical challenges waiting to be explored. The general ridged structure observed on the fingertip is common to all glabrous skin, but the local ridge mechanics might still differ: glabrous skin on the foot sole exhibits some morphological differences in order to support large weights that might well influence its mechanical response (Boyle et al., 2019). For example, the morphology of transverse ridges (running orthogonal to and connecting limiting with intermediate ridges) differs across regions on the foot sole (Nagashima and Tsuchida, 2011) and very likely from the hand (Yamada et al., 1996). Our method should be directly applicable to study deformations of these ridges, though three-dimensional observations might be needed to resolve some of the open questions. Hairy skin, in contrast, differs from glabrous skin in that the stratum corneum is much thinner. It also lacks the clearly organised ridge structure but exhibits more loosely oriented skin folds instead, which very likely also serve a mechanical function (Leyva-Mendivil et al., 2015) and in principle are amenable to study using OCT.
+
+Materials and methods
+
+Participants
+
+Ten healthy participants (3 males, average age 20.5 years) participated in the experiment after providing informed consent. Due to low imaging quality for data from one participant, which precluded consistent tracking, all sliding experiments included data from nine participants; the static protocol was run on a subset of five participants. The experiment was performed on the subjects’ left middle finger. Before any trial, the finger was thoroughly cleaned with water and dried carefully, and a thin layer of petroleum jelly was applied to moisturize the skin; this helped prevent repeated stick-slip events while sliding the surface. Environmental conditions during the test were controlled with 20°C room temperature and 50% relative humidity. The study protocol received ethical approval from The University of Sheffield Research Ethics Committee (ethics number 039144). All experiments took place in the Skin Barrier Research Facility, operated by Sheffield Dermatology Research at the Royal Hallamshire Hospital in Sheffield, UK.
+
+Experimental setup
+
+The experimental setup for the present study was adapted from the design of an earlier study (Lee et al., 2020). Transparent plates were secured by a support rig fixed on a linear stage that could move in both distal and proximal directions with respect to the participant’s fingertip, allowing the plate to slide against the finger. The fingertip was glued onto a finger holder to maintain its position during the acquisitions. The support rig was mounted on a force plate (HE6X6–10, Advanced Mechanical Technology, Inc) to measure the load along the axes parallel and perpendicular to the direction of the movement and along the axis normal to the plate surface. The plates were made from polymethyl methacrylate (PMMA) and were 30 × 40 × 0.5 mm in size (produced by Shape Technology S.r.l., Casale Monferrato, Italy). One plate was flat, while the two others had an embossed oriented half-circular edge (1 mm base diameter and 0.4 mm height) or an engraved oriented groove (1 mm base diameter and 0.3 mm depth) traversing the middle of the surface (see Figure 1F).
+
+Prior to each trial, the plate specimens were cleaned with deionized water and dried thoroughly with paper towels. The participant’s finger was secured in a finger holder, which was positioned in such a way that the flat part of the fingertip distal to the whorl made initial contact with the plate as it was lowered onto the fingertip. The scanner was positioned such that its scan path aligned with the distal-proximal axis of the plate, targeting the centre line of the fingerpad so that the fingerprint ridges were oriented orthogonally to the line scan. In the static loading experiment, the plate was initially positioned in contact with the participant’s fingertip without exerting any pressure (∼0 N). Afterward, the load was manually incrementally increased in 0.5 N steps, reaching a maximum of 3.5 N. At each step, 20 frames were recorded. In the sliding experiments, before commencing the imaging acquisition in each trial, the plate was manually lowered onto the participant’s fingertip until a normal load of 0.2 N was reached. During each trial, the plate was moved 7.6 mm in each direction (proximal to distal and vice versa) four times at a constant speed of 0.8 mm/s. For these experiments, imaging focused on the central flat part of the contact area, such that all fingerprint ridges visible in the imaged region were in contact with the plate throughout the trial.
+
+Image acquisition and pre-processing
+
+For image acquisition, we utilized the Vivosight OCT system (Michelson Diagnostics, Kent), which is clinically approved and features a Fourier domain with a 20 kHz swept-source laser at 1300 nm center wavelength. The image capture rate was 10 frames per second, and the dimension of each image was 895 × 483 pixels with 256 gray levels with a 4.5 µm lateral and 5 µm axial resolution.
+
+Following the acquisition, we preprocessed the images using the cv2 library in Python. Firstly, we normalized the brightness and increased the contrast by applying histogram equalization. Then, to further enhance the contrast and adjust the image saturation, we performed a gamma transformation (γ=5). Lastly, we removed noise while preserving sharp edges by applying a bilateral filter (diameter of pixel neighborhood: 5, sigmaColor: 110, sigmaSpace: 190).
+
+Tracking of individual ridge deformation
+
+In each frame of the experiment, the top and bottom of each ridge within the field of view were semi-automatically tracked at three levels: the surface, the border between the stratum corneum and viable epidermis, and the junction between the dermis and epidermis. As imaging slices were 4 mm wide, often 8–9 ridges were visible concurrently. For each set of frames obtained during a single trial, a portion of the frames, ranging between 25–50% of the total, were manually annotated using the Python polygonal annotation library Labelme (Wada, 2021). The annotated frames were then used to train a DeepLabCut model to automatically estimate the position of each tracked point in the remaining frames (Nath et al., 2019). The accuracy of the models, on average, was 2.96 pixels on the training set and 14.64 pixels on the test set. We then manually reviewed the automatic annotations to correct any inaccuracies that might have arisen from automatic tracking. To measure the deformation of individual sub-surface ridges, the tracked points were used to create a triangular mesh for each ridge in the field of view. The mesh consisted of 8 facets per ridge, divided between the stratum corneum and viable epidermis and between the proximal and distal flanks of each ridge.
+
+Movement phase classification
+
+To study the skin movement during the transits of the plate, we analyzed the displacement of the tracked points from frame to frame. We calculated the horizontal and vertical components of the skin velocity, vx and vy, respectively, by measuring the displacement along the x-axis and y-axis. To determine the velocity components for each ridge, we averaged the velocities of the nine tracked points belonging to that ridge, resulting in vxridge and vyridge.
+
+For the flat plate trials, four phases were identified by analyzing the horizontal component of the velocity vxridge:
+
+Sticking proximally (vxplate<0, vxridge<0): the plate is moving in distal to proximal direction, and the skin is sticking to the plate.
+
+Slipping proximally (vxplate<0, vxridge=0): the plate is moving in distal to proximal direction, and it is slipping over the stationary skin.
+
+Sticking distally (vxplate>0, vxridge>0): the plate is moving in proximal to distal direction, and the skin is sticking to the plate.
+
+Slipping distally (vxplate>0, vxridge=0): the plate is moving in proximal to distal direction, and it is slipping over the stationary skin.
+
+To identify the transition between sticking and slipping phases, we took the positive and negative extrema of the first derivative of vxridge as markers. Each trial consisted of four plate transits in each direction, resulting in a total of 16 successive phases. We selected the central nphase frames for each phase to ensure an equal number of frames for each occurrence of a single phase during the subsequent mesh averaging. We chose nphase as the minimum duration of each phase among its four repetitions. The time spent in either phase varied markedly across participants (range: 11.4–82.7%, mean: 44.7%). These differences are partly attributable to differences in skin mechanics across participants (e.g. moisture level) but also depend on the precise location of the imaging site on the fingertip, as previous research has shown that stable contact is lost progressively over time across the whole fingertip during the transition from stick to slip (Delhaye et al., 2014).
+
+For trials using the feature plates, all frames where vxridge≠0 were discarded to retain only data where the skin was fully slipping under the plate. Then, by examining the vertical component of the skin speed vyridge, four phases were classified for every ridge mesh separately:
+
+full slipping (vyridge=0): before and after approaching the feature
+
+approaching the feature (vyridge>0 for the groove plate and vyridge<0 for the edge plate)
+
+moving away from the feature (vyridge<0 for the groove plate and vyridge>0 for the edge plate)
+
+under the plate feature (frames in between the two previous phases, vyridge=0)
+
+In each trial, there were a total of 40 successive phases, as each of the five phases identified occurred in each of the eight transits of the plate. Again, the central nphase frames were selected for each phase in order to consider the subsequent mesh averaging an equal number of frames in each occurrence of a single phase.
+
+Strain computation
+
+The mesh coordinates of each ridge in each frame were centered around the origin by subtracting from the coordinates of any tracked point in a ridge, the average of the coordinates across all the points in that ridge. Then, to obtain a single stereotypical ridge shape for every phase, the mesh coordinates of each ridge were averaged across all the ridges in a frame and all the frames in the same phase. Displacement field gradients were calculated for each triangle in the mesh,
+
+between two consecutive phases for the flat plate trials
+
+between the initial slipping phase and every other phase for the feature plates.
+
+Green-Lagrange strains were estimated from the displacement gradient by the equations:(1) εxx=∂u∂x+0.5[(∂u∂x)2+(∂v∂x)2]
+
+(2) εyy=∂v∂y+0.5[(∂u∂y)2+(∂v∂y)2]
+
+(3) εxy=0.5(∂u∂y+∂v∂x)+0.5(∂u∂x∂u∂y+∂v∂x∂v∂y)
+
+where εxx and εyy are the horizontal and vertical strain, εxy is the shear strain, and u and v are the displacements along x and y axes, respectively.
+
+The principal components of the strain, e1 and e2, were obtained by eigenvalue decomposition of the strain matrix ε, as reported in Delhaye et al., 2016. The principal strain decomposition consists of a rotation of the reference coordinates so that the shear strain is canceled and the axial strains take their maximal and minimal value. Thus, the principal components e1 and e2 represent the maximum tensile and compressive deformation along perpendicular axes.
+
+From the principal strain components, we computed the variation in the area of every triangle composing the mesh as:(4) ea=e1+e22
+
+As a measure of overall deformation during sliding of the flat surface, we calculate the maximum shear strain as:(5) es=e1−e22
+
+Statistics
+
+Statistical tests were run in Python using the scipy.stats package. As distributions were skewed, we used non-parametric analyses throughout the study. Bonferroni corrections were used when multiple comparisons were made.
+
+Funding Information
+
+This paper was supported by the following grants:
+
+https://ror.org/00k4n6c32 Horizon 2020 Framework Programme 10.3030/813713 to Giulia Corniani, Hannes P Saal.
+
+https://ror.org/0439y7842 Engineering and Physical Sciences Research Council EP/R001766/1 to Zing S Lee, Matt J Carré, Roger Lewis.
+
+https://ror.org/03q83t159 Fonds De La Recherche Scientifique - FNRS to Benoit P Delhaye.
+
+Acknowledgements
+
+We would like to thank Simon Danby and Paul Andrew for making the Skin Barrier Research Facility available and Mia Rupani for assistance with data processing.
+
+Additional information
+
+Competing interests
+
+Author contributions
+
+Ethics
+
+Additional files
+
+MDAR checklist
+
+Data availability
+
+All OCT data and main analysis code are available at Dryad, https://doi.org/10.5061/dryad.0vt4b8hbz.
+
+The following dataset was generated:
+
+Corniani G Lee ZS Carré MJ Lewis R Delhaye B Saal HP 2025 Data and code from: Sub-surface deformation of individual fingerprint ridges during tactile interactions Dryad Digital Repository 10.5061/dryad.0vt4b8hbz PMC12677895 41342686
+
+DOI: 10.7554/eLife.93554.3.sa0
+
+eLife Assessment
+
+Pruszynski J Andrew Reviewing Editor Western University Canada
+
+Keywords: Compelling
+Keywords: Important
+
+By leveraging optical coherence tomography this study provides important insight into the deformation of human fingertip ridges when contacting raised features such as edges and contours. The study provides compelling evidence that such features tend to cause deformation and relative movement of what the authors term ridge flanks rather than bending of the ridges themselves.
+
+DOI: 10.7554/eLife.93554.3.sa1
+
+Reviewer #2 (Public review):
+
+Reviewer
+
+Summary:
+
+The authors investigate sub-skin surface deformations to a number of different, relevant tactile stimuli, including pressure and moving stimuli. The results demonstrate and quantify the tension and compression applied from these types of touch to fingerprint ridges, where pressure flattens the ridges. Their study further revealed that on lateral movement, prominent vertical shearing occurred in ridge deformation, with somewhat inconsistent horizontal shear. This also shows how much the deeper skin layers are deformed in touch, meaning the activation of all cutaneous mechanoreceptors, as well as the possibility of other deeper non-cutaneous mechanoreceptors.
+
+Strengths:
+
+The paper has many strengths. As well as being impactful scientifically, the methods are sound and innovative, producing interesting and detailed results. The results reveal the intricate workings of the skin layers to pressure touch, as well as sliding touch over different conditions. This makes it applicable to many touch situations and provides insights into the differential movements of the skin, and thus the encoding of touch in regards to the function of fingerprints. The work is very clearly written and presented, including how their work relates to the literature and previous hypotheses about the function of fingerprint ridges. The figures are very well-presented and show individual and group data well. The additional supplementary information is informative and the video of the skin tracking demonstrates the experiments well.
+
+Weaknesses:
+
+There are very few weaknesses with the work; rather the authors detail well the limitations in the discussion. Therefore, this opens up lots of possibilities for future work.
+
+Impact/significance:
+
+Overall, the work will likely have a large impact on our understanding of the mechanics of the skin. The detail shown in the study goes beyond current understanding, to add profound insights into how the skin actually deforms and moves on contact and sliding over a surface, respectively. The method could be potentially applied in many other different settings (e.g. to investigate more complex textures, how skin deformation changes with factors like dryness and aging). This fundamental piece of work could therefore be applied to understand skin changes and how these impact on touch perception. It can further be applied to understand skin mechanoreceptor function better and model these. Finally, the importance of fingertip ridges is well-detailed, demonstrating how these play a role in directly shaping our touch perception and how they can shape the interactions we have with surfaces.
+
+DOI: 10.7554/eLife.93554.3.sa2
+
+Reviewer #3 (Public review):
+
+Reviewer
+
+Summary:
+
+The publication presents unique in-vivo images of the upper layer of the epidermis of glabrous skin when a flat object compresses or slides on the fingertip. The images are captured using OCT and show the strain that fingerprints experience during mechanical stimulation.
+
+The most important finding is, in my opinion, that fingerprints undergo pure compression/tension without horizontal shear, suggesting that the shear stress caused by tangential load is transferred to the deeper tissues and ultimately to the mechanoreceptors (SA-I / RA-I).
+
+Strengths:
+
+Fascinating new insights into the mechanics of glabrous skin. To the best of my knowledge, this is the first experimental evidence of the mechanical deformation of fingerprints when subjected to dynamic mechanical stimulation. The OCT measurement allows unprecedented measurement of skin depth, whereas previous works were limited to tracking surface deformation.
+
+The robust data analysis reveals the continuum mechanics underlying the deformation of the fingerprint ridges.
+
+Weaknesses:
+
+I do not see any major weaknesses. The work is mainly experimental and is rigorously executed.
+
+DOI: 10.7554/eLife.93554.3.sa3
+
+Author response
+
+Corniani Giulia Author University of Sheffield Sheffield United Kingdom
+
+Lee Zing S Author University of Sheffield Sheffield United Kingdom
+
+Carré Matt J Author University of Sheffield Sheffield United Kingdom
+
+Lewis Roger Author University of Sheffield Sheffield United Kingdom
+
+Delhaye Benoit Author UCLouvain Brussels Belgium
+
+Saal Hannes P Author University of Sheffield Sheffield United Kingdom
+
+The following is the authors’ response to the original reviews.
+
+Reviewer #1 (Public Review):
+
+Summary:
+
+This manuscript uses optical coherence tomography (OCT) to visualize tissue microstructures about 1-2 mm under the finger pad skin surface. Their geometric features are tracked and used to generate tissue strains upon skin surface indentation by a series of transparent stimuli both normal and tangential to the surface. Then movements of the stratum corneum and the upper portion of the viable epidermis are evaluated. Based upon this data, across a number of participants and ridges, around 300 in total, the findings report upon particular movements of these tissue microstructures in various loading states. A better understanding of the mechanics of the skin microstructures is important to understand how surface forces propagate toward the locations of mechanoreceptive end organs, which lie near the edge of the epidermis and dermis, from which tactile responses of at least two peripheral afferents originate. Indeed, the microstructures of the skin are likely to be important in shaping how neural afferents respond and enhance their sensitivity, receptive field characteristics, etc.
+
+Strengths:
+
+The use of OCT in the context of analyzing the movements of skin microstructures is novel. Also novel and powerful is the use of distinct loading cases, e.g., normal, tangential, and stimulus features, e.g., edges, and curves. I am unaware of other empirical visualization studies of this sort. They are state-of-the-art in this field.
+
+Moreover, in addition to the empirical imaging observations, strain vectors in the tissues are calculated over time.
+
+Weaknesses:
+
+The interpretation of the results and their framing relative to the overall hypotheses/questions and prior works could be articulated more clearly. In particular, the major findings of the manuscript are in newly describing a central concept regarding "ridge flanks," but such structures are neither anatomically nor mechanistically defined in a clear fashion. For example, "... it appears that the primary components of ridge deformation and, potentially, neural responses are deformations of the ridge flanks and their relative movement, rather than overall bending of the ridges themselves." From an anatomical perspective, I think what the authors mean by "ridge flanks" is a differential in strain from one lateral side of a papillary ridge to the other. But is it unclear what about the continuous layers of tissue would cause such behaviors. Perhaps a sweat duct or some other structure (not visible to OCT) would subdivide the "flanks" of a papillary ridge somehow? If not due to particular anatomy, then is the importance of the "ridge flank" due to a mechanistic phenomenon of some sort? Given that the findings of the manuscript center upon the introduction of this new concept, I think a greater effort should be made to define what exactly are the "ridge flanks." It is clear from the results, especially the sliding case, that there is something important that the manuscript is getting at with this concept.
+
+We apologize for the confusion around our use of ‘ridge flanks’. To recap the overall goal briefly, we wanted to measure the deformation of papillary ridges and their associated sub-surface structures to different tactile stimuli. Capturing these deformations and comparing them against different proposed ideas, for example bending (horizontal shear) of the entire ridge versus differential deformations of different sub-parts, constrains neural activation mechanisms, has implications for how well tactile stimuli can be spatially resolved on the skin, and for whether sub-surface deformations can be easily predicted from surface movements alone. Our mesh was dense enough to compare the stratum corneum and the viable epidermis directly, where we expected some differences due to their previously documented mechanical differences, as well as the ridge flanks, which refers to the two (proximal and distal) sides of a single papillary ridge and their associated structure in the SC and VE (as correctly surmised by the reviewer). Differential behaviour across ridge flanks might be seen, because various observations of the surface of the stratum corneum had suggested mechanical differences between the papillary ridges and the grooves dividing them, potentially leading to differential deformations of these two halves depending on which direction they were facing tissue with different mechanical properties.
+
+We now provide a clearer definition of ridge flanks in Figure 1 and in the main text. Importantly, existing prior research is better connected to our own investigation in the Introduction and we now specifically explain why we investigate ridge flanks.
+
+The OCT used herein cannot visualize deep and fully into what the manuscript refers to as a "ridge"(note others have previously broken apart this concept apart into "papillary", "intermediate" and "limiting" ridges) near locations of the mechanoreceptive end organs lie at the epidermal-dermal border. Therefore, the OCT must make inferences about the movements of these deeper tissues, but cannot see them directly, and it is the movements of these deeper tissues that are likely driving the intricacies of neural firing. Note the word "ridge" is used often in the manuscript's abstract, introduction, and discussion but the definition in Fig. 1 and elsewhere differs in important ways from prior works of Cauna (expert in anatomy). Therefore, the manuscript should clarify if "ridge" refers to the papillary ridge (visible at the exterior of the skin), intermediate ridge (defined by Cauna as what the authors refer to as the primary ridge), and limiting ridge (defined by Cauna as what the authors refer to as the secondary ridge). What the authors really mean (I think) is some combination of the papillary and intermediate ridge structures, but not the full intermediate ridge. The manuscript acknowledges this in the "Limitations and future work" section, stating that these ridges cannot be resolved. This is important because the manuscript is oriented toward tracking this structure. It sets up the narrative and hypotheses to evaluate the prior works of Cauna, Gerling, Swensson, and others who all directly addressed the movement of this anatomical feature which is key to understanding ultimately how stresses at these locations might move the peripheral end organs (i.e., Merkel cells, Meissner corpuscles).
+
+Thank you for these observations. Indeed, our terminology was not consistent. We have now switched to Cauna’s terminology and added additional labels in Figure 1, explaining all mentioned structures in the main text. We have also changed the language in many instances in the main text to make it clearer whether we are referring to individual anatomical ridges (papillary, limiting, etc.) or the whole structure. Additionally, it is now clearer from the start which features are tracked, and we specifically state that intermediate ridges are excluded from our tracking.
+
+Regarding the intermediate ridge, it indeed plays a big role in Cauna’s lever hypothesis. Given the intermediate ridge is excluded from our analysis, we can neither prove nor disprove this hypothesis in our current work. However, there are many mechanical mysteries to solve regarding the structures directly above, which are the main focus of this paper. We have rewritten the introduction to make these questions clearer. For example, Cauna observed pliability of the papillary ridges in surface experiments. Swensson found differential expression patterns of keratin in epidermis tissue in and above the intermediate ridges, but the direct mechanical consequences that are proposed in their paper concern the behaviour of papillary ridges, rather than relying on a mechanical role of intermediate ridges. Even Cauna’s lever idea implies specific deformation of the stratum corneum, which would be measurable in our study, as the upper handle of the ‘lever’ needs turning. We observed little movement in accordance with this idea, putting the lever mechanism into question. While this does not rule out a mechanical role of the intermediate ridge, these findings constrain its potential mechanisms.
+
+Reviewer #2 (Public Review):
+
+Summary:
+
+The authors investigate sub-skin surface deformations to a number of different, relevant tactile stimuli, including pressure and moving stimuli. The results demonstrate and quantify the tension and compression applied from these types of touch to fingerprint ridges, where pressure flattens the ridges. Their study further revealed that on lateral movement, prominent vertical shearing occurred in ridge deformation, with somewhat inconsistent horizontal shear. This also shows how much the deeper skin layers are deformed in touch, meaning the activation of all cutaneous mechanoreceptors, as well as the possibility of other deeper non-cutaneous mechanoreceptors.
+
+Strengths:
+
+The paper has many strengths. As well as being impactful scientifically, the methods are sound and innovative, producing interesting and detailed results. The results reveal the intricate workings of the skin layers to pressure touch, as well as sliding touch over different conditions. This makes it applicable to many touch situations and provides insights into the differential movements of the skin, and thus the encoding of touch in regards to the function of fingerprints. The work is very clearly written and presented, including how their work relates to the literature and previous hypotheses about the function of fingerprint ridges. The figures are very well-presented and show individual and group data well. The additional supplementary information is informative and the video of the skin tracking demonstrates the experiments well.
+
+Weaknesses:
+
+There are very few weaknesses in the work, rather the authors detail well the limitations in the discussion. Therefore, this opens up lots of possibilities for future work.
+
+We thank the reviewer for these encouraging comments.
+
+Impact/significance:
+
+Overall, the work will likely have a large impact on our understanding of the mechanics of the skin. The detail shown in the study goes beyond current understanding, to add profound insights into how the skin actually deforms and moves on contact and sliding over a surface, respectively. The method could be potentially applied in many other different settings (e.g. to investigate more complex textures, and how skin deformation changes with factors like dryness and aging). This fundamental piece of work could therefore be applied to understand skin changes and how these impact touch perception. It can further be applied to understand skin mechanoreceptor function better and model these. Finally, the importance of fingertip ridges is well-detailed, demonstrating how these play a role in directly shaping our touch perception and how they can shape the interactions we have with surfaces.
+
+Reviewer #3 (Public Review):
+
+Summary:
+
+The publication presents unique in-vivo images of the upper layer of the epidermis of the glabrous skin when a flat object compresses or slides on the fingertip. The images are captured using OCT, and are the process of recovering the strain that fingerprints experience during the mechanical stimulation.
+
+The most important finding is, in my opinion, that fingerprints undergo pure compression/tension without horizontal shear, hinting at the fact that the shear stress caused by the tangential load is transferred to the deeper tissues and ultimately to the mechanoreceptors (SA-I / RA-I).
+
+Strengths:
+
+Fascinating new insights into the mechanics of glabrous skin. To the best of my knowledge, this is the first experimental evidence of the mechanical deformation of fingerprints when subjected to dynamic mechanical stimulation. The OCT measurement allows an unprecedented measurement of the depth of the skin whereas previous works were limited to tracking the surface deformation. - The robust data analysis reveals the continuum mechanics underlying the deformation of the fingerprint ridges.
+
+Weaknesses:
+
+I do not see any major weaknesses. The work is mainly experimental and is rigorously executed. Two points pique my curiosity, however:
+
+(1) How do the results presented in this study compare with previous finite element analysis? I am curious to know if the claim that the horizontal shear strain is transferred to the previous layer is also captured by these models. The reason is that the FEA models typically use homogeneous materials and whether or not the behavior in-silico and in-vivo matches would offer an idea of the nature of the stratum corneum.
+
+Very few modeling studies have examined combined normal and tangential loading of the fingertip. Additionally, results are often expressed in terms of Von Mises stresses, and not deformation [1,2], making direct comparison challenging. Nevertheless, one multilayered study [3] supports our finding that the largest deformations are found in deeper tissues.
+
+(1) Shao, F., Childs, T. H. C., Barnes, C. J. & Henson, B. Finite element simulations of static and sliding contact between a human fingertip and textured surfaces. Tribology International 43, 2308–2316 (2010).
+
+(2) Tang, W. et al. Investigation of mechanical responses to the tactile perception of surfaces with different textures using the finite element method. Advances in Mechanical Engineering 8, (2016).
+
+(3) Amaied, E., Vargiolu, R., Bergheau, J. M. & Zahouani, H. Aging effect on tactile perception: Experimental and modelling studies. Wear 332–333, 715–724 (2015).
+
+(2) Was there a specific reason why the authors chose to track only one fingerprint? From the method section, it seems that nothing would have prevented tracking a denser point cloud and reconstructing the stain on a section of the skin rather than just one ridge. With such data, the author could extend their analysis to multiple ridges interaction and get a better sense of the behavior of the entire strip of skin.
+
+We apologise for the confusion regarding this point. While in our illustration and the accompanying videos, we only show a single tracked ridge for clarity, we do indeed track all visible ridges in every frame. As imaging slices were 4 mm wide, often 8-9 ridges were visible concurrently. However, during the sliding experiments the skin was sometimes dragged along with the stimulus, causing some ridges to disappear from view for certain periods and then re-enter the frame. This would make it difficult to expand the analysis to multiple ridges, but in any case, we found neighbouring ridges to behave very consistently within a given trial, so that their mechanical behaviour (relative to the tactile feature, if any) could be averaged in the analysis.
+
+Reviewer #1 (Recommendations For The Authors):
+
+Discussion, line 213, "Thus, the primary mechanism through which the ridge conforms to the object involves the relative movement and shearing of the ridge flanks, rather than relying on the groves as articulated joints." I don't see this as definitely proven in the imaging and analysis. This could be a hypothesis to come from this work for further evaluation but is a quite strong statement not obviously supported by the evidence.
+
+We have rephrased this statement as a proposal for further testing:
+
+“Therefore, we propose that the primary mechanism through which a ridge conforms to an object might involve the relative movement and shearing of the ridge flanks, rather than relying on the grooves as articulated joints.”
+
+Discussion, line 220, "Our findings strongly indicate that the majority of the surface movement of the skin was observed by deeper tissue rather than surface layers of the skin." But since there are no measurements of such tissues, or of collagen bundle tightening, etc. it is not obvious to me how this can be proven as it is not directly observable and was not modeled.
+
+We have reworded this paragraph to be more cautious and have included potential avenues for future testing of this idea:
+
+“It is possible that the majority of the surface movement of the skin was absorbed by deeper tissues rather than the surface layers of the skin imaged in the present study. If that is the case, recent modeling work has suggested that tissue deformations are highly dependent on the orientation of collagen fibers in these tissues (Duprez et al., 2024), which might be amenable to tracking in future OCT work to test this idea directly. Additionally, previous work investigating tactile afferent responses to tangential skin movements has reported strong activation of SA-2 receptors, thought to measure skin stretch mainly in deeper tissues (Saal et al., 2025), providing further indirect evidence.”
+
+Figure 1, A. As noted elsewhere, there are issues with the naming of the anatomy, and there is no definition of the concept of "ridge flanks." Also, it does not indicate the depth point to which OCT can resolve.
+
+We have updated and expanded the labels in Figure 1A to clarify the anatomy (along with changes in the text described above). Figure 1C now includes a sentence about the resolvability of features below the mesh:
+
+“Detail view of a single OCT frame showing ridged skin structure and clear boundary between the stratum corneum and viable epidermis. A mesh covering the stratum corneum and the upper part of the viable epidermis (without the intermediate ridge) is overlaid spanning a single papillary ridge. The border between the viable epidermis and dermis is less clearly delineated, but some deeper features are resolved less well.”
+
+The concept of a ridge flank is now illustrated in Figure 1B(i) and Figure 1B(iv), and referred to in both the caption and main text. Updated figure caption text:
+
+“These deformations need not apply to the whole ridge structure but might affect different parts separately, e.g. via shearing in different directions across both ridge flanks as shown on the far right
+
+(see darker shading to highlight a single ridge flank).”
+
+Updated text in the main manuscript:
+
+“Additionally, if there are indeed mechanical differences between papillary ridges and their neighbouring grooves at the level of the stratum corneum, this might result in differential movements of the two sides of each papillary ridge, here referred to as ridge flanks (see Figure 1B-iv, right, for a potential example).”
+
+Note that Figure 4B also includes an illustration of this concept.
+
+Figure 1, B. This mechanical representation does not capture the entirety of the papillary-intermediate ridge unit in question, as set up by the authors in the introduction. Also, in the caption it is not ridge deformation, but upper SC and VE deformation. And the OCT cannot resolve the whole ridge.
+
+We have reworded the figure caption”
+
+“Potential deformations of the tracked ridge structure, including the stratum corneum and the bulk of the viable epidermis, during tactile interactions, with arrows indicating the directions of relative deformation. [...]”
+
+Importantly, the main manuscript text has been rewritten in the introduction section to clarify our research question and how much of the sub-surface ridge structure is tracked:
+
+“From a mechanical standpoint, these conflicting interpretations raise the question of how the outermost two skin layers typically deform at the resolution of single papillary ridges, whether by tension, compression, or shear (see examples in Figure 1B). Additionally, such deformations might apply to individual papillary ridges and all their sub-surface structures equally, for example horizontal shearing that bends the papillary ridge in a certain direction, while levering its sub-surface aspects in the opposite direction. Conversely, individual parts of the ridge structure might deform differently. For example, the viable epidermis might deform to a different extent or in different directions due to its lower stiffness and different morphology. Additionally, if there are indeed mechanical differences between papillary ridges and their neighbouring grooves at the level of the stratum corneum, this might result in differential movements of the two sides of each papillary ridge, here referred to as ridge flanks (see Figure 1B-iv, right, for a potential example). To empirically address these questions, we employed Optical Coherence Tomography (OCT) to precisely measure the sub-surface deformation of individual fingerprint ridges in response to a variety of mechanical events. Specifically, we focused on the stratum corneum and the bulk of the viable epidermis (excluding intermediate ridges), which could be robustly resolved and tracked by our setup.”
+
+Figure 1, C: While it is noted in the caption that the locations of the intermediate and limiting ridges, as well as the collagen bundles, are clearly visible, it is not clear to me, although the caption uses these words. This is especially the case below the orange mesh. From the picture, and because this is not labeled, it leaves it up to my interpretation, it seems like the secondary ridge (limiting) is larger than the primary (intermediate).
+
+We have reworded the caption as follows:
+
+“Detail view of a single OCT frame showing ridged skin structure and clear boundary between the stratum corneum and viable epidermis. A mesh covering the stratum corneum and the upper part of the viable epidermis (without the intermediate ridge) is overlaid spanning a single papillary ridge. The border between the viable epidermis and dermis is less clearly delineated.”
+
+Indeed, while the intermediate ridge was often visible in the OCT images, its size was rather inconsistent and it could appear as larger or smaller than the limiting ridge, while in histological images it is generally shown as larger (however note that there is somewhat limited data). This difference might be due to imaging artifacts, e.g. limited visibility into the deeper tissues, might reflect individual differences between participants, or could indicate that intermediate ridges are not of a consistent height in the (out-of-plane) direction along a given ridge. We have clarified this in the Limitations section of the Discussion:
+
+“[...] while we could confidently track landmarks associated with the stratum corneum, we could not reliably identify intermediate ridges in the viable epidermis, though they were visible in some of the frames, limiting the depth of the fitted mesh. We hypothesize that the additional depth of these ridges combined with their slender morphology might have degraded the signal. 3D OCT imaging (see below) might help to resolve these features in future work and settle open questions regarding their precise morphology.”
+
+Figure 1, D, and E: How do these measurements compare with the literature? They seem reasonable to me based on a cursory review, but there is a need to directly compare, especially since measurements in this context with the OCT are novel and could be valuable.
+
+We have clarified this in the main text and added more references to the existing literature:
+
+“We measured an average ridge width of 0.47 mm across participants (Figure 1D), consistent with previous studies (Moore, 1989; Ohler and Cummins, 1942). Average skin layer thickness was 0.38 mm for the stratum corneum and 0.12 mm for the viable epidermis across our dataset (Figure 1E), again in agreement with previous studies using both in vivo imaging and ex vivo histology (Fruhstorfer et al., 2000; Lintzeri et al., 2022; Maiti et al., 2020).”
+
+Abstract 4th sentence's structure makes me think that hundreds of individual fingerprint ridges can be tracked at the same time. Perhaps it could be tweaked to clearly indicate that hundreds were tracked between trials between participants.
+
+We have changed the sentence to now read:
+
+“Here, we used optical coherence tomography to image and track sub-surface deformations of hundreds of individual fingerprint ridges across ten participants and four individual contact events at high spatial resolution in vivo.”
+
+Introduction, 1st sentence, the fingertip per se is not an organ, though the skin is an organ.
+
+Changed the wording from “organ” to “structure”.
+
+Introduction, 1st sentence, "... that convert skin deformations ..." Need to add word skin to be clear.
+
+Done.
+
+Introduction, 3rd paragraph, "Alternately, the grooves may be stiffer or less ...". In this paragraph, and this sentence in particular, Cauna is cited and the words groves and ridges are used. But this is not adequately explained. Cauna had distinct terminology, where he referred to papillary, intermediate, and limiting ridges, that exist in addition to ready ridges. It is important because the manuscript uses the word "ridges" in a non-specific way. This is done not just here but throughout the manuscript, and is central to the questions which can be addressed with OCT.
+
+Anatomy has been better defined and more extensively labelled in Figure 1A, including labels for ‘papillary ridges’ and ‘grooves’. We have reworded this paragraph to better explain the concepts and how they relate to the subsequent analyses in the paper
+
+“Consequently, the mechanical response of the skin below its immediate surface remains largely unknown, leading to conflicting interpretations in the literature. For instance, it has been proposed that the papillary ridges are stiffer than the neighbouring grooves (Swensson et al., 1998), which might imply that normal loading of the skin might not affect the ridges’ profile appreciably. Conversely, other observations have suggested that the grooves are relatively stiff, allowing the papillary ridges to deform considerably (Cauna, 1954; Johansson and LaMotte, 1983). However, the sub-surface consequences of this putative pliability during object contact or stick-to-slip transitions (see e.g. Delhaye et al., 2016) are unclear: the whole ridge structure might bend as proposed in Cauna’s lever mechanism (Cauna, 1954), but this view has proved controversial (see e.g. Gerling and Thomas, 2008), with direct empirical evidence lacking.”
+
+Figure 1. Avoid red-green dots for colorblind accessibility. PMMA is not in the caption.
+
+We have switched the colors of the mechanoreceptors in panel A to a colorblind-friendly scheme. We now also specify the material of the plates in the figure 1 caption.
+
+Results, line 102. "... papillary ridge structure...." Is this the ridge to which is being referred?
+
+In conjunction with the updated labeling in Figure 1A, we have updated the terminology throughout the paper to be more consistent.
+
+Results, line 99. "We noted a small increase in the area of the strateum corneum, which was likely an artifact due to the fit of the mesh to the ridge's curvature ..." There is very little discussion of Fig. F's finding related to an increase in area in the SC and decrease in the VE. It makes me question if this finding in this panel is an artifact. With stiff tissue like stratum corneum, how would the area increase?
+
+This finding could be a measurement artifact or it could be the result of skin from neighbouring regions pushing into the imaged space. We have reworded the brief description in the Results:
+
+“We noted a small increase in the area of the stratum corneum, which was possibly an artifact due to the imperfect fit of the mesh to the ridge's curvature (but see Discussion for an alternative explanation).”
+
+Additionally, we have added a short section in the Discussion in the Limitations section:
+
+“Some of our tactile interactions might have caused skin deformations out-of-plane that were thus not measurable. For example, the slight increase in thickness of the stratum corneum under normal load might be explained as a measurement artifact due to the coarse nature of the mesh fitted, but could alternatively reflect tissue from out-of-plane regions pushing into the imaged space. Indeed, recent surface measurements of the skin's behaviour during initial object contact have reported compression of the skin in the plane parallel to its surface (Doumont et al., 2025), which would result in increasing thickness, assuming that the stratum corneum is incompressible. Future studies could consider creating three-dimensional reconstructions of the fingerprint structure to study such effects.”
+
+Figure 3. The colors used in slip and stick are not colorblind accessible.
+
+We have changed the background colors in Figure 3A,B,C to a colorblind accessible version.
+
+Results, line 151, "Thus, most of this shearing must be sustained by deeper tissues." But there are no direct observations as such. Also, in the next sentence, "collagen fiber bundles" are referred to in a non-specific way. This section is highly speculative with no systematic visualization of these structures, and should probably be moved to the discussion.
+
+We have reworded this sentence to be more cautious. We have now also highlighted collagen fiber bundles visible in the figure. Systematic analysis of these is beyond the scope of the present study, as these were not tracked, but might be possible in future studies. The reworded sentence reads as follows:
+
+“Thus, it is possible that shearing is sustained by deeper tissues, an effect that could be tested in future studies by directly tracking the angle and orientation of collagen fiber bundles anchoring the epidermis to deeper tissues (see highlighted examples in Figure 3B).”
+
+Results, line 161, " Horizontal shear ..." do you mean surface shear, per the Fig. 1 definition?
+
+For consistency, we have changed the labels to ‘Horizontal shear’ and ‘Vertical shear’ in Figure 1A(iii) and Figure 1A(iv) as these are the terms used throughout the paper.
+
+Discussion, line 198, "... flatten even at relatively low forces." This is an interesting point and it would be useful to note how low exactly.
+
+We have reworded this sentence to better reflect the findings described earlier:
+
+“We found that individual ridges tended to flatten considerably at relatively low forces of 0.5 N, with higher forces increasing deformations only moderately.”
+
+Reviewer #2 (Recommendations For The Authors):
+
+Minor comments that could improve the paper even further
+
+In the abstract, it may be good to specify that the stimuli were all applied to the finger, this was not an active, self-generated tactile interaction, e.g. change 'in response to a variety of tactile stimuli' to 'in response to a variety of passively-applied tactile stimuli'.
+
+Done.
+
+Comment on the grey/blue colours in the figures. I like the combination of blue/orange for different conditions, but sometimes the blue is very difficult to see against the grey background. Is there any way of making the grey background shading lighter and/or the blue darker/more vivid?
+
+We have changed the color of the SC mesh to a darker shade of blue, which is more easily distinguished from the grey background. This applies to figures 2B/C, 3D, 4A/B/D/E, and all supplementary figures.
+
+Methods. Could you please add a little more detail about exactly where the images were taken, e.g. in the exact middle of the fingerpad, at the fingertip? Did you line up the skin fingerprint ridges to be in a plane? It is just to better understand how the stimulus moved against the skin, which itself is rounded, and whether it was at a point where the ridges were relatively linear or curved.
+
+We have added the following text in the “Experimental set-up” section of the Methods:
+
+“The participant's finger was secured in a finger holder, which was positioned in such a way that the flat part of the fingertip distal to the whorl made initial contact with the plate as it was lowered onto the fingertip. The scanner was positioned such that its scan path aligned with the distal-proximal axis of the plate, targeting the centre line of the fingerpad so that the fingerprint ridges were oriented orthogonally to the line scan.”
+
+and
+
+“For these experiments, imaging focused on the central flat part of the contact area, such that all fingerprint ridges visible in the imaged region were in contact with the plate throughout the trial.”
+
+Methods. There is no section about statistics, yet you do use them in the paper. It may be good to add a few details in the methods to outline the package you used to do the statistics, as well as why you chose the tests you carried out.
+
+We have added a new Statistics section at the end of the Methods:
+
+“Statistical tests were run in Python using the scipy.stats package. As distributions were skewed, we used non-parametric analyses throughout the study. Bonferroni corrections were used when multiple comparisons were made.”
+
+A very minor point. Discussion, line 210: 'In this study...' is vague, which study exactly? It is preferable to be more precise, e.g. 'In the present/current study...'.
+
+Fixed.
+
+Discussion. One point you may want to add is the possibility of looking at other skin regions. For example, would this approach work on the palm, on border glabrous/hairy skin, on various hairy skin sites, and on the foot? The possibilities could be endless if it could be applied anywhere, but it may depend on the technical positioning and skin itself. However, it would be interesting to know.
+
+We have added the following text at the end of the Discussion section:
+
+“Finally, while we focused on the fingertip only, many other skin regions present interesting mechanical challenges waiting to be explored. The general ridged structure observed on the fingertip is common to all glabrous skin, but the local ridge mechanics might still differ: glabrous skin on the foot sole exhibits some morphological differences in order to support large weights that might well influence its mechanical response (Boyle et al., 2019). For example, the morphology of transverse ridges (running orthogonal to and connecting limiting with intermediate ridges) differs across regions on the foot sole (Nagashima and Tsuchida, 2011) and very likely from the hand (Yamada et al., 1996). Our method should be directly applicable to study deformations of these ridges, though three-dimensional observations might be needed to resolve some of the open questions. Hairy skin in contrast differs from glabrous skin in that the stratum corneum is much thinner. It also lacks the clearly organised ridge structure, but exhibits more loosely oriented skin folds instead, which very likely also serve a mechanical function (Leyva-Mendivil et al., 2015) and in principle are amenable to study using OCT.”
+
+In the last lines of the discussion, you mention the possible effects of skin moisturization. The Tomlinson et al. paper refers to the hydration of the skin with regard to water, which I would say is a slightly different factor. I think you can mention this paper and talk about the water level of the skin/hydration, but also add specifically that moisturization (i.e. by an emollient, humectant, or occlusive substance) is another factor to consider (e.g. effects found by Dione et al, 2023 Sci Rep). Overall, these two points relate to the dryness of the skin and the humidity of surfaces being contacted, therefore you could expand on both.
+
+Thank you for the correction! We now mention both skin hydration and moisturization separately in this section.
+
+No competing interests declared.
+
+Conceptualization, Data curation, Software, Formal analysis, Investigation, Visualization, Methodology, Writing – original draft, Writing – review and editing.
+
+Conceptualization, Resources, Software, Methodology.
+
+Conceptualization, Resources, Funding acquisition, Writing – review and editing.
+
+Conceptualization, Resources, Funding acquisition, Writing – review and editing.
+
+Conceptualization, Software, Formal analysis, Supervision, Methodology, Writing – review and editing.
+
+Conceptualization, Data curation, Supervision, Funding acquisition, Methodology, Writing – original draft, Writing – review and editing.
+
+Ten healthy participants (3 males, average age 20.5 years) participated in the experiment after providing written informed consent, including consent to publish the recorded data. The study protocol received ethical approval from The University of Sheffield Research Ethics Committee (ethics number 039144).
+
+
+References
+
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+Swensson O Langbein L McMillan JR Stevens HP Leigh IM McLean WH Lane EB Eady RA 1998 Specialized keratin expression pattern in human ridged skin as an adaptation to high physical stress The British Journal of Dermatology 139 767 775 10.1046/j.1365-2133.1998.02499.x 9892940
+Tomlinson SE Lewis R Liu X Texier C Carré MJ 2011 Understanding the friction mechanisms between the human finger and flat contacting surfaces in moist conditions Tribology Letters 41 283 294 10.1007/s11249-010-9709-y
+Wada K 2021 Wkentaro/labelme: v4.6.0 Zenodo 10.5281/zenodo.5711226
+Willemet L Kanzari K Monnoyer J Birznieks I Wiertlewski M 2021 Initial contact shapes the perception of friction PNAS 118 2109109118 10.1073/pnas.2109109118 PMC8670444 34857635
+Willemet L Huloux N Wiertlewski M 2022 Efficient tactile encoding of object slippage Scientific Reports 12 13192 10.1038/s41598-022-16938-1 35915135 PMC9343352
+Witney AG Wing A Thonnard JL Smith AM 2004 The cutaneous contribution to adaptive precision grip Trends in Neurosciences 27 637 643 10.1016/j.tins.2004.08.006 15374677
+Yamada N Kashima Y Inoué T 1996 Scanning electron microscopy of the basal surface of the epidermis of human digits Cells Tissues Organs 155 242 248 10.1159/000147812 8883535
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+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Nanoscale Adv
+Journal ID: Nanoscale Adv
+NLM Journal ID: 101738708
+Journal ID: NA
+
+Nanoscale Advances
+
+EISSN: 2516-0230
+Publisher: Royal Society of Chemistry
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC13182842
+PMID: 42158722
+DOI: 10.1039/d6na00038j
+Article ID: d6na00038j
+Article version: 1
+Subjects: Chemistry
+
+Comparative analysis of the water-based nanofluids in semi-circular heat transfer systems for thermohydraulic performance evaluation
+
+https://orcid.org/0000-0001-7862-8197 Ali Ussama a c
+https://orcid.org/0000-0003-4492-200X Janajreh Isam a b
+a Mechanical and Nuclear Engineering Department, Khalifa University of Science and Technology Abu Dhabi 127788 United Arab Emirates isam.janajreh@ku.ac.ae
+b Center for Membrane and Advanced Water Technology, Khalifa University of Science and Technology Abu Dhabi 127788 United Arab Emirates
+c Mechanical Engineering Department, University of Engineering and Technology Lahore 54890 Pakistan
+Electronic publication date: 2026 May 18
+Received 2026 Jan 16; Accepted 2026 Apr 1
+Copyright: This journal is © The Royal Society of Chemistry
+Copyright year: 2026
+Copyright holder: RSC
+
+License: This article is licensed under a Creative Commons Attribution 3.0 Unported Licence. You can use material from this article in other publications without requesting further permissions from the RSC, provided that the correct acknowledgement is given.
+License URL: https://creativecommons.org/licenses/by/3.0/
+
+Funding: Khalifa University of Science, Technology and Research 10.13039/501100004070 Unassigned
+pubstatus: Advance Article
+
+Ÿ==============================Ÿ
+This study presents a comprehensive numerical investigation of the thermohydraulic behavior of seven water-based nanofluids, Al, Al2O3, Cu, CuO, graphene (G), graphene oxide (GO), and hexagonal boron nitride (hBN), within a two-dimensional semi-circular cavity under a transitional regime. Using the transition SST K–ω model in the ANSYS Fluent software, simulations were conducted at a Reynolds number of 2500, incorporating nanoparticles at concentrations ranging from 0.5% to 5% by volume. The thermophysical properties were modeled using the established correlations. Key performance indicators included the convective heat transfer coefficient, Nusselt number, cavity wall temperature, thermal effectiveness, pressure drop, pumping power, and thermal performance factor (TPF). Results revealed that G/water and hBN/water nanofluids consistently outperformed others, delivering up to 53% and 42% heat transfer enhancement, respectively, with minimal hydraulic penalties. In contrast, Cu/water and CuO/water nanofluids, while thermally effective, exhibited a significant pressure drop and energy cost. Al/water, Al2O3/water, and GO/water demonstrated limited thermal gains relative to their pumping demands. These results highlight the importance of balancing the thermal conductivity, dispersion stability, and hydrodynamic performance in the nanofluid design, particularly for applications in electronics cooling and compact heat exchange systems.
+
+Graphene and hBN water-based nanofluids exhibit the highest thermohydraulic performance in a semi-circular cavity, achieving up to 53% heat-transfer enhancement with a moderate pressure drop compared with the Al, Al2O3, Cu, and CuO nanofluids.
+
+1. Introduction
+
+In recent decades, the pursuit of enhanced thermal performance in engineering systems has gained extensive research attention in advanced heat transfer fluids. Among these, nanofluids, which are colloidal suspensions of nanoparticles within conventional base fluids such as water, ethylene glycol, or oil, have emerged as a groundbreaking innovation.1,2 First introduced by Choi and Eastman in 1995,3,4 nanofluids exhibit significantly improved thermophysical properties compared with their base fluids, primarily due to the high thermal conductivity and large surface area of their dispersed nanoparticles.5,6 These enhancements lead to greater convective heat transfer coefficients, improved thermal conductivity, and better energy efficiency, especially in compact and high-flux thermal systems.7,8 Furthermore, nanofluids offer potential advantages such as reduced size and weight of heat exchangers9,10 and the capability to tailor fluid properties by selecting appropriate nanoparticle types, sizes, and concentrations. Therefore, nanofluids are now considered highly suitable for a wide array of applications, including electronic cooling,11,12 fabrication of automotive radiators,13 solar thermal collection,14 and advanced manufacturing processes.15
+
+Among the most widely researched oxide-based nanofluids, aluminum oxide (Al2O3) nanofluids have consistently demonstrated notable thermal performance enhancements in various engineering systems.16–18 The high surface area, thermal conductivity, and chemical stability of Al2O3 nanoparticles make them an effective choice for augmenting convective heat transfer. Vajjha et al. (2010)19 conducted a numerical investigation to assess the thermal performance of Al2O3 and CuO nanofluids in an ethylene glycol–water mixture under laminar flow conditions through flat tubes of an automotive radiator. Their findings showed a notable improvement in the convective heat transfer coefficient when using nanofluids compared with the base fluid. Specifically, the Al2O3 nanofluid at a volume concentration of 10% exhibited an average heat transfer coefficient approximately 91% higher than that of the base fluid. Additionally, the study found that both the local and average friction factors, as well as the convective heat transfer coefficients, increased with the nanoparticle concentration. Similarly, Elsebay et al.20 conducted a numerical study to investigate the impact of Al2O3 and CuO nanoparticles on the thermal and hydraulic performance of nanofluids flowing through the flat tubes of an automobile radiator. Their findings revealed that both nanofluids significantly enhanced the average heat transfer coefficient by up to 45% for Al2O3 and 38% for CuO compared with pure water. However, the improvements came at the cost of increased friction factor and pressure drop, particularly at higher nanoparticle concentrations. A resizing analysis further showed that the radiator tube length could be reduced by 11.7% for Al2O3 and 9.8% for CuO, maintaining the same cooling performance. Despite the benefit of more compact radiator design, the study noted a substantial increase in pumping power (up to 80%), emphasizing the trade-off between thermal enhancement and hydraulic efficiency. Similarly, Andreozzi et al.21 explored Al2O3/water nanofluids in ribbed channels under turbulent conditions and noted that the thermal performance improved consistently with the increase in particle concentration, though at the cost of higher pressure losses.
+
+In a numerical study by Lima-Téllez et al.,22 an Al2O3/water nanofluid was employed in a photovoltaic (PV) cooling channel equipped with baffles. The authors reported that a 10% volume concentration of Al2O3 nanofluid reduced the operating temperature of the PV panel by up to 15%, while increasing the electrical efficiency by approximately 4% at low Reynolds numbers (Re). In a separate numerical investigation using the lattice Boltzmann method, Mohebbi et al.23 found that although Al2O3 nanofluids showed slightly inferior performance than CuO nanofluids in heat transfer effectiveness, they still yielded significant Nusselt number improvements, especially at higher Reynolds numbers and particle concentrations. Furthermore, Alshukri et al.24 numerically assessed turbulent flow in baffled channels and confirmed that Al2O3 nanofluids at 4% volume fraction offered substantial thermal performance gains while maintaining acceptable hydraulic losses, reinforcing their suitability for high-Reynolds applications. Although aluminum (Al) nanoparticles are generally less stable in water than aluminum oxide (Al2O3) due to their higher reactivity and tendency to oxidize, they have nonetheless been investigated in studies for their high thermal conductivity and potential to enhance convective heat transfer.25 Jamal-Abad et al.26 conducted an experimental investigation on Al/water nanofluids in spiral coils and found that the thermal conductivity increased by up to 22% at a volume concentration of 2.23%, accompanied by a notable rise in the Nusselt number. Interestingly, although the friction factor increased slightly with the nanoparticle concentration, it remained close to that of the base fluid, implying a negligible pressure drop penalty for Al/water nanofluids.
+
+Copper (Cu)-based nanofluids have demonstrated superior thermal performance compared to other metallic nanofluids due to copper's high intrinsic thermal conductivity.27–29 In the study by Jamal-Abad et al.,26 Cu/water nanofluids outperformed Al/water counterparts, offering up to 26% enhancement in thermal conductivity at 2.23% volume concentration. While the friction factor did increase slightly with the nanoparticle concentration, it remained within practical limits for most engineering systems. Additionally, Nouari et al.30 conducted a numerical study of Cu/water nanofluid jet cooling in an inverted T-shaped channel and found that increasing the nanoparticle concentration significantly improved the Nusselt number across a wide range of Reynolds numbers. Their findings further confirmed that Cu/water nanofluids offer efficient thermal management solutions in compact electronic cooling systems, where space and thermal loading are both constrained.
+
+Copper oxide (CuO) nanofluids are more commonly studied than those containing metallic copper, primarily due to their greater colloidal stability in aqueous suspensions and superior cost-effectiveness compared to pure copper nanoparticles.31 Numerous studies have confirmed the superior performance of CuO/water nanofluids in both laminar and turbulent heat transfer applications. Mohebbi et al.23 conducted a comparative numerical study using the lattice Boltzmann method in a channel with extended surfaces, where CuO/water nanofluids outperformed Al2O3- and TiO2-based alternatives in terms of heat transfer augmentation. Their results showed that increasing the nanoparticle concentration from 0% to 5% led to a significant increase in the average Nusselt number, especially at higher Reynolds numbers, confirming the strong temperature-dependent performance of CuO nanofluids. Furthermore, Karami et al.32 conducted a numerical investigation into the turbulent flow of CuO/water nanofluids in grooved cylindrical channels, with particular focus on how the nanoparticle concentration affects thermal performance. Their results confirmed that increasing the CuO volume fraction from 0% to 4% consistently improved the average Nusselt number across all tested geometries and Reynolds numbers, indicating enhanced convective heat transfer. The study also noted that higher nanoparticle concentrations led to increased fluid viscosity and density, which in turn increased the friction factor and pressure drop, especially in grooved channels. Similarly, Lima-Téllez et al.22 numerically investigated CuO nanofluids in a photovoltaic panel cooling system with baffles. Their findings showed that CuO-based nanofluids yielded a high thermal efficiency improvement, up to 5.67% over water, at low Reynolds numbers, reinforcing the suitability of CuO nanofluids in low-flow-rate thermal applications. In turbulent flow regimes, Alshukri et al.24 examined CuO/water nanofluids flowing through baffled rectangular channels and observed a 10.3% improvement in the heat transfer coefficient compared to water alone, with a thermal performance factor approaching 2 at Re = 5000.
+
+Besides the traditional Al- and Cu-based nanofluids, graphene-based nanofluids have garnered increasing attention due to graphene's extraordinary thermal conductivity, high aspect ratio, and surface area, making them especially suitable for high-performance cooling applications.33–35 Almutter et al.36 used molecular dynamics simulations to study the impact of graphene nanoparticle size on Brownian displacement and thermophoretic behavior in water-based graphene nanofluids. They reported that increasing the nanoparticle size from 0.5 nm to 1 nm led to enhanced Brownian motion and thermophoresis, which translated to a substantial rise in thermal conductivity from 0.36 to 0.51 W m−1 K−1, reinforcing the efficiency of larger graphene nanoplatelets in promoting convective heat transfer. Arzani et al.37 performed both experimental and numerical analyses to explore how various parameters affect the thermal behavior of water-based graphene nanoplatelet (GNP) nanofluids flowing through an annular channel. Their results revealed that a GNP concentration of 0.1% by weight (wt%), among 0% to 0.1%, yielded the greatest improvement in the convective heat transfer coefficient, showing a 22% increase compared to pure water. However, they also noted that higher nanoparticle concentrations led to a rise in the friction factor, which in turn caused a noticeable increase in pressure loss throughout the system. Similarly, AbdRabbuh et al.38 performed both experimental and CFD studies on GNP nanofluids in aqueous solutions functionalized using gallic acid. They tested the thermal performance of an annular passage with various nanoparticle concentrations. The nanofluids exhibited an enhancement in thermal conductivity of up to 18.25%, accompanied by a 12.11% increase in the convective heat transfer coefficient at a concentration of 0.1 wt%. The pressure drop also increased with the nanoparticle concentration, but the performance index was highest at 0.025 wt%, indicating the best balance between thermal gain and pumping cost.
+
+Graphene oxide (GO), a derivative of graphene, offers enhanced dispersibility in water due to its oxygen-containing functional groups, and has been widely adopted in nanofluid applications demanding stable suspensions.39–41 Bai et al.42 examined the convective heat transfer performance and stability of graphene oxide/water nanofluids in a simulated spacecraft fluid loop. Their results showed that the nanofluids exhibited enhanced convective heat transfer compared to the base fluid, particularly in the 298–358 K temperature range, where the structure of the GO remained stable. The Nusselt number of the nanofluid was up to 43% higher than that of water at low heating powers. In another study, Yusuf et al.43 examined GO nanofluids in solar collectors using ionic liquid and water mixtures. Their findings showed that GO/water nanofluids exhibited significant thermal enhancement, but the use of ionic liquids further amplified the energy efficiency, achieving up to 37.4% improvement over water.
+
+Hexagonal boron nitride (hBN), often referred to as “white graphene” due to its structural similarity with graphene, has recently emerged as a promising nanomaterial for enhancing the thermal performance in heat transfer systems44–46. With properties such as high thermal conductivity, excellent chemical stability, and electrical insulation, hBN has proven to be an effective additive in water-based nanofluids.47–49 Büyükalaca et al.50 conducted numerical investigations into the use of hBN/water nanofluids in photovoltaic thermal (PVT) collectors and found that at 0.18% volume fraction, thermal efficiency improved significantly, while the electrical efficiency continued to increase with the increase in hBN concentration. hBN/water is marginally better than the graphene/water nanofluids with regard to both thermal and energy efficiencies. Similarly, Rizwan et al.51 experimentally evaluated a gravitational water vortex heat exchanger using hBN/water nanofluids and observed a maximum heat transfer rate increase from 8490 W to 9998 W, highlighting the strong potential of hBN nanofluids in industrial heat exchange applications. Furthermore, Sofiah et al.52 applied a response surface method (RSM) to optimize the performance of a PVT system using hBN/water nanofluids, reporting an electrical efficiency of 7.43% and a thermal efficiency of 73.82% under optimal flow and irradiance conditions.
+
+Despite the growing body of research on nanofluids, comparative studies that systematically evaluate the thermal and hydrodynamic behaviors of multiple nanofluids under identical conditions remain limited. The present study aims to fill this gap by offering a comprehensive comparative assessment of seven distinct water-based nanofluids: Al, Al2O3, Cu, CuO, graphene (G), graphene oxide (GO), and hexagonal boron nitride (hBN), within a controlled semi-circular cavity geometry. This approach allows for a direct and meaningful comparison of their performance in terms of heat transfer enhancement and flow characteristics. Table 1 provides an overview of the water stability and heat transfer potential of the selected nanoparticles used in this work. Stability in water is influenced by factors such as chemical reactivity and surface functionalization, while thermal conductivity and dispersion quality determine the overall heat transfer potential of each nanofluid. The semi-circular cavity, used as the computational domain, closely resembles configurations found in electronics cooling, microchannel heat sinks, and curved duct flows in compact energy systems. Its smooth geometry and potential for uniform heat distribution make it suitable for emerging applications in the thermal management of electronic devices and solar thermal collectors. The rest of the paper is organized as follows: Section 2 outlines the computational methodology used in this study, including turbulence modeling and boundary conditions. Section 3 presents and discusses the results, focusing on key performance metrics such as heat transfer coefficient, cavity wall temperature, Nusselt number, pumping power, and thermal performance factor. Finally, Section 4 provides the main conclusions drawn from this study.
+
+Table 1 Summary of the stabilities and thermal characteristics of the nanoparticles used in this study
+
+Nanoparticle	Stability in water	Heat transfer potential	
+Aluminum (Al)	Poor stability due to high reactivity. Prone to oxidation and agglomeration53	High thermal conductivity, but poor dispersion limits practical usage despite strong heat transfer potential54	
+Aluminum oxide (Al2O3)	Very stable, chemically inert and well-dispersed. Widely used in nanofluids55	Moderate conductivity. Widely used due to its balance of thermal performance and excellent stability56	
+Copper (Cu)	Poor stability, oxidizes and sediments quickly without surfactants57	Extremely high conductivity, but poor dispersion makes it unstable for long-term applications58	
+Copper oxide (CuO)	More stable than Cu. Good dispersion in water59	Lower conductivity, but offers a good balance between thermal performance and stability60	
+Graphene (G)	Low stability, prone to agglomeration unless stabilized with surfactants or functionalization61	Very high theoretical conductivity. Excellent heat transfer potential but difficult to stabilize62	
+Graphene oxide (GO)	Good stability due to oxygen functional groups which enhance its water compatibility63	Lower conductivity, but more practical due to higher stability compared with graphene64	
+Hexagonal boron nitride (hBN)	Chemically stable in water, but may require surfactants or functionalization to disperse well65	High thermal conductivity. Good potential, although cost and dispersion can be limiting factors66	
+
+2. Methodology
+
+2.1. Governing equations
+
+The present study solves the steady-state, incompressible, single-phase transitional flow of nanofluids in a two-dimensional (2D) semi-circular cavity using ANSYS Fluent. The governing equations include mass, momentum, and energy conservation, along with turbulence modeling via the transition SST K–ω model. Nanofluids are assumed to be Newtonian, with the thermophysical properties calculated based on the nanoparticle concentration. The governing equations are expressed in Cartesian coordinates (x, y). For incompressible, steady-state flow, the continuity equation is as follows:1
+
+where ρ is the fluid density, and u and v are the velocity components in the x- and y-directions, respectively. The momentum equations in the x- and y-directions are given as follows:2a
+
+2b
+
+where P is the static pressure, µ is the dynamic viscosity, and µt is the turbulent viscosity. The steady-state energy equation is given as follows:3
+
+where T is the temperature, cp is the specific heat capacity, k is the thermal conductivity, and kt is the turbulent thermal conductivity. The transport equations for the turbulent kinetic energy (K) and the specific dissipation rate (ω) are as follows:4a
+
+4b
+
+where GK and Gω are the generation terms, YK and Yω are the dissipation terms, Dω accounts for cross-diffusion, and σk and σω are the turbulent Prandtl numbers for K and ω equations, respectively.
+
+2.2 Thermophysical properties
+
+In this study, nanofluids are modeled as single-phase homogeneous mixtures, with their effective thermophysical properties computed based on the established empirical correlations. The base fluid is water, and the nanoparticles used include aluminum (Al), aluminum oxide (Al2O3), copper (Cu), copper oxide (CuO), graphene (G), graphene oxide (GO), and hexagonal boron nitride (hBN), all with a mean particle diameter of 10 nm. Nanoparticle volume fractions (ϕ) considered were 0.5%, 1%, 3%, and 5%. The following equations were used to calculate the nanofluid properties, based on Corcione et al.67
+
+Density of the Nanofluid:5 ρnf = ϕρp + (1 − ϕ)ρbf,5
+
+where ρnf is the density of the nanofluid, ρp is the density of the nanoparticle, and ρbf is the density of the base fluid (water). The term ϕ represents the volume fraction of the nanoparticles dispersed in the base fluid.
+
+Specific Heat Capacity of the Nanofluid:6
+
+where cp,nf denotes the specific heat capacity of the nanofluid. The symbols cp,p and cp,bf refer to the specific heat capacities of the nanoparticle and the base fluid, respectively.
+
+Viscosity of the Nanofluid:7
+
+where µnf is the dynamic viscosity of the nanofluid and µbf is the viscosity of the base fluid. dp is the diameter of the nanoparticle, while dbf is the molecular diameter of the base fluid, calculated as follows:8
+
+where M is the molecular weight of water (0.018015 kg mol−1) and NA is Avogadro's number (6.022 × 1023 mol−1).
+
+Thermal Conductivity of the Nanofluid (Corcione Correlation67):9
+
+where knf is the thermal conductivity of the nanofluid, and kbf and kp are the thermal conductivities of the base fluid and the nanoparticle, respectively. T is taken as the inlet temperature (300 K), Tfr is the freezing point of water (273 K), Prbf is the Prandtl number of the base fluid, and Rep is the particle Reynolds number given as follows:10
+
+where kB is the Boltzmann constant (1.3806 × 10−23 J K−1). It must be noted that the Corcione model is valid for spherical nanoparticles in the range of 10–150 nm with a concentration ≤5%.
+
+For nanofluids containing graphene (G), graphene oxide (GO), and hexagonal boron nitride (hBN), the nanomaterials are not spherical, but exist in the form of nanoplatelets or 2D flakes. As such, the widely used Corcione model, which assumes spherical particles, may not yield accurate predictions for these types of nanofluids. To address this, the present study utilizes the Hamilton–Crosser model68 to estimate the effective thermal conductivity, incorporating the effect of particle shape via a sphericity factor. A similar approach has been adopted in previous studies.69–71 The remaining thermophysical properties (density, specific heat, and viscosity) were computed using the same equations as used for spherical particles, as these properties are not as strongly affected by shape.
+
+Thermal Conductivity of the Nanofluid (Hamilton–Crosser Model68):11
+
+where n is the shape factor defined as n = 3/ξ and ξ is the sphericity of the particle. For nanoplatelets, ξ is taken as 0.15 in this study, resulting in n ≈ 20. This high value of n reflects the low sphericity and high aspect ratio of platelet-like particles. A sensitivity analysis was conducted by varying ξ between 0.10 and 0.20 around the baseline value of ξ = 0.15. In addition, the influence of platelet viscosity modeling was assessed using the Krieger–Dougherty relation 72 with intrinsic viscosity and maximum packing fraction values reported in the literature.73,74 The detailed results of these sensitivity analyses are presented in Appendix A. The results indicate that variations in cavity wall temperature, thermal performance factor, and thermal effectiveness remain small, confirming that the primary conclusions of this study are not significantly affected by reasonable variations in nanoparticle morphology assumptions.
+
+The Reynolds number and Prandtl number of the nanofluid are given as follows:12
+
+13
+
+where v is the inlet velocity and L in the characteristic length (inlet width). The average convective heat transfer coefficient (h) is calculated using Newton's law of cooling, which is mathematically represented as follows:14
+
+where q″ represents the heat flux, Tw denotes the mean temperature of the heated wall, and Tb indicates the average working fluid bulk temperature. To evaluate the average Nusselt number (Nu), the following relation is used:15
+
+where Lw is the length of the cavity wall. Table 2 presents the thermophysical properties of water and the nanoparticles utilized in this study. The thermal effectiveness and thermal performance factor (TPF) are calculated as follows:16
+
+17
+
+where Tout, Twall, and Tin are the outlet temperature, cavity wall temperature, and inlet temperature, respectively. Nu and ΔP refer to the Nusselt number and pressure drop obtained using the nanofluid, while Nu0 and ΔP0 denote the Nusselt number and pressure drop calculated for the base fluid (water) under identical operating conditions. The thermal performance factor defined in eqn (17) is a widely used thermohydraulic evaluation index that combines heat-transfer enhancement with the associated pressure-drop penalty.75–78
+
+Table 2 Thermophysical properties of water and the nanoparticles used in this study
+
+Material	Density ρ (kg m−3)	Specific heat cp (J kg−1 K−1)	Thermal conductivity k (W m−1 K−1)	
+Water (base fluid)	998.8	4182	0.611	
+Aluminum (Al)	2700	900	237	
+Aluminum oxide (Al2O3)	3970	765	40	
+Copper (Cu)	8933	385	400	
+Copper oxide (CuO)	6000	540	18	
+Graphene (G)	2250	2100	2500	
+Graphene oxide (GO)	1800	670	5	
+Hexagonal boron nitride (hBN)	2200	700	60	
+
+2.3. Numerical method
+
+The computational domain consists of a two-dimensional, semi-circular cavity with a top-centered vertical inlet and two symmetric outlets located at both ends of the horizontal top wall, as illustrated in Fig. 1. The diameter of the semi-circular cavity is denoted by D, while the inlet width is set to D/20 and extends vertically by D/4. This geometric configuration is representative of flow conditions found in electronics cooling applications and curved thermal ducts. A uniform velocity inlet boundary condition was applied at the vertical inlet at a constant temperature of 300 K, corresponding to a Reynolds number of 2500 based on the inlet width and water as the base fluid. This Reynolds number indicates a transitional flow regime, making the choice of the transition SST K–ω model particularly suitable for capturing near-wall effects and transition to turbulence within the curved cavity. At the cavity wall, a constant heat flux boundary condition of q″ = 50 000 W m−2 was imposed to simulate an externally heated surface, and all other walls were considered adiabatic. The two outlets were modeled as pressure outlets with zero-gauge pressure, allowing for symmetric discharge from the domain. The working fluid was either pure water or one of the seven different water-based nanofluids, each consisting of dispersed nanoparticles (Al, Al2O3, Cu, CuO, G, GO, and hBN) with a fixed particle size of 10 nm. Nanoparticle volume concentrations of 0%, 0.5%, 1%, 3%, and 5% were considered.
+
+Fig. 1 Computational domain illustrating the curved cavity geometry along with the locations of the inlet and outlets.
+
+Although nanofluids are inherently two-phase systems, previous studies79,80 have shown that they exhibit a behavior more similar to that of pure fluids than that of liquid–solid mixtures. Therefore, in this study, a single-phase model was adopted, treating the nanofluid as a continuum with effective thermophysical properties derived from those of the base fluid and nanoparticles. All nanofluids were also assumed to behave as classical Newtonian fluids, consistent with the single-phase approach.81,82 The flow was solved under steady-state conditions using the pressure-based solver in ANSYS Fluent. The SIMPLE algorithm was applied for pressure–velocity coupling. All spatial discretization schemes were set to second-order accuracy, and gradients were computed using the least squares cell-based method. A convergence criterion of 10−6 was applied to all residuals. Mesh refinement was focused near the cavity wall to resolve steep gradients in the boundary layer.
+
+The use of a two-dimensional, steady-state formulation is justified by the geometric symmetry of the semi-circular cavity and the study's primary objective, i.e., to compare the steady thermohydraulic performance of various nanofluids under identical boundary conditions. Although minor secondary motions may exist in curved geometries, prior studies79,80,82 have shown that for moderate Reynolds numbers and symmetric configurations, two-dimensional steady simulations capture the mean flow and heat transfer characteristics with good agreement to full three-dimensional or transient results. Moreover, the SST K-ω turbulence model effectively accounts for near-wall and transitional effects within a steady framework. Since both the inlet velocity and wall heat flux are constant, the system evolves toward a quasi-steady-state thermal equilibrium, making the steady-state assumption physically representative of the time-averaged behavior. This modeling approach ensures an appropriate balance between physical fidelity and computational efficiency for the multi-nanofluid comparative analysis performed in this study.
+
+The key assumptions adopted in developing the mathematical model are summarized as follows.
+
+• The flow is considered two-dimensional and incompressible.
+
+• The nanofluid is treated as a single-phase, Newtonian fluid with uniform and constant thermophysical properties.
+
+• The nanoparticles are uniformly dispersed, maintaining consistent size and shape throughout the domain.
+
+• Thermal equilibrium is assumed between the nanoparticles and the base fluid, forming a homogeneous mixture.
+
+• The effective thermophysical properties of the nanofluid are considered isotropic and temperature-independent. This assumption is justified by the small bulk-fluid temperature rise observed in the present simulations, with a maximum variation of approximately 0.86 K, which results in negligible changes in fluid properties.
+
+• The top surface of the cavity is assumed to be adiabatic.
+
+These assumptions are consistent with those adopted in several prior studies on nanofluids.83–86 Since the primary objective of the present work is a comparative assessment of different nanofluids under identical operating conditions, the use of these assumptions is considered appropriate and does not affect the relative performance trends reported.
+
+2.4 Mesh independence study
+
+To establish confidence in the accuracy of the numerical simulations, a mesh independence study was performed using four different mesh densities, as summarized in Table 3. All meshes were generated as structured quadrilateral grids, with a refined mesh spacing near the cavity wall to adequately resolve the steep velocity and thermal gradients expected in the boundary layer regions due to the applied heat flux. A visual representation of the baseline mesh used for the simulations is shown in Fig. 2. The refinement near the heated cavity wall was specifically designed to ensure that the dimensionless wall distance (y+) remained below 1 across the entire heated surface, thereby fully resolving the viscous sublayer. This resolution satisfies the requirements of the SST K–ω model, which employs a low-Reynolds-number formulation near the wall without relying on wall functions, ensuring the accurate prediction of near-wall flow and thermal gradients.
+
+Table 3 Mesh independence results showing variation in the heat transfer coefficient and cavity temperature for different mesh densities
+
+Mesh designation	No. of elements	Heat transfer coefficient (W m−2 K−1)	Difference in heat transfer coefficient (%)	Cavity temperature (K)	Difference in cavity temperature (%)	
+Coarse 1	8960	3269.5	8.50	316.70	0.41	
+Coarse 2	21 968	3139.8	4.20	317.25	0.23	
+Baseline	34 304	3035.6	0.74	317.82	0.05	
+Fine	84 048	3013.3	—	317.99	—	
+
+Fig. 2 Structured computational mesh with a refined spacing near the heated cavity wall.
+
+The comparison was based on two key output parameters: the average convective heat transfer coefficient at the cavity wall and the mean cavity wall temperature. As presented in Table 3, the transition from the Coarse 1 mesh to the Fine mesh results in a progressive reduction in the deviation of both the heat transfer coefficient and cavity temperature from Fine mesh values. Notably, the differences become marginal beyond the Baseline mesh, indicating mesh-independent behavior. Specifically, the difference in heat transfer coefficient between the Baseline and Fine meshes was only 0.74%, while the difference in average cavity wall temperature was a negligible 0.05%. Given this minimal variation and the significantly reduced computational cost compared to the Fine mesh, the Baseline mesh was selected for all subsequent simulations. This mesh provides a practical balance between the solution accuracy and the computational efficiency.
+
+2.5 Model validation
+
+To ensure the accuracy and reliability of the numerical model developed in this study, model validation was performed by replicating the experimental results of AbdRabbuh et al.,38 who investigated the thermal and hydrodynamic performance of water and graphene nanofluids in a fully circular pipe under transitional flow conditions. The experimental configuration of AbdRabbuh et al.38 was replicated numerically using distilled water as the working fluid. The same thermophysical properties, pipe geometry, and inlet conditions were adopted, covering Reynolds numbers in the range of 2500–4500. Two CFD models were implemented: (i) a full 3D pipe model and (ii) a 2D axisymmetric representation of the same geometry. In both cases, identical boundary conditions and the transition SST K–ω turbulence model were employed. The numerical results were compared with the experimental data in terms of the average Nusselt number (Nu) and the pressure drop per unit pipe length (ΔP/L). As shown in Fig. 3, both the 3D and 2D axisymmetric simulations reproduce the experimental trends very well over the entire Reynolds number range. The 3D model exhibits a very close agreement with the measurements, whereas the 2D axisymmetric model slightly overpredicts both Nu and ΔP/L. The observed deviations can be attributed to several factors. First, while the reference study by AbdRabbuh et al.38 was experimental in nature, the present work employs a CFD simulation, which inherently involves modeling assumptions such as idealized boundary conditions, mesh discretization, and turbulence model approximations. Additionally, experimental uncertainties such as slight variations in material properties or pipe surface roughness could contribute to discrepancies. The numerical model, on the other hand, assumes smooth walls and fully developed flow conditions. Despite these differences, the overall agreement between the datasets confirms the reliability of the current numerical framework for predicting thermal and hydrodynamic behavior in similar flow configurations.
+
+Fig. 3 Validation of the present numerical model against the results of AbdRabbuh et al.38 for a circular annular pipe with water as the working fluid at various Reynolds numbers: (left) average Nusselt number (Nu) and (right) pressure drop per unit pipe length (ΔP/L).
+
+In addition to the comparison with the external experimental data, the present 2D model was tested against a full 3D simulation of the semi-circular cavity configuration. The 3D domain, shown in Fig. 4, was generated by extruding the 2D geometry in the spanwise direction while maintaining the same boundary conditions. The average heat transfer coefficient at the heated wall, cavity-average temperature, outlet bulk temperature, and total pressure drop were evaluated from both simulations. As summarized in Table 4, the maximum deviation between the 2D and 3D predictions is 2.84% for the heat transfer coefficient, whereas the differences in cavity temperature, outlet temperature, and pressure drop remain below 1%. These discrepancies are well within the typical numerical uncertainty bounds for CFD simulations, and confirm that the 2D formulation captures the dominant thermohydraulic behavior of the semi-circular cavity. Therefore, the 2D model is adopted for the subsequent parametric investigation of water-based nanofluids, providing an appropriate balance between the computational efficiency and the predictive accuracy.
+
+Fig. 4 3D semi-circular cavity geometry and computational mesh used to assess the validity of the 2D numerical model.
+
+Table 4 Comparison of the key thermohydraulic parameters predicted by the 2D and 3D models for water at Re = 2500 in the semi-circular cavity
+
+Parameter	2D model	3D model	Difference (%)	
+Heat transfer coefficient (W m−2 K−1)	3035.64	3121.88	2.84	
+Cavity temperature (K)	317.82	316.66	0.365	
+Outlet temperature (K)	300.82	300.80	0.00665	
+Pressure drop (Pa)	98.43	99.10	0.681	
+
+3. Results and discussion
+
+This section presents and discusses the effect of the inlet position and the thermohydraulic performance of various nanofluids in a semi-circular cavity. The analysis encompasses seven water-based nanofluids: Al, Al2O3, Cu, CuO, graphene (G), graphene oxide (GO), and hexagonal boron nitride (hBN), with volume concentrations ranging from 0.5% to 5%.
+
+3.1. Effect of inlet position
+
+To assess the influence of geometric modification on the flow behavior and heat transfer efficiency, a preliminary investigation was conducted to evaluate the effect of inlet position within the semi-circular cavity. Three configurations were tested using water as the working fluid: (i) a top inlet, (ii) an inlet placed at a quarter depth from the top of the cavity, and (iii) an inlet positioned at half depth from the top of the cavity. All other parameters, including the inlet velocity (corresponding to Re = 2500), inlet temperature (300 K), and cavity heating conditions, were kept constant.
+
+Table 5 summarizes the results in terms of average convective heat transfer coefficient, mean cavity temperature, outlet temperature, and pressure drop. While the changes in thermal parameters are relatively minor, a clear trend emerges with the increasing inlet depth: the average heat transfer coefficient decreases from 3274.2 W m−2 K−1 (top) to 3035.6 W m−2 K−1 (half-depth), accompanied by a rise in mean cavity temperature and a slight increase in outlet temperature. Conversely, the pressure drop decreases significantly, from 126.9 Pa (top inlet) to 98.4 Pa (half-depth inlet). This trade-off reflects a shift in flow dynamics within the cavity. As the inlet is placed deeper into the cavity, the incoming jet is less effective at sweeping along the heated cavity wall, resulting in diminished convective transport and reduced thermal performance. However, this configuration minimizes the pressure drop due to the shorter acceleration path and more favorable flow development. These observations are supported by the pressure contours in Fig. 5 and temperature fields in Fig. 6. The top-inlet configuration shows a more concentrated high-pressure region in front of the inlet. In contrast, the half-depth inlet promotes a gentler flow, reducing flow resistance but also limiting thermal extraction.
+
+Table 5 Effect of inlet position on the average convective heat transfer coefficient, cavity temperature, outlet temperature, and pressure drop at Re = 2500 using water
+
+Inlet position	Heat transfer coefficient (W m−2 K−1)	Cavity temperature (K)	Outlet temperature (K)	Pressure drop (Pa)	
+Top	3274.2	316.58	300.77	126.92	
+Quarter	3262.06	316.72	300.78	110.59	
+Half	3035.64	317.82	300.82	98.43	
+
+Fig. 5 Pressure contour maps for different inlet positions of (a) top, (b) quarter-depth, and (c) half-depth.
+
+Fig. 6 Temperature contour maps inside the cavity for different inlet positions of (a) top, (b) quarter-depth, and (c) half-depth.
+
+Given the significant disparity in pressure drop (over 22% reduction from top to half-depth) and the modest loss in thermal performance (∼7% reduction in convective heat transfer coefficient and only 0.4% drop in cavity temperature), the half-depth inlet was selected for subsequent nanofluid simulations. This geometry provides a more energy-efficient platform, particularly important considering the added viscosity and associated pressure penalties introduced by nanoparticle-laden fluids.
+
+3.2 Thermal performance
+
+Fig. 7 presents the variation in the convective heat transfer coefficient (h) and the normalized Nusselt number (Nu/Nu0), where Nu0 corresponds to the Nusselt number obtained using the base fluid (water). A clear enhancement in thermal performance is observed upon the introduction of nanoparticles, especially with the increasing volume concentration (ϕ). Similar enhancement trends with the increasing nanoparticle volume fraction have been widely reported in experimental and numerical studies of nanofluid convection flows.19,26,37,87,88
+
+Fig. 7 Variation in the convective heat transfer coefficient (h) and normalized Nusselt number (Nu/Nu0) with the nanoparticle volume concentration (ϕ).
+
+Among all nanofluids, graphene/water shows the most significant improvement, with the convective heat transfer coefficient reaching ∼4700 W m−2 K−1 at 5% concentration, corresponding to an increase of 53% over water. The normalized Nusselt number also peaks for graphene at 1.53, highlighting its excellent capacity to augment convective heat transport. The second-best performer is hBN/water, which achieves a convective heat transfer coefficient of 4303 W m−2 K−1, representing a 42% enhancement over water. These improvements are attributed to their high thermal conductivities (as shown in Table 6) and unique platelet morphology, which promotes rapid in-plane conduction and increases the surface area for heat exchange.
+
+Table 6 Thermophysical properties of the water-based nanofluids at 5% volume concentration
+
+Nanofluid	Density ρnf (kg m−3)	Specific heat cp,nf (J kg−1 K−1)	Thermal conductivity knf (W m−1 K−1)	
+Water (base fluid)	998.8	4182	0.611	
+Al/water	1083.8	3773.2	0.764	
+Al2O3/water	1147.3	3590.8	0.756	
+Cu/water	1395.5	2966.7	0.7664	
+CuO/water	1248.8	3307.1	0.7526	
+G/water	1061.3	3961.3	1.2509	
+GO/water	1038.8	3877.7	0.7746	
+hBN/water	1058.8	3820.2	1.1397	
+
+Interestingly, although copper (Cu) nanoparticles possess a significantly higher intrinsic thermal conductivity (∼400 W m−1 K−1) than hexagonal boron nitride (hBN) nanoparticles (∼60 W m−1 K−1), the Cu/water nanofluid exhibits inferior thermal performance. At 5% concentration, the convective heat transfer coefficient for Cu/water is 3687 W m−2 K−1, which is notably lower than that of hBN/water. This is because the effective thermal conductivity of the Cu/water nanofluid at 5% concentration (0.7664 W m−1 K−1) is actually lower than that of hBN/water (1.1397 W m−1 K−1), highlighting the importance of nanoparticle dispersion and interaction with the base fluid over intrinsic properties alone. CuO/water, though less conductive, exhibits similar trends and begins to plateau after 3%, suggesting diminishing returns due to increased flow resistance and energy dissipation.
+
+Al/water and Al2O3/water demonstrate relatively low enhancements. Al/water, while possessing good intrinsic conductivity, is chemically unstable and prone to agglomeration in aqueous media, which may reduce its effective surface area. Al2O3/water, though more stable, exhibits a modest gain (3413 W m−2 K−1 at 3%) that flattens beyond 3%. This plateau behavior indicates that viscous effects begin to offset thermal gains at higher concentrations. The poorest performer is GO/water, which shows minimal improvement. Although GO/water is chemically more stable than G/water, its significantly lower conductivity outweighs any stability benefit, leading to a convective heat transfer coefficient value of 3308 W m−2 K−1 at 5%.
+
+The enhancement trends are non-linear, suggesting that beyond certain concentration thresholds, further nanoparticle addition either provides minimal benefit or may even deteriorate thermal performance due to increased viscosity, reduced effective Reynolds number, and potential onset of micro-scale flow instabilities.
+
+Fig. 8(a) displays the average cavity wall temperature for all nanofluids, serving as an indirect indicator of heat transfer efficiency. Lower wall temperatures indicate better convective removal of heat from the wall–fluid interface. At 5% volume concentration, Graphene/water and hBN/water significantly reduce the wall temperature to 311.8 K and 312.7 K, respectively, compared to water's 317.8 K. These reductions are consistent with the convective heat transfer coefficient and Nu/Nu0 trends in Fig. 7. For other nanofluids such as Cu/water, CuO/water, and Al2O3/water, the temperature drops are more modest (314.6 K, 315.5 K, and 316.1 K, respectively), while GO/water yields negligible reduction (316.6 K). Notably, wall temperature decreases significantly up to 3% concentration for most nanofluids, after which a plateau or slight increase is observed. This is due to increasing viscosity which decreases the effective Reynolds number. The interplay of reduced temperature and increasing pumping demands at high concentrations is a central trade-off in nanofluid optimization.
+
+Fig. 8 (a) Average cavity wall temperature and (b) average outlet nanofluid temperature as a function of the nanoparticle volume concentration (ϕ).
+
+Fig. 8(b) presents the corresponding average outlet nanofluid temperature as a function of nanoparticle volume concentration. The outlet temperature increases slightly with the increase in concentration for most nanofluids due to improved heat absorption from the heated cavity wall. However, the overall temperature rise remains small because of the relatively high flow rate associated with the transitional Reynolds number (Re = 2500). The maximum outlet bulk temperature increase observed is approximately 0.86 K relative to the inlet temperature (300 K) for the GO/water nanofluid at 5% concentration. This limited temperature rise confirms that the working fluid experiences only a modest thermal gain while effectively transporting heat away from the cavity wall.
+
+The temperature contours presented in Fig. 9 provide visual support for the quantitative analysis. Nanofluids such as Cu/water, G/water, and hBN/water demonstrate noticeably thicker thermal boundary layers and more uniform thermal diffusion along the heated cavity wall than the base fluid (water). Notably, the G/water and hBN/water nanofluids exhibit steeper temperature gradients near the wall, signifying enhanced local heat flux and more efficient thermal boundary layer transport. Moreover, the high-temperature zone typically observed adjacent to the cavity wall in the water and Cu/water cases is significantly suppressed in the G/water configuration. This reduction in thermal hotspots reflects the superior thermal conductivity and convective transport of graphene-enhanced nanofluids, leading to more effective and evenly distributed heat extraction.
+
+Fig. 9 Temperature contour maps within the semi-circular cavity for (a) water, (b) Cu/water, (c) G/water, and (d) hBN/water nanofluids at 5% concentration.
+
+Fig. 10 presents the thermal effectiveness, computed using eqn (16), which quantifies the extent to which the cooling fluid utilizes the available thermal potential for heat absorption. Water shows a baseline effectiveness of 4.6%. G/water and hBN/water nanofluids achieve the highest values (6.7% and 6.5%, respectively) at 5% volume concentration. Cu/water and CuO/water provide intermediate effectiveness (5.3% and 5.5%, respectively), while Al/water, Al2O3/water, and GO/water remain below 5.2%.
+
+Fig. 10 Thermal effectiveness of the nanofluids as a function of the nanoparticle volume concentration (ϕ).
+
+This trend directly reflects the cumulative effect of enhanced convective heat transfer coefficient, reduced wall temperature, and favorable nanoparticle properties. Thermal effectiveness shows saturation behavior for Al/water and Al2O3/water beyond 3%, mirroring earlier thermal indicators. Al/water, Al2O3/water, and GO/water show low performance due to their limited heat transfer ability.
+
+3.3 Pressure drop and pumping power
+
+The impact of nanoparticle addition on flow resistance is comprehensively evaluated in Fig. 11, which presents both the normalized pressure drop (ΔP/ΔP0) and the corresponding pumping power required for each nanofluid.
+
+Fig. 11 Normalized pressure drop (ΔP/ΔP0) and pumping power variations with the nanoparticle volume concentration (ϕ).
+
+Among all the tested nanofluids, the Cu/water nanofluid exhibits the highest pressure drop, reaching 1.40 times that of the base fluid at a 5% volume concentration. This is closely followed by CuO/water, which shows a normalized pressure drop 1.29 times that of the base fluid. These elevated values are primarily attributed to the high densities of copper-based nanofluids, which increase the inertial resistance to flow. As a result, wall shear stresses are significantly elevated, necessitating greater pumping power to maintain a constant flow rate. In contrast, G/water and hBN/water nanofluids exhibit only moderate increases in pressure drop, with values around 1.13 times that of water. This indicates a more favorable thermohydraulic balance, where substantial thermal benefits are achieved without imposing excessive hydraulic penalties. This behavior is due to the unique platelet-like morphology and high aspect ratio of these nanoparticles. Their lower densities compared to metallic nanoparticles also help maintain the fluid momentum and reduce the overall flow resistance.
+
+The associated pumping power requirements, shown on the secondary y-axis of Fig. 11, follow a similar trend. Cu/water and CuO/water nanofluids require the highest input energy, reaching 0.345 W and 0.316 W, respectively, at 5% concentration. G/water and hBN/water, despite their high thermal performance, require less than 0.28 W, confirming their suitability for applications where both thermal enhancement and energy efficiency are desired. Al/water and GO/water nanofluids not only exhibit low pumping power demands but also provide limited thermal enhancement, as discussed in Fig. 7 and 8, thereby reducing their overall effectiveness in performance-critical systems. This shows the importance of balancing thermal gains with hydrodynamic costs. Nanofluids such as G/water and hBN/water offer the most promising profiles, achieving meaningful thermal improvements while maintaining manageable increases in pressure drop and pumping power. Conversely, while copper-based nanofluids may enhance heat transfer, their high hydraulic demands could limit their practicality in energy-sensitive or compact flow systems.
+
+The pressure contours in Fig. 12 support the quantitative findings. For water, GO/water, and hBN/water, the high-pressure zones are localized near the bottom wall directly in front of the inlet, while the pressure within the cavity remains relatively low. In contrast, Cu/water displays a more pronounced and expanded high-pressure region, accompanied by elevated pressure levels throughout the cavity. This distribution reflects greater flow resistance and is consistent with the higher pressure drop and pumping power observed for Cu-based nanofluids.
+
+Fig. 12 Pressure contour maps inside the cavity for (a) water, (b) Cu/water, (c) G/water, and (d) hBN/water nanofluids at 5% concentration.
+
+3.4. Thermal performance factor
+
+Fig. 13 shows the Thermal Performance Factor (TPF) for the nanofluids used in this study. It reflects the net benefit of nanofluid use by combining heat transfer gain and flow penalty into a single metric, and is calculated according to eqn (17).
+
+Fig. 13 Plot of the thermal performance factor (TPF) of nanofluids versus nanoparticle volume concentration (ϕ).
+
+Among all the tested nanofluids, graphene (G/water) demonstrates the most favorable performance, achieving a TPF of approximately 1.47 at 5% concentration. This highlights graphene's ability to deliver substantial thermal enhancement while incurring only a modest increase in pressure drop. hBN/water follows closely with a TPF of ∼1.36, reinforcing its potential as a high-efficiency coolant. The high aspect ratio and anisotropic thermal conductivity of these nanoplatelet structures contribute to significant heat transfer improvements without causing substantial increases in flow resistance.
+
+In contrast, Cu/water, while thermally effective as seen in earlier metrics, records a lower TPF of ∼1.08 at 5%. This drop in performance is directly linked to its higher pressure drop, which consequently reduces the overall benefit when energy costs are considered. CuO/water, Al/water, Al2O3/water, and GO/water nanofluids exhibit TPF values near 1.05, suggesting that the thermal gains offered by these nanofluids are nearly offset by the accompanying increase in pumping power. The combined results from Fig. 4–12 highlight that selecting a nanofluid is a multi-objective optimization task.
+
+4. Limitations and future work
+
+The present work is based on a two-dimensional, steady-state, single-phase approach with temperature-independent thermophysical properties. Although the present analysis was conducted at Re = 2500, previous experimental and numerical studies in the transitional regime (Re ≈ 2000–4000) have shown that increasing the Reynolds number generally enhances convective heat transfer for both base fluids and nanofluids while preserving similar relative performance trends among different nanofluids.89,90 Formulation-specific effects such as surfactants or nanoparticle surface functionalization, which may influence dispersion stability and viscosity in practical nanofluids, were not explicitly considered in the present numerical framework. While these assumptions enable a clear comparative evaluation among different nanofluids with manageable computational cost, they may not capture transient, three-dimensional, or particle–fluid interaction effects that can occur in real systems. Future studies should therefore extend the analysis to three-dimensional and transient domains, incorporating two-phase or particle-tracking models and temperature-dependent properties to more accurately represent nanofluid behavior under dynamic thermal loads. Experimental validation under similar geometric and operating conditions is also recommended to further substantiate the numerical predictions and refine the modeling framework for practical applications.
+
+5. Conclusions
+
+In this study, a two-dimensional numerical investigation was conducted to evaluate the thermohydraulic performance of various water-based nanofluids within a semi-circular cavity under transitional flow conditions. Using the transition SST K–ω model in ANSYS Fluent, simulations were performed at a Reynolds number of 2500. The base fluid was water, and nanoparticles included Al, Al2O3, Cu, CuO, G, GO, and hBN, introduced at volume concentrations of 0.5%, 1%, 3%, and 5%. Thermophysical properties were modeled using established empirical correlations appropriate for spherical and platelet-shaped particles. The key findings of this study are as follows.
+
+• Graphene/water and hBN/water nanofluids exhibited the highest thermal enhancement, achieving heat transfer coefficients up to 53% and 42% higher than water, respectively. Their superior performance is attributed to high thermal conductivity, anisotropic morphology, and moderate flow resistance.
+
+• Copper-based nanofluids (Cu/water and CuO/water) demonstrated reasonable thermal improvement but were hindered by significant increases in pressure drop and pumping power, limiting their applicability in energy-sensitive systems. Al/water and Al2O3/water nanofluids, despite offering moderate conductivity, showed only marginal improvements in heat transfer.
+
+• Graphene oxide (GO), while stable in water, offered limited thermal benefits, and its performance plateaued at higher concentrations, underscoring the importance of balancing stability with conductive potential.
+
+• The thermal performance factor identified G/water and hBN/water as the most efficient nanofluids, with TPF values of 1.47 and 1.36, respectively, at 5% concentration, demonstrating an optimal trade-off between thermal gain and hydraulic penalty.
+
+• Temperature and pressure contours supported the quantitative results, showing improved thermal uniformity and reduced hotspot formation for high-performance nanofluids like G/water and hBN/water, while highlighting elevated flow resistance in Cu-based nanofluids.
+
+These results demonstrate that nanofluid selection is a multi-objective optimization problem, requiring a balance between thermal conductivity, viscosity, stability, and nanoparticle morphology. The semi-circular cavity results presented here are particularly relevant for compact thermal systems, such as microchannel coolers, electronic device heat sinks, and solar thermal collectors, where both heat transfer and flow efficiency are paramount.
+
+Conflicts of interest
+
+There are no conflicts to declare.
+
+A. Appendices
+
+A1. Sensitivity analysis of platelet morphology and viscosity model
+
+A1.1. Sensitivity to nanoparticle sphericity in the Hamilton–Crosser model
+
+The Hamilton–Crosser model accounts for particle shape through the sphericity parameter (ξ). Since graphene (G), graphene oxide (GO), and hBN nanoparticles exhibit platelet-like morphologies, the assumed sphericity may influence the predicted effective thermal conductivity. In this study, a baseline value of ξ = 0.15 was adopted, and a sensitivity analysis was performed by varying ξ between 0.10 and 0.20. The resulting variations in cavity wall temperature, thermal performance factor (TPF), and thermal effectiveness at ϕ = 5% are summarized in Table 7. The results indicate that the predicted thermohydraulic performance is not significantly sensitive to the assumed sphericity. For G/water and hBN/water nanofluids, the maximum change in cavity wall temperature is below 0.51%, while thermal effectiveness and TPF vary by less than approximately 14% and 16%, respectively. For the GO/water nanofluid, the sensitivity is even smaller, with TPF changes below 1.3% and wall temperature variations below 0.07%. These results indicate that the overall conclusions regarding the superior performance of platelet-based nanofluids do not significantly change within a realistic range of platelet morphologies.
+
+Table 7 :Sensitivity of the thermohydraulic performance of platelet-based nanofluids to the particle sphericity (ξ) in the Hamilton–Crosser thermal conductivity model at 5% volume fraction
+
+Nanofluid (ϕ = 5%)	Sphericity (ξ)	Cavity wall temperature (K)	Percentage difference in cavity wall temperature (%)	TPF (–)	Percentage difference in TPF (%)	Effectiveness (%)	Percentage difference in effectiveness (%)	
+hBN/water	0.1	311.5	0.40	1.51	11.10	7.10	9.67	
+hBN/water	0.15	312.8	Reference	1.36	Reference	6.48	Reference	
+hBN/water	0.2	313.7	0.29	1.27	6.69	6.09	5.92	
+G/water	0.1	310.2	0.51	1.70	15.84	7.61	13.79	
+G/water	0.15	311.8	Reference	1.47	Reference	6.69	Reference	
+G/water	0.2	313.0	0.35	1.34	8.58	6.18	7.62	
+GO/water	0.1	316.4	0.07	1.07	1.27	5.23	1.03	
+GO/water	0.15	316.6	Reference	1.05	Reference	5.17	Reference	
+GO/water	0.2	316.8	0.06	1.04	1.13	5.12	1.05	
+
+A1.2. Sensitivity to platelet viscosity model
+
+The viscosity of platelet-based nanofluids depends on the particle aspect ratio and packing characteristics. To evaluate the influence of viscosity modeling assumptions, a sensitivity analysis was performed using the Krieger–Dougherty viscosity model,72 given as follows:A1
+
+where [η] is the intrinsic viscosity and ϕm is the maximum packing fraction. In the present study, the viscosity calculated from eqn (7) corresponds to [η] = 6.04 and ϕm = 0.17 in the Krieger–Dougherty viscosity model for ϕ = 5%. These values fall within the literature ranges reported for platelet suspensions, including the values proposed by Kasgoz et al.73 and Claypole et al.74Table 8 compares the predicted viscosity, cavity wall temperature, thermal performance factor, thermal effectiveness, and pumping power obtained using these parameter sets. The results show that the predicted thermohydraulic behavior is only weakly sensitive to the viscosity model parameters. The nanofluid viscosity varies less than 4.4%, leading to changes below 0.07% in cavity wall temperature, 1.5% in TPF and effectiveness, and 0.5% in pumping power. These small deviations confirm that the main conclusions of the study are not significantly affected by reasonable variations in platelet viscosity modeling.
+
+Table 8 Sensitivity of the predicted thermohydraulic performance to platelet viscosity modeling using the Krieger–Dougherty relation at a nanoparticle volume fraction of ϕ = 5%. Percentage differences relative to the present study are shown in parentheses
+
+Reference	Intrinsic viscosity [η]	Maximum packing fraction (ϕm)	Viscosity (Pa s−1)	Cavity wall temperature (K)	TPF	Effectiveness (%)	Pumping power (W)	
+Kasgoz et al.73	5.4	0.189	0.001217 (4.40%)	311.64 (0.067%)	1.494 (1.79%)	6.77 (1.13%)	0.275 (0.93%)	
+Present work	6.04	0.17	0.001273 (reference)	311.85 (reference)	1.468 (reference)	6.69 (reference)	0.278 (reference)	
+Claypole et al.74	6.37	0.151	0.00131 (2.91%)	311.99 (0.047%)	1.450 (1.19%)	6.63 (0.84%)	0.280 (0.58%)	
+
+Supplementary Material
+
+NA-OLF-D6NA00038J-s001
+
+This research was funded by the Center for Membrane and Advanced Water Technology, Khalifa University of Science and Technology (KU-CMAT).
+
+Data availability
+
+The data supporting this article have been included as part of the supplementary information (SI). Supplementary information is available. See DOI: https://doi.org/10.1039/d6na00038j.
+
+
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diff --git a/corpus/psychology/text/94a50a67c27157f4.txt b/corpus/psychology/text/94a50a67c27157f4.txt
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index 0000000000000000000000000000000000000000..e7b7cc2e3b61ed8991593402c73144c14d7f923d
--- /dev/null
+++ b/corpus/psychology/text/94a50a67c27157f4.txt
@@ -0,0 +1,76 @@
+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Diagnostics (Basel)
+Journal ID: Diagnostics (Basel)
+NLM Journal ID: 101658402
+Journal ID: diagnostics
+
+Diagnostics
+
+EISSN: 2075-4418
+Publisher: Multidisciplinary Digital Publishing Institute (MDPI)
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC13114527
+PMID: 42072874
+DOI: 10.3390/diagnostics16081177
+Article ID: diagnostics-16-01177
+Article version: 1
+Subjects: Correction
+
+Correction: Urbano et al. Comparison of Serum and Cerebrospinal Fluid Neurofilament Light Chain Concentrations Measured by Ella™ and Lumipulse™ in Patients with Cognitive Impairment. Diagnostics 2024, 14, 2408
+
+https://orcid.org/0000-0003-1490-5508 Urbano Teresa 1 2 †
+https://orcid.org/0009-0006-4863-0716 Maramotti Riccardo 3 4 5 †
+https://orcid.org/0000-0001-6698-5437 Tondelli Manuela 3 6 *
+https://orcid.org/0000-0001-5057-0181 Gallingani Chiara 3 6
+Carbone Chiara 3 6
+https://orcid.org/0009-0008-1235-3782 Iacovino Najara 3 6
+https://orcid.org/0000-0003-1055-8908 Vinceti Giulia 6
+Zamboni Giovanna 3 6
+Chiari Annalisa 6 ‡
+https://orcid.org/0000-0001-5006-3294 Bedin Roberta 1 3 6 ‡
+1 Neuroimmunology Laboratory, Department of Biomedical, Metabolic and Neural Sciences, University of Modena and Reggio Emilia, Baggiovara Hospital, 41126 Modena, Italy; teresa.urbano@unimore.it (T.U.); roberta.bedin@unimore.it (R.B.)
+2 Environmental, Genetic and Nutritional Epidemiology Research Center (CREAGEN), Department of Biomedical, Metabolic and Neural Sciences, University of Modena and Reggio Emilia, 41125 Modena, Italy
+3 Department of Biomedical, Metabolic and Neural Sciences, University of Modena and Reggio Emilia, 41125 Modena, Italy; riccardo.maramotti@unimore.it (R.M.); gallinganichiara@gmail.com (C.G.); chiara.carbone@unimore.it (C.C.); najara.iacovino@unimore.it (N.I.); giovanna.zamboni@unimore.it (G.Z.)
+4 Department of Physics, Informatics and Mathematics, University of Modena and Reggio Emilia, 41125 Modena, Italy
+5 Department of Mathematics and Computer Science, University of Ferrara, 44121 Ferrara, Italy
+6 Neurology Unit, Baggiovara Hospital, 41126 Modena, Italy; gvinceti@gmail.com (G.V.); chiari.annalisa@aou.mo.it (A.C.)
+* Correspondence: manuela.tondelli@unimore.it† These authors contributed equally to this work.
+
+‡ These authors contributed equally to this work.
+
+Electronic publication date: 2026 Apr 16
+Publication date: 2026 Apr
+Volume: 16
+Issue: 8
+Electronic Location ID: 1177
+Received 2026 Mar 26; Accepted 2026 Mar 27
+Copyright: © 2026 by the authors.
+Copyright year: 2026
+License: Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Erratum for: Comparison of Serum and Cerebrospinal Fluid Neurofilament Light Chain Concentrations Measured by Ella™ and Lumipulse™ in Patients with Cognitive Impairment 14 21 29 10 2024 2408 Diagnostics 10.3390/diagnostics14212408 PMC11544876 39518375
+
+Ÿ==============================Ÿ
+In the original publication [1], there was a transcription error in the mathematical expressions of the conversion formulae between the Lumipulse™ and Ella™ assays derived from the Passing–Bablok regression model. A correction has been made to Section 3 Results, Paragraphs 7 and 8 with equations, as follows:
+
+When only Ella™ is available, the formulae used to obtain the corresponding value in Lumipulse™ (y) in relation to Ella™ (x) arey(Lumipulse™) = 0.8261 × x(Ella™) − 45.38 (for CSF)
+
+y(Lumipulse™) = 0.5775 × x(Ella™) + 7.543 (for serum)
+
+On the other hand, when only Lumipulse™ (y) is available, the formulae used to obtain the corresponding Ella™ (x) value arex(Ella™) = 1.211 × y(Lumipulse™) + 45.38 (for CSF)
+
+x(Ella™) = 1.732 × y(Lumipulse™) − 7.543 (for serum)
+
+The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.
+
+Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.
+
+
+Reference
+
+1. Urbano T. Maramotti R. Tondelli M. Gallingani C. Carbone C. Iacovino N. Vinceti G. Zamboni G. Chiari A. Bedin R. Comparison of Serum and Cerebrospinal Fluid Neurofilament Light Chain Concentrations Measured by Ella™ and Lumipulse™ in Patients with Cognitive Impairment Diagnostics 2024 14 2408 10.3390/diagnostics14212408 39518375 PMC11544876
diff --git a/corpus/psychology/text/9f3272b322a49b17.txt b/corpus/psychology/text/9f3272b322a49b17.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a4730a33d3a1a590840499b0d8ff26aa418ae081
--- /dev/null
+++ b/corpus/psychology/text/9f3272b322a49b17.txt
@@ -0,0 +1,8 @@
+Emotional Composition Of Sleep-Related Out-Of-Body Experiences In Relation To Sleep Paralysis And Lucid Dreaming
+
+Sleep-related out-of-body experiences (OBEs) occupy an ambiguous position between sleep paralysis and lucid dreaming. OBEs are often considered part of the vestibular-motor component of sleep paralysis, but they also share features with lucid dreaming, including vivid internally generated experience, heightened awareness, and perceived agency. Here, we examined whether the emotional composition of sleep-related OBEs is closer to sleep paralysis, closer to lucid dreaming, or distinguishable from both.
+We analysed 666 participant-by-experience-type emotional reports corresponding to OBEs, sleep paralysis, and lucid dreams. Emotional variables were coded as binary presence/absence indicators. The main multivariate analyses focused on reports containing at least one discrete emotion, yielding 658 reports: 184 OBEs, 210 sleep paralysis reports, and 264 lucid dream reports. Emotional composition was assessed using Jaccard dissimilarity, non-metric multidimensional scaling, PERMANOVA, multivariate dispersion, and emotion-by-group association analyses. Responses indicating absence of emotion were analysed separately.
+Emotional composition differed significantly across OBEs, sleep paralysis, and lucid dreams. Descriptively, the OBE–lucid dream contrast showed the smallest observed pairwise effect size, whereas contrasts involving sleep paralysis showed larger observed effects. Sleep paralysis was associated with high-arousal negative emotions, particularly fear, terror, and anxiety, and showed the most homogeneous emotional profile. Lucid dreams were associated with happiness, love, hope, and sexual energy. OBEs were distinguished by peace/tranquility and, to a lesser extent, euphoria. Absence-of-emotion responses were rare and did not account for the multivariate pattern.
+Sleep-related OBEs were not emotionally reducible to sleep paralysis. Their emotional profile was consistent with greater affective similarity to lucid dreams than to sleep paralysis, while remaining distinguishable from both. These findings suggest that emotional composition provides an informative axis for characterizing sleep-related altered states of consciousness.
+
+Keywords: out-of-body experience; sleep paralysis; lucid dreaming; dream emotions; altered states of consciousness.
diff --git a/corpus/psychology/text/a2a07f5167c603cc.txt b/corpus/psychology/text/a2a07f5167c603cc.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9855b7914f8bf0de316931e8840d355e945c0766
--- /dev/null
+++ b/corpus/psychology/text/a2a07f5167c603cc.txt
@@ -0,0 +1,3 @@
+How mouse cursor tracking contributes to the psychological validation of the drift diffusion model
+
+As a well-established cognitive model of human decision-making, the drift diffusion model (DDM) offers a psychologically intuitive account of the decision-making process by virtue of its four basic parameters. However, the reliance of the DDM on endpoint measures (response times and accuracy) creates a conceptual gap to its process-oriented account, which needs to be bridged with the help of independent process-tracing methods. In two studies, we deployed mouse cursor tracking with the aim of validating the psychological interpretation of the basic DDM parameters drift rate, threshold separation, and non-decision time.  In a first preregistered study, 88 participants completed 90 trials of a random dot kinematogram (RDK). Partial least square regression was applied in order to predict between-subject variation in the three DDM parameters with the help of 18 established cursor measures. We found support for the psychological interpretation of threshold separation and non-decision time, confirming the results of a previous study, while the analyses of drift rate remained inconclusive. In a second study, we further explored the predictability of drift rate both between subjects and task conditions. Drift rate could be validated within-subjects but not between-subject pointing to an under-specification in the psychological interpretation of the drift rate. Our results further strengthen our psychological understanding of the DDM, point towards conceptual ambiguities in both cursor measures and diffusion modelling, and encourage further joint application of cognitive models and process-tracing methodology.
diff --git a/corpus/psychology/text/a490065e6a380296.txt b/corpus/psychology/text/a490065e6a380296.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c1e9f9fddc78299a832a8d7f030ec362b26c40a7
--- /dev/null
+++ b/corpus/psychology/text/a490065e6a380296.txt
@@ -0,0 +1,52 @@
+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: PLOS Glob Public Health
+Journal ID: PLOS Glob Public Health
+NLM Journal ID: 9918283779606676
+Journal ID: plos
+
+PLOS Global Public Health
+
+EISSN: 2767-3375
+Publisher: PLOS
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC11687884
+PMID: 39739890
+DOI: 10.1371/journal.pgph.0004155
+Article ID: PGPH-D-24-03027
+Article version: 1
+Subjects: Correction
+
+Correction: Exploring ethical practice in NGOS on mental health research in Malawi
+
+Amos Action
+Guerra Cristobal
+Reid Corinne
+Toro Edgardo
+Calia Clara
+Electronic publication date: 2024 Dec 31
+Publication date: 2024
+Volume: 4
+Issue: 12
+Electronic Location ID: e0004155
+Copyright: © 2024 Amos et al
+Copyright year: 2024
+Copyright holder: Amos et al
+License: This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Erratum for: Exploring ethical practice in NGOS on mental health research in Malawi 4 4 11 4 2024 e0003001 PLOS Global Public Health 10.1371/journal.pgph.0003001 PMC11008845 38603700
+Figure count: 0
+Table count: 0
+Page count: 1
+
+Ÿ==============================Ÿ
+The affiliation for the fourth author is incorrect. The correct affiliation is not indicated. Edgardo Toro is not affiliated with #4 but with: Pontificia Universidad Católica de Valparaiso, Escuela de Trabajo Social, Chile.
+
+
+Reference
+
+1 Amos A , Guerra C , Reid C , Toro E , Calia C (2024) Exploring ethical practice in NGOS on mental health research in Malawi. PLOS Glob Public Health 4(4): e0003001. doi: 10.1371/journal.pgph.0003001 38603700 PMC11008845
diff --git a/corpus/psychology/text/a66eab2529d76b2f.txt b/corpus/psychology/text/a66eab2529d76b2f.txt
new file mode 100644
index 0000000000000000000000000000000000000000..af05035cb301eb6fd17ff837ac82b559695c5d3c
--- /dev/null
+++ b/corpus/psychology/text/a66eab2529d76b2f.txt
@@ -0,0 +1,3 @@
+Social Origins of the Self: Mutual Gaze at 12 Months Predicts Self-Recognition and Fronto-Temporoparietal Connectivity at 18 Months
+
+A central question in developmental science concerns how a reflective, conceptual self emerges. Theoretical accounts propose that infants' early experiences as the object of caregiver attention — particularly through mutual gaze — scaffold the development of objective self-awareness, possibly via maturation of fronto-temporoparietal networks implicated in self-referential processing. The present longitudinal study examined associations among early mutual gaze experience, fronto-temporoparietal functional connectivity, and mirror self-recognition during the second year of life. Mother–infant dyads (N = 107) participated in a 10-min free-play interaction at 12 months, from which mother-to-infant, infant-to-mother, and mutual gaze durations were micro-coded. Task-free functional connectivity within a fronto-temporoparietal network (FTPN) was assessed at 12 and 18 months using fNIRS, and mirror self-recognition was tested at 18 months as an index of self-awareness. Bayesian analyses revealed moderate evidence that infants who experienced more mutual gaze with their mothers at 12 months were more likely to be classified as mirror recognisers at 18 months. Mutual gaze at 12 months also predicted left-hemisphere and bilateral FTPN connectivity at 18 months. We did not replicate previously reported group differences in FTPN connectivity between mirror recognisers and non-recognisers. Together, these findings provide longitudinal evidence that early experience as the object of caregiver attention is associated with the emergence of self-awareness and the development of brain networks implicated in self-referential processing. This supports theoretical accounts situating the origins of objective self-awareness in early dyadic social experience.
diff --git a/corpus/psychology/text/adf8ccef9ce4ec12.txt b/corpus/psychology/text/adf8ccef9ce4ec12.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7c8d9a99e4d873dfc2b1928e0796e1add2e63aab
--- /dev/null
+++ b/corpus/psychology/text/adf8ccef9ce4ec12.txt
@@ -0,0 +1,3 @@
+Rethinking Age Differences in ERP Word Predictability Effects During Reading: Evidence from Meta-Analysis
+
+Electroencephalography (EEG) studies of reading often report smaller and delayed neural responses to word predictability in older adults, particularly in the N400 and later frontal positivity components of event-related potential (ERP) measures. These findings have been interpreted as evidence for age-related declines in the use of contextual information during language comprehension. However, this contrasts with eye-movement research, which typically shows preserved or enhanced use of context in older readers. One possible explanation is methodological. Many EEG studies use rapid serial visual presentation (RSVP), where words are presented one at a time at a fixed pace. This limits natural reading behaviors that may be especially important for older adults. To evaluate this possibility, we conducted a meta-analysis of 12 EEG studies examining age differences in word predictability effects during sentence reading. RSVP studies were compared with studies using more naturalistic presentation methods. On average, older adults showed smaller and delayed N400 predictability effects than younger adults, replicating the standard ageing pattern. Critically, presentation method moderated these effects. RSVP studies consistently showed smaller and delayed predictability effects in older adults, whereas more naturalistic paradigms showed comparable effects across age groups and sometimes larger effects in older adults. No reliable age differences were observed in late frontal positivity effects. These findings suggest that widely reported age-related reductions in EEG word-predictability effects may reflect experimental constraints rather than a general decline in contextual processing during reading. Under more natural reading conditions, older adults appear to retain the ability to use prior context effectively.
diff --git a/corpus/psychology/text/b33e811a7b357390.txt b/corpus/psychology/text/b33e811a7b357390.txt
new file mode 100644
index 0000000000000000000000000000000000000000..0e8d6d31bfe040696c87b799655e5ab96b5ab00d
--- /dev/null
+++ b/corpus/psychology/text/b33e811a7b357390.txt
@@ -0,0 +1,322 @@
+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Int J Mol Sci
+Journal ID: Int J Mol Sci
+NLM Journal ID: 101092791
+Journal ID: ijms
+
+International Journal of Molecular Sciences
+
+EISSN: 1422-0067
+Publisher: Multidisciplinary Digital Publishing Institute (MDPI)
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC13566312
+PMID: 42737655
+DOI: 10.3390/ijms27177758
+Article ID: ijms-27-07758
+Article version: 1
+Subjects: Article
+
+Comparative Proteomic Analysis of the Striatum in Heterozygous and Null DAT Knockout Rats
+
+https://orcid.org/0000-0002-3675-0597 Mittenberg Alexey G. Validation Methodology Investigation Writing – original draft 1
+https://orcid.org/0009-0005-2866-9106 Belskaya Anastasia D. 2
+Shabelnikov Sergey V. Methodology Investigation 1
+https://orcid.org/0000-0002-2074-9081 Fesenko Zoya S. 2
+https://orcid.org/0009-0009-2267-4990 Sylko Polina A. Investigation 2
+Gainetdinov Raul R. Writing – review & editing Supervision Funding acquisition 2
+https://orcid.org/0000-0003-0724-887X Volnova Anna B. 2 3
+https://orcid.org/0000-0002-0101-1065 Vaganova Anastasia N. Conceptualization Software Validation Formal analysis Data curation Writing – original draft Writing – review & editing Visualization 2 *
+Costa Mario Academic Editor
+1 Institute of Cytology of the Russian Academy of Sciences, Tikhoretskiy Prospekt, 4, 194064 St. Petersburg, Russia; mittenberg@incras.ru (A.G.M.);
+2 Institute of Translational Biomedicine, St. Petersburg State University, Universitetskaya Nab. 7/9, 199034 St. Petersburg, Russia st101564@student.spbu.ru (P.A.S.);
+3 Center for Transgenesis and Genome Editing, St. Petersburg State University, Universitetskaya Nab. 7/9, 199034 St. Petersburg, Russia
+* Correspondence: a.n.vaganova@spbu.ru
+Electronic publication date: 2026 Aug 29
+Publication date: 2026 Sep
+Volume: 27
+Issue: 17
+Electronic Location ID: 7758
+Received 2026 Jul 23; Revised 2026 Aug 26; Accepted 2026 Aug 27
+Copyright: © 2026 by the authors.
+Copyright year: 2026
+License: Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Keywords: neurodevelopmental disorders, ADHD, proteome, DAT, ASD, dopamine, striatum
+
+Funding: Russian Science Foundation https://ror.org/03y2gwe85 21-75-20069-P Saint Petersburg State University https://ror.org/023znxa73 148723091 This study was funded by the Russian Science Foundation grant 21-75-20069-P (A.G.M., A.D.B., Z.S.F., A.B.V., A.N.V.); maintenance and genotyping of laboratory animals were supported by Saint Petersburg State University research project grant 148723091, St. Petersburg, Russia (R.R.G. and P.A.S). The APC was funded by Russian Science Foundation grant no. 21-75-20069-P and Saint Petersburg State University research project 148723091 (St. Petersburg, Russia) equally.
+
+Ÿ==============================Ÿ
+Deregulation of striatal neurotransmission is a key pathogenetic mechanism in neurodevelopmental disorders such as attention deficit hyperactivity disorder (ADHD) and autism. In the present study, we applied a proteomic approach to demonstrate shifts in striatal protein expression in rats with heterozygous (DAT-Het) and homozygous (DAT-KO) dopamine transporter (DAT) gene knockouts. These animals model dose-dependent ADHD- and autism-like behaviors, ranging from slightly increased activity and social disturbances in DAT-Het rats to a pronounced phenotype in DAT-KO rats. We revealed pronounced changes in the proteomic profiles of both groups, associated primarily with deregulation of proteins involved in energy and carbon metabolism. Furthermore, we identified changes in vesicular transport proteins specific to DAT-KO and DAT-Het rats. Since these changes involved SNARE complex components, we evaluated SNARE mRNA expression in our models and public transcriptomic data for mouse models of neurodevelopmental disorders, including Mbd5 gene haploinsufficiency and a polygenic model of ADHD. No significant changes in mRNA levels were revealed in any model. Thus, the identified protein expression changes likely depend on post-transcriptional mechanisms. These data suggest a deregulation of metabolism in DAT-Het rats, which becomes more pronounced in DAT-KO rats.
+
+1. Introduction
+
+The striatum plays an important role in decision-making and action selection, primarily based on glutamatergic inputs from the cortex, thalamus, and limbic regions, as well as dopaminergic afferents from the substantia nigra pars compacta (SNc) and ventral tegmental area (VTA) [1,2,3]. The main targets of cortical inputs in the striatum are GABAergic spiny projection neurons (SPNs), which represent 95% of the total neuronal population [3]. The remaining 5% of striatal neurons are regulatory interneurons, including cholinergic, fast-spiking, low-threshold-spiking, and several minor subtypes [3,4]. Both SPNs and striatal interneurons express different subtypes of DA receptors and receive dopaminergic innervation [5]. At the same time, around 80% of dopaminergic synapses are also associated with other presynaptic terminals in synaptic hub structures. These dopamine hub synapses are formed with cholinergic (14%), GABAergic (26%), and glutamatergic synapses (42%) [6].
+
+Attention deficit hyperactivity disorder (ADHD) is one of the most common comorbid disorders of autism spectrum disorder (ASD) that can accompany autism [7]. Thus, up to 70% of individuals with ASD also present ADHD [8]. The recognition of this fact has led to the introduction of the term ‘AuDHD’ to describe people who have both autism and ADHD [9]. Currently, both diseases are considered as neurodevelopmental disorders, and their high comorbidity is suggested to be related to the common pathogenic mechanisms.
+
+Dysregulation of dopaminergic activity in the striatum is a possible cause of a number of pathological conditions and neurodevelopmental disorders. In rodent models, methamphetamine self-administration [10], high alcohol preference [11], and antipsychotic administration [12] are associated with differentially expressed and phosphorylated synaptic components in the striatum. Neurodevelopmental disorders, including ADHD and ASD, are accompanied with altered volumes of the striatum and its subregions (e.g., the putamen, caudate and n. accumbens), as well as changes in the density of striatal neurons [13,14]. These alterations can cause an imbalance between sensorimotor and cognitive inputs, leading to social and motor impairments [15,16,17,18]. Furthermore, neurodevelopmental disorders are associated with altered connectivity between brain structures, including compromised structural integrity of corticostriatal tracts [14,19,20,21,22], aberrant striatum activity [23,24], and increased local functional connectivity between striatal subregions [25].
+
+Clinical studies indicate that ADHD individuals may exhibit anomalous cross-regulation between cortical and striatal D2/3 receptors [26], while ASD subjects display increased DRD2 expression within the striatum [27]. A study of adult patients with ADHD found differences in cortical thickness that correlated with the severity of their symptoms [28].
+
+Currently, there are a number of animal models of ASD that exhibit autistic-like behavior characteristics. All of these models are characterized by impaired social interactions, repetitive stereotypical behavior patterns, and memory and attention deficits [29]. Although animal models do not fully replicate the characteristics of ASD, some researchers have suggested that autistic behavior in humans may result from dysfunction in the midbrain dopaminergic system [30]. In particular, in the ASD model rats acquired by prenatal valproate exposure, a reduction in tyrosine hydroxylase (TH) content has been observed in the striatum. Despite TH being the key enzyme for dopamine synthesis, which is limiting for dopamine production, increased dopamine levels were found in the striatum and, as well, in the frontal cortex, cerebellum, and pons in rats after prenatal valproate exposure. By contrast, decreased dopamine levels were found in the hippocampus, midbrain, and serum of these animals [21,27].
+
+Animal models of ADHD are also being actively developed to find new adequate approaches to the treatment of this disease [31]. It is believed that this syndrome is associated with impaired dopamine signaling in the striatum [32,33], with the dopamine reuptake transporter (DAT) playing a key role in this process [34,35]. Genetically modified animal models with impaired dopamine homeostasis mimic some of the symptoms of ADHD [36].
+
+Dopamine transporter knockout (DAT-KO) mice [33,36] and rats [37] were created to investigate disorders rooted in disrupted dopamine transmission. The absence of DAT prevents dopamine reuptake, significantly prolonging dopamine release from the synaptic cleft and increasing extracellular dopamine levels in the striatum. Homozygous DAT-KO rats exhibit an approximately eight-fold elevation in extracellular striatal dopamine concentrations [37]. As a result, dopamine levels in the synaptic clefts of DAT-KO rats are increased, but the total dopamine concentration in the striatum, midbrain, and spinal cord tissues is reduced, and dysregulation of serotonin neurotransmission has also been evidenced [38].
+
+As a result of these abnormalities in monoamine signaling, DAT-KO rats exhibit a distinct phenotype characterized by pronounced motor hyperactivity with attentional deficits [35,37,39,40] (as seen in ADHD patients), stereotypy and cognitive rigidity [22,41] (characteristic of ASD), sexual behavioral disturbances [42], and the manifestation of asocial-like autistic phenotypes [43]. Animals also demonstrated impairments in learning and spatial memory [44], and involuntary attention (prepulse inhibition and sensorimotor filtering) [37,45].
+
+Rats with a deficiency of the DAT gene can be considered a model of neurodevelopmental disorders, exhibiting specific behavioral and neurobiological features that align with ADHD and autism spectrum disorders. Additionally, these rats display reduced body size and weight, along with postural alterations, relative to their WT littermates. Thus, DAT-KO animals serve as models of specific behavioral phenotypes that mimic the characteristics of ADHD and ASD. At the same time, given the established links between DAT dysfunction and neuropsychiatric pathology, DAT-KO animals, including mice and rats, serve as translational models for neurodevelopmental disorders.
+
+Of particular note are heterozygous (DAT-Het) littermates, who retain one functional allele and exhibit milder physiological abnormalities [28] but still have severe impairments in social behavior [43].
+
+Proteomic analysis of synaptosomes isolated from the striatum of DAT-KO rats and their wild-type littermates previously revealed the decreased relative abundance of several proteins, including proteins involved in axonal–dendritic transport, postsynaptic modulation of chemical synaptic transmission, and regulation of receptor-mediated endocytosis [46]. The present study investigates the global, whole-tissue striatal proteome, which was not described previously in the DAT-KO rats. Furthermore, we expand the experimental design by introducing DAT-heterozygous rats to capture intermediate disease phenotypes and uncover novel homeostatic adaptations. DAT-Het rats exhibit intermediate molecular changes in the striatum and other brain regions [47,48,49], accompanied by significantly less pronounced behavioral disturbances compared to their homozygous DAT-KO counterparts.
+
+Considering the previously described molecular and functional disturbances in the striatum of dopamine transporter knockout rats, this study aims to characterize the proteomic changes in this structure in homo- (DAT-KO) and heterozygous (DAT-Het) DAT knockout rats. Taking into account that the striatum represents the primary anatomical site for DAT expression and signaling, the molecular alterations and compensatory mechanisms triggered by DAT dysfunction will compromise the overall function of this structure, ultimately leading to subsequent downstream impairments and distinct phenotypic manifestations. Therefore, we performed the profiling of the striatal proteome to improve the understanding the molecular background of DAT knockout-related features in rats. To capture global alterations in the striatal proteome, an untargeted label-free proteomic screening of pooled striatal lysates was performed using LC-MALDI analysis. Next, we quantitatively measured the expression of target mRNAs in striatal tissue obtained from homozygous and heterozygous DAT knockout rats using RT-PCR.
+
+2. Results
+
+2.1. LC-MALDI Proteomic Profiling of DAT-Deficient Rats’ Striatum
+
+The peptide samples fractionated on a nano-LC system (Eksigent NanoLC Ultra 2D+ system, Sciex, Darmstadt, Germany) were analyzed with an AB Sciex 5800 TOF/TOF instrument operated in the positive ion mode. The LC-MALDI analysis of striatal lysates yielded a diverse set of proteins with distinct distribution profiles across the experimental groups (Figure 1).
+
+We identified 186 proteins in striatal lysate, including 15 unique proteins for WT rats, 2 unique proteins for DAT-KO rats, and 8 unique proteins for DAT-Het rats. Additionally, seven proteins were identified in both DAT-Het and DAT-KO rats but were not revealed in WT rats (Supplementary Table S1). Thus, only 97 proteins were identified mutually; 169, 163, and 117 were identified in WT, DAT-Het, and DAT-KO rats, respectively. Of note, the semi-quantitative assay did not reveal a gradual decrease in protein content and diversity in DAT-Het and DAT-KO rats compared to WT samples. Some proteins, which were not identified in DAT-KO rats, seem to be overproduced in DAT-Het samples compared to WT.
+
+2.2. KEGG Pathway Enrichment Analysis of Differentially Expressed Proteins in DAT Knockout Rats
+
+To expand the number of enriched terms, we included all proteins whose expression levels were up- or downregulated by at least 1.5-fold in DAT-Het or DAT-KO rats compared to their WT littermates. Considering that pathway dysregulation may involve the downregulation of some gene products accompanied by an increase in the expression of other pathway components, we included both upregulated and downregulated proteins simultaneously (Figure 2A,B).
+
+The enrichment results were highly concordant between DAT-Het and DAT-KO rats. Specifically, we identified widespread dysregulation of energy and glucose metabolism, accompanied by changes in the expression of several proteins involved in nervous system function, such as Lamc1, Ncam1, Slc1a2, and others. Such combinations of differentially expressed proteins resulted in the significant enrichment of these clusters with components related to neurodegenerative disease-specific KEGG pathways. Because the number of significantly downregulated proteins was higher in DAT-KO samples, the enrichment results were more complex in this group (Figure 2B) compared to the DAT-Het rats (Figure 2A). In both studied genotypes, the enrichment cores of the identified pathways consisted predominantly of downregulated proteins.
+
+One of the most neuron-specific expression shifts observed in the DAT-KO and DAT-Het groups involved the synaptic vesicle cycle pathway, particularly within the machinery regulating exocytosis and vesicle interaction with the presynaptic membrane, including SNARE components. DAT-Het striatal samples were characterized by a decreased level of Vamp2 protein, which is a part of this complex, and in DAT-KO rats, another part of this complex, Stx1b, was decreased. Additionally, Stxbp1, which interacts with Stx1b, was also decreased in DAT-KO rats’ striatal samples. Thus, we additionally performed a targeted analysis of the mRNA expression of genes associated with the SNARE complex, as described below. The mapping of enrichment results for differently expressed proteins in DAT-KO and DAT-Het striatum samples on the synaptic vesicle cycle KEGG pathway is represented in Supplementary Figure S1.
+
+2.3. SNARE Complex Gene mRNA Expression in the Striatum in DAT-KO Rats
+
+To evaluate the transcriptional regulation of the SNARE complex, we quantified the mRNA expression of Stx1b, Stxbp1, Snap25, Snap23, Vamp2, Cplx1, Cplx2, Cplx3, and Syt1 genes in striatal tissue harvested from the DAT knockout rat line using RT-qPCR. No significant differences in expression levels were observed among wild-type (WT), heterozygous (DAT-Het), and homozygous (DAT-KO) rats (Figure 3).
+
+2.4. GEO Data Search and Analysis
+
+An initial search of the GEO database [44] retrieved 79 entries, from which four GEO SuperSeries records were excluded. Following a rigorous filtering process to eliminate non-relevant or incomplete datasets—such as single-cell RNA sequencing data, in vitro studies, non-striatal samples, small sample sizes (n < 5 per experimental group), or a lack of behavioral validation confirming relevance to ADHD and/or ASD—six candidate reports were retained for further evaluation. Of these, four datasets were subsequently excluded due to the unavailability of raw count tables. Ultimately, two specific RNA-seq datasets (explicitly listed in Table 1) met all criteria and were selected for downstream comparative analysis.
+
+Consistent with the RT-qPCR data from the DAT knockout rats, no significant differences were observed in the expression of Stx1b, Stxbp1, Snap25, Snap23, Vamp2, Cplx1, Cplx2, Cplx3, and Syt1 genes in these animal models of neurodevelopmental disorders compared to their respective wild-type littermates (Figure 4).
+
+3. Discussion
+
+Recently, several specific features of striatal morphology and function were revealed in DAT-KO rats, which are considered a model for ADHD and manifestations of other neurodevelopmental and psychiatric diseases in humans. These rats demonstrate a pronounced volume loss in the dorsal striatum, pronounced hyperconnectivity in the cortico-striatal circuit, and an increase in extracellular dopamine concentrations accompanied by a decrease in total dopamine content [46,48]. In the present study, we evaluated the changes in the proteomic profile of both DAT-KO rats with pronounced behavioral disturbances and DAT-Het rats, which demonstrate mild hyperactivity and social abnormalities under experimental conditions. These data expand the previous study, which estimated the synaptosomal proteome in DAT-KO rats and revealed the decreased relative abundances of proteins involved in axo-dendritic transport, postsynaptic modulation of chemical synaptic transmission, and regulation of receptor-mediated endocytosis [46].
+
+As expected, the alterations observed in DAT-KO rats were more pronounced compared to those in their DAT-Het littermates. Striatal samples from DAT-KO rats lost the expression of significantly more proteins compared to WT rats. At the same time, in DAT-Het rats, the expression of several proteins was upregulated or downregulated rather than completely lost compared to WT. Interestingly, 17 proteins that were not identified in WT rats were revealed in the DAT-insufficient littermates (Figure 1).
+
+Both DAT-haploinsufficient and DAT-KO rats demonstrate changes in the expression of proteins related to neurodegenerative diseases. These associations were revealed by KEGG pathway enrichment analysis and depend on the deregulation of basic energetic mitochondrial metabolism, accompanied by expression changes in several proteins involved in neurotransmitter signaling. Among the latter is the glial transporter Slc1a2, which clears glutamate from the extracellular space. Its expression increases in both knockout variants. At the same time, monoamine oxidase A (Maoa), which metabolizes dopamine and regulates its levels [50], is downregulated in both DAT-Het and DAT-KO animals in our study.
+
+The primary striatal proteomic differences identified between WT rats and DAT-Het/DAT-KO rats are heavily associated with mitochondrial function and carbon metabolism. The principal role of mitochondria is energy production via the oxidative phosphorylation (OXPHOS) pathway. Within the brain, neurons largely rely on OXPHOS for ATP production, whereas astrocytes preferentially depend on glycolysis [51]. Beyond energy supply, mitochondria are critically involved in reactive oxygen species (ROS) production, intracellular Ca2+ homeostasis, and apoptosis; consequently, mitochondrial dysfunction encompasses aberrant energy metabolism, oxidative damage, and compromised lipid metabolism [51].
+
+Despite differences in their core symptoms and diagnostic criteria, ASD and ADHD frequently co-occur, sharing underlying metabolic endophenotypes. For instance, mitochondrial DNA copy number (mtDNA-cn) has been proposed as a complex biomarker reflecting mitochondrial activity, which is predominantly under nuclear genetic control [52,53]. While approximately 5% of children with ASD are diagnosed with classic mitochondrial disease, a significantly larger proportion exhibits subclinical mitochondrial dysfunction [54,55]. Taken together, these insights reinforce the notion that neurodevelopmental pathologies are closely linked to neuronal dysfunction arising from oxidative stress, mitochondrial impairment [56], and the dysregulation of cerebral glucose metabolism [57].
+
+We also revealed differences in the expression of synaptic vesicle machinery proteins in DAT-deficient rats. In both genotypes, several proteins involved in this process were markedly decreased or completely lost (i.e., became undetectable using the applied method). However, the identified proteomic profiles were genotype-specific. Stx1b and Stxbp1, which are involved in SNARE complex functioning, were downregulated in DAT-KO rats. At the same time, in DAT-Het rats, the disturbances in this pathway were milder; however, these rats demonstrated a loss of Vamp2 expression, which, like Stx1b, is part of the SNARE complex.
+
+The SNARE complex is the core machinery driving synaptic vesicle exocytosis. It consists of SNAP-25, vesicle-associated membrane proteins (VAMPs), and syntaxins, alongside key regulatory elements such as synaptotagmins (SYTs) [58]. For instance, complexins stabilize the core SNARE bundle in a highly fusogenic state, maintaining a primed vesicle pool primed for rapid, synchronous release upon calcium influx sensed by SYT [58,59,60,61]. Furthermore, Syntaxin 1A (STX1A) is essential for anchoring presynaptic membrane fusion, while the entire complex is subsequently disassembled by the NSF ATPase and its cofactor, SNAP, to allow vesicle recycling [62]. Notably, across various ASD and ADHD models, the expression levels of several vesicular transport proteins, including SNAP-25, STX1A, STX1B, and VAMP2, are significantly altered [63,64,65].
+
+Studies on postmortem human samples and various animal models of neurodevelopmental disorders consistently demonstrate that genes governing synapse maintenance and neurotransmission are dysregulated under these conditions. Specifically, prominent changes in SNARE abundance have been documented in striatal tissue [58]. The identified decrease in expression in SNARE complex components and associated protein Stxbp1 may be interpreted as an adaptation for the hyperdopaminergic striatum state in these animals. However, it also may be related to the decrease in general neurotransmission activity in the striatum, mirroring the gradual decompensation of the striatal function in DAT-Het and DAT-KO rats.
+
+In animal models of neurodevelopmental disorders, a discrepancy between the protein and gene expression data in brain structures suggests post-transcriptional or post-translational modifications [66]. At the same time, the identified discrepancy between qPCR and proteomics data may be related to the complex nature of striatal samples, which consist of both striatal neurons and projections from distant brain structures, such as the substantia nigra or motor cortex. Thus, the identified differences in SNARE protein profiles, as well as other differences between WT, DAT-KO, and DAT-Het rats, may be related to gene transcription deregulation outside the striatum.
+
+The presented results should be interpreted within the context of several study limitations.
+
+While this discovery-based approach allowed for a broad mapping of the proteome, it relies on data that can be influenced by ionization efficiency rather than absolute protein concentration. Consequently, the observed changes reflect relative differences in protein expression across genotypes rather than exact absolute quantities, necessitating subsequent targeted validation for specific candidates. Second, the semi-quantitative screening in this study was performed using a pooled sample strategy, which limits the application of stringent statistics. Therefore, our analysis focuses on identifying robust, large-scale trends and co-regulated pathways rather than individual biological variance and single-protein shifts. Another limitation of the method is the preferential detection of highly abundant proteins; data regarding low-abundance receptors or upstream regulators that initiate downstream signaling pathways and physiological processes may be under-represented due to low protein abundance, insufficient signal quality, poor peptide ionization, limited MS coverage, or other technical factors. As well, our analysis included proteins exhibiting relatively subtle expression changes (less than a 2-fold change) in DAT knockout animals relative to controls; notably, RT-qPCR may lack the sensitivity required to robustly detect such minor fluctuations at the mRNA level. Simultaneously, data regarding post-translational modifications are incomplete in the present study and were omitted from the global analysis. Nevertheless, critical proteins mediating synaptic transmission are known to undergo S-nitrosylation in the striatum, including VAMP2/synaptobrevin, SNAP-25, CPLX1, and SYT1. For instance, CPLX1 undergoes S-nitrosylation, which induces functional and synaptic localization changes that may alter its interaction with the SNARE complex [64], alongside other modifications. Finally, we focused specifically on the vesicular transport alterations as the neuron-specific process, deliberately leaving the complex shifts in systemic metabolic regulation outside the scope of the present study.
+
+Despite certain limitations, our findings demonstrated highly consistent trends across both DAT knockout groups. These results indicate that the model effectively recapitulates neurodevelopmental disorders at the molecular level. Furthermore, the identified changes in proteins critical for vesicular transport and energy metabolism warrant further investigation, offering potential biomarkers to assess therapeutic efficacy in translational studies utilizing this model.
+
+4. Materials and Methods
+
+4.1. Animals
+
+Striatal samples were collected from 5-month-old male rats and categorized into three genotypes: homozygous DAT knockout (DAT-KO, n = 5 for proteomic studies and n = 7 for RT-PCR), heterozygous DAT knockout (DAT-Het, n = 5 for proteomic studies and n = 7 for RT-PCR), and wild-type controls (WT, n = 5 for proteomic studies and n = 7 for RT-PCR). The DAT-KO line was derived by mating heterozygous parents, with genotypes verified according to an established protocol. Animals were maintained in individually ventilated cages (IVC; RAIR IsoSystem World Cage 500, Lab Products, Inc., Seaford, DE, USA) under standard conditions: a 12 h light/dark cycle (lights on at 09:00), a 22 ± 1.0 °C ambient temperature, and 50–70% relative humidity. Food and water were provided ad libitum.
+
+For sampling, rats were humanely sacrificed by decapitation under deep anesthesia induced by 1% isoflurane in 100% oxygen (Chemical Iberica Produktos Veterinarios, Salamanca, Spain). For proteomic studies, dissected striatal tissues were immediately placed into liquid nitrogen for protein preservation. For RT-PCR, samples were immediately stored in ExtractRNA solution (Evrogern, Moscow, Russia). All animal experiments adhered to ethical regulations and received approval from the Institutional Animal Care and Use Committee of Saint Petersburg State University (protocol no. 131-03-6, 25 April 2025).
+
+4.2. Sample Preparation and Label-Free LC-MALDI Mass Spectrometry
+
+Whole-tissue striatum tissue samples were homogenized on ice using a Silent Crusher S homogenizer (Heidolph Instruments, Schwabach, Germany) in a lysis buffer containing 10 M urea, 2% CHAPS, 0.5 mM phenylmethylsulfonyl fluoride (PMSF), 0.01× protease inhibitor cocktail cOmplete™ Protease Inhibitor Cocktail (Roche Diagnostics, Mannheim, Germany), and 1% DeStreak reagent (Cytiva, Marlborough, MA, USA). The resulting homogenates were subjected to ultrasonication.
+
+To evaluate sample quality, aliquots of the protein extracts were analyzed via SDS-PAGE according to the Laemmli method. Protein aliquots were mixed with a 4× loading buffer (0.5 M Tris-HCl, pH 6.8, 2% SDS) and rhodamine dye, incubated for 10 min at 37 °C, and loaded onto a 10% polyacrylamide gel. Electrophoresis was performed in a Tris-glycine running buffer (25 mM Tris, 192 mM glycine, 0.1% SDS, pH 8.3) using a Mini-PROTEAN Tetra Cell system (Bio-Rad Laboratories, Hercules, CA, USA). Gels were stained with Coomassie Brilliant Blue G-250 and subsequently destained with 7% acetic acid. Protein molecular weights were estimated using pre-stained protein markers (10–180 kDa, SolarBio Science & Technology, Beijing, China). Protein quantification was normalized against a known concentration of the protein marker.
+
+Protein samples were solubilized in 8 M urea. Proteins were reduced with 10 mM DTT for 30 min, alkylated with 25 mM IAA for 45 min in the dark at room temperature, and then digested with modified trypsin (Trypsin Gold, Promega, Madison, WI, USA). Overnight digestion was performed at 37 °C at a specific enzyme-to-protein ratio, ensuring the final urea concentration was below 1 M. The resulting peptides were desalted and concentrated usin Strata-X 30 mg solid-phase extraction tubes (Phenomenex, Torrance, CA, USA). Eluted fractions were supplemented with 10 μL of 50 mg/mL D-glucose to aid subsequent rehydration and dried in a rotor vacuum evaporator (Martin Christ, Osterode am Harz, Germany). Then, digests were resuspended in 25 μL of 1% (v/v) aqueous formic acid. Following filtration through a 0.2 μm PVDF filter, peptide concentrations for mass spectrometry were determined by UV extinction at 205 and 280 nm.
+
+Chromatographic separation was achieved on a nano-LC system (Eksigent NanoLC Ultra 2D+, Sciex, Darmstadt, Germany) equipped with a Chromolith CapRod RP-18e HR reversed-phase column (0.1 mm × 150 mm, Merck, Darmstadt, Germany). A total peptide load of 1000 ng was resolved using a 44 min linear gradient of 6.5–43% mobile phase B at a flow rate of 400 nL·min−1. Mobile phases consisted of A (water with 0.2% v/v TFA) and B (80% v/v acetonitrile in water). Effluent was continuously mixed at 2.4 μL·min−1 with a matrix solution containing 9 mg·mL−1 CHCA in 85% acetonitrile and 0.2% (v/v) TFA, supplemented with two calibration standards, bradykinin 2–9 (30 pM·mL−1) and ACTH 18–39 (60 pM·mL−1), at a flow rate of 2.4 μL·min−1. A micro-fraction collector deposited 1 mm spots every 2 s, yielding a 44 × 16 array of 704 targets per run. Prior to subsequent injections, the column was washed with a gradient (0–100–100% B for 5 min and 2 min, respectively, at a flow rate of 600 nL·min−1) and equilibrated to 0% B for 3.5 min before subsequent injections.
+
+Targeted plates were analyzed using a TOF/TOF 5800 System (Sciex) in positive ion mode with the MALDI stage set to continuous motion. MS spectra were acquired at a laser intensity of 3300 (500 shots/spectrum; 250 shots/sub-spectrum). For MS/MS analysis, the intensity was increased to 4600 using a DynamicExit algorithm with a high spectral quality threshold, capped at 1000 shots/spectrum (250 shots/sub-spectrum). Up to 25 top precursor ions per spot within a mass range of 750–3500 Da and an S/N > 40 were selected for fragmentation.
+
+Protein Pilot 5.0.1 software (Sciex, Darmstadt, Germany) with the Paragon algorithm in thorough mode was used for the MS/MS spectra search against the Uniprot rat database. Carbamidomethyl cysteine was set as a fixed modification. False discovery rate (FDR) analysis was performed by analyzing reversed sequences using the embedded PSEP tool, with the threshold for strictly confident protein and peptide identification set at FDR < 1%. The MS/MS data was converted to mzidentml format for further analysis using Scaffold 4.0 software. Protein relative abundance was determined using an untargeted, label-free intensity-based quantification strategy. Relative protein expression levels across the experimental samples (DAT-KO, DAT-Het, and WT) were calculated based on the summation of precursor peptide ion intensities (total ion current, TIC) extracted by Scaffold 4.0 software. To account for systematic run-to-run variations and slight differences in sample loading, total intensity normalization was applied across all mass spectrometry runs.
+
+All samples were analyzed in technical triplicate. Proteins were included in the final list of accepted identifications only if they were detected in all replicates of at least one experimental group. Protein abundance differences between the DAT-deficient lineages and the WT control group were subsequently expressed as fold change (FC) values. Due to the sample pooling strategy, missing value imputation was not performed; proteins undetected in a specific group pooling were treated as below the limit of detection, with unique proteins requiring at least 2 unique peptides for confident identification. The mass spectrometry proteomics data have been deposited at Mendeley Data, V1, https://doi.org/10.17632/6tsdm23n2y.1.
+
+4.3. Functional Enrichment and KEGG Pathway Analysis
+
+All proteins whose expression levels were up- or downregulated by at least 1.5-fold in DAT-Het or DAT-KO rats compared to their WT littermates were considered differentially expressed.
+
+Kyoto Encyclopedia of Genes and Genomes (KEGG) pathway enrichment analysis was performed on clusters of proteins whose expression levels were up- or downregulated by at least 1.5-fold in DAT-Het or DAT-KO rats compared to their WT littermates. Enrichment analysis and visualization of the results were performed using the clusterProfiler (v.4.6.0) R package [67], which is designed to conduct over-representation analysis (ORA) to determine which a priori-defined gene sets are significantly enriched in the data. The enrichKEGG function with default arguments was applied, using all genes listed in the database as the background. A cnetplot visualization within clusterProfiler was used to represent the enrichment networks.
+
+4.4. Gene Expression Omnibus Database Search
+
+The RNAseq data were mined from the public database GEO from NCBI [68] by the search request ("neostriatum"[MeSH Terms] OR "corpus striatum"[MeSH Terms] OR Striatum[All Fields]) AND ((((((((ASD[All Fields] OR ("autistic disorder"[MeSH Terms] OR autism[All Fields])) OR ("autistic disorder"[MeSH Terms] OR autistic[All Fields])) OR ("attention deficit disorder with hyperactivity"[MeSH Terms] OR ADHD[All Fields])) OR ("attention"[MeSH Terms] OR attention[All Fields])) OR hyperactivity[All Fields]) OR neurodevelopmental[All Fields]) OR neurodevelopment[All Fields]) AND "Expression profiling by high throughput sequencing"[Filter] AND ("10"[n_samples] : "10000"[n_samples])) AND ("Expression profiling by high throughput sequencing"[Filter] AND ("10"[n_samples] : "10000"[n_samples])) in the GEO DataSets repository. The inclusion criteria were as follows: (1) at least 5 striatal samples per study subgroup in the dataset, including intact WT samples; (2) the datasets represent the expression profiles of native samples, and data for single-cell RNA sequencing or cell fractions were excluded; (3) clear description of behavioral abnormalities matching ASD or ADHD phenotypes in the dataset description or associated papers; and (4) raw count data are available.
+
+4.5. Transcriptomic Data Analysis
+
+Data from the GEO repository were obtained as raw counts, which were utilized for differential expression analysis (DEA) and subsequently converted to counts per million (CPM) for visualization.
+
+DEA was performed using the quasi-likelihood (QL) F-test framework in the edgeR (v. 4.6.2) R package [69]. Low-expressed genes were removed prior to analysis using the filterByExpr function with default parameters. Library sizes were normalized using the calcNormFactors function via the trimmed mean of M-values (TMM) method. p-values were adjusted using the Benjamini–Hochberg procedure, and genes with a false discovery rate (FDR) < 0.05 were identified as differentially expressed genes (DEGs).
+
+4.6. RNA Extraction, Reverse Transcription, and qPCR Analysis
+
+Total RNA was isolated from striatal specimens using ExtractRNA reagent (Evrogen, Moscow, Russia) according to the manufacturer’s guidelines. A NanoDrop 2000 spectrophotometer (Thermo Scientific, Waltham, MA, USA) was employed to evaluate RNA concentration and purity.
+
+Next, 300 ng of total RNA from each sample was converted into complementary DNA (cDNA). Reverse transcription was executed with the MMLV Reverse Transcriptase kit (Evrogen, Moscow, Russia) under recommended conditions.
+
+Table 2 lists the gene-specific primers used in this work. Real-time amplification was performed on a CFX96 Touch Real-Time PCR Detection System (Bio-Rad, Hercules, CA, USA) in at least two independent runs per cDNA sample. Transcript levels of ND1–ND6 were determined using the qPCRmix-HS SYBR master mix (Evrogen, Moscow, Russia). The qPCR program consisted of 40 cycles of denaturation at 95 °C for 10 s, annealing at 60 °C for 15 s, and elongation at 72 °C for 30 s with simultaneous fluorescence data collection. Amplicons were subjected to melting curve analysis using the default instrument settings to verify the specificity of the PCR products.
+
+4.7. Statistical Analysis
+
+Relative gene expression levels were quantified utilizing the 2−ΔΔCt methodology. The process commenced with the acquisition of cycle threshold (Ct) values for every sample. Subsequently, ΔCt values were established by subtracting the Ct of the internal control gene (Hprt) from that of the gene of interest. To obtain ΔΔCt, the average Ct value for each gene within the wild-type cohort was then subtracted from these ΔCt values. The ultimate relative expression levels were then derived by calculating 2−ΔΔCt.
+
+Each experimental run was duplicated, and the mean values were employed for subsequent statistical processing. Prior to comparative analysis, data distribution normality was verified using the Shapiro–Wilk test. Discrepancies in normalized expression were analyzed either by a Student’s t-test (for data conforming to a normal distribution with p > 0.05 across all groups) or a Mann–Whitney U test, incorporating a Holm–Bonferroni correction for multiple comparisons. Outlier data points, identified through the interquartile range (IQR) criterion, were excluded from further examination.
+
+5. Conclusions
+
+In the present study, protein expression profiles were compared in striatal samples derived from rats with different doses of DAT gene knockout, which is suggested to be a model for neurodevelopmental disorders. In both DAT-deficient groups, i.e., DAT haploinsufficiency or null DAT knockout, basic carbohydrate and energy metabolism seems to be deregulated in the striatum compared to their WT littermates. These results align with current literature data, pointing out that energy and carbohydrate metabolism is impaired in ADHD and ASD subjects, as well as in rodent models of neurodevelopmental conditions. Expectedly, the deregulation pattern was more pronounced in homozygous DAT-KO rats than in DAT-Het animals. Additionally, a specific downregulation of proteins involved in synaptic vesicular transport was revealed in DAT-deficient rats. Considering the previously described decrease in SNARE complex-related proteins in the striatum of patients with neurodevelopmental disorders and relevant animal models and the high expression of proteins Syn1 and Stxbp1 identified in DAT-deficient rats, we additionally estimated mRNA expression for genes involved in SNARE functioning in DAT-Het and DAT-KO rats, as well as in public transcriptomic data. However, we did not identify any significant changes in the mRNA expression for these proteins. These results do not contradict the proteomic results, because a plethora of processes in neural tissues are regulated on a post-transcriptional level. Thus, we demonstrate that in DAT-deficient rats representing models of neurodevelopmental conditions, the energy metabolism of striatal tissue seems to be impaired, while the more pronounced phenotype in DAT-KO rats is also associated with the suppression of synaptic transmission. These features may be considered as biomarkers for further translational studies.
+
+Acknowledgments
+
+The research was supported by the research Resource Center Molecular and Cell Technologies of St. Petersburg State University. Breeding and support of DAT-KO rats were performed by the Resource Center Vivarium of St. Petersburg State University, St. Petersburg, Russia.
+
+Supplementary Materials
+
+The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/ijms27177758/s1.
+
+Author Contributions
+
+Conceptualization, A.N.V., Z.S.F. and A.B.V.; methodology, A.N.V., A.G.M. and S.V.S.; software, A.N.V.; validation, A.N.V., A.G.M. and A.B.V.; formal analysis, A.N.V.; investigation, A.D.B., A.G.M., Z.S.F., S.V.S. and P.A.S.; resources, A.B.V. and A.G.M.; data curation, A.N.V.; writing—original draft preparation, A.N.V. and A.G.M.; writing—review and editing, A.N.V., A.B.V. and R.R.G.; visualization, A.N.V.; supervision, R.R.G.; project administration, A.B.V.; funding acquisition, A.B.V. and R.R.G. All authors have read and agreed to the published version of the manuscript.
+
+Institutional Review Board Statement
+
+The animal study protocol was approved by the Saint Petersburg State University Ethical Committee for Animal Research (no. 131-03-6; approval date: 25 April 2025).
+
+Informed Consent Statement
+
+Not applicable.
+
+Data Availability Statement
+
+The mass spectrometry proteomics data have been deposited at Mendeley Data, V1, https://doi.org/10.17632/6tsdm23n2y.1, and Zenodo, https://doi.org/10.5281/zenodo.21873293.
+
+Conflicts of Interest
+
+The authors declare no conflicts of interest.
+
+Figure 1 Semi-quantitative analysis of proteomic data in DAT knockout rats. Relative expression levels in heterozygous (Het) and homozygous (KO) DAT knockout rats are presented as fold change (FC) compared to WT. An FC of 1 (i.e., the same level as in WT) is marked by red dotted lines. Proteins that are over- or under-represented by a factor of two or more compared to WT (FC > 2 or FC < 0.5) are indicated.
+
+Figure 2 KEGG pathway enrichment analysis of proteins exhibiting altered expression in DAT-Het (A) and DAT-KO (B) rats compared to their WT littermates.
+
+Figure 3 Expression of SNARE complex genes in the striatum of DAT knockout rats. Relative mRNA expression levels in wild-type (WT), heterozygous (Het), and homozygous (KO) DAT knockout rats are presented as 2−ΔΔCt-normalized values.
+
+Figure 4 Expression of SNARE complex genes in mouse striatum samples represented in GEO116752 and GSE144277 GEO datasets. CPM—count per million.
+
+ijms-27-07758-t001_Table 1 Table 1 RNAseq datasets included in the analysis.
+
+GEO ID	Title	Platform	Sample	Model	
+GEO116752	Striatal transcriptome of a mouse model of ADHD reveals a pattern of synaptic remodeling	Illumina HiSeq 2500	5 control and 5 model animals, 6.5 months old, male	To model ADHD polygenically, a mouse line was generated through selective breeding for high home-cage activity. Relative to controls, these high-active mice display hyperactivity and motor impulsivity that are successfully reversed by amphetamine administration [11].	
+GSE144277	Functional genomic consequences of MBD5 knockdown in mouse brain and CRISPR-derived neurons [mouse]	Illumina HiSeq 2000	8 control and 10 model animals, 8 weeks old, male and female	The Mbd5 gene encodes methyl-CpG-binding domain protein 5, which is structurally associated with ASD; its heterozygous deficiency in mice (Mbd5+/GT causes craniofacial dysmorphism, cognitive disabilities, impaired motor functions, and aberrant social behaviors [44].	
+
+ijms-27-07758-t002_Table 2 Table 2 Primers and probes were used for quantitative RT-PCR in DAT-KO and DAT-Het rat study.
+
+Target	Forward Primer	Reverse Primer	
+Cplx1	ATG CGG CAG GGC ATA CGA GAT A	TGC CTT CTG AGT TGG CCT CCA T	
+Cplx2	TGA GAA GGT CCG GCA GCA GAT T	CAG TGG CCC CGG CAG ATA TTT G	
+Cplx3	ACA AGG GGG ACG GAG ACA AGT C	CCC TGA AGT GAC TCC GTA GCG T	
+Vamp2	CCC TGC ACC TCC TCC AAA TC	GAT AGC TTC TGG TCC CGC TC	
+Snap23	GCA ACA TGG GGT GAT GGT GGA G	AGG ATG CTG CCC ACT TGA GTC A	
+Snap25	GTG GCT TCA TCC GCA GGG TAA C	GAG GTT TCC GAT GAT GCC GCT C	
+Stx1b	CCG AGG CTG CAT CGA GAA ACT G	CCG GAC CTT GTT TGC CGT CTT T	
+Stxbp1	AAC AAA CTC ATC CAG CAC GCC C	GCG TAG TGT GGA ATC CGT GAC G	
+Syt1	ACG CTG TCC CGA AAG TTT GTG G	GCA AAA CCC TGG TGA TGG CTG T	
+rStx1a	CGT AGC GGA GGG AGA AGC AGA T	TCC AAC TCC TCA CTG GTC GTG G	
+Hprt	CTC ATG GAC TGA TTA TGG ACA GGA C	GCA GGT CAG CAA AGA ACT TAT AGC C	
+
+Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.
+
+
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+43. Adinolfi A. Zelli S. Leo D. Carbone C. Mus L. Illiano P. Alleva E. Gainetdinov R.R. Adriani W. Behavioral Characterization of DAT-KO Rats and Evidence of Asocial-like Phenotypes in DAT-HET Rats: The Potential Involvement of Norepinephrine System Behav. Brain Res. 2019 359 516 527 10.1016/j.bbr.2018.11.028 30472113
+44. Kurzina N.P. Aristova I.Y. Volnova A.B. Gainetdinov R.R. Deficit in Working Memory and Abnormal Behavioral Tactics in Dopamine Transporter Knockout Rats during Training in the 8-Arm Maze Behav. Brain Res. 2020 390 112642 10.1016/j.bbr.2020.112642 32428629
+45. Ptukha M. Fesenko Z. Belskaya A. Gromova A. Pelevin A. Kurzina N. Gainetdinov R.R. Volnova A. Effects of Atomoxetine on Motor and Cognitive Behaviors and Brain Electrophysiological Activity of Dopamine Transporter Knockout Rats Biomolecules 2022 12 1484 10.3390/biom12101484 36291693 PMC9599468
+46. Savchenko A. Müller C. Lubec J. Leo D. Korz V. Afjehi-Sadat L. Malikovic J. Sialana F.J. Lubec G. Sukhanov I. The Lack of Dopamine Transporter Is Associated With Conditional Associative Learning Impairments and Striatal Proteomic Changes Front. Psychiatry 2022 13 799433 10.3389/fpsyt.2022.799433 35370807 PMC8971526
+47. Sylko P.A. Gromova A.A. Fesenko Z.S. Kanov E.V. Volnova A.B. Gainetdinov R.R. Vaganova A.N. Altered Co-Expression Patterns of Mitochondrial NADH-Dehydrogenase Genes in the Prefrontal Cortex of Rodent ADHD Models Int. J. Mol. Sci. 2025 26 11079 10.3390/ijms262211079 41303563 PMC12652654
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diff --git a/corpus/psychology/text/ba51a2d7bcd92b71.txt b/corpus/psychology/text/ba51a2d7bcd92b71.txt
new file mode 100644
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--- /dev/null
+++ b/corpus/psychology/text/ba51a2d7bcd92b71.txt
@@ -0,0 +1,51 @@
+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Comput Math Methods Med
+Journal ID: Comput Math Methods Med
+NLM Journal ID: 101277751
+Journal ID: cmmm
+
+Computational and Mathematical Methods in Medicine
+
+ISSN: 1748-670X
+EISSN: 1748-6718
+Publisher: Wiley
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC10718916
+PMID: 38094445
+DOI: 10.1155/2023/9847256
+Article version: 1
+Subjects: Retraction
+
+Retracted: Cognitive Function and Vitamin D Status in the Chinese Hemodialysis Patients
+
+Methods in Medicine Computational and Mathematical cmmm@hindawi.com
+
+Publication date: 2023
+Electronic publication date: 2023 Dec 6
+Volume: 2023
+Electronic Location ID: 9847256
+Received 2023 Dec 5; Accepted 2023 Dec 5
+Copyright: Copyright © 2023 Computational and Mathematical Methods in Medicine.
+Copyright year: 2023
+License: This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Retraction of: Cognitive Function and Vitamin D Status in the Chinese Hemodialysis Patients 2022 9 9 2022 2175020 Computational and Mathematical Methods in Medicine 10.1155/2022/2175020 PMC9481383 36118837
+
+Ÿ==============================Ÿ
+This article has been retracted by Hindawi, as publisher, following an investigation undertaken by the publisher [1]. This investigation has uncovered evidence of systematic manipulation of the publication and peer-review process. We cannot, therefore, vouch for the reliability or integrity of this article.
+
+Please note that this notice is intended solely to alert readers that the peer-review process of this article has been compromised.
+
+Wiley and Hindawi regret that the usual quality checks did not identify these issues before publication and have since put additional measures in place to safeguard research integrity.
+
+We wish to credit our Research Integrity and Research Publishing teams and anonymous and named external researchers and research integrity experts for contributing to this investigation.
+
+The corresponding author, as the representative of all authors, has been given the opportunity to register their agreement or disagreement to this retraction. We have kept a record of any response received.
+
+
+1 Zhang J. Hu J. Zhou R. Xu Y. Cognitive Function and Vitamin D Status in the Chinese Hemodialysis Patients Computational and Mathematical Methods in Medicine 2022 2022 6 10.1155/2022/2175020 2175020 36118837 PMC9481383
diff --git a/corpus/psychology/text/bbdbe3a9072564d3.txt b/corpus/psychology/text/bbdbe3a9072564d3.txt
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--- /dev/null
+++ b/corpus/psychology/text/bbdbe3a9072564d3.txt
@@ -0,0 +1,277 @@
+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Bioengineering (Basel)
+Journal ID: Bioengineering (Basel)
+NLM Journal ID: 101676056
+Journal ID: bioengineering
+
+Bioengineering
+
+EISSN: 2306-5354
+Publisher: Multidisciplinary Digital Publishing Institute (MDPI)
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC13405351
+PMID: 42510466
+DOI: 10.3390/bioengineering13070801
+Article ID: bioengineering-13-00801
+Article version: 1
+Subjects: Article
+
+Patient-Specific Finite Element Analysis of Ventral Incisional Hernia Repair: Biomechanical Investigation of the Cause of Recurrence
+
+Ezechukwu Tochukwu Bright 1
+Luo Yigang 2 *
+Sakib Sadman 1
+Ogbeyemi Akinola 1
+Odeyemi Jethro 1
+Song Nara 3
+https://orcid.org/0000-0001-7973-8769 Zhang Wenjun 1 4 *
+Liao Jun Academic Editor
+1 Division of Biomedical Engineering, College of Engineering, University of Saskatchewan, Saskatoon, SK S7N 5A9, Canada xns319@usask.ca (S.S.); akinola.ogbeyemi@usask.ca (A.O.); jethro.odeyemi@usask.ca (J.O.)
+2 Division of General Surgery, College of Medicine, University of Saskatchewan, Saskatoon, SK S7N 5A9, Canada
+3 Biomedical Sciences, College of Medicine, University of Saskatchewan, Saskatoon, SK S7N 5A9, Canada; vyb871@mail.usask.ca
+4 School of Mechanical Engineering, Donghua University, Shanghai 200051, China
+* Correspondence: yil872@mail.usask.ca (Y.L.); chris.zhang@usask.ca (W.Z.)
+Electronic publication date: 2026 Jul 13
+Publication date: 2026 Jul
+Volume: 13
+Issue: 7
+Electronic Location ID: 801
+Received 2026 May 4; Revised 2026 Jun 23; Accepted 2026 Jun 26
+Copyright: © 2026 by the authors.
+Copyright year: 2026
+License: Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Keywords: finite element method, stress, suture, tissue biomechanics, ventral incisional hernia
+
+Funding: This research received no external funding.
+
+Ÿ==============================Ÿ
+Ventral incisional hernia is a frequent postoperative complication following abdominal surgery, with recurrence largely driven by biomechanical factors such as elevated intra-abdominal pressure and stress concentration at the suture–mesh–tissue interface. This study presents a patient-specific finite element analysis (FEA) framework to investigate stress transfer mechanisms within ventral incisional hernia repair systems under physiologically relevant loading conditions. A patient-specific abdominal wall geometry was reconstructed from computed tomography images and modeled as a nonlinear hyper-elastic material using a second-order Ogden formulation. Polypropylene surgical meshes and sutures were represented using finite elements, and an intra-lay mesh placement with a midline incision was simulated. Loading conditions corresponding to regular breathing, forceful breathing, and heavy-load lifting were applied. The results reveal that stress concentrations consistently localize at the sutures, with stress magnitudes increasing markedly under higher physiological loads. Under heavy lifting, suture stresses approached the material yield limit, whereas mesh stresses remained comparatively low. These findings identify suture failure as a critical mechanical factor contributing to hernia recurrence and highlight the importance of postoperative load management and improved support strategies. This work provides a basis for more comprehensive future patient-specific analyses.
+
+1. Introduction
+
+The abdominal wall serves as a critical structural and functional barrier, protecting the intra-abdominal organs from mechanical injury and maintaining abdominal integrity [1]. Following surgical interventions, the muscular and fascial layers of the abdominal wall may undergo weakening or disruption, leading to a reduction in tensile strength [2]. This compromised structural integrity can result in the formation of a defect through which intra-abdominal tissues or organs may protrude, giving rise to a ventral hernia. Clinically, a ventral hernia is characterized by the protrusion of abdominal contents through a weakened or defective region of the abdominal musculature or fascial layers [3].
+
+Ventral incisional hernia is a common postoperative complication, with reported incidence rates ranging from approximately 3% to 20% among patients undergoing abdominal surgical repair [4,5]. Despite advances in surgical techniques, recurrence of incisional hernia remains a persistent clinical challenge and is widely recognized as a multifactorial phenomenon influenced by patient-related, surgical, and biomechanical factors [6]. Over several decades, extensive efforts have been made to reduce hernia recurrence following abdominal surgery through a variety of repair strategies, including procedures performed with or without prosthetic mesh reinforcement.
+
+The two most widely adopted surgical approaches for incisional hernia repair are open surgical repair and laparoscopic repair [7]. In an open surgical repair, an incision is made directly over the hernia defect, and a prosthetic mesh is sutured to reinforce the weakened abdominal wall. This approach is commonly employed for both small and large hernias, particularly in patients with a history of previous hernia repairs [8]. In contrast, laparoscopic repair involves the insertion of small cannulas (laparoscopic ports) through the abdominal wall, allowing the surgeon to access and repair the defect using minimally invasive instruments [9]. During a laparoscopic repair, the hernia defect is closed and, depending on the clinical indication, a mesh may be placed to provide additional reinforcement.
+
+Despite the clinical success of both open and laparoscopic techniques, recurrence remains a significant concern. Following surgery, patients are exposed to various physiological loading conditions during routine activities such as lifting, coughing, sneezing, and strenuous use of thbe abdominal muscles [10]. These activities generate elevated intra-abdominal pressures and mechanical stresses on sutures and implanted meshes. Over time, repeated loading can lead to suture failure, mesh displacement, or loss of fixation, thereby compromising the integrity of the repair and increasing the likelihood of hernia recurrence. In many cases, excessive stress concentration at the suture–mesh–tissue interface results in tearing of sutures or gradual migration of the mesh from its original position, ultimately leading to reherniation.
+
+The motivation of the present study is to advance technological and biomechanical understanding aimed at reducing the recurrence of ventral incisional hernia following surgical repair. To address this challenge, this work develops a mathematical and computational framework capable of simulating stress distributions within the abdominal wall, sutures, and surgical mesh under physiologically relevant loading conditions. The primary objective of this study was to construct a finite element model of the abdominal wall–suture–mesh system to evaluate the mechanical response when intra-abdominal contents exert pressure on the repaired hernia site. Finite element analysis (FEA) [11,12] was employed to characterize stress transfer mechanisms and deformation behavior within the repair construct.
+
+To achieve this objective, established procedures reported in the literature were adopted and applied to the modeling and reconstruction of the abdominal wall. Anatomical data were obtained from medical imaging of a male subject with a mean body mass index (BMI) of less than 25 kg/m2 and an age range between 19 and 23 years, processed using the open-source imaging software 3D Slicer. This study contributes to the field of surgical biomechanics by integrating computational modeling, numerical simulation, and mechanical analysis to provide insight into stress-induced failure mechanisms in ventral incisional hernia repair. The findings aim to inform improved surgical strategies and device designs that may reduce recurrence rates and enhance long-term clinical outcomes.
+
+Compared with previous finite element studies of abdominal wall biomechanics, the present work introduces several features that enhance the physiological relevance of the analysis. First, a patient-specific three-dimensional abdominal wall geometry reconstructed from computed tomography images was employed rather than simplified generic geometries. Second, the nonlinear mechanical behavior of the abdominal wall was represented using a second-order Ogden hyperelastic constitutive model, which more accurately captures the deformation characteristics of soft biological tissues. Third, clinically relevant polypropylene mesh and suture configurations were incorporated to simulate the mechanical interactions occurring at the repair site. In addition, loading conditions corresponding to different physiological states were considered to reproduce the mechanical effects associated with daily activities. These features enable a more realistic assessment of stress transfer mechanisms and provide insight into the role of suture stress concentrations as a potential cause of ventral incisional hernia recurrence.
+
+2. Methodology
+
+In this study, a step-by-step finite element analysis (FEA) workflow was developed to simulate ventral incisional hernia repair by integrating patient-specific abdominal wall geometry with surgical mesh and suture representations. The methodology includes image-based geometry reconstruction, model preprocessing, material definition, mesh generation, and the application of clinically relevant loading and boundary conditions to evaluate stress transfer within the repair system.
+
+2.1. Image Acquisition and Geometry Reconstruction
+
+A comprehensive review of existing finite element-based studies on abdominal wall biomechanics was conducted to guide model development. Anatomical reconstruction of the abdominal wall was performed using computed tomography (CT) imaging data from a male subject with a normal body mass index (BMI < 25 kg/m2) and age range between 19 and 23 years. The imaging data was obtained and processed using 3D Slicer (Version: 4.11), an open-source platform widely used for biomedical image analysis [13].
+
+The CT images were acquired using a Siemens SOMATOM Definition Flash (Siemens Healthineers, Forchheim, Germany) with a slice thickness of 1 mm, tube voltage of 120 kVp, tube current of 200 mA, pixel spacing of 0.742 mm × 0.742 mm, and an image resolution of 512 × 512 pixels. These imaging parameters ensured adequate spatial resolution for reconstructing the abdominal wall geometry and associated anatomical structures.
+
+The CT images were segmented to reconstruct the abdominal contents and muscular layers. Both manual and semi-automatic segmentation techniques were employed to ensure accurate delineation of anatomical structures. The resulting three-dimensional (3D) models were exported in STL format for subsequent preprocessing and finite element modeling.
+
+2.2. Segmentation of the Abdominal Wall
+
+Segmentation was performed using the Segment Editor module in 3D Slicer, which enables the conversion of 2D medical images into 3D anatomical geometries based on tissue-specific intensity thresholds. The abdominal wall muscles were segmented as regions of interest in both 2D slice views and 3D space. In this paper, the editor tools were used to segment the muscle layer of the abdominal wall as shown in Figure 1.
+
+Although the abdominal wall consists of four distinct muscle groups—rectus abdominis (RA), external oblique (EO), internal oblique (IO), and transversus abdominis (TrA) [14]—these layers were represented as a single equivalent muscle layer in the present model to reduce computational complexity and facilitate convergence of the finite element simulations. Furthermore, the available CT images did not provide sufficient information to accurately distinguish the fiber orientations and anisotropic properties of the individual muscle layers. Similar homogenized representations have been adopted in previous biomechanical studies when patient-specific information regarding layer thickness and fiber architecture is unavailable [15,16]. While this simplification preserves the overall mechanical response of the abdominal wall, it is recognized that neglecting the anisotropic behavior of the individual muscle layers may influence the magnitude and localization of stresses, particularly in regions surrounding the mesh–suture interface where stress concentrations occur. Therefore, the present model is intended to capture the overall stress transfer mechanisms within the repair system rather than predict exact local tissue stresses. Future work will incorporate multilayer anisotropic constitutive models to provide a more physiologically realistic representation of the abdominal wall.
+
+2.3. Geometry Cleanup and Preprocessing
+
+The STL geometry generated from segmentation was imported into ANSYS (Version: 2020 R2) SpaceClaimfor preprocessing (Figure 2). Due to common STL-related issues such as inverted normals, intersecting triangles, and irregular edges, geometry cleanup was performed prior to finite element modeling. The abdominal wall was converted into a shell representation by extracting the inner surface, merging surface patches, and assigning a uniform thickness corresponding to the selected muscle layer thickness (Figure 3). The shell offset was defined toward the bottom surface to represent the physiological orientation of the abdominal wall. This preprocessing step ensured numerical stability and compatibility with shell-based finite element analysis.
+
+2.4. Surgical Mesh and Suture Modeling
+
+A synthetic, non-degradable polypropylene (PP) surgical mesh was selected for this study, reflecting its widespread clinical use in ventral incisional hernia repair [17,18]. The mesh was modeled as a woven structure and assumed to exhibit isotropic mechanical behavior [19]. A square mesh geometry measuring 125 mm × 125 mm was generated in SolidWorks 2021 based on dimensions reported in the literature [20]. The mesh porosity was defined to exceed 1 mm to reduce the risk of fibrotic tissue entrapment [21].
+
+The mesh geometry was imported into ANSYS (Version: 2020 R2) SpaceClaimand simplified using beam extraction techniques (Figure 4) to reduce computational cost. The mesh fibers were represented as circular beam elements with a diameter of 0.8 mm. Similarly, the sutures were modeled as monofilament, non-absorbable polypropylene materials. The sutures were represented using beam elements with a circular cross-section of 0.7 mm in diameter. Beam representations were selected for both the mesh and the sutures to achieve computational efficiency while preserving mechanical fidelity.
+
+2.5. Mesh Placement and Incision Configuration
+
+The intra-lay (intraperitoneal onlay mesh, IPOM) placement technique was adopted, wherein the mesh is positioned beneath the abdominal muscle layer and outside the peritoneum. This approach minimizes muscle trauma and is commonly employed in clinical practice. A midline incision configuration was selected, as it is the most frequently used incision type in open abdominal surgeries. Specifically, an upper midline incision was modeled (Figure 5). The finite element model was restricted to the abdominal muscle layer, surgical mesh, and sutures to focus on stress transfer mechanisms at the repair site.
+
+The complete 3D geometry of the abdominal wall, showing the midline incision, intra-lay placement of the mesh, and sutures, was converted into beam and shell elements in Ansys SpaceClaim, as shown in Figure 6.
+
+2.6. Constitutive Model of the Abdominal Muscle
+
+The abdominal muscle layer was modeled as a nonlinear, nearly incompressible hyper-elastic material. A second-order Ogden constitutive model was employed to characterize the stress–strain behavior of the muscle tissue [22]. This model is well suited for biological soft tissues and has been validated in prior biomechanical studies. Specifically, the Ogden material parameters were adopted from the published literature and defined using four constants, μ1, μ2, α1, and α2, which were estimated as 0.0439 MPa, −0.236 MPa, 9.82, and −1.00, respectively [23]. These parameters were implemented within the finite element solver to capture the nonlinear deformation response of the abdominal wall under loading.
+
+2.7. Finite Element Mesh Generation
+
+Finite element meshing was performed using ANSYS (Version: 2020 R2) Meshing. Geometry defeaturing and virtual topology operations were applied to remove small edges and irrelevant features that could degrade mesh quality. To ensure accurate stress transfer between the sutures and the abdominal wall, topology sharing was implemented at the suture–wall interface (Figure 7). Prior to the final simulations, several global mesh sizes were examined to assess the sensitivity of the numerical results to mesh density. A mesh convergence study was performed by comparing the predicted stress distributions obtained from progressively refined meshes. It was observed that further refinement beyond the selected mesh size resulted in only negligible changes in the calculated stress values while substantially increasing computational cost and solution time. Therefore, a global element size of 60 mm was considered sufficient to provide accurate and numerically stable results. Localized refinement was automatically applied in regions of contact between the mesh, sutures, and the abdominal wall to improve stress resolution in areas of interest. Beam and shell elements were used consistently throughout the model to achieve an appropriate balance between solution accuracy and computational efficiency.
+
+2.8. Loading and Boundary Conditions
+
+To simulate physiological loading conditions associated with activities such as coughing, deep breathing, and physical exertion, external loads were applied to the repaired abdominal wall. Fixed boundary conditions were assigned to the suture vertices, as well as the top and bottom edges of the abdominal wall, to represent anatomical constraints (Figure 8). Displacement was constrained in the x- and z-directions, allowing motion only along the y-axis (Figure 9).
+
+In the present study, physiological loading was represented by a uniformly distributed pressure acting normal to the inner surface of the abdominal wall in the negative y-direction, thereby simulating the mechanical effects of intra-abdominal pressure. The pressure levels were selected based on physiological loading conditions reported in the literature and corresponded to different levels of abdominal activity. The resultant force associated with each loading condition was obtained by integrating the distributed pressure over the loaded area. Three loading states were considered, representing regular breathing, forceful breathing, and heavy-load lifting. These loading conditions corresponded to equivalent resultant forces of 16.05 N, 38.25 N, and 74.3 N, respectively. This loading configuration enabled the evaluation of stress distribution and deformation behavior under clinically relevant conditions and provided a more physiologically realistic representation of the mechanical environment experienced by the abdominal wall–mesh–suture system.
+
+3. Results and Discussion
+
+This section presents the finite element simulation results of the abdominal wall–mesh–suture system under physiologically relevant loading conditions and discusses the resulting stress distribution patterns. The findings are interpreted to identify critical mechanical failure mechanisms associated with ventral incisional hernia recurrence and to relate the numerical outcomes to clinical observations.
+
+3.1. Physiological Loading Conditions on the Abdominal Wall
+
+An internal report conducted by the College of Medicine at the University of Saskatchewan investigated the magnitude of forces exerted on the abdominal wall under different physiological conditions [24]. The objective of the study was to quantify abdominal wall loading during three expiratory states: regular breathing, forceful breathing, and heavy-load lifting. Participants were tested non-invasively using a dynamometer, and the resulting force ranges are summarized in Table 1. The findings indicated that forces ranging from 11.2 N to 25.1 N were generated during regular breathing, while higher force magnitudes were observed during forceful breathing and heavy-load lifting.
+
+In the present finite element analysis, physiological loading was represented by a uniformly distributed pressure acting over the abdominal surface rather than by concentrated point forces. The resultant force generated by the distributed pressure was used to characterize each physiological state. Based on the average values obtained from the experimental measurements, equivalent resultant forces of 16.05 N, 38.25 N, and 74.3 N were considered for the regular breathing state, forceful breathing state, and heavy-load lifting state, respectively. Thus, the applied loads represent the mechanical effects of intra-abdominal pressure associated with different physiological activities and provide a more realistic description of the loading environment experienced by the abdominal wall–mesh–suture system.
+
+3.2. Stress Analysis Framework
+
+Stress develops within a structure when external forces induce internal resistance to deformation. In surgical hernia repair, suturing the mesh to the abdominal muscle layer introduces localized stress concentrations, which may influence the mechanical stability of the repair. To account for the increased stiffness associated with suturing and mesh reinforcement, a stiffness factor of 0.2 was assigned to both the sutures and the surgical mesh in the model. The stress distribution within the model was evaluated using the von Mises stress criterion, which is commonly employed to assess yielding behavior in ductile materials such as polypropylene.
+
+3.3. Stress Distribution During the Regular Breathing State (RBS)
+
+During the regular breathing state, an average force of 16.05 N was applied to the internal surface of the abdominal muscle layer, modeled using shell elements. The muscle layer was mechanically connected to the surgical mesh and sutures through mesh connections to enable effective force transfer across the system.
+
+The von Mises stress contours (Figure 10, Figure 11 and Figure 12) revealed that the highest stress concentrations occurred at the suture edges, followed by the contact regions between the sutures and the abdominal wall. These regions of maximum stress were identified by red-shaded areas in the contour plots. Such stress concentrations suggest potential sites of mechanical failure, particularly under repetitive or excessive loading conditions. Elevated stress at the suture–tissue interface may also indicate suboptimal suturing techniques or excessive suture tension.
+
+The nonlinear contact interaction between the suture and the abdominal wall significantly influenced stress distribution. The sutures in the model served to secure the surgical mesh beneath the incision site, and any increase in the applied load led to corresponding increases in localized stress. Failure of the polypropylene sutures is expected if the stress exceeds their yield strength of approximately 2.8 MPa. In comparison, stress observed within the surgical mesh was considerably lower than those in the sutures, indicating that the mesh experienced less mechanical demand during regular breathing.
+
+3.4. Stress Distribution During the Forceful Breathing State (FBS)
+
+During the forceful breathing state, an average load of 38.25 N was applied to the model. The resulting stress contours (Figure 13, Figure 14 and Figure 15) demonstrated increased stress magnitudes compared to the regular breathing state. Stress concentrations remained primarily localized at the suture edges and at the suture–muscle contact regions. Notably, stresses at the suture edges were consistently higher than those observed in the surrounding contact areas, highlighting the susceptibility of sutures to mechanical overload during elevated physiological activity.
+
+3.5. Stress Distribution During Heavy-Load Lifting
+
+The highest stress levels were observed during the heavy-load lifting state, where an average force of 74.3 N was applied to the model. The stress contours (Figure 16) showed pronounced stress concentrations at the sutures, contact interfaces, and, to a lesser extent, within the surgical mesh. These results indicate that lifting heavy loads substantially increases the mechanical demand on the repair system, thereby elevating the risk of suture failure and mesh displacement.
+
+3.6. Deformation and Displacement Analysis
+
+Under the regular breathing state, only minor deformation was observed, indicating that the repair system was able to maintain adequate structural stability under normal physiological loading conditions. As the loading increased to the forceful breathing state, the magnitude of displacement increased correspondingly, although the deformation remained localized within the vicinity of the repair site. The greatest displacement occurred during heavy-load lifting, reflecting the higher mechanical demand imposed on the abdominal wall–mesh–suture system.
+
+The progressive increase in displacement with increasing loading conditions demonstrates that deformation behavior is strongly influenced by intra-abdominal pressure. Although the surgical mesh provided structural reinforcement, excessive loading resulted in larger deformations and increased stress concentrations around the fixation points. These findings suggest that excessive postoperative loading may compromise the mechanical stability of the repair and contribute to the development of recurrence.
+
+3.7. Comparative Analysis of Stress Across Physiological States
+
+A comparative assessment of stress magnitudes across the three physiological states demonstrated a clear increasing trend: (1) Regular Breathing State<Forceful Breathing State<Heavy Load Lifting State
+
+This progression confirms that activities involving higher intra-abdominal pressure generate significantly greater stress within the hernia repair system. The sutures consistently experienced the highest stress concentrations across all loading conditions, followed by the suture–muscle contact regions and the surgical mesh. These findings underscore the critical role of suture integrity in preventing hernia recurrence and highlight the importance of postoperative activity management to minimize excessive loading on repaired abdominal walls.
+
+From a clinical perspective, the results suggest that optimization of suture spacing may play an important role in improving the mechanical stability of hernia repairs. Smaller suture spacing may promote more uniform load sharing among fixation points and reduce localized stress concentrations, thereby decreasing the likelihood of suture pull-through or rupture. Conversely, widely spaced sutures may result in higher stresses being transmitted to individual fixation points, increasing the risk of mechanical failure.
+
+The present findings also emphasize the importance of the mesh fixation strategy. Alternative fixation configurations and improved load distribution mechanisms may reduce stress concentrations at the mesh–suture interface and enhance the long-term integrity of the repair construct. Appropriate mesh positioning and fixation patterns could therefore contribute to reducing recurrence rates and improving clinical outcomes.
+
+Furthermore, the observed increase in stress under heavy-load lifting conditions highlights the importance of postoperative rehabilitation and activity management. Patients recovering from ventral incisional hernia repair should avoid excessive abdominal loading during the early stages of healing, as strenuous activities and heavy lifting may expose the sutures to stresses approaching their mechanical limits. Consequently, controlled rehabilitation protocols and a gradual return to physical activity may be essential for preserving repair integrity and minimizing the risk of recurrence.
+
+3.8. Limitations
+
+Several limitations of the present study should be acknowledged [25,26,27]. First, the abdominal wall was represented as a single equivalent isotropic hyperelastic layer rather than as four distinct muscle layers, namely the rectus abdominis, external oblique, internal oblique, and transversus abdominis. Although this simplification reduced computational complexity and facilitated convergence of the patient-specific finite element model, it may influence the magnitude and localization of stresses, particularly near the mesh–suture interface where stress concentrations are highest. Furthermore, the anisotropic behavior and fiber orientations of the individual muscle layers were not considered because such information could not be reliably obtained from the available CT images.
+
+Second, the loading conditions employed in the simulations were simplified by assuming a uniformly distributed intra-abdominal pressure acting over the abdominal surface. In reality, intra-abdominal pressure varies spatially and temporally and may be influenced by patient posture, breathing patterns, and different physical activities. Consequently, the applied loading conditions represent an approximation of the physiological environment rather than an exact reproduction of in vivo conditions.
+
+Third, the present study focused primarily on stress transfer mechanisms within the abdominal wall–mesh–suture system and did not consider time-dependent tissue remodeling, healing processes, or the viscoelastic effects of biological tissues. These factors may influence the long-term mechanical behavior of the repair and contribute to hernia recurrence.
+
+Finally, experimental validation of the numerical predictions has not yet been performed. Although the simulation results are in agreement with clinical observations regarding the role of suture failure in recurrent hernias, further validation using physical phantoms, cadaveric specimens, and animal models is required to establish the reliability and predictive capability of the developed finite element framework. Future studies will focus on incorporating multilayer anisotropic constitutive models, dynamic loading conditions, and experimental validation to provide a more physiologically realistic representation of ventral incisional hernia repair.
+
+4. Conclusions
+
+This study investigated the mechanical behavior of a ventral incisional hernia repair system using a finite element analysis (FEA) model incorporating the abdominal wall, surgical mesh, and sutures under physiologically relevant loading conditions. The primary objective was to evaluate stress transfer within the repair system when intra-abdominal contents exert pressure on the weakened abdominal wall during activities such as breathing and heavy lifting. The developed FEA framework successfully captured the stress distribution within the system and provided insight into the mechanical factors contributing to hernia recurrence.
+
+The results demonstrated that the highest stress concentrations consistently occurred at the sutures rather than within the mesh or the surrounding abdominal wall tissue. As the applied loading increased, particularly under conditions simulating heavy lifting, the stresses within the sutures progressively approached their yield strength. These findings indicate that suture failure is a critical mechanical trigger for the recurrence of ventral incisional hernias. Importantly, this numerical outcome aligns closely with empirical clinical observations reported by surgeons, who commonly identify suture rupture or pull-through as the primary failure mode in recurrent hernia cases, especially in patients exposed to high postoperative loads.
+
+From a clinical perspective, the findings suggest that optimization of suture spacing and mesh fixation strategies may play an important role in reducing stress concentrations and improving the long-term stability of the repair. More uniform load distribution achieved through appropriate fixation patterns could potentially decrease the likelihood of suture overload and recurrence. Furthermore, the results emphasize the importance of postoperative rehabilitation and activity management. Avoidance of excessive abdominal loading during the early healing period, particularly during heavy lifting and strenuous activities, may help preserve repair integrity and improve long-term surgical outcomes. Therefore, the developed model has potential value as a predictive tool for surgical planning and postoperative care strategies.
+
+The agreement between the FEA predictions and clinical experience strengthens the credibility of the developed model and highlights its usefulness for understanding the biomechanical mechanisms associated with ventral incisional hernia recurrence. Future research will extend this work in several directions. First, a more anatomically realistic abdominal wall model incorporating all four muscle layers with distinct anisotropic mechanical properties will be developed to better represent in vivo behavior. Second, a dynamic FEA framework will be introduced to capture large deformations and time-dependent loading associated with daily activities. Third, experimental validation using physical phantoms and animal models will be conducted to further assess the reliability and accuracy of the numerical predictions. Finally, ongoing work aims to develop an adaptive “smart” postoperative abdominal binder capable of real-time load modulation, offering personalized mechanical support and potentially reducing the risk of hernia recurrence.
+
+Author Contributions
+
+Conceptualization, T.B.E., Y.L., S.S. and W.Z.; methodology, T.B.E., S.S., W.Z., A.O., J.O. and N.S.; software, T.B.E., Y.L., S.S. and W.Z.; validation, T.B.E., S.S., W.Z., A.O., J.O. and N.S.; software, T.B.E., Y.L., S.S. and W.Z.; formal analysis, T.B.E., S.S. and W.Z., Akinola and Ogbeyemi, J.O. and N.S.; writing—original draft preparation, S.S. and T.B.E.; writing—review and editing, T.B.E., Y.L., S.S. and W.Z. ; methodology, T.B.E., S.S., W.Z., A.O., J.O. and N.S. ; visualization, T.B.E., Y.L., S.S. and W.Z. ; methodology, T.B.E., S.S., W.Z., A.O., J.O. and N.S.; supervision, Y.L. and W.Z.; project administration, Y.L. and W.Z.; funding acquisition, Y.L. and W.Z. All authors have read and agreed to the published version of the manuscript.
+
+Data Availability Statement
+
+No new data were created or analyzed in this study. Data sharing is not applicable to this article.
+
+Conflicts of Interest
+
+The authors declare no conflict of interest.
+
+Figure 1 Segmentation and 3D Reconstruction of Abdominal Organs and Skeletal Structures in 3D Slicer.
+
+Figure 2 Preprocessing of STL File in ANSYS SpaceClaim.
+
+Figure 3 Creating Shell Element (Extracted Surface).
+
+Figure 4 Beam Element for Surgical Mesh.
+
+Figure 5 The Midline Incision.
+
+Figure 6 The complete Three-Dimensional Geometry (Beam and Shell Elements).
+
+Figure 7 Generated Finite Element Mesh of the Abdominal Wall Model.
+
+Figure 8 Fixed Supports.
+
+Figure 9 Mesh Displacement and Convergence Plot.
+
+Figure 10 Stress on the suture during the regular breathing state.
+
+Figure 11 Stress around the areas of contact between the suture and the wall (RBS).
+
+Figure 12 Stress on the surgical mesh during the regular breathing state.
+
+Figure 13 Equivalent stress distribution in the sutures during forceful breathing and heavy lifting.
+
+Figure 14 Finite Element Stress Analysis of the Surgical Mesh During Forceful Breathing and Heavy-Load Lifting.
+
+Figure 15 Contact stress distribution on the abdominal wall under forceful breathing and heavy lifting.
+
+Figure 16 Variation in von Mises Stress Under Regular Breathing, Forceful Breathing, and Heavy Lifting.
+
+bioengineering-13-00801-t001_Table 1 Table 1 Force ranges exerted on the abdominal wall under different physiological conditions (male participants) [24].
+
+Participant No.	Regular Breathing—Expiration (N)	Forceful Breathing—Expiration (N)	Heavy Lifting (N)	
+1	13.7	33.3	51.2	
+2	11.2	51.8	40.7	
+3	11.2	33.3	77.3	
+4	16.3	30	64.5	
+5	15.2	28.6	83.4	
+6	15.4	53.1	78.2	
+7	17.7	30.9	56.9	
+8	21.6	38.2	82.7	
+9	25.1	44.4	85.9	
+10	13.1	38.9	122.2	
+
+Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.
+
+
+References
+
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+2. Persichetti P. Ciarrocchi S. Brunetti B. Abdominal Wall Surgery Textbook of Plastic and Reconstructive Surgery Maruccia M. Giudice G. Springer Cham, Switzerland 2022 10.1007/978-3-030-82335-1_26
+3. Miller H.J. Novitsky Y.W. Ventral hernia and abdominal release procedures Elsevier eBooks Elsevier Amsterdam, The Netherlands 2019 571 589 10.1016/b978-0-323-40232-3.00052-2
+4. Lindmark M. Strigård K. Löwenmark T. Dahlstrand U. Gunnarsson U. Risk Factors for Surgical Complications in Ventral Hernia Repair World J. Surg. 2018 42 3528 3536 10.1007/s00268-018-4642-6 29700567 PMC6182761
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+6. Tigora A. Radu P.A. Garofil D.N. Bratucu M.N. Zurzu M. Paic V. Ioan R.G. Surlin V. Margaritescu D. Badoiu S.C. Modern Perspectives on Inguinal Hernia Repair: A narrative review on surgical techniques, mesh selection and fixation strategies J. Clin. Med. 2025 14 4875 10.3390/jcm14144875 40725568 PMC12295799
+7. Awaiz A. Rahman F. Hossain M.B. Yunus R.M. Khan S. Memon B. Memon M.A. Meta-analysis and systematic review of laparoscopic versus open mesh repair for elective incisional hernia Hernia 2015 19 449 463 10.1007/s10029-015-1351-z 25650284
+8. Deerenberg E.B. Timmermans L. Hogerzeil D.P. Slieker J.C. Eilers P.H.C. Jeekel J. Lange J.F. A systematic review of the surgical treatment of large incisional hernia Hernia 2015 19 89 101 10.1007/s10029-014-1321-x 25380560
+9. Takata M.C. Duh Q. Laparoscopic inguinal hernia repair Surg. Clin. N. Am. 2008 88 157 178 10.1016/j.suc.2007.10.005 18267168
+10. Mogoanta S.S. Paitici S. Mogoanta C.A. Postoperative Follow-Up and Recovery after Abdominal Surgery IntechOpen eBooks IntechOpen London, UK 2021 10.5772/intechopen.97739
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+12. Cao L. Dolovich A.T. Schwab A.L. Herder J.L. Zhang W.J. Towards a Unified Design Approach for both Compliant Mechanisms and Rigid-Body Mechanisms: Module Optimization ASME J. Mech. Des. 2015 137 122301 10.1115/1.4031294
+13. Fedorov A. Beichel R. Kalpathy-Cramer J. Finet J. Fillion-Robin J. Pujol S. Bauer C. Jennings D. Fennessy F. Sonka M. 3D Slicer as an image computing platform for the Quantitative Imaging Network Magn. Reson. Imaging 2012 30 1323 1341 10.1016/j.mri.2012.05.001 22770690 PMC3466397
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+15. Tahan N. Khademi-Kalantari K. Mohseni-Bandpei M.A. Mikaili S. Baghban A.A. Jaberzadeh S. Measurement of superficial and deep abdominal muscle thickness: An ultrasonography study J. Physiol. Anthropol. 2016 35 17 10.1186/s40101-016-0106-6 27553830 PMC4995748
+16. Noguchi T. Demura S. Relationship between Abdominal Strength Measured by a Newly Developed Device and Abdominal Muscle Thickness Adv. Phys. Educ. 2014 4 70 76 10.4236/ape.2014.42010
+17. Rastegarpour A. Cheung M. Vardhan M. Ibrahim M.M. Butler C.E. Levinson H. Surgical mesh for ventral incisional hernia repairs: Understanding mesh design Plast. Surg. 2016 24 41 50 10.1177/229255031602400110 PMC4806756 27054138
+18. Procter L. Falco E.E. Fisher J.P. Roth J.S. Abdominal wall hernias and biomaterials Studies in Mechanobiology, Tissue Engineering and Biomaterials Springer Berlin/Heidelberg, Germany 2009 425 447 10.1007/978-3-642-00534-3_19
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diff --git a/corpus/psychology/text/bc75c9fabc4ffedd.txt b/corpus/psychology/text/bc75c9fabc4ffedd.txt
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--- /dev/null
+++ b/corpus/psychology/text/bc75c9fabc4ffedd.txt
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+Shared research materials in psychology are widely downloaded but often difficult to reuse
+
+Open science reforms have made posting data and code common, but are shared materials actually used, and easily reused? Treating download counts of Open Science Framework (OSF) supplements as a usage index, I analysed 1,660 articles from four psychology journals (Cognition, Psychological Science, Journal of Experimental Social Psychology, Journal of Memory and Language) across three years (2015, 2020, 2025). OSF sharing rose from 9% in 2015 to 52% in 2025. Among 392 papers with download data, materials were downloaded a median of 152 times; only 1% went undownloaded. Download volume was associated with citation count and altmetric attention. Availability did not ensure easy reuse: only 40% of repositories provided documentation, 34% were flagged for a hard-coded file path, and 42% referenced a missing file — shortcomings that did not improve as sharing grew. Altogether, shared materials are being used, but often not easily reusable.
diff --git a/corpus/psychology/text/c10096127eb96c32.txt b/corpus/psychology/text/c10096127eb96c32.txt
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+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Front Psychol
+Journal ID: Front Psychol
+NLM Journal ID: 101550902
+Journal ID: Front. Psychol.
+
+Frontiers in Psychology
+
+EISSN: 1664-1078
+Publisher: Frontiers Media SA
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC12226827
+PMID: 40620923
+DOI: 10.3389/fpsyg.2025.1636749
+Article version: 1
+Subjects: Psychology, Correction
+
+Correction: Analysis of drug and health resource use before and after COVID-19 lockdown in a population undergoing treatment for depression or anxiety
+
+Lear-Claveras Ana 1
+Clavería Ana 2 3 4 *
+Couso-Viana Sabela 3 4
+Nabbe Patrice 5
+Oliván-Blázquez Bárbara 1 4 6
+1 Institute for Health Research Aragón (IIS Aragón) , Zaragoza , Spain
+2 I-Saúde Group, South Galicia Health Research Institute , Vigo , Spain
+3 Vigo Health Area, SERGAS , Vigo , Spain
+4 Network for Research on Chronicity, Primary Care, and Health Promotion (RICAPPS) , Barcelona , Spain
+5 Département Universitaire de Médecine Générale, ER 7479 SPURBO (Soins Primaires, Santé Publique, Registre des Cancers de Bretagne Occidentale), Université de Bretagne Occidentale , Brest , France
+6 Department of Psychology and Sociology, University of Zaragoza , Zaragoza , Spain
+Edited and reviewed by: Changiz Mohiyeddini, Oakland University William Beaumont School of Medicine, United States
+
+*Correspondence: Ana Clavería anaclaveriaf@gmail.com
+Electronic publication date: 2025 Jun 20
+Publication date: 2025
+Volume: 16
+Electronic Location ID: 1636749
+Received 2025 May 28; Accepted 2025 Jun 4
+Copyright: Copyright © 2025 Lear-Claveras, Clavería, Couso-Viana, Nabbe and Oliván-Blázquez.
+Copyright year: 2025
+Copyright holder: Lear-Claveras, Clavería, Couso-Viana, Nabbe and Oliván-Blázquez
+License: This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Erratum for: Analysis of Drug and Health Resource Use Before and After COVID-19 Lockdown in a Population Undergoing Treatment for Depression or Anxiety 13 5 4 2022 861643 Frontiers in Psychology 10.3389/fpsyg.2022.861643 PMC9037328 35478736
+Keywords: COVID-19, depression, anxiety, quarantine, lifestyle, primary health care
+Figure count: 0
+Table count: 0
+Equation count: 0
+Reference count: 0
+Page count: 2
+
+section-at-acceptance: Health Psychology
+
+Ÿ==============================Ÿ
+In the published article, there were several instances where the text was incomplete. Additional wording has been included in certain parts of the text for added clarification.
+
+Corrections have been made to Discussion, Paragraphs 8, 9, 10 and 11.
+
+This text previously stated:
+
+Any study should be interpreted with caution. Our choice was to analyze the changes in behavior over a short period, between 6 months before and 6 months after lockdown, by collating the modification of the use of the care system and of anti-depressant and anxiety drugs. Starting from a postula: these increases reflect not only the increase in psychological suffering in these patients but also, they may be a proxy for the increase in prevalences of depression in general population.
+
+Although the sample size was large, the mean age of the sample was high (61.7 years). The duration of the study may not be long enough to see variations in the severity of depression. Depression is a disease that sets in gradually. While anxiety is subject to greater variability. But the significant increase in the use of anxiolytics is a warning sign. Studies should be continued to confirm or not the increase in the prevalence of depression, possibly expected thereafter.
+
+Our source of information was a registry: the ECR. But this is not enough to provide objective information on the impact of the pandemic on the mental health of patients. To ensure the diagnosis of depression, the use of validated scales [Goldberg Anxiety and Depression Scale (GADS), Hamilton Anxiety Rating Scale, Beck Anxiety Inventory, etc.] will be necessary. In addition, it would be interesting to organize a qualitative research to complement this analysis. A cohort study using diagnostic tools to perform the sampling would be very useful in answering this question: are we on the cusp of an increase in depression in the general population due to the pandemic and which ones are the measures to deal with it?
+
+Finally, the number of statistical tests and calculated p-values in this article is large and therefore needs to be confirmed in further studies.
+
+The corrected paragraphs 8, 9, 10 and 11 are shown below.
+
+Any study should be interpreted with caution. Our choice was to analyze the changes in behavior over a short period, between 6 months before and 6 months after lockdown, by collating the modification of the use of the care system and of anti-depressant and anxiety drugs. Starting from a postula: these increases reflect not only the increase in psychological suffering in these patients but also, they may be a proxy for the increase in prevalences of depression in general population. But it is relevant to highlight that this study uses an observational design, which does not allow for causal inferences. This is particularly important in the context of assessing COVID-19 lockdown effects, where multiple confounding factors may have influenced the outcomes.
+
+Although the sample size was large, the mean age of the sample was high (61.7 years), and the age range of our sample was 87 years, with a minimum age of 16 years and a maximum age of 103 years. However, since real-world data (RWD) was used, all individuals who met the inclusion criteria were included. Therefore, this reflects the actual mean age of the population with depression in Aragon (Spain) before the start of the pandemic. The duration of the study may not be long enough to see variations in the severity of depression. The six-month comparison period may not be sufficient to capture long-term changes, especially in conditions such as depression that often require extended observation. This timeframe may have affected the detection of meaningful trends since depression is a disease that sets in gradually. While anxiety is subject to greater variability. But the significant increase in the use of anxiolytics is a warning sign. Studies should be continued to confirm or not the increase in the prevalence of depression, possibly expected thereafter.
+
+Our source of information was a registry: the ECR. But this is not enough to provide objective information on the impact of the pandemic on the mental health of patients. To ensure the diagnosis of depression, the use of validated scales [Goldberg Anxiety and Depression Scale (GADS), Hamilton Anxiety Rating Scale, Beck Anxiety Inventory, etc.] will be necessary. This relates to the following limitation: the analysis did not adequately adjust for key confounders, such as differences in the severity of depression or anxiety, or changes in healthcare policies during the pandemic. Since there are no data on depression severity in the medical records, this factor could not be adjusted for. The absence of standardized assessments of symptom severity in electronic clinical records (ECRs) further limits the interpretation of outcomes. However, as there were no changes in the relevant medication guideline protocols issued by health authorities during the study period, it may be inferred that general practitioners tend to adjust medication upward in response to worsening symptoms of anxiety and depression, particularly following the initial titration period after a drug has been prescribed. Nevertheless, this cannot be definitively established based on the available data. Therefore, these findings should be interpreted with caution.
+
+Finally, the number of statistical tests and calculated p-values in this article is large and therefore needs to be confirmed in further studies. A comparison at two time points of related samples (paired Student T-test) has been used, and for those variables with fewer number of observations than 100, Wilcoxon rank test was used. Some researcher consider that this may increases the risk of Type I errors.
+
+Additionally, a correction has also been made to Conclusion, Paragraph 1.
+
+This paragraph previously stated:
+
+This study offers contributions, from a long-term perspective, with regard to the knowledge of the repercussions of lockdown measures on the use of drugs and health care resources, in a sample of patients undergoing active treatment for anxiety and/or depression, according to the ECR.
+
+The corrected paragraph is shown below.
+
+This study offers contributions, from a short-term perspective, with regard to the knowledge of the repercussions of lockdown measures on the use of drugs and health care resources, in a sample of patients undergoing active treatment for anxiety and/or depression, according to the ECR. However, the use of data from Electronic Clinical Records to investigate patients with anxiety and depression may have limitations.
+
+The authors apologize for these errors and state that these do not change the scientific conclusions of the article in any way. The original article has been updated.
+
+Publisher's note
+
+All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.
+
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+Is conscious perception necessary to direct attention? A replication of Jiang et al. (2006): Stage 2 Registered Report
+
+The relationship between attention and consciousness has been debated for decades. Observing attentional biases induced by visual stimuli below the conscious threshold is one way of providing evidence for the independence of attention and conscious perception. Among such studies, Jiang et al. (2006) found a strong priming effect below the objective conscious threshold with high sensitivity, in showing attentional biases to nude images suppressed by continuous flash suppression (CFS). In our replication, we found moderate Bayesian evidence for the unconscious attraction from opposite sex nude images below the subjective conscious threshold in heterosexual participants. This supports the theory that attention and consciousness are dissociable, and the idea that sexually attractive visual stimuli capture attention even when rendered unconscious. The results have been checked for computational reproducibility by an independent statistician, full report at https://osf.io/dr35v/files/te58h.
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+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Cureus
+Journal ID: Cureus
+NLM Journal ID: 101596737
+
+Cureus
+
+EISSN: 2168-8184
+Publisher: Cureus Inc.
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC13198936
+PMID: 42186616
+DOI: 10.7759/cureus.107667
+Article version: 1
+Subjects: Cardiology, Public Health, Internal Medicine
+
+Living With Symptom Experiences in Patients With Heart Failure: A Scoping Review
+
+Muacevic Alexander
+Adler John R
+Fukuda Tomohide 1
+Hosogaya Junichi 2
+Imai Yoshie 3
+Murakami Yoshie 4
+1 Faculty of Nursing, Musashino University, Tokyo, JPN
+2 Department of Nursing, Kawaguchi Cardiovascular and Respiratory Hospital, Saitama, JPN
+3 Faculty of Medicine, Tokushima University, Tokushima, JPN
+4 Faculty of Nursing and Medical Care, Keio University, Tokyo, JPN
+Tomohide Fukuda t-fukuda@musashino-u.ac.jp
+Electronic publication date: 2026 Apr 24
+Publication date: 2026 Apr
+Volume: 18
+Issue: 4
+Electronic Location ID: e107667
+Accepted 2026 Apr 23
+Copyright: Copyright © 2026, Fukuda et al.
+Copyright year: 2026
+Copyright holder: Fukuda et al.
+License: This is an open access article distributed under the terms of the Creative Commons Attribution License CC-BY 4.0., which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+This article is available from https://cureus.com/articles/482662-living-with-symptom-experiences-in-patients-with-heart-failure-a-scoping-review
+Keywords: heart failure, patient reported experience, self-care, symptom experience, symptom recognition
+
+Funding: This work was supported by JSPS KAKENHI Grant Number 25K13944.
+
+Ÿ==============================Ÿ
+Heart failure is a long-term progressive disease affecting millions of people worldwide, imposing physical, psychological, and social burdens on patients and their families. Symptom recognition, which refers to awareness and understanding of bodily changes, is a key aspect of self-care; however, how patients and their families live with symptoms and deal with them in their daily lives remains unclear. This review aimed to summarise the current knowledge on how patients with heart failure and their caregivers experience, notice, and manage symptoms in daily life, and to identify the knowledge gaps that make timely and appropriate care difficult.
+
+This scoping review followed the frameworks of Arksey and O’Malley and the Preferred Reporting Items for Systematic Reviews and Meta-Analyses extension for Scoping Reviews guidelines. Four databases (PubMed, CINAHL, PsycINFO, and Ichushi-Web) were searched for peer-reviewed studies published between 2010 and 2025. Studies focusing on the symptom experiences of adult patients with heart failure and their caregivers were included. Two reviewers independently screened and extracted the data, which were organised into main themes.
+
+Of the 2,057 studies, 19 were included (14 qualitative, three cross-sectional, and two mixed-method). Findings were grouped into five categories: symptom experiences, in which breathlessness, tiredness, and swelling were often accepted as normal; detection and barriers, in which vague or small changes were often missed; family and caregiver roles, in which families sometimes encouraged early care-seeking but sometimes delayed it; management factors, including cognition, family support, healthcare complexity, and treatment burden; and knowledge and system gaps, including low body awareness, delays in severe cases, and limited attention to contextual factors.
+
+Managing heart failure symptoms depends not only on medical knowledge but also on psychological, social, and contextual factors. Interventions should go beyond education by correcting normalisation, reducing the treatment burden, and combining human support with technology. Building multilayered strategies that link knowledge and action is essential for reducing readmissions and improving quality of life.
+
+Introduction and background
+
+Heart failure is a chronic and progressive disease that affects millions of people worldwide and seriously impacts the lives of both patients and their caregivers [1]. Patients with heart failure often experience several symptoms simultaneously, such as breathlessness, fatigue, and swelling. These symptoms limit daily activities, cause psychological distress, and often lead to social isolation, resulting in a significant decrease in quality of life [2,3].
+
+Therefore, promoting self-care behaviours among patients with heart failure is essential to prevent symptom worsening and improve clinical outcomes [4]. Among these behaviours, symptom perception, or the ability to notice and understand physical changes, is central to effective self-care management. Early recognition and appropriate response to symptoms can strongly influence health outcomes [5,6]. However, symptom perception is not only about medical knowledge; it depends deeply on how patients personally experience and interpret their symptoms.
+
+Symptom experience is not limited to physical sensation. It includes aspects of self-perception, role performance, and social connections [3]. Fatigue is a continuous and disabling symptom that restricts daily life and decreases a patient's sense of self-efficacy. In addition, the appearance and management of symptoms are strongly associated with social determinants of health, such as access to health care, financial burden, and the presence of social support networks [7]. These findings show that the symptom experiences of patients with heart failure are complex processes involving biological, social, and emotional dimensions.
+
+Despite this understanding, many studies have focused on symptom recognition or self-care behaviours, whereas few have systematically examined how patients live with and experience symptoms in their daily lives. Comprehensive research mapping the lived experiences of heart failure symptoms from the patient's perspective remains limited.
+
+International clinical guidelines emphasise the importance of adopting a patient-centred approach to heart failure care [8]. Understanding patients' subjective experiences of symptoms is essential for designing effective medical interventions and building care systems that truly reflect the realities of patients' daily lives. A scoping review approach was selected to map the breadth of methodologically heterogeneous evidence on lived symptom experiences across qualitative, mixed-methods, and survey-based studies. Therefore, this scoping review aimed to explore and integrate existing studies on how patients with heart failure experience symptoms in their daily lives - encompassing both their subjective experiences and the perceptual processes through which they detect signs of worsening. Through this review, we aim to provide foundational knowledge for developing comprehensive and responsive nursing care models based on patients' lived experiences of symptoms.
+
+To achieve this aim, three interrelated review questions were formulated, anchored in the lived experience of heart failure symptoms in daily life: (1) how adults with heart failure and their families experience and detect symptoms and signs of worsening in daily life; (2) what individual, social, and contextual factors shape how patients and their families manage these symptom experiences in everyday settings; and (3) what knowledge and system-level gaps hinder the translation of symptom experiences and detection into timely and appropriate responses.
+
+Review
+
+Review questions
+
+This scoping review addressed three interrelated questions anchored in the lived experience of heart failure symptoms in daily life: (1) How do adults with heart failure and their families experience and detect worsening symptoms in daily life? (2) What individual, social, and contextual factors shape how patients and their families manage these symptom experiences in everyday settings? (3) What knowledge and system-level gaps hinder the translation of symptom experiences and detection into timely and appropriate responses?
+
+Methodology
+
+Study Design
+
+This scoping review followed the methodological framework proposed by Arksey and O’Malley [9], which was later refined by Levac et al. [10]. It was conducted in accordance with the Preferred Reporting Items for Systematic Reviews and Meta-Analyses extension for Scoping Reviews (PRISMA-ScR) guidelines [11].
+
+This review aimed to systematically search, organise, and integrate existing studies that examined how patients with heart failure - across ejection fraction phenotypes (heart failure with reduced ejection fraction (HFrEF), heart failure with mildly reduced ejection fraction (HFmrEF), and heart failure with preserved ejection fraction (HFpEF)) - experience and manage their symptoms in their daily lives. To define the research questions and eligibility criteria, we applied the Population, Concept, and Context (PCC) framework as follows: Population - adult patients diagnosed with heart failure and their caregivers; Concept - symptom experiences in daily life; Context - adults living in community settings, excluding those receiving end-of-life or palliative care.
+
+Eligibility Criteria
+
+Studies were included if they met the following criteria: (1) targeted adult patients diagnosed with heart failure of any ejection fraction phenotype (HFrEF, HFmrEF, or HFpEF), or heart failure not otherwise specified, or their family members and caregivers; (2) explored symptom experiences in daily life; (3) were published as full-text, peer-reviewed articles in English or Japanese. The exclusion criteria were as follows: (1) studies that only examined the effects of symptom management interventions without exploring patients’ experiences; (2) studies involving patients living with mechanical circulatory support; (3) studies focusing on populations other than heart failure patients (e.g., caregivers or healthcare professionals only); (4) studies limited to end-of-life or palliative care settings; and (5) review articles (including integrative, narrative, systematic, and scoping reviews), to restrict the synthesis to primary evidence and avoid double-counting of findings already represented in included primary studies.
+
+Search Strategy
+
+A comprehensive literature search was conducted using four electronic databases: PubMed, CINAHL, PsycINFO, and Ichushi-Web. The search was performed from May 1 to May 31, 2025, and included studies published between January 1, 2010, and April 30, 2025. Eligible studies were limited to peer-reviewed articles published in English or Japanese, reflecting the linguistic competencies of the review team and thereby enabling reliable full-text assessment and nuanced interpretation of qualitative accounts. Search terms included combinations of keywords related to heart failure (e.g., “heart failure”), symptom experiences (e.g., “symptom experience,” “lived experience”), and daily life (e.g., “daily life,” “everyday life”). Boolean operators (AND, OR) were used to combine these terms. The complete PubMed search strategy is provided in Supplementary Appendix S1; equivalent strategies were adapted for the other databases. Additionally, reference lists of relevant studies were hand-searched to identify further eligible literature that may not have appeared in the database searches.​​​​​​
+
+Selection of Sources of Evidence
+
+The selection process was conducted in two stages. In the first stage, two independent reviewers (TF and JH) independently screened the titles and abstracts of all identified studies based on predefined eligibility criteria. Inter-rater reliability was assessed using both per cent agreement and Cohen’s κ; the observed agreement was 85.5%, and κ = 0.71 (95% CI: 0.68-0.75). In the second stage, the same reviewers independently assessed the full texts of the selected studies for eligibility. Disagreements were resolved through discussion, and when consensus could not be reached, a third reviewer (YM or YI) made the final decision. The selection process was illustrated using a PRISMA flow diagram.​​​​​​
+
+Data Charting and Synthesis
+
+Data from the included studies were collected using a standardised data extraction form developed by the research team. The form recorded key information such as author, year of publication, study design, country or region, participant characteristics, study objectives, symptom experiences explored, and major findings related to the review questions. Two reviewers independently extracted the data, and any discrepancies were resolved through discussion. Extracted data were synthesised using a descriptive qualitative approach: findings were summarised by key concepts, types of symptom experiences, and contextual factors, and were integrated both in tables and in descriptive text. The five thematic categories presented in the Results were derived inductively through iterative discussion among the reviewers. In this review, consistent with the primary aim of mapping the breadth rather than appraising the strength of available evidence, a formal critical appraisal of included studies was not conducted. To address the third review question, knowledge gaps were charted from the limitations and future research recommendations reported within the included studies.
+
+Results
+
+A total of 2,057 records were identified in the four electronic databases. After removing duplicates, 1,562 articles were screened based on their title and abstract. Based on the inclusion and exclusion criteria, 1,436 studies were excluded. The remaining 126 full-text articles were reviewed in detail, and 19 studies were included in this scoping review (Figure 1). Of the 19 included studies, 14 were qualitative, three were cross-sectional, and two used mixed methods.​​​​​
+
+Figure 1 PRISMA-ScR flow diagram
+
+PRISMA-ScR: Preferred Reporting Items for Systematic Reviews and Meta-Analyses Extension for Scoping Reviews
+
+The general characteristics of the included studies are presented in Table 1. Across the included studies, patients with heart failure and their families or caregivers described diverse and complex experiences related to symptoms and their recognition of worsening conditions. To provide an integrated understanding of these findings, the results were organised into five categories: (1) symptom experiences; (2) processes and barriers to symptom detection; (3) involvement of family and caregivers; (4) factors influencing symptom management; and (5) knowledge and system gaps.​​​​​
+
+Table 1 Characteristics of included studies
+
+Author, year, country	Design	Main focus	Key findings	
+Walthall et al. (2016) [12], UK	Qualitative	Heart failure patients' experience and management of breathlessness	Breathlessness is a central symptom of life for heart failure patients, involving fear and limitation, and patients cope with it alone while attempting to live with it.	
+Taylor et al. (2017) [13], UK	Qualitative	To explore symptom onset and diagnostic meaning of "heart failure" from the patient's perspective in the heart failure diagnostic pathway	Patients are prone to overlooking initial symptoms and experience intense anxiety regarding the diagnostic label "heart failure." Educational support promoting early recognition and understanding of the diagnosis is crucial.	
+Jones et al. (2012) [14], USA	Qualitative	The perceptions, experience, and meaning of fatigue as a distressing symptom of chronic heart failure.	Fatigue for heart failure patients is not merely tiredness but an internal experience embodying a "reduction of vital life-force" and "loss of physical strength." It is often poorly understood by others and accompanied by feelings of isolation.	
+Xu et al. (2018) [15], USA	Qualitative	Heart failure patients' symptom interpretation and response patterns.	Patients often fail to accurately judge the severity of their symptoms and tend to overlook ambiguous cues, especially because initial symptoms are frequently unrecognised.	
+Riegel et al. (2018) [16], USA	Mixed methods	Factors related to symptom recognition in chronic heart failure patients.	The ability of heart failure patients to recognise symptoms is influenced more by cognitive function, supportive environment, and decision-making skill than by knowledge alone. Support for symptom detection is key to preventing deterioration.	
+Palmer et al. (2023) [17], Australia	Qualitative	To explore in-depth experiences and emotions of people with heart failure within the context of self-care.	Fear, shame, and lack of understanding impede self-management, while heart failure patients live with "heartache" (emotional distress) and a "sense of failure”.	
+Shogaki et al. (2024) [18], Japan	Qualitative	Experience of acute exacerbation and recovery from heart failure.	Heart failure patients become intensely conscious of bodily abnormalities during acute exacerbation, and their central concern shifts to daily life during the recovery phase, but verbalising the experience deepens self-understanding.	
+Ivynian et al. (2024) [19], Australia	Mixed methods	How do illness perceptions influence coping responses and self-care behaviours that lead to delayed care-seeking?	Delayed care-seeking when heart failure patients experience symptoms is deeply related to inaccurate illness perceptions, such as attributing symptoms to "not being ill" or "age or fatigue," and emotion-focused coping strategies like denial and avoidance.	
+Schumacher et al. (2018) [20], Canada	Qualitative	Symptom recognition, interpretation, and response among heart failure patients living in the community.	Heart failure patients accept symptom worsening as "part of daily life" and cope by resting or adjusting their routine, consequently overlooking signs of deterioration. This process of symptom "normalization" is the background for delayed care-seeking and decreased functional capacity.	
+Riegel et al. (2013) [21], USA	Qualitative	Naturalistic decision making) and their course regarding symptoms in adults with chronic heart failure.	Decision-making in heart failure patients is an accumulation of "naturalistic decisions" rooted in experience, where self-management is formed through situation awareness, mental simulation of actions, and evaluation of outcomes.	
+Heo et al. (2021) [22], USA	Qualitative	Heart failure patients' symptom perception and support needs.	Patients responded to various symptoms like breathlessness and oedema using diverse strategies, including medication and position change, but many lacked knowledge, felt uncertain about efficacy, and often adopted a "wait-and-see" approach depending on the situation.	
+Lee et al. (2013) [23], USA	Cross sectional	The association between mild cognitive dysfunction and self-care/care-seeking behaviours in symptomatic heart failure patients.	Heart failure patients with mild cognitive dysfunction are less likely to translate perceived symptoms into action or care-seeking. Even mild cognitive impairment is a factor impeding self-management.	
+Min et al. (2023) [24], Korea	Qualitative	To explore in-depth experiences and emotions of people with heart failure within the context of self-care.	Heart failure patients engaged in "fragile yet continuous efforts" explored amidst anxiety from a sudden diagnosis and physical constraints, supported by family and healthcare providers. Psychological and family support served as motivation for self-care.	
+Sethares et al. (2014) [25], USA	Cross sectional	Factors associated with delay in seeking care for acute decompensated heart failure	Delay in seeking care among heart failure patients is influenced not by medical factors, but by psycho-social factors such as "wait-and-see" behaviour and the response of family members	
+Sano and Majima (2018) [26], Japan	Qualitative	Self-management process in elderly male patients with chronic heart failure who have avoided re-hospitalisation for over 2 years.	Elderly male heart failure patients strive to maintain their desired lifestyle while preventing symptom worsening, engaging in trial and error between personal preferences and constraints to achieve this.	
+Reeder et al. (2015) [27], USA	Qualitative	How heart failure patients perceive worsening symptoms and respond as self-care	Heart failure patients find it difficult to link vague bodily changes to their disease, often resorting to self-directed coping which can lead to deterioration.	
+Austin et al. (2022) [28], UK	Cross sectional	The association between heart failure symptoms and the burden of treatment (BoT)	The higher the severity of symptoms like breathlessness and fatigue in heart failure patients, the greater the perceived burden associated with self-care activities such as diet, exercise, and utilisation of healthcare services. Symptoms are not merely indicators of disease status, but significantly influence overall treatment and life, restricting patients' role function and quality of life.	
+Sevilla-Cazes et al. (2018) [29], USA	Qualitative	Patient and caregiver challenges to heart failure home management and perceived reasons for readmission	Instead of "failing to follow instructions," patients are "attempting to come to terms with the illness in their own way." Readmission is not a "self-management failure" but a rational choice where the patient assesses their limits and seeks to regain safety.	
+Hall et al. (2014) [30], USA	Qualitative	Heart failure patients’perceptions and use of technology to manage disease symptoms.	While heart failure patients are accustomed to in-home measuring devices, there are psychological and practical barriers to using information and communication technology (ICT) or remote monitoring. Promoting technology utilisation requires the prerequisites of ensuring patient trust, understanding, and a supportive environment.	
+
+Symptom Experiences
+
+Across the included studies, patients with heart failure described symptom experiences that were frequent, burdensome, and deeply embedded in daily life. Breathlessness and fatigue were among the most commonly reported symptoms. Shortness of breath (85%), fatigue (53%), and oedema (42%) were the most frequently recognised pre-admission symptoms among the 60 patients interviewed by Reeder et al. [27], and breathlessness on exertion affected 82% and fatigue 85% of the 333 community-dwelling patients in the SYMPACT survey [28]. However, the meaning patients attributed to these symptoms was often more important than the symptoms themselves. Symptom experiences were not simply physical events; rather, they involved subjective interpretation, emotional responses, and ongoing adjustments to everyday living.
+
+Breathlessness was the most pervasive and disabling symptom, reported as a daily experience across virtually all included studies [12]. Its character differed markedly across disease phases: acute episodes were described in terms of terror, suffocation, and a sense of drowning, whereas chronic breathlessness gradually constricted the texture of everyday life, limiting activities such as bathing, climbing stairs, and sleeping. Night-time was particularly burdensome, with patients lying awake in fear, unable to lie flat. Despite its severity, many patients under-reported breathlessness to healthcare professionals and concealed its extent from family members, often managing it through self-devised strategies such as adjusting posture or slowing their pace [12]. Patients tended to seek help only when breathlessness became acute or severely disrupted daily activities; gradual increases in breathlessness during routine exertion were frequently attributed to ageing, deconditioning, or comorbid conditions rather than cardiac deterioration [13].
+
+Fatigue was similarly prevalent but proved far more resistant to accurate interpretation. Rather than using clinical terminology, patients preferred expressions conveying low energy, physical depletion, or a loss of vital force [14]. Because fatigue was experienced as an entirely internal phenomenon - invisible to family, friends, and clinicians alike - patients frequently felt misunderstood, isolated, and reluctant to raise the symptom in healthcare encounters. The existential dimension of fatigue was particularly striking: it functioned as an embodied barometer of mortality, experienced as a diminishment of life itself rather than a symptom to be reported and treated [14]. Across multiple studies, fatigue was consistently misattributed to ageing or overexertion, a pattern that significantly delayed recognition of clinical deterioration [13,14].
+
+While patients were monitored for fluid retention through daily weighing and ankle inspection, these objective indicators were unreliable guides to action. When presented with vignette scenarios, patients could identify acute breathlessness as requiring urgent intervention but struggled considerably with more gradual symptoms such as weight gain and ankle swelling, often responding with palliative measures rather than seeking clinical advice [15]. Consistent with this, longitudinal monitoring revealed that nearly half of patients showed a mismatch between objectively measured thoracic fluid accumulation and their own subjective perception of congestion [16]. Those who interpreted symptoms more accurately engaged in what has been termed body listening - an attentive, experience-based attunement to subtle internal signals - and demonstrated higher decision-making skill and stronger social support [16].
+
+The emotional dimensions of symptom experience were equally consequential. Living with heart failure generated a sustained burden of fear, uncertainty, shame, and guilt that shaped daily decision-making and healthcare engagement [17]. Both the experience of symptoms and the diagnostic label “heart failure” itself evoked associations with imminent death, in some cases discouraging patients from discussing their condition openly with family or clinicians [13,17]. In a phenomenological study conducted in Japan, patients reflecting on the period preceding emergency hospitalisation recalled vague bodily signals - unusual fatigue, changes in urine character, hoarseness - that had remained unrecognised as signs of worsening, illustrating how early warning symptoms are readily absorbed into the background of everyday life rather than interpreted as clinically meaningful [18].
+
+Processes and Barriers to Symptom Detection
+
+Patients consistently experienced difficulty in recognising the worsening of heart failure symptoms, and this difficulty operated through several interrelated mechanisms rather than a single barrier.
+
+A primary and cross-cutting barrier was the progressive normalisation of symptoms through daily habituation. Symptoms initially perceived as alarming became incorporated into the fabric of everyday life as they recurred without acute consequence [19,20]. Patients built tolerance incrementally - comparing new sensations against a continuously adjusted baseline of familiarity - while simultaneously enacting three active coping strategies through which normalisation was reinforced: resting to resolve symptoms in real time, reorganising daily routines to avoid symptomatic episodes, and progressively relinquishing valued roles [20]. Although each strategy temporarily restored a sense of control, their cumulative effect was a reduction in exertional activity that obscured the physiological signals necessary for accurate self-monitoring.
+
+Closely linked to normalisation was the systematic misattribution of symptoms to non-cardiac causes. Breathlessness, fatigue, and oedema were consistently attributed to ageing, deconditioning, or comorbid conditions rather than cardiac deterioration [19,20]. This misattribution was not simply a knowledge deficit; it was reinforced by ambiguous symptom presentations, particularly when overlapping conditions such as respiratory illness or constipation produced sensations indistinguishable from heart failure exacerbation [19]. In the absence of clear perceptual anchors, patients defaulted to wait-and-see behaviour - monitoring symptoms passively while deferring decisions according to severity, mood, or the availability of family members - a pattern documented consistently across qualitative and mixed-methods studies [20-22].
+
+Cognitive function emerged as a critical modifying variable in this process. Using a cardiovascular-specific cut-off on the Montreal Cognitive Assessment, patients with mild cognitive dysfunction demonstrated 21.5% worse self-care management scores and 51% worse consulting behaviours compared with cognitively intact counterparts [23]. The brain regions most affected by the haemodynamic consequences of heart failure overlap substantially with those governing decision-making, suggesting that cognitive vulnerability operates as a largely invisible amplifier of the barriers described above.
+
+Underpinning all of these processes was the naturalistic character of self-care decision-making itself. Rather than reasoning analytically about symptoms, patients relied on situation awareness and mental simulation grounded in personal experience [21]. Crucially, uncertainty and ambiguity - both pervasive features of heart failure symptom presentation - consistently directed this process toward passive responses. Comparison with previous hospitalisations reinforced inaction: patients who judged their current condition as less severe than a prior crisis concluded that intervention was premature [21].
+
+The included studies also described circumstances in which detection proceeded more successfully. Patients who interpreted and responded appropriately to worsening symptoms were distinguished by higher decision-making skill and better-quality social support, in contrast to those who struggled with recognition and action [16]. The post-recovery period following an acute exacerbation emerged as a distinctive window in which patients could articulate and contextualise prior bodily experiences when prompted, even though these same experiences had remained below the threshold of conscious awareness during routine daily life [18]. Accumulated experience with prior symptomatic episodes further supported detection: memory of concrete physical sensations, emotions, and imagery allowed some patients to rapidly re-appraise new symptoms, shortening appraisal and illness delays even when initial attributions had been inaccurate [19].
+
+These findings collectively indicate that symptom detection in heart failure is neither linear nor primarily knowledge-dependent. It is shaped by the erosion of perceptual sensitivity through normalisation, cognitive vulnerability, and the inherent uncertainty of experiential decision-making in daily life - a combination that frequently delays recognition until deterioration becomes critical.
+
+Involvement of Family and Caregivers
+
+Family members and caregivers played a structurally ambivalent role in heart failure symptom management - simultaneously enabling and impeding timely care-seeking - and this duality was a consistent finding across both qualitative and quantitative studies.
+
+The facilitative dimension of family involvement was most evident in crisis situations. When symptoms reached a threshold that could no longer be managed at home, families actively intervened: accompanying patients to consultations, contacting emergency services, and taking immediate action to support patients [24,25]. Family members were consulted in 87% of cases when patients first noticed symptom changes, and an active family response was associated with significantly shorter delay times compared with a passive one [25]. Caregivers also monitored patients' daily activities, helped manage dietary restrictions, and functioned as a practical scaffold for self-care - particularly for older adults for whom independent management had become physically challenging [24].
+
+However, family involvement also generated its own barriers. When mild or gradual symptoms were present, both patients and those around them tended toward wait-and-see responses, and a passive response from others was identified as an independent predictor of treatment-seeking delay, increasing delay time by nearly 38 hours compared with an active response [25]. Patients' pervasive shame, guilt, and fear of being a burden led them to actively conceal symptoms from family members, particularly those who had witnessed prior cardiac events and responded with heightened anxiety [17]. Paradoxically, family members' visible worry and protectiveness sometimes contributed to patients' emotional distress and could reinforce concealment rather than disclosure [17]. This relational complexity was also captured in the dynamic of conflict and gratitude, whereby, despite genuine appreciation for caregivers' support, sustained dependency generated interpersonal friction and diminished patients' sense of autonomy [24].
+
+Locally embedded social norms also influenced symptom management within everyday relationships. In a qualitative study of older male patients in Japan, self-management was shaped by social obligations that frequently competed with medical recommendations [26]. Adherence to dietary and lifestyle advice was negotiated against contextual demands such as workplace meals, alcohol consumption at social gatherings, and the maintenance of established role identities. Patients tended to adopt a process of trial and error, with selective disclosure of their condition and partial dietary modification rather than strict adherence [26]. These observations indicate that locally specific social norms may operate as additional determinants of self-management alongside family support and caregiver behaviour.
+
+Taken together, these findings indicate that the contribution of family and social context to symptom management in heart failure is neither uniformly supportive nor uniformly obstructive. Its character depends on the emotional climate between patients and caregivers, the severity and visibility of symptoms, and the social and contextual norms that frame what constitutes acceptable help-seeking and disclosure.
+
+Factors Influencing Symptom Management
+
+Symptom management in daily life was shaped by an interplay of individual, social, structural, and technological factors, none of which operated in isolation.
+
+At the individual level, cognitive function was a central determinant of whether perceived symptoms were translated into self-care action. Patients with even mild cognitive impairment demonstrated blunted responses to worsening symptoms and were substantially less likely to initiate care-seeking behaviours compared with cognitively intact counterparts [23]. Illness perception operated alongside cognition as a distinct barrier: patients who attributed symptoms to ageing, fatigue, or temporary states - rather than to heart failure - tended to adopt emotion-focused coping strategies such as denial and avoidance, which structurally delayed care-seeking [19]. Crucially, even when patients sensed that something was not quite right, many were unable to specify what was wrong, and instead attributed their deteriorating condition to changes in diet or medications rather than to worsening disease [27]. This misattribution meant that more than 40% of patients experienced symptoms for at least two weeks before seeking care [27]. Decision-making in this context was rarely analytical; rather, it followed a naturalistic pattern grounded in situation awareness and mental simulation derived from accumulated personal experience [21].
+
+Social factors functioned as both protective and inhibitory forces. When family members drew attention to symptom changes, patients were more likely to seek care early; conversely, families responding passively - whether adopting a wait-and-see approach or not encouraging medical contact - substantially delayed help-seeking [25]. Beyond crisis response, the ongoing presence of family caregivers served as an essential source of practical and emotional support, providing patients with the motivation to sustain daily self-care efforts even amid physical constraints and uncertainty [24]. For patients living alone, this protective function was largely absent, and competing domestic obligations - such as caring for pets or dependants - could directly compete with care-seeking, leading to further delay [19].
+
+Structural and system-level factors compounded individual vulnerabilities. Complex medical access routes, insufficient discharge education, and confusing self-management protocols collectively increased the burden of treatment, eroding patients' capacity for home-based self-care [28,29]. Quantitative evidence from the SYMPACT study demonstrated this burden concretely: among the specific domains of self-care engagement, exercise carried the highest burden score, followed by diet and difficulty with healthcare services - domains in which over half of patients reported receiving no professional guidance [28]. Furthermore, the emotional impact of engaging with self-care regimens showed a moderate-to-strong association with symptom severity, suggesting that the psychological cost of maintaining daily management routines may itself become a barrier to adherence [28]. Importantly, readmission in this context was not primarily a failure of adherence; patients often engaged in a cycle of limit testing, in which uncertain symptom improvement and unclear instructions led to progressive reduction in self-management capacity, and hospitalisation ultimately became a rational choice made from a position of distress rather than negligence [29]. A parallel cycle of despair was also identified: patients who experienced worsening symptoms despite perceived good adherence developed hopelessness and frustration, which further eroded their self-management behaviours [29]. Non-pharmacological self-care, including salt and fluid restriction, daily weighing, and exercise, was similarly constrained by the interacting patient-, condition-, therapy-, and system-level factors captured in the treatment-burden framework [29].
+
+Technological tools emerged as a potential resource for bridging these gaps; however, their integration into daily symptom management remained uneven. Although patients were generally familiar with and used over-the-counter home monitoring devices such as blood pressure cuffs and scales, daily weighing - a cornerstone of heart failure self-management - remained poorly maintained, in part because patients failed to associate it with fluid retention and disease worsening [30]. Barriers to broader technology use included financial costs, mistrust of device-generated information, low digital literacy, privacy concerns, and a strong preference for physician-validated information over independent use of digital tools [30]. Notably, technology acceptance was considerably higher when its use was initiated or endorsed by healthcare providers, suggesting that technology integration must be embedded within relational care rather than offered as a standalone solution [30]. These findings collectively indicate that effective symptom management cannot be achieved through any single strategy but requires multilayered support that simultaneously addresses personal interpretation, relational context, system complexity, and the conditions under which patients can meaningfully and safely engage with technology. 
+
+Knowledge and System Gaps
+
+The studies included in this review collectively reveal persistent gaps at both the individual knowledge level and the healthcare system level, which together sustain a knowledge-action gap - the distance between what patients nominally understand about heart failure and what they can act upon in daily life.
+
+At the level of somatic knowledge, a fundamental problem is the disconnect between explicit disease understanding and embodied symptom awareness. Riegel et al. demonstrated this gap objectively: 44% of patients showed a symptom-hemodynamic mismatch, with objective evidence of fluid retention failing to correspond to subjective symptom perception [16]. Qualitative analysis from the same study identified two distinct response patterns - patients able to interpret and respond appropriately to symptoms were characterised by higher decision-making skill and better quality social support, whereas those who struggled tended to attribute symptoms to comorbidities, await the emergence of expected patterns, and delay treatment for days or more [16]. Underlying this objective-subjective gap is a deficit in somatic awareness itself. Patients often reported a vague sense that “something was not quite right” but were unable to specify the underlying change and commonly misattributed symptoms to diet or medication changes rather than to worsening heart failure, with over 40% experiencing symptoms for at least two weeks before seeking care [27]. The translation of such awareness into action was further blunted in patients with mild cognitive dysfunction, who showed 21.5% worse self-care management and 51% worse consulting behaviours than their cognitively intact counterparts [23].
+
+Shogaki et al.'s phenomenological study extended this insight by revealing that patients could recall pre-hospitalisation bodily changes - including altered urine characteristics, subtle throat discomfort, and diffuse malaise - only when explicitly prompted during the post-recovery period [18]. In daily life, these experiences had remained below the threshold of conscious awareness, absorbed within habitual bodily routines. This finding suggests that somatic knowledge does not develop automatically through disease experience; without active facilitation, the body's early warning signals remain unarticulated and therefore unactionable [18].
+
+Compounding this, post-discharge education practices were insufficiently targeted to support patients' ability to bridge this gap. Prior episodes of acute exacerbation did not reliably translate into improved symptom perception in subsequent episodes; patients tended to re-normalise recurrent symptoms rather than update their interpretive framework [19,20]. Riegel et al. further identified that patients with poor self-care maintenance were not necessarily symptomatic, suggesting that standard educational approaches focused on symptom checklists may fail to develop the body listening skills that characterise more capable self-managers [16]. Shogaki et al. similarly showed that the period immediately following recovery from acute exacerbation represents a unique window for education, during which patients - when asked - could begin to articulate and contextualise their bodily experiences, potentially establishing a foundation for improved symptom perception after discharge [18]. Xu et al. confirmed that deficits in somatic awareness were not consistently addressed by routine heart failure education [15].
+
+At the system level, structural barriers further widened the knowledge-action gap. Healthcare complexity - including competing demands from multiple comorbidities, fragmented follow-up arrangements, and unclear guidance on when to contact providers - contributed substantially to delayed care-seeking even among patients who had recognised symptom changes [29]. These system-level factors interacted with individual knowledge deficits in mutually reinforcing ways: patients uncertain whether their symptoms warranted action were simultaneously navigating a system that provided insufficient behavioural guidance. Beyond these structural factors, the contextual fit of self-care guidance shaped what patients could realistically enact. Sano and Majima illustrated this vividly among older Japanese men with heart failure, who continually negotiated between medical recommendations and locally embedded social obligations. Avoiding meals out with colleagues, drinking at workplace gatherings, and restricting traditional high-sodium foods such as sashimi with soy sauce or pickled dishes proved deeply difficult. Many consequently prioritised social belonging and personal preferences over strict adherence, accepting some risk of decompensation as an acceptable trade-off [26]. Such contextually mediated trade-offs illustrate how self-care guidance developed without attention to local dietary practices, social roles, and gendered expectations may be only partially actionable, narrowing its applicability in heterogeneous populations.
+
+Taken together, these findings indicate that bridging the knowledge-action gap in heart failure requires more than information transfer. Education must be experientially grounded - supporting patients in articulating and connecting their own bodily experiences to their disease - and delivered at strategically optimal moments, particularly during the post-recovery period, when patients are most receptive to reflecting on and reinterpreting their bodily experience [18]. At the system level, contextually responsive guidance and clear behavioural protocols for symptom response are essential if improved awareness is to translate into timely action.
+
+Discussion
+
+This scoping review integrated the findings of 19 studies that explored how patients with heart failure and their families or caregivers experience, detect, and manage symptoms in daily life, and the knowledge gaps that influence these processes. This review revealed that symptom experiences in heart failure are not merely medical or biological events. They are deeply shaped by subjective perceptions, family dynamics, social backgrounds, and healthcare system constraints, such as complex access routes and insufficient discharge education. These intertwined factors demonstrate that symptom management in heart failure is a multidimensional process that goes beyond clinical explanations. The following discussion addresses three perspectives based on the review questions: (1) symptom experiences and detection of worsening signs; (2) individual, social, and contextual factors influencing symptom management; and (3) knowledge and system gaps related to symptom experiences, detection, and responses.
+
+Symptom Experiences and Detection of Worsening Signs
+
+Symptom experiences in patients with heart failure were closely associated with daily restrictions and psychological distress, in addition to typical symptoms such as breathlessness, fatigue, oedema, and sleep disturbance. McHorney et al. [1] reported that these symptoms often interfered with social activities and family interactions and were associated with anxiety and depression. Patients tended to accept such changes as a new normal; however, this acceptance sometimes increased the risk of overlooking worsening signs or delaying medical visits. Fry et al. [31] reported that patients frequently confused early symptoms with other illnesses or ageing, resulting in a delayed response. For patients with multiple comorbidities, it was difficult to determine whether cough or fatigue indicated heart failure deterioration.
+
+Thus, recognising symptoms is not simply sensory awareness but a process that involves cognitive interpretation and adaptation to daily life. Santos et al. [5] defined symptom detection as a complex process of monitoring bodily changes, interpreting their meaning, and linking them to actions, noting that many patients struggle with this process. This review confirmed that symptom recognition is shaped by personal experience and life context rather than physical sensations alone. What patients consider abnormal differs individually and is strongly influenced by their daily routines and past experiences. Therefore, effective support for early detection should respect how patients give meaning to their experiences while helping them transform awareness into concrete self-care behaviours.
+
+While much of the included literature foregrounded barriers to detection, our synthesis also identified experiential learning from prior episodes, decision-making skill coupled with responsive social support, and the post-recovery period as recurrent mechanisms underlying successful detection [16,18,19]. These positive mechanisms suggest that strategies to improve timely symptom response should not focus solely on removing barriers but also on actively strengthening the experiential, relational, and reflective resources through which detection succeeds. Importantly, the included studies did not report formal metrics of detection accuracy, timeliness, or sensitivity; characterising successful detection through such measures remains an important direction for future primary research.
+
+Individual, Social, and Contextual Factors Influencing Symptom Management
+
+Symptom management in patients with heart failure is influenced by individual psychological traits and living conditions, as well as by social resources, contextual factors, and patients' experience of healthcare complexity. Clark et al. [32] demonstrated that successful self-management, such as weight monitoring and salt restriction, was dependent not only on knowledge or motivation but also on family support and relationships with healthcare providers. Thus, self-care is not performed by the patient alone; rather, the availability of daily support strongly affects whether these behaviours can be maintained.
+
+For patients with multiple chronic conditions, complex medication schedules and the need to visit several clinics are often significant barriers [33]. Such burdens can reduce motivation for self-care and increase the risk of worsening symptoms. Symptom management is often perceived as an overly complicated task by older adults and those with limited social resources. Greenhalgh et al. [34] noted that although technologies such as remote monitoring could make symptom management more efficient, some patients perceive these systems as cold care, which undermines a sense of reassurance. This suggests that the introduction of technology does not always align with patients' personal values or expectations of care.
+
+Health-seeking behaviours and self-management were influenced by sex, age, and social background; however, these factors showed inconsistent patterns across studies [35]. Overall, heart failure management is shaped by the interplay between systemic constraints and social contexts, requiring multilayered approaches beyond individual-level interventions.
+
+Knowledge and System Gaps Related to Symptom Experiences, Detection, and Responses
+
+The included studies suggest several recurring gaps in the clinical, cognitive, and contextual understanding of how patients with heart failure experience, detect, and respond to symptoms. These gaps were derived through interpretive synthesis of the included studies, consistent with the scoping review framework; systematic mapping against an established self-care theory would be a valuable direction for future research. Self-management of heart failure involves multiple processes - monitoring, recognition, interpretation, and response - which are inherently difficult for many patients. Patients with low somatic awareness may delay seeking medical attention when their symptoms worsen, which increases the risk of cardiovascular events. When patients lack sufficient knowledge, they may misinterpret breathlessness or fatigue as a result of stress or ageing, hindering appropriate self-care behaviours [5].
+
+Patients with New York Heart Association (NYHA) Class III or IV heart failure tend to become accustomed to their symptoms, leading to a slower recognition of deterioration and delayed hospital visits [36]. This finding highlights the need for further studies to clarify the mechanisms underlying the delay in patients with advanced disease. Moreover, Schumacher et al. [20] reported that even after receiving education, patients continued to normalise their symptoms, indicating that knowledge alone was insufficient for behavioural change. This suggests the presence of cognitive barriers between symptom recognition and action, underscoring the need to improve educational approaches.
+
+Patients' contextual beliefs and social values shape how they understand and respond to symptoms; however, the included studies suggest that these factors have received limited attention in existing heart failure research [37]. Future strategies should focus on understanding patients' contextual and social perspectives and incorporating them into care. Multilayered interventions that combine contextually responsive education and personalised support may be needed to bridge the gap between cognitive understanding and concrete behavioural change.
+
+Limitations
+
+This review has several methodological limitations. First, a formal critical appraisal of included studies was not conducted, in keeping with the aim of mapping the breadth of available evidence; consequently, the synthesis should be read as a descriptive map rather than as a comparative assessment of study quality. Second, inclusion was not stratified by ejection fraction phenotype, as most primary studies did not report phenotype-specific symptom data, and our findings therefore reflect heart failure as a broad clinical entity. Third, eligibility was restricted to peer-reviewed articles in English and Japanese, reflecting the review team's linguistic competencies; evidence from regions whose dominant languages fall outside this scope may be underrepresented, limiting the geographic and cultural diversity of the synthesis.
+
+Conclusions
+
+This scoping review revealed that the processes of experiencing, detecting, and responding to symptoms among patients with heart failure are not merely biological phenomena. They are closely shaped by patients' subjective interpretations, family relationships, and perceptions of healthcare complexity, with social and contextual factors also likely to play a role. Patients often perceive vague and gradually progressing symptoms as part of their daily life. Whether patients notice these signs is shaped not only by medical knowledge but also by the personal meanings and rhythms of everyday living. Symptom management is influenced not only by individual factors such as cognitive function and self-efficacy, but also by social and healthcare-related factors, including family involvement, treatment burden, complexity of care pathways, and attitudes toward technology. Low somatic awareness, delayed care-seeking in advanced cases, and limited attention to social and contextual factors may further contribute to a gap between knowledge and action.
+
+For clinical practice, several practical implications emerge from these findings: educational programs that help counter normalisation bias through family participation or scenario-based learning; consistent post-discharge action plans and clear communication systems; reduction of treatment burden through simplified medication and visit schedules; use of technology in ways that preserve human relationships rather than creating cold care; and individualised support that considers patients' personal and social contexts. Future research should longitudinally examine how patients' meaning-making leads to care-seeking behaviour within family, social, and system contexts, and evaluate multilayered interventions that bridge the gap between recognition and action in symptom management.
+
+Disclosures
+
+Author Contributions
+
+Appendices
+
+Appendix S1
+
+PubMed Search Strategy
+
+Database: PubMed Search date: May 2025 Publication date filter: 1 January 2010 to 30 April 2025 (applied via PubMed's date limit) Language filter: English
+
+Search string: ("heart failure"[MeSH] OR "heart failure"[tiab] OR "cardiac failure"[tiab]) AND ("symptom experience"[tiab] OR "lived experience"[tiab] OR "symptom perception"[tiab] OR "symptom recognition"[tiab] OR "symptom management"[tiab] OR "illness experience"[tiab] OR "patient experience"[tiab] OR "subjective experience"[tiab] OR "symptoms"[tiab]) AND ("daily life"[tiab] OR "everyday life"[tiab] OR "activities of daily living"[MeSH] OR "self care"[MeSH] OR "self-management"[tiab] OR "quality of life"[MeSH] OR "patient perspective"[tiab] OR "patient-centered"[tiab]) AND (English[lang]) NOT ("palliative care"[MeSH] OR "terminal care"[MeSH] OR "hospice care"[MeSH] OR "end of life"[tiab])
+
+Notes: [MeSH] = Medical Subject Heading (controlled vocabulary); [tiab] = title/abstract field tag; [lang] = language filter
+
+Japanese-language literature was retrieved separately via Ichushi-Web using equivalent concept blocks adapted for that database's syntax. Equivalent search strategies were adapted for CINAHL and PsycINFO according to each database’s syntax and indexing system.
+
+Conflicts of interest: In compliance with the ICMJE uniform disclosure form, all authors declare the following:
+
+Payment/services info: This work was supported by JSPS KAKENHI Grant Number 25K13944.
+
+Financial relationships: All authors have declared that they have no financial relationships at present or within the previous three years with any organizations that might have an interest in the submitted work.
+
+Other relationships: All authors have declared that there are no other relationships or activities that could appear to have influenced the submitted work.
+
+Concept and design:  Tomohide Fukuda
+
+Acquisition, analysis, or interpretation of data:  Tomohide Fukuda, Junichi Hosogaya, Yoshie Imai, Yoshie Murakami
+
+Drafting of the manuscript:  Tomohide Fukuda
+
+Critical review of the manuscript for important intellectual content:  Tomohide Fukuda, Junichi Hosogaya, Yoshie Imai, Yoshie Murakami
+
+Supervision:  Yoshie Murakami
+
+
+References
+
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+2 Symptom burden in heart failure: assessment, impact on outcomes, and management Heart Fail Rev Alpert CM Smith MA Hummel SL Hummel EK 25 39 22 2017 27592330 10.1007/s10741-016-9581-4 PMC6042838
+3 Patients experience of fatigue in advanced heart failure Contemp Nurse Walthall H Floegel T Boulton M Jenkinson C 71 82 55 2019 30961451 10.1080/10376178.2019.1604147
+4 A systematic review of patient heart failure self-care strategies J Cardiovasc Nurs Harkness K Spaling MA Currie K Strachan PH Clark AM 121 135 30 2015 24651683 10.1097/JCN.0000000000000118
+5 Symptom perception in heart failure: a scoping review on definition, factors and instruments Eur J Cardiovasc Nurs Santos GC Liljeroos M Dwyer AA 100 117 19 2020 31782668 10.1177/1474515119892797
+6 Symptom perception in heart failure - interventions and outcomes: a scoping review Int J Nurs Stud Santos GC Liljeroos M Dwyer AA 103524 116 2021 32063295 10.1016/j.ijnurstu.2020.103524
+7 Addressing social determinants of health in the care of patients with heart failure: a scientific statement from the American Heart Association Circulation White-Williams C Rossi LP Bittner VA 0 63 141 2020 10.1161/CIR.0000000000000767 32349541
+8 2021 ESC guidelines for the diagnosis and treatment of acute and chronic heart failure Eur Heart J McDonagh TA Metra M Adamo M 3599 3726 42 2021 34447992 10.1093/eurheartj/ehab368
+9 Scoping studies: towards a methodological framework Int J Soc Res Methodol Arksey H O'Malley L 19 32 8 2005
+10 Scoping studies: advancing the methodology Implement Sci Levac D Colquhoun H O'Brien KK 69 5 2010 20854677 10.1186/1748-5908-5-69 PMC2954944
+11 PRISMA extension for scoping reviews (PRISMA-ScR): checklist and explanation Ann Intern Med Tricco AC Lillie E Zarin W 467 473 169 2018 30178033 10.7326/M18-0850
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+13 From breathless to failure: symptom onset and diagnostic meaning in patients with heart failure - a qualitative study BMJ Open Taylor CJ Hobbs FD Marshall T Leyva-Leon F Gale N 0 7 2017 10.1136/bmjopen-2016-013648 PMC5353318 28283487
+14 The experience of fatigue as a distressing symptom of heart failure Heart Lung Jones J McDermott CM Nowels CT Matlock DD Bekelman DB 484 491 41 2012 22652166 10.1016/j.hrtlng.2012.04.004
+15 Using vignettes to understand heart failure self-care J Clin Nurs Xu J Arruda S Gallo JJ 3554 3560 27 2018 29943481 10.1111/jocn.14581 PMC6448145
+16 A mixed methods study of symptom perception in patients with chronic heart failure Riegel B Dickson VV Lee CS 107 114 47 2018 10.1016/j.hrtlng.2017.11.002 PMC5857218 29304990
+17 The heartache of living with failure: the experience of people with chronic heart failure Collegian Palmer K Bowles KA Morphet J 286 292 30 2023
+18 Lived bodily experience of worsening heart failure from acute exacerbation to recovery: a phenomenological study Kobe J Med Sci Shogaki J Fukuda A Matsuba S Saito N Miyawaki I 0 55 70 2024 10.24546/0100489736 PMC11216660 38936877
+19 The role of illness perceptions in delayed care-seeking in heart failure: a mixed-methods study Int J Nurs Stud Ivynian SE Ferguson C Newton PJ DiGiacomo M 104644 150 2024 38016267 10.1016/j.ijnurstu.2023.104644
+20 Heart failure self-management and normalizing symptoms: an exploration of decision making in the community Heart Lung Schumacher C Hussey L Hall V 297 303 47 2018 29699706 10.1016/j.hrtlng.2018.03.013
+21 Qualitative analysis of naturalistic decision making in adults with chronic heart failure Nurs Res Riegel B Dickson VV Topaz M 91 98 62 2013 23154659 10.1097/NNR.0b013e318276250c
+22 Self-care strategies and interventions needed in patients with heart failure: from patient perspectives - a qualitative study Eur J Cardiovasc Nurs Heo S Moser DK Lennie TA 540 546 20 2021 34008023 10.1093/eurjcn/zvaa033
+23 Blunted responses to heart failure symptoms in adults with mild cognitive dysfunction J Cardiovasc Nurs Lee CS Gelow JM Bidwell JT Mudd JO Green JK Jurgens CY Woodruff-Pak DS 534 540 28 2013 23013837 10.1097/JCN.0b013e31826620fa
+24 A qualitative study on the self-care experiences of people with heart failure West J Nurs Res Min D Lee J Ahn JA 646 652 45 2023 37085988 10.1177/01939459231169102
+25 Factors associated with delay in seeking care for acute decompensated heart failure J Cardiovasc Nurs Sethares KA Sosa ME Fisher P Riegel B 429 438 29 2014 24088620 10.1097/JCN.0b013e3182a37789
+26 Self-management of congestive heart failure among elderly men in Japan Int J Nurs Pract Sano M Majima T 0 24 2018 10.1111/ijn.12653 29667310
+27 Symptom perceptions and self-care behaviors in patients who self-manage heart failure J Cardiovasc Nurs Reeder KM Ercole PM Peek GM Smith CE 0 7 30 2015 10.1097/JCN.0000000000000117 PMC4116472 24335834
+28 SYMptoms in chronic heart failure imPACT on burden of treatment (SYMPACT): a cross-sectional survey ESC Heart Fail Austin RC Schoonhoven L Koutra V Richardson A Kalra PR May CR 2279 2290 9 2022 35451208 10.1002/ehf2.13904 PMC9288776
+29 Heart failure home management challenges and reasons for readmission: a qualitative study to understand the patient's perspective J Gen Intern Med Sevilla-Cazes J Ahmad FS Bowles KH 1700 1707 33 2018 29992429 10.1007/s11606-018-4542-3 PMC6153210
+30 Heart failure patients' perceptions and use of technology to manage disease symptoms Telemed J E Health Hall AK Dodd V Harris A McArthur K Dacso C Colton LM 324 331 20 2014 24483939 10.1089/tmj.2013.0146 PMC3968876
+31 The implications of living with heart failure; the impact on everyday life, family support, co-morbidities and access to healthcare: a secondary qualitative analysis BMC Fam Pract Fry M McLachlan S Purdy S Sanders T Kadam UT Chew-Graham CA 139 17 2016 27670294 10.1186/s12875-016-0537-5 PMC5037641
+32 Determinants of effective heart failure self-care: a systematic review of patients' and caregivers' perceptions Heart Clark AM Spaling M Harkness K Spiers J Strachan PH Thompson DR Currie K 716 721 100 2014 24548920 10.1136/heartjnl-2013-304852
+33 Understanding patients' experiences of treatment burden in chronic heart failure using normalization process theory Ann Fam Med Gallacher K May CR Montori VM Mair FS 235 243 9 2011 21555751 10.1370/afm.1249 PMC3090432
+34 Understanding heart failure; explaining telehealth - a hermeneutic systematic review BMC Cardiovasc Disord Greenhalgh T A'Court C Shaw S 156 17 2017 28615004 10.1186/s12872-017-0594-2 PMC5471857
+35 Non-symptom-related factors contributing to delay in seeking medical care by patients with heart failure: a narrative review J Card Fail Gravely S Tamim H Smith J Daly T Grace SL 779 787 17 2011 21872149 10.1016/j.cardfail.2011.05.003 PMC4490893
+36 Delay in seeking medical care for worsening heart failure symptoms: predictors and association with cardiac events Eur J Cardiovasc Nurs Lin CY Hammash M Miller JL Schrader M Mudd-Martin G Biddle MJ Moser DK 454 463 20 2021 33580784 10.1093/eurjcn/zvaa032
+37 Culture and the understanding of advanced heart failure: a mixed-methods systematic review Collegian Alassoud B Johnston B Hogg K 459 470 27 2020
diff --git a/corpus/psychology/text/c911583b7551d2fd.txt b/corpus/psychology/text/c911583b7551d2fd.txt
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@@ -0,0 +1,351 @@
+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Membranes (Basel)
+Journal ID: Membranes (Basel)
+NLM Journal ID: 101577807
+Journal ID: membranes
+
+Membranes
+
+EISSN: 2077-0375
+Publisher: Multidisciplinary Digital Publishing Institute (MDPI)
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC13515136
+PMID: 42646228
+DOI: 10.3390/membranes16080253
+Article ID: membranes-16-00253
+Article version: 1
+Subjects: Article
+
+Separation of Taurine and Sodium Sulfate from Simulated Mother Liquor by Electrodialysis and Process Optimization
+
+Zhu Huiting Writing – original draft Data curation Methodology Conceptualization Software Validation
+Cao Douyan Validation Investigation Data curation
+https://orcid.org/0000-0002-2773-7200 Zhao Jigang Writing – review & editing Conceptualization Investigation Visualization Supervision *
+Koter Stanisław Academic Editor
+School of Chemical Engineering, East China University of Science and Technology, Shanghai 200237, China; zhu_huiting829@163.com (H.Z.); y30230233@mail.ecust.edu.cn (D.C.)
+* Correspondence: zjg@ecust.edu.cn
+Electronic publication date: 2026 Jul 23
+Publication date: 2026 Aug
+Volume: 16
+Issue: 8
+Electronic Location ID: 253
+Received 2026 Jun 21; Revised 2026 Jul 20; Accepted 2026 Jul 21
+Copyright: © 2026 by the authors.
+Copyright year: 2026
+License: Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Keywords: electrodialysis, taurine, sodium sulfate, desalination, process integration
+
+Funding: This research received no external funding.
+
+Ÿ==============================Ÿ
+To address the high energy demand and product losses associated with separating taurine from sodium sulfate (Na2SO4) in the ethylene oxide route to taurine, electrodialytic desalination of a simulated taurine/Na2SO4 mother liquor was investigated. The effects of applied voltage, circulation flow rate, and initial feed concentration on the desalination rate, product purity, taurine recovery, current efficiency, specific energy consumption, and membrane productivity were evaluated. Ion-transport behavior was further examined using COMSOL Multiphysics® 6.3. At 14 V, a circulation flow rate of 200 L/h, and initial taurine and Na2SO4 concentrations of 100 and 68 g/L, respectively, the process achieved a taurine purity of 99.8% and a recovery of 98.9%. The specific electrical energy consumption of the electrodialysis unit was 0.56 kWh/kg Na2SO4, and the membrane productivity was 0.49 kg Na2SO4/(m2·h). One of the key findings of this work is that the low-salt stage plays a dominant role in process economics. This observation led to a simple endpoint-control strategy. The ED operation is stopped when the Na2SO4 concentration in the dilute compartment drops to about 2 g/L. This avoids prolonged operation under inefficient conditions and reduces ED energy consumption by 16.5%. Within the binary simulated system and the defined cost boundary, the proposed process provided a higher taurine recovery and a lower estimated separation cost than the conventional crystallization route. These results demonstrate the laboratory-scale feasibility of electrodialysis for desalting simulated taurine mother liquor.
+
+1. Introduction
+
+Taurine (2-aminoethanesulfonic acid) is a sulfur-containing amino acid with several physiological functions and is widely used in infant formula, functional beverages, pharmaceuticals, and feed additives [1,2,3]. With the growing demand for health-related products and fine chemicals, increasingly stringent requirements are being placed on the purity, recovery, and environmental performance of taurine production processes [4]. Taurine is currently produced mainly by the ethylene oxide route, which uses readily available raw materials and is well established at the industrial scale. However, this route generates a substantial amount of sodium sulfate (Na2SO4) as a by-product. Efficient separation of taurine and Na2SO4 with low energy consumption and minimal product loss is therefore essential for increasing product recovery, reducing process energy demand, and alleviating the wastewater-treatment burden.
+
+Conventional taurine separation processes rely mainly on phase-change operations, including evaporation, concentration, cooling crystallization, and recrystallization. These processes separate taurine from Na2SO4 primarily on the basis of differences in solubility and its temperature dependence. However, as reported in studies on amino acid solubility and crystallization behavior, the presence of inorganic salts can significantly influence the solubility and nucleation kinetics of amino acids through salting-in/out effects and co-crystallization, which may compromise separation performance in practical operations [5,6]. In industrial practice, multiple crystallization or recrystallization steps are often required to ensure product purity, while mother liquor recycling is used to improve the overall recovery [7]. These measures increase the evaporation duty, energy consumption, and wastewater-treatment burden. Conventional crystallization therefore involves an inherent trade-off among product purity, recovery, and energy efficiency, which constrains the development of more sustainable and intensified taurine production processes.
+
+Ion-exchange-based technologies have recently been investigated for separating taurine from Na2SO4 [8,9,10]. Electrodialysis (ED) is an electrically driven membrane process in which ions are selectively transported through ion-exchange membranes, and it has been applied to the desalination of organic acids, amino acids, and fermentation broths [11,12,13,14]. In a taurine/Na2SO4 solution, Na+ and SO42− migrate through cation-exchange membranes (CEMs) and anion-exchange membranes (AEMs), respectively, into the concentrate compartment. Near neutral pH, taurine has a degree of dissociation below 10−5 and exists predominantly as a zwitterion with a low net charge, which favors its retention in the dilute compartment. ED may therefore reduce the number of phase-change steps required in conventional crystallization, thereby lowering the separation energy and improving taurine recovery.
+
+Early studies on ED separation of taurine from Na2SO4 demonstrated the technical feasibility of this approach. Konarev reported that introducing ED into taurine production markedly improved product quality, eliminated energy-intensive operations, and removed poisonous gas emissions [15]. In an early investigation, Zhao et al. achieved a taurine purity of 98.5% and a recovery of 78.1% from a taurine/Na2SO4 mixed solution using ED [16]. More recently, Eliseeva and Kharina comprehensively reviewed electromembrane desalination of amino acid solutions, examining the influence of various mineral cations (Na+, K+, NH4+) and anions (NO3−, SO42−, Cl−) on ion transport and membrane current–voltage characteristics [17]. Studies on phenylalanine-salt systems have further revealed that electroconvection at overlimiting current modes can increase amino acid loss, and that membrane ion-exchange resin content significantly affects separation efficiency [18].
+
+Studies on ED applied to the taurine/Na2SO4 system have been primarily limited to feasibility validation. The effects of operating parameters on mass-transfer behavior under high salt concentrations remain insufficiently understood. Endpoint regulation of the ED process coupled with crystallization for energy consumption control has not been reported, and the specific advantages of ED over crystallization have not been quantitatively evaluated. In this study, conventional ED was used to desalt a binary simulated taurine/Na2SO4 mother liquor. The effects of applied voltage, circulation flow rate, and initial feed concentration on the desalination rate, taurine purity and recovery, specific energy consumption, and membrane productivity were systematically evaluated. Ion-transport behavior was examined using a COMSOL Multiphysics® model, and the effect of endpoint selection on process energy consumption was analyzed. We hypothesize that the deterioration of ED performance is mainly governed by concentration-dependent transport limitation rather than membrane selectivity loss. Therefore, identifying the critical salt concentration and establishing an endpoint-control strategy may provide a more energy-efficient route. The results provide experimental data for evaluating ED as a potential separation step in the production of taurine by the ethylene oxide route.
+
+2. Materials and Methods
+
+2.1. Materials and Equipment
+
+Taurine (TAU, analytical grade) was supplied by Luofu Pharmaceutical Technology Co., Ltd., Jiaxing, China. Anhydrous sodium sulfate (Na2SO4, purity ≥ 99.9%) was obtained from Shanghai Titan Scientific Co., Ltd., Shanghai, China. Deionized water was produced in-house. Formaldehyde, phenolphthalein, and a standardized NaOH solution (0.1 mol/L) were purchased from Shanghai Macklin Biochemical Technology Co., Ltd., Shanghai, China.
+
+An SED-30 laboratory-scale electrodialysis stack (Shanghai Sanji New Material Co., Ltd., Shanghai, China) was used. The stack was equipped with polyethylene (PE)-based anion-exchange membranes functionalized with quaternary ammonium groups and PE-based cation-exchange membranes functionalized with sulfonic acid groups. The spacer used in the stack is of a square-mesh support type with a grid size of 1 cm × 1 cm and a filament width of 1 mm. The electrode material is Ti/Pt (titanium-coated platinum). The principal equipment specifications are listed in Table 1.
+
+2.2. Electrodialysis Setup and Procedure
+
+The experiments were conducted in batch ED mode. The dilute reservoir was filled with 1 L of a mixed solution containing taurine and Na2SO4 at a fixed mass ratio of 1:0.68 to simulate the industrial mother liquor from the ethylene oxide route. The concentrate reservoir was initially filled with 1 L of deionized water. The interconnected electrode loop serving both the anode and cathode was filled with 1 L of a 3 wt.% Na2SO4 solution to limit pH changes caused by electrode reactions. Deionized water was used in the concentrate compartment at the beginning of each batch experiment. Although this practice inevitably increased the initial electrical resistance of the stack and may have temporarily reduced the current efficiency, it was adopted to establish a well-defined initial state with zero background salt concentration. This allowed the salt flux across the membranes to be quantified directly from conductivity changes in the concentrate stream. Figure 1 schematically shows the separation principle of taurine and Na2SO4 by electrodialysis.
+
+The circulation flow rates in the dilute and concentrate loops were set to the same value ((50–200 L/h) as specified for each experiment), whereas the electrode-loop flow rate was fixed at 100 L/h. After the flow rates had stabilized, the initial conductivity, temperature, and pH were recorded. The DC power supply was then switched on at the prescribed voltage (8–16 V). During operation, Na+ and SO42− through the CEM and AEM, respectively, into the concentrate compartment, while taurine was largely retained in the dilute compartment. Conductivity, pH, temperature, stack voltage, and current were recorded every 5 min. Each run was terminated when the current decreased to 0.1 A. At the end of the run, 100 g samples were collected from both the dilute and concentrate reservoirs, dried at 80 °C for 4 h and subsequently at 60 °C for 12 h, and sealed for analysis. Each experiment was performed in triplicate. Desalination-rate data are reported as medians, whereas recovery, purity, energy consumption, and membrane productivity are reported as mean values. The desalination rate is reported as the median value of triplicate runs because the conductivity readings exhibited relatively large fluctuations toward the end of the experiments, particularly when the salt concentration became low, and the use of the mean would have introduced bias due to these endpoint deviations. The median, being less sensitive to extreme fluctuations, provides a more representative description of the desalination trend.
+
+2.3. Limit Current Density Measurement
+
+The limiting current density (ilim) was determined using the current–voltage curve method [19]. A 2 L solution containing 68 g/L Na2SO4 (100 g/L taurine) corresponding to the salt concentration in the simulated mother liquor, was prepared. The dilute and concentrate reservoirs were each filled with 1 L of this solution, and the outlets were cross-connected to maintain approximately constant concentrations during the measurement. The electrode loop was filled with 1 L of 3 wt.% Na2SO4 solution. The applied voltage was increased stepwise from 3 V to higher values in increments of 1 V and the steady-state current was recorded at each voltage. As shown in Figure 2, the intersection associated with the marked change in slope of the current–voltage curve corresponded to an approximate limiting current density of 16.24 mA/cm2 at 15.4 V.
+
+The ilim measured under constant-concentration conditions provides a practical reference for selecting the applied voltage, rather than a fixed threshold that applies uniformly throughout the entire batch desalination process. In actual operation, the dilute compartment concentration decreases continuously, and the ilim varies accordingly. Therefore, a current density that exceeds the measured ilim under steady-state conditions may not necessarily cause concentration polarization when the bulk concentration is high, while a current density below the measured ilim may still cause polarization when the salt concentration becomes low. The actual current density evolution during each run is therefore the more relevant indicator for assessing polarization.
+
+Above approximately 15 V, the current–voltage curve exhibits a second slope increase, which deviates from the classical plateau behavior expected for simple salt solutions. At overlimiting current densities, water dissociation at the membrane surface generates H+ and OH− ions, which interact with taurine molecules through protonation/deprotonation, increasing the number of charged species available for ion transport [20]. This barrier effect allows the current to rise further despite mass-transfer limitations.
+
+2.4. COMSOL Simulation
+
+2.4.1. Model Setup and Parameters
+
+A two-dimensional mass-transfer model of the ED cell was developed using the Electrodeposition Module in COMSOL Multiphysics®. Ion transport was described by the Nernst–Planck equation (Equation (1)), and ionic mobility (um,i) was calculated from the Nernst–Einstein relationship (Equation (2)) [21]:(1) Ji = −Di (dCidx + ziCiFRTdφdx + Cidlnγidx)
+
+(2) um,i=DiRT
+
+where Ji (mol/(m2·s)) is the total flux of ion i, Di (m2/s) is the diffusion coefficient, γi is the activity coefficient, Ci (mol/m3) the concentration, zi is the charge number, F the Faraday constant (96,485 C/mol), R is the gas constant [8.314 J/(mol∙K)], T the temperature (K), and dφ/dx is the electric-potential gradient. In the present model, the activity-coefficient term in Equation (1) was retained only for completeness of the theoretical framework. For practical implementation, ideal solution behavior was assumed (γi = 1) and the activity-coefficient gradient was neglected. This simplification is acceptable for qualitative trend analysis, which is the primary purpose of the simulation in this study.
+
+Figure 3a shows a schematic two-dimensional ED unit. The region enclosed by the dashed rectangle was selected as the computational domain, as illustrated in Figure 3b. Donnan equilibrium was imposed at the membrane/solution interfaces, and charge conservation was represented using the water-based electroneutrality condition. The computational domain of the two-dimensional model is shown in Figure 3b, covering one ED unit cell (one dilute channel flanked by cation- and anion-exchange membranes and adjacent concentrate channels) [22]. The boundary layers adjacent to the membrane surfaces are not pre-defined but emerge from the simulation as regions of steep concentration gradients, reflecting the onset of concentration polarization. The positive flux direction is defined as from the dilute to the concentrate side (left to right in Figure 3b).
+
+Taurine transport is not explicitly simulated because taurine is predominantly zwitterionic and electrically neutral under the experimental pH conditions, and its retention is confirmed by the high purity and recovery values obtained from titration. The principal model parameters are listed in Table 2, including the ionic diffusion coefficients [23], membrane thickness, channel width, and operating variables corresponding to the experimental ranges.
+
+2.4.2. Mesh Independence
+
+Mesh independence test was evaluated by monitoring the average Na+ concentration at the CEM surface on the cathode side. As shown in Figure 4, the calculated concentration became effectively independent of the mesh when the number of elements exceeded 8250. Accordingly, a mesh containing 8250 elements was used in subsequent simulations to balance numerical accuracy and computational cost.
+
+The COMSOL model presented here was developed as a qualitative interpretation tool to visualize the ion-transport behavior predicted by the Nernst–Planck equations under different operating conditions. The model has not been quantitatively validated against experimental data, and its outputs are intended to illustrate the trends observed in the experiments rather than to provide accurate quantitative predictions. Quantitative validation would require detailed inputs such as membrane transport properties, boundary-layer thickness, and concentration-dependent diffusion coefficients which are beyond the scope of the present study.
+
+2.5. Data Analysis
+
+To quantify the Na2SO4 concentration, a calibration curve was first established. A series of Na2SO4 standard solutions was prepared, and the Na+ concentration of each solution was accurately determined by ICP-MS. The corresponding Na2SO4 concentration was then calculated from the Na+ content. The conductivity of each standard solution was also measured using a calibrated conductivity meter. A regression equation was fitted between the measured conductivity and the Na2SO4 concentration, as shown in Equation (3) (R2 = 0.99):(3) C = 176.19−176.061+(σ/182.19)0.93
+
+where C (g/L) is the Na2SO4 concentration and σ (mS/cm) the conductivity. In subsequent ED experiments, the Na2SO4 concentration was determined from the measured conductivity using this calibration curve, without repeating ICP-MS analysis for each sample.
+
+Taurine was quantified by titration with standardized NaOH solution in the presence of formaldehyde. Taurine is a zwitterionic amino acid and cannot be directly titrated with a strong base. When formaldehyde is added, it reacts with the amino group (-NH2) of taurine to form N-methylol derivatives, which eliminates the basicity of the amino group and releases protons. This allows the sulfonic acid group (-SO3H) to be titrated with standardized NaOH solution [24]. The endpoint was determined by a color change in phenolphthalein. Taurine purity (W, %) and recovery (X, %) were calculated by:(4) W=ΔV1−ΔV0CNaOH×Mm0100%
+
+(5) X=1−m2×W1m1×100%
+
+where ΔV1 and ΔV0 (L) are the volumes of NaOH solution consumed for the sample and the blank respectively; CNaOH is the NaOH concentration (0.1 mol/L); M is the molar mass of taurine (125.147 g/mol); m0 (g) is the sample mass (0.2 g); m1 (g) is the initial mass of taurine in the dilute compartment; m2 (g) is the total solute mass recovered from the concentrate compartment; and W1 (%) is the taurine mass fraction in the concentrate compartment determined by titration. The recovery (X, %) is calculated as the fraction of taurine retained in the dilute compartment.
+
+The method was validated under the experimental conditions. The average recovery was 100.2% (RSD = 0.42%, n = 3), and the RSD for repeated measurements was below 0.5%. These results confirm that the titration method is reliable and suitable for taurine quantification in this study.
+
+Current efficiency (CE, %), specific energy consumption for Na2SO4 removal (EC, kJ/kg Na2SO4) and membrane productivity [MP, kg Na2SO4/(h·m2)] were calculated by [25]:(6) CE =∆n·e·F/N∫0 t  I dt
+
+(7) EC=∫0 t U·I dt/m
+
+(8) MP=3600·m/(t·A·N)
+
+where n (mol) is the amount of transferred Na+ or SO42−, e is the charge number, N is the number of cell pairs (10), I (A) is the current, U (V) is the stack voltage, t (s) is the operating time, A (m2) is the effective membrane area of one membrane sheet, and m (kg) is the mass of Na2SO4 mass in the concentrate compartment at the end of the run. In this case, the average Na2SO4 flux was used to represent membrane productivity.
+
+The estimated separation cost (USD/kg taurine) included electricity, steam (for subsequent concentration/crystallization), and membrane replacement. The membrane price was 220 USD/m2 based on a supplier quotation, and the assumed membrane service life was 5 years. The membrane-replacement cost (MC, USD/kg taurine) was calculated as follows:MC = (220 × 2 × 0.68)/(5 × 8000 × MP)(9)
+
+where MP is the membrane productivity [kg Na2SO4/(m2·h)], and “8000” is the assumed annual operating time (h), “0.68” represents the mass ratio of Na2SO4 to taurine in the feed (taurine: Na2SO4 = 1:0.68), The factor “×2” accounts for the fact that each cell pair in the electrodialysis stack consists of two membranes: one cation-exchange membrane and one anion-exchange membrane. Electricity and steam prices were taken as 0.1 USD/kWh and 37 USD/t, respectively, based on representative industrial prices in first-tier Chinese cities.
+
+3. Results and Discussion
+
+3.1. Effect of Applied Voltage
+
+At a baseline circulation flow rate of 150 L/h, the feed to the dilute compartment contained 68 g/L Na2SO4 and 100 g/L of taurine. The applied voltage was varied from 8 to 16 V (8, 10, 12, 14, and 16 V) to evaluate its effect on the separation performance.
+
+As shown in Figure 5a, the desalination rate increased as the applied voltage increased from 8 to 14 V. The simulated Na+ flux profiles in Figure 6 are presented as qualitative illustrations of the effect of applied voltage on the ion transport. The nearly flat regions at 0.0004 and 0.0013 m correspond to the ion-exchange membranes, whereas the regions with changing slopes on either side represent the membrane/solution boundary layers. While the simulations show a clear increase in Na+ flux with increasing unit voltage (from 1 to 3 V), consistent with the experimental desalination trends, the absolute flux values should not be interpreted as validated predictions due to the simplified nature of the model and the lack of quantitative calibration against the present experimental system.
+
+When the voltage was further increased to 16 V, the desalination rate decreased. This behavior cannot be explained fully by the simplified ion-migration model and was therefore interpreted in conjunction with current density. To further examine the role of current density, the current density during each desalination run was recorded and plotted against time (Figure 5d). The peak current density increased with increasing applied voltage, which is expected from Ohm’s law. At 8–12 V, the current density curves remained relatively stable throughout the run, indicating that ion transport proceeded without significant mass-transfer limitation. At 14 V and 16 V, however, the curves became much steeper, reflecting a more rapid decline in current density as desalination progressed. The super-linear increase in current at higher voltages is characteristic of the overlimiting current regime in ion-exchange membrane systems. Water dissociation and electroconvection at the membrane/solution interface generate additional charge carriers and enhance mass transfer, respectively, leading to a current rise that exceeds the linear Ohm’s law prediction [20].
+
+Notably, although 16 V gave the highest peak current density among all tested voltages, it did not result in a higher desalination rate than 14 V (Figure 5a). This apparent contradiction suggests that the additional current at 16 V did not contribute effectively to salt removal; instead, a considerable fraction of the applied current was consumed by side reactions such as water dissociation at the membrane/solution interfaces. This behavior is a typical manifestation of concentration polarization: once the operation exceeds the limiting current density, further voltage increase enhances parasitic processes rather than ion migration, leading to a decrease in current efficiency and an overall loss of desalination performance. In contrast, at 14 V, the balance between driving force and mass transfer was more favorable, resulting in the highest effective desalination rate among the conditions tested [26,27].
+
+Within the investigated voltage range, 14 V therefore provided a comparatively high desalination rate. As shown in Figure 5b, the differences in product purity among the voltage conditions were less than 0.2 percentage points, and all purities exceeded 99.5%. The highest measured purity was 99.7% at 14 V. The small variation among the voltage conditions may be attributable to slight differences in the endpoint reached in each run. The taurine recovery at 14 V was 98.7%, and no monotonic relationship between recovery and voltage was observed. Figure 7 indicates that taurine loss was affected by both operating time and current. The data in Figure 7 were collected from the run at 10 V, which was selected as an intermediate voltage level among the tested range. A higher voltage shortened the separation time and may therefore have reduced passive diffusive loss of taurine [28]; however, it also increased the current and may have promoted taurine transport associated with ion migration. These competing effects are consistent with the observed variation in taurine recovery.
+
+Figure 5c shows that the applied voltage affected both the specific energy consumption and membrane productivity. The energy consumption per unit mass of Na2SO4 removed increased with voltage. This trend is likely associated with Joule heating: higher currents generate more resistive heat in the membranes and solution, thereby reducing current efficiency. The solution temperature increased slightly with increasing applied voltage (Table 3). The observed temperature rise ranged from 0.3 °C (at 8 V) to 1.4 °C (at 16 V), consistent with the expected Joule heating effect. However, given the small magnitude of these changes and the fact that all temperatures remained well below the membrane manufacturer’s recommended limit (40 °C), the thermal effect is unlikely to have significantly influenced membrane performance or separation efficiency under the tested conditions [29].
+
+A paired t-test between the 8 V and 16 V groups gave p > 0.05, indicating that the temperature differences observed across the voltage range were not statistically significant at the 95% confidence level. This suggests that the thermal effect was minor under the present operating conditions. Therefore, the decline in current efficiency can also be attributed to other factors. Although the current increased with applied voltage, the current efficiency decreased slightly at higher voltages because a larger fraction of the applied current may be consumed by water dissociation and counter-ion transport rather than by Na2SO4 removal. Second, the higher current density at elevated voltages may have promoted concentration polarization near the membrane surfaces, increasing the membrane resistance and thus the energy required per unit of salt removed. Joule heating was a minor side-effect rather than a primary contributor to the observed increase in energy consumption. The dominant factor governing the voltage-dependence of energy consumption was therefore the trade-off between increased driving force and reduced current efficiency. In electrodialysis, temperature influences both membrane conductivity and ion mobility [30]. Higher temperatures generally increase ionic diffusivity and reduce solution viscosity, which can enhance ion transport across the membrane and improve current efficiency. However, as shown in Table 3, the solution temperature in all experiments remained below 40 °C, which is within the safe operating range specified by the membrane manufacturer. A portion of the additional energy at higher voltages may also be dissipated through electrode overpotential and ohmic losses at the electrode/solution interface [31], as well as through water dissociation associated with concentration polarization. The dominant factor governing the voltage-dependence of energy consumption was therefore the trade-off between increased driving force and reduced current efficiency.
+
+Increasing the applied voltage also shortened the separation time substantially, thereby reducing the membrane area required to achieve a specified production capacity. Within an appropriate voltage range, increasing the voltage can therefore reduce the membrane cost per unit mass of product.
+
+For an illustrative annual taurine production capacity of 500 t and an annual operating time of 8000 h, the production rate would be 62.5 kg taurine/h, and the Na2SO4 removal rate would be 42.5 kg/h. The estimated ED separation costs under these conditions are summarized in Table 4. Based on the separation performance and the estimated electricity and membrane replacement costs, 14 V gave the lowest combined cost among the tested voltages within the defined accounting boundary. This cost estimation considers only electricity and membrane replacement, and does not include other capital or operating costs.
+
+3.2. Effect of Circulation Flow Rate
+
+At an applied voltage of 14 V and an initial Na2SO4 concentration of 68 g/L in the dilute feed, the circulation flow rate was varied among 50, 100, 150, and 200 L/h (corresponding to linear velocities of 1.5, 3.1, 4.6, and 6.2 cm/s, respectively). The effects of circulation flow rate on the desalination profile, product quality and economic indicators are shown in Figure 8. Increasing the flow rate had only a minor effect on the overall desalination rate, although a slight increase was observed during the initial stage, when the concentrate compartment contained deionized water. The simulation results in Figure 9 indicate that flow velocity had a limited effect on the ion flux but reduced the boundary-layer thickness, consistent with the experimental trends. According to the Nernst–Planck framework, a higher flow velocity decreases the diffusion-boundary-layer thickness and accelerates ion transport from the bulk solution to the membrane surface [32]. The taurine purity consequently increased slightly with flow rate (Figure 8b). The taurine recovery at 50 L/h was lower than those obtained at the higher flow rates. This result may be associated with weaker hydrodynamic mixing and a longer residence time of taurine near the membrane interface, which could increase its probability of crossing the membrane.
+
+As shown in Figure 8c, increasing the circulation flow rate slightly increased the electrical energy consumption. Nevertheless, 200 L/h provided the highest taurine purity (99.8%) and recovery (98.9%) together with a comparatively high membrane productivity, and it was therefore selected for subsequent experiments. At this flow rate, the membrane-surface linear velocity was 6.2 cm/s. For process scale-up, the membrane-surface linear velocity, rather than the volumetric flow rate alone, should be used as the principal hydrodynamic scaling parameter. The effect of flow rate on separation performance was weaker than that of applied voltage; however, excessively low flow rates should be avoided because they may increase mass-transfer limitations within the stack.
+
+3.3. Effect of Initial Feed Concentration
+
+At a circulation flow rate of 150 L/h and an applied voltage of 14 V, the initial Na2SO4 concentration in the feed was varied among 34, 42.5, 51, 59.5, and 68 g/L. The taurine/Na2SO4 mass ratio was maintained at 1:0.68 in all experiments. The concentration-dependence experiments were conducted at a circulation flow rate of 150 L/h, which was the same condition used in the voltage optimization experiments to maintain a consistent hydrodynamic baseline.
+
+Figure 10 shows the effect of the initial feed concentration on ED performance. Because the initial salt loads differed among the experimental groups, the desalination curves alone could not be used to compare the intrinsic desalination rates directly. Transient simulations were therefore performed (Figure 11). The simulation results indicated that the desalination rate increased with initial concentration. As with the voltage simulations, the transient desalination profiles shown in Figure 11 are intended for qualitative interpretation of the concentration effect trends and have not been quantitatively validated against the present experimental data. Consequently, although the initial Na2SO4 concentration was doubled from 34 to 68 g/L, the time required to reach the experimental endpoint increased by only approximately 15 min rather than doubling. Comparison of Figure 5a, Figure 8a and Figure 10a show that desalination rate remained relatively stable at high salinity but decreased at low salt concentrations.
+
+As shown in Figure 10b, the taurine recovery varied non-monotonically with feed concentration. Increasing the feed concentration exerted competing effects on the separation. a higher concentration increased the mass-transfer driving force and ion flux and reduced the solution resistance, resulting in a higher average current and a faster desalination rate (Figure 12). On the other hand, at high concentrations, the increased osmotic pressure and weaker Donnan exclusion may reduce membrane permselectivity [33,34], enhance water transport, and increase taurine loss, thereby decreasing product purity and recovery. Because the taurine/Na2SO4 mass ratio was held constant, both solute concentrations changed simultaneously, which may have contributed to the rebound in recovery at the highest concentration. Additional experiments in which the taurine concentration is held constant while only the Na2SO4 concentration is varied are required to isolate the effect of salt concentration on taurine loss.
+
+Within the investigated range, an initial Na2SO4 concentration of 68 g/L provided a strong mass-transfer driving force without a pronounced loss of selectivity. Considering the desalination rate, product quality, and membrane productivity (Figure 10c), 68 g/L Na2SO4 was selected as the feed concentration for the subsequent experiments.
+
+3.4. Separation Endpoint and Process-Control Analysis
+
+At 14 V, a circulation flow rate of 200 L/h (corresponding to a membrane-surface linear velocity of 6.2 cm/s), and initial concentrations of 68 g/L Na2SO4 and 100 g/L taurine, the taurine purity and recovery were 99.8% and 98.9%, respectively. The specific electrical energy consumption was 2022.3 kJ/kg Na2SO4 (0.56 kWh/kg Na2SO4) and 0.49 kg Na2SO4/m2·h. Additional experiments were conducted under the optimized operating conditions. Figure 13 shows the evolution of current efficiency and the conductivities of the dilute and concentrate compartments during ED.
+
+The current efficiency was substantially lower at the beginning and end of the batch than during the middle stage. The maximum current efficiency, 93.5% during 10–15 min, was observed when the conductivities of the two compartments were similar. The low initial current efficiency was attributed primarily to the high electrical resistance of the deionized water initially present in the concentrate compartment. For continuous operation, the salt concentration in the concentrate compartment should be maintained at a level corresponding to a conductivity above 15 mS/cm to avoid excessive resistance and low current efficiency.
+
+A decrease in current efficiency near the end of batch operation is difficult to avoid completely. Because the final product is crystalline taurine, the subsequent crystallization step can be operated so that trace Na2SO4 remains in the mother liquor rather than co-crystallizing with taurine. Terminating ED before the desalination efficiency decreases sharply can therefore improve equipment utilization and reduce energy consumption. On the basis of the dilute-conductivity curve and current-efficiency profile in Figure 13, 30 min was selected as the preferred endpoint for this system. At this time, the dilute conductivity was 1.27 mS/cm, corresponding to an Na2SO4 concentration of 1.93 g/L. Setting the endpoint at approximately 2 g/L Na2SO4 reduced the ED energy consumption by 16.5% relative to continued operation to the original endpoint.
+
+To implement this endpoint-control strategy, the subsequent evaporation–crystallization step should be adjusted so that the solution is not evaporated to complete dryness. Instead, a small amount of water should be retained to keep part of the Na2SO4 in the liquid phase, and the concentrated mother liquor can then be recycled to the ED step. This strategy may support high taurine purity and recovery while enabling closed-loop mother-liquor circulation. Its feasibility was demonstrated only for the binary simulated taurine/Na2SO4 system. The present study was conducted with a binary simulated system. Industrial taurine mother liquor typically contains additional impurities such as sodium isethionate, sodium iminodisulfonate, ethylene glycol, and polyethylene glycol [33]. These impurities may affect the ED process through several mechanisms. First, studies on amino acid electrodialysis have shown that prolonged contact between ion-exchange membranes and organic solutes can lead to structural changes in the membrane material and irreversible performance decay [17]. Second, the presence of additional ionic species (sodium iminodisulfonate) may compete with Na+ and SO42− for transport through the membranes, potentially reducing the selectivity for salt removal and increasing taurine loss. Third, the accumulation of non-volatile impurities in the recycled mother liquor during closed-loop operation may require additional purification steps to maintain process stability. Therefore, before industrial implementation, the long-term stability of membrane performance, effective cleaning protocols, and impurity accumulation management must be further investigated using real mother liquor or impurity-spiked simulated solutions [35].
+
+3.5. Comparison with Conventional Crystallization
+
+The selected ED process followed by evaporation drying was compared with a conventional multistage crystallization process on the basis of an annual taurine production capacity of 500 t [9]. The raw synthesis mother liquor contained taurine and Na2SO4 at a mass ratio of 1:0.68. For the crystallization route, the recycled mother liquor contained 20% of the initial taurine mass, whereas the ED feed was diluted to a taurine mass fraction of 8.6% on the basis of the selected operating conditions. The results calculated per kilogram of taurine product are summarized in Table 5. A crystallization data from an industrial process package and calculated by the authors. ED total energy = ED electrical energy (0.56 kWh/kg) + evaporation energy (7.02 kWh/kg). Evaporation energy was estimated from water latent heat assuming 100% thermal efficiency. Auxiliary energies are not included. Within the defined accounting boundary, the ED route provided a higher taurine recovery and lower estimated energy consumption and separation cost.
+
+As shown in Table 5, most of the energy consumption of the ED route arose from the subsequent evaporation step (7.02 kWh/kg taurine). The product obtained by direct evaporation drying after ED had a slightly lower purity than the recrystallized product from the conventional route and could be subjected to an additional polishing crystallization step if required. Within the stated accounting boundary, which excluded labor, maintenance, cleaning, and waste-liquor treatment, the ED route increased taurine recovery by 7.4 percentage points, reduced the specific energy consumption by 2.7 kWh/kg taurine, and lowered the estimated separation cost by 0.08 USD/kg taurine compared with conventional crystallization. However, this comparison is simplified and does not include auxiliary energy or long-term membrane replacement costs.
+
+To assess the robustness of the economic evaluation, a simple sensitivity analysis was performed on the key assumptions listed above (Table 6). Each parameter was varied individually within a reasonable range while keeping all others at their baseline values, and the resulting change in the estimated separation cost was recorded.
+
+As summarized in Table 6, the separation cost is most sensitive to steam price and membrane lifetime: increasing the steam price increases the cost by 25%, while reducing the membrane lifetime from 5 to 3 years increases the cost by 8.3%. In contrast, the ED separation cost is relatively insensitive to electricity price membrane price and annual operating hours have a moderate impact (+2.1%). Within the selected variation ranges, the ED separation cost remained consistently lower than that of conventional crystallization.
+
+4. Conclusions
+
+The laboratory-scale ED process was evaluated for separating taurine from Na2SO4 in a binary simulated mother liquor. Under the selected conditions (an applied voltage of 14 V, a circulation flow rate of 200 L/h, an initial Na2SO4 concentration of 68 g/L, and an initial taurine concentration of 100 g/L), the process achieved a taurine purity of 99.8% and a recovery of 98.9%. Compared with the conventional route within the defined accounting boundary (Table 5), the calculated taurine recovery increased by 7.4 percentage points.
+
+Beyond process optimization, this study provides a practical strategy for process control: using approximately 2 g/L Na2SO4 in the dilute compartment as the separation endpoint. Unlike most previous ED studies that focus primarily on parametric optimization, we have quantitatively demonstrated that the low-salt stage is the dominant factor governing process energy efficiency. Setting the endpoint at 2 g/L Na2SO4 avoided inefficient operation at low salt concentrations and reduced the ED-unit energy consumption by approximately 16.5%. This endpoint-control strategy is simple, requires no additional equipment, and can be readily implemented in industrial practice. The estimated specific energy consumption and separation cost were lower by 2.7 kWh/kg taurine and 0.08 USD/kg taurine, respectively, than those of the conventional crystallization route. Coupling ED with controlled evaporation-crystallization may also reduce the direct discharge of salt-containing mother liquor. If higher product purity is required, a polishing crystallization step can be incorporated.
+
+These results demonstrate the feasibility of electrodialytic desalination for a binary simulated taurine/Na2SO4 stream and indicate that an ED-crystallization process warrants further evaluation using real mother liquor and long-term continuous operation. In industrial taurine mother liquor, organic impurities and inorganic scaling may cause membrane fouling. Although various cleaning strategies exist, complete restoration of membrane performance is often difficult. Membrane lifetime under such conditions remains unknown and requires long-term pilot studies. Finally, it is acknowledged that the COMSOL model presented in this study has not been quantitatively validated against experimental data. The model is intended as a qualitative tool to support the interpretation of experimental trends rather than as a predictive simulation. Future studies with more comprehensive model parameters and systematic experimental validation could extend the quantitative capabilities of the modeling approach.
+
+Author Contributions
+
+Conceptualization, H.Z.; methodology, H.Z.; software, H.Z.; validation, H.Z., D.C.; investigation, D.C.; data curation, H.Z. and D.C.; writing—original draft preparation, H.Z.; writing—review and editing J.Z.; supervision, J.Z. All authors have read and agreed to the published version of the manuscript.
+
+Institutional Review Board Statement
+
+Not applicable.
+
+Informed Consent Statement
+
+Not applicable.
+
+Data Availability Statement
+
+The data supporting the findings of this study are included in the article. Additional numerical data are available from the corresponding author upon reasonable request.
+
+Conflicts of Interest
+
+The authors declare no conflicts of interest.
+
+Figure 1 Schematic of the electrodialysis process for separating taurine and Na2SO4. The orange arrows indicate the flow in the dilute compartment, and the blue arrows indicate the flow in the concentrate compartment.
+
+Figure 2 Determination of the limiting current density from the current–voltage curve. The red and black dashed lines are auxiliary lines indicating the intersection point where the slope of the current–voltage curve changes.
+
+Figure 3 (a) Schematic of one electrodialysis unit; (b) two-dimensional COMSOL model. Orange arrows indicate the flow in the dilute compartment; blue arrows indicate the flow in the concentrate compartment; black arrows indicate the direction of ion migration.
+
+Figure 4 Mesh-independence test.
+
+Figure 5 Effects of applied voltage on (a) the desalination profile, (b) taurine purity and recovery, and (c) specific energy consumption and membrane productivity, (d) current density.
+
+Figure 6 Simulated effect of applied voltage on the Na+ flux.
+
+Figure 7 Relationship between taurine loss, operating time, and current (data obtained at 10 V).
+
+Figure 8 Effects of circulation flow rate on (a) the desalination profile, (b) taurine purity and recovery, and (c) specific energy consumption and membrane productivity.
+
+Figure 9 Simulated effect of circulation velocity on the Na+ flux.
+
+Figure 10 Effects of initial feed concentration on (a) the desalination profile, (b) taurine purity and recovery, and (c) specific energy consumption and membrane productivity.
+
+Figure 11 Simulated effect of initial concentration on the desalination profile.
+
+Figure 12 Simulated effect of initial concentration on the Na+ flux.
+
+Figure 13 Changes in current efficiency and compartment conductivity during electrodialysis.
+
+membranes-16-00253-t001_Table 1 Table 1 Specifications of the SED-30 electrodialysis system.
+
+Parameters	Value	
+Cell pairs	10	
+Spacer thickness (mm)	0.75	
+Spacer size (cm2)	16 × 21	
+Membrane thickness (mm)	0.10–0.12	
+The commercial name of AEM	AC	
+The commercial name of CEM	CC	
+Membrane resistance of AEM (Ω∙cm2)	4.0–5.0	
+Membrane resistance of CEM (Ω∙cm2)	2.0–3.0	
+Effective membrane size (cm2)	12 × 17.5	
+Permselectivity (%)	96	
+Operating temperature range (°C)	<40	
+Operating pH range	1–9	
+Rectifier Output	30 V DC × 10 A	
+
+membranes-16-00253-t002_Table 2 Table 2 Parameters used in the electrodialysis model.
+
+Parameters	Value	
+Na+ diffusion coefficient (m2/s)	1.33 × 10−9	
+SO42− diffusion coefficient (m2/s)	1.06 × 10−9	
+Temperature (K)	298	
+Domain Height (m)	0.1	
+Membrane thickness (mm)	0.1	
+Compartment width (mm)	0.75	
+membrane ion concentration (mol/m3)	1000	
+
+membranes-16-00253-t003_Table 3 Table 3 Solution temperature before and after electrodialysis at different applied voltages (mean ± SD, n = 3).
+
+Voltage (V)	Initial Temperature (°C)	Final Temperature
+(°C)	Temperature Increase (°C)	
+8	24.8 ± 0.2	25.1 ± 0.2	0.3 ± 0.1	
+10	23.5 ± 0.0	23.8 ± 0.2	0.3 ± 0.1	
+12	22.1 ± 0.1	22.6 ± 0.3	0.5 ± 0.2	
+14	24.1 ± 0.2	25.1 ± 0.2	1.0 ± 0.2	
+16	24.6 ± 0.1	26.0 ± 0.3	1.4 ± 0.3	
+
+membranes-16-00253-t004_Table 4 Table 4 Effect of applied voltage on the estimated electrodialysis separation cost.
+
+Voltage (V)	Electricity Cost (USD/kg Taurine)	Membrane Cost (USD/kg Taurine)	Total Cost
+(USD/kg Taurine)	
+8	0.021	0.086	0.107	
+10	0.030	0.049	0.079	
+12	0.036	0.034	0.070	
+14	0.041	0.027	0.068	
+16	0.050	0.030	0.080	
+
+membranes-16-00253-t005_Table 5 Table 5 Comparison of the conventional crystallization and electrodialysis routes. Mass- and cost-based quantities are reported per kilogram of taurine.
+
+Parameter	Crystallization	Electrodialysis	
+Taurine purity (%)	100	99.8	
+Taurine recovery (%)	91.3	98.9	
+Waste generation (kg/kg taurine)	1.08	0 1	
+Specific energy consumption (kJ/kg taurine)	10.1	7.4	
+Electricity cost (USD/kg taurine)	0.12	0.04	
+Steam cost (USD/kg taurine)	0.44	0.41	
+Membrane cost (USD/kg taurine)	-	0.03	
+Estimated separation cost (USD/kg taurine)	0.56	0.48	
+1 “0” waste refers to no direct discharge of salt-containing mother liquor under the defined closed-loop assumption and does not imply zero liquid discharge.
+
+membranes-16-00253-t006_Table 6 Table 6 Sensitivity analysis of key economic parameters on the estimated ED separation cost.
+
+Parameter	Variation	Crystallization Cost (USD/kg Taurine)	Change from Baseline	ED Cost (USD/kg Taurine)	Change from Baseline	
+Baseline	-	0.56	-	0.48	-	
+Electricity price	+30%	0.60	7.1%	0.49	2.1%	
+Steam price	+30%	0.69	17.9%	0.60	25%	
+Membrane lifetime	3 year	0.56	-	0.52	8.3%	
+Membrane price	+30%	0.56	-	0.49	2.1%	
+Annual operating hours	6000 h	0.56	-	0.49	2.1%	
+
+Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.
+
+
+References
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+2. Cao T.Y. Zhang W.Y. Wang Q. Wang C. Ma W. Zhang C. Ge M. Tian M. Yu J. Jiao A. Cancer SLC6A6-mediated taurine uptake transactivates immune checkpoint genes and induces exhaustion in CD8+ T cells Cell 2024 187 2288 2304 10.1016/j.cell.2024.03.011 38565142
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+13. Martí C.M.C. Ruiz G.M. Pérez H.V. On the selective transport of mixtures of organic and inorganic anions through anion-exchange membranes: A case study about the separation of nitrates and citric acid by electrodialysis Sep. Purif. Technol. 2025 354 128951 10.1016/j.seppur.2024.128951
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diff --git a/corpus/psychology/text/cda8efbd91c71f26.txt b/corpus/psychology/text/cda8efbd91c71f26.txt
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+++ b/corpus/psychology/text/cda8efbd91c71f26.txt
@@ -0,0 +1,5 @@
+SocialPulse: On-Device Detection of Social Interactions in Naturalistic Settings Using Smartwatch Sensing
+
+Social interactions are fundamental to well-being, yet automatically detecting them in daily life—particularly using wearables—remains underexplored. Most existing systems are evaluated in controlled settings, focus primarily on in-person interactions, or rely on restrictive assumptions (e.g., requiring multiple speakers within fixed temporal windows), limiting generalizability to real-world use. We present an on-watch interaction detection system designed to capture diverse interactions in naturalistic settings. A core component is a foreground speech detector trained on a public dataset. Evaluated on over 100,000 labeled foreground speech and background sound instances, the detector achieves a balanced accuracy of 85.51%, outperforming prior work by 5.11%.
+
+We evaluated the system in a real-world deployment (N=38), with over 900 hours of total smartwatch wear time. The system detected 1,691 interactions, 77.28% were confirmed via participant self-report, with durations ranging from under one minute to over one hour. Among correct detections, 81.45% were in-person, 15.7% virtual, and 1.85% hybrid. We further developed a 15-second window-level audio-only model that enables faster interaction prediction, achieving a balanced accuracy of 90.39% and a sensitivity of 91.01% on 33,698 labeled windows. These results demonstrate the feasibility of real-world interaction sensing and open the door to adaptive, context-aware systems responding to users’ dynamic social environments.
diff --git a/corpus/psychology/text/ced807f9c47254fb.txt b/corpus/psychology/text/ced807f9c47254fb.txt
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@@ -0,0 +1,451 @@
+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Biomed Eng Online
+Journal ID: Biomed Eng Online
+NLM Journal ID: 101147518
+
+BioMedical Engineering OnLine
+
+EISSN: 1475-925X
+Publisher: BMC
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC13374303
+PMID: 42458460
+DOI: 10.1186/s12938-026-01598-3
+Article ID: 1598
+Article version: 1
+Subjects: Research
+
+Computational mechanobiological model combining epiphyseal, apophyseal, and appositional growth and inner bone remodeling of the juvenile femur
+
+https://orcid.org/0000-0002-4428-4848 Lipphaus Andreas andreas.lipphaus@rub.de
+1 2
+Tröbs Ralf-Bodo 3
+Klimek Matthias 1 4
+Selkmann Sascha 1
+Witzel Ulrich 1
+1 https://ror.org/04tsk2644 grid.5570.7 0000 0004 0490 981X Biomedical Engineering Lab, Ruhr University Bochum, Bochum, Germany
+2 Clinic of Pediatric Surgery, St. Mary’s Hospital Witten, Witten, Germany
+3 Department of General-, Visceral- and Pediatric Surgery, St. Vinzenz Krankenhaus Paderborn, Paderborn, Germany
+4 https://ror.org/01856cw59 grid.16149.3b 0000 0004 0551 4246 Clinic for Trauma, Hand and Reconstructive Surgery, Institut für Muskuloskelettale Medizin, University Hospital Münster, Münster, Germany
+Electronic publication date: 2026 Jul 15
+Publication date: 2026
+Volume: 25
+Electronic Location ID: 94
+Received 2025 Jul 27; Accepted 2026 Jun 21
+Copyright: © The Author(s) 2026
+Copyright year: 2026
+License: Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Keywords: Biomechanics, Finite element, Bone growth, Endochondral ossification, Growth plate, Femoral neck isthmus, In silico modeling, Pediatric orthopedics
+
+Funding: https://doi.org/10.13039/501100001659 Deutsche Forschungsgemeinschaft 445465815
+
+Funding: Ruhr-Universität Bochum (1007) Open Access funding enabled and organized by Projekt DEAL.
+
+issue-copyright-statement: © BioMed Central Ltd., part of Springer Nature 2026
+
+Ÿ==============================Ÿ
+In silico models for simulating bone growth based on mechanical or non-mechanical epigenetic factors are widely used. In this study, a well-known mechanobiological model, which states that octahedral shear stress accelerates longitudinal bone growth and hydrostatic stress retards it, is applied to a finite element model of the femur of an 8-year-old boy. Proximal and distal epiphyseal plates as well as the growth plate of the greater trochanter, cartilaginous growth at the femoral isthmus, and appositional bone growth are included in the model. Furthermore, changes in the density of the cancellous bone in the metaphyses are modeled based on Wolff's law using compressive stresses as the mechanical stimulus. Muscle forces during a dynamic gait cycle were determined for nine discrete loading cases by optimizing to minimize bending stress. The highest stresses in the femoral shaft were determined as medial compressive stresses with a maximum of −33.2 MPa. Highest internal axial load in the shaft was 985 N during loading response. The simulated bone growth resulted in an increase in femur length of 23.7 mm and a decrease in femoral neck angle by −1.4°, anteversion angle by −2.4°, and lateral distal femur angle by −1.6° per year. Growth of the apophysis of the greater trochanter resulted in an unchanged articulo-trochanteric distance. The bone remodeling led to an increase in bone density, particularly in the medial proximal metaphysis. The consideration of different growth mechanisms allowed a comprehensive simulation of femoral growth with high agreement with anthropometric data. Possible applications are the simulation of the correction of deformities.
+
+Introduction
+
+In children, longitudinal bone growth occurs at the cartilaginous epiphyseal plates by endochondral ossification [1]. These growth plates are located at the end of the long bones between the metaphysis and the epiphysis and can be divided into horizontal zones. Next to the epiphysis, the resting zone contains stem-like cells and secretes morphogens influencing the alignment of the proliferative chondrocytes and inhibiting their terminal differentiation [2]. The finite proliferative capacity of resting chondrocytes leads to growth deceleration and finally epiphyseal fusion by growth plate senescence as children age [3]. The resting zone is followed by the proliferation zone, where chondrocytes rapidly divide, form columns of flattened, disc-shaped chondrocytes, and synthesize new matrix [4]. Toward the end of the proliferative zone, chondrocytes enlarge and take a more spherical shape forming the hypertrophic zone [5]. Two main hypotheses of ossification at the end of the hypertrophic zone involve either the apoptosis of hypertrophic chondrocytes followed by invasion of osteoblast precursors by the vascular system or transdifferentiation of chondrocytes to osteoblasts [6]. Appositional growth increases the thickness or diameter of the bone. In this mechanically stimulated process, osteoblasts deposit new matrix on the periosteal and endosteal surfaces and differentiate into osteocytes [7].
+
+Bone growth in children is orchestrated by various mechanical [8, 9] and non-mechanical factors like inflammation [10], growth [11] and sex hormones [12], and genetics [13]. Several studies investigated the rate of longitudinal growth in the growth plates as a function of static or dynamic loading. The Hueter–Volkmann law states that epiphyseal growth is increased by tensile stress and retarded by compressive stress acting at the growth plate [14]. While in some animal models only minor femoral length differences are reported due to different physiological dynamic loadings [15], a growth retardation of 52–63% is observed in paralyzed embryonic chicks due to a lack of mechanical stimulation [16]. In animal models, a linear relationship between sustained tensile and compressive stresses and acceleration and deceleration of growth was observed [17]. This effect is due to reduced numbers of both proliferative and hypertrophic chondrocytes and increases approximately linearly with time [18]. The effect of cyclic or intermittent loading is still not fully understood: while some studies found no significant bone length differences with different exercises in rats [19], others reported an increase in the length of radius and ulna in the dominant arm of professional tennis players [20]. Smith experimentally determined the principal stress directions in the epiphyses and concluded that the stress trajectories often are orthogonal to the direction of bone growth [21]. A second hypothesis is that due to the low stiffness of the cartilage under load, a deformity occurs and that growth proceeds in the direction of the distortion of the cartilage columns as long as this is too small to lead to tissue damage [22–24]. Pauwels proposed that deformities, especially after fractures, lead to asymmetric growth by uneven loading of the epiphyseal plate and thereby works to correct these deformities [25]. Carter and Wong proposed a mechanobiological model that epiphyseal growth is inhibited by dynamic hydrostatic compression and accelerated by octahedral shear stress. They defined the osteogenic index as the sum of maximum octahedral shear stress and minimum hydrostatic stress overall load cases and calculated the resulting growth as the product of the osteogenic index and the mechanical growth rate [26].
+
+Endochondral growth primarily causes functional adaptations through angular adaptations till the fusion of the growth plates. In contrast, bone formation and resorption optimize bone density and volume, especially in childhood, but also in adults. Appositional growth occurring at the periosteum is influenced by local strains [27]. Higher loading is associated with greater periosteal growth [28]. Thereby, the bone's diameter increases, and not only the axial strength but in particular the strength of bone in bending and torsion is increased. Indeed, previous finite element simulations suggested that torsional load is the most important stimulus in forming the medullary cavity [29]. In adults, periosteal formation is seen in regions stressed with more than 20 MPa [30] or 1500 με [31]. Above a threshold of about 4000 με overload resorption occurs and bone density decreases. In growing bones exercise leads to a higher cortical area, while disuse results in decreased cortical area compared to normal developing bones [32]. However, due to the lower Young's modulus, higher deformations occur [33]. In addition, the threshold of bone formation is lower. A study in adolescent rats has reported significant and prolonged bone formation with strains of 850 με [34]. Overall, mechanically controlled growth patterns allow the bone to adapt to its mechanical needs. Thereby, bending stresses can be reduced to achieve lightweight design [30, 35, 36].
+
+Based on finite element models, several computational approaches were established to simulate bone growth due to metabolic and mechanobiological signaling. Early models depicted either the biochemical or the mechanobiological component of growth. Heegard et al. used a pure mechanobiological model to simulate prenatal joint development [37], bone straightening [38], and epiphyseal growth of the distal femur [39]. Based on this, the development of bone deformities resulting from pathologies such as cerebral palsy [40], cam deformity [41], and developmental dysplasia of the hip [42–44] has been simulated. A similar approach was developed by Stokes et al. and uses tensile or compressive axial stresses to describe the longitudinal bone growth [45]. Alonso et al. presented a mechanobiological model simulating epiphyseal growth and remodeling after virtual implantation of staples for hemiepiphysiodesis [46]. In the latest models, reaction–diffusion equations of morphogens and mechanobiological approaches were combined to model the embryonic development of synovial joints and the femur [47–49]. Also, changes in bone density of the trabecular bone in the proximal femur of children have been modeled [50, 51], resulting in an increase in bone mineral density on the medial side of the femoral neck [52].
+
+The proximal femur has three growth plates: the growth plate located between the metaphysis and the femoral head, the trochanteric growth plate, and the femoral neck isthmus [53]. Because chondral growth is faster than periosteal growth, the cartilage of the femoral neck isthmus is necessary to compensate for length growth and shape the femoral metaphysis. The growth of the trochanteric apophysis affects the statics of the hip joint as the hip resultant force is mainly defined by the body weight and the hip abductors attached to the greater trochanter. The force resultant at the greater trochanter is formed by forces through a muscle sling of the vastus lateralis with the opposing gluteus medius and minimus and the iliotibial band [54], reducing bending in both the femoral shaft and near the hip joint. Growth of the greater trochanter results in a reduction of the femoral neck–shaft angle [55], and subsequently, epiphysiodesis of the greater trochanter has been described as a treatment for infantile coxa vara [56]. The morphological changes during growth allow the bone to maintain physiological loading and a constant cartilage load [57].
+
+Current in silico models either focus on very early phases of bone development or focus on a single growth mechanism. For transition into clinical practice, a more comprehensive model is needed. As the greater trochanter plays an important role in the biomechanics of the hip, it is of interest to include its growth in in silico models of bone development. Therefore, this study aims to develop a mechanobiological model of the growth of the juvenile femur including all growth plates, appositional growth of the femoral shaft, and inner remodeling. Stresses and internal axial loading are calculated during gait and muscle forces are optimized to reduce bending stresses. For validation, growth predicted by the in silico model is compared to several in vivo anthropometric measurements.
+
+Results
+
+Optimization of muscle forces
+
+Before the growth simulation was initiated, muscle forces were calculated using a bending minimization approach (Table 1). Two peaks in axial load at midshaft, the first during loading response and the second during terminal stance (Fig. 1) were associated with peaks in muscle forces of the gluteal muscles and the iliopsoas and iliacus muscles, respectively. Table 1 Resultant muscle forces in Newton (N) for all nine load cases in an 8-year-old boy using a bending minimization approach. Muscle forces are rounded to full numbers. Forces below 1 N are considered as no muscle activation (-). Additionally, resulting axial loading is given for all load cases
+
+Muscle/load case	1	2	3	4	5	6	7	8	9	
+Adductor brevis	4	–	–	–	–	–	–	–	32	
+Adductor longus	1	–	–	–	–	–	–	2	34	
+Adductor magnus	10	52	–	–	–	–	–	–	–	
+Biceps femoris	45	–	–	–	–	18	96	64	37	
+Gastrocnemius lateralis	11	–	–	–	–	55	125	37	–	
+Gastrocnemius medialis	9	–	–	–	–	123	372	32	–	
+Gemellus	-	2	6	5	3	9	9	–	12	
+Gluteus maximus	11	188	235	152	35	2	–	–	-	
+Gluteus medius	–	131	609	368	282	266	206	109	23	
+Gluteus minimus	–	10	64	27	27	59	60	57	12	
+Iliacus	–	–	–	–	–	137	880	524	244	
+Pectineus	–	–	–	–	–	–	–	–	5	
+Piriformis	–	14	62	17	8	29	67	12	29	
+Psoas	–	–	–	–	–	3	208	64	169	
+Quadratus femoris	11	4	2	–	–	–	–	–	–	
+Vastus intermedius	–	23	47	28	13	–	–	–	–	
+Vastus lateralis	–	100	191	94	16	–	–	–	–	
+Vastus medialis	–	45	86	43	8	–	–	–	–	
+Axial loading	316	727	985	575	586	656	924	592	206	
+
+Fig. 1 Course of the axial load for all nine load cases. The respective phases of the gait cycle are shown accordingly. Axial forces range between 200 and 985 N at midshaft with peaks at the end of loading response and terminal stance
+
+Finite element analysis of the physiological superposition of all nine load cases in the initial model of the femur of an 8-year-old shows that 3rd principal stresses are highest in the proximal femur on the medial side (Fig. 2a, b). In contrast, compression in the distal femur is mostly homogeneously distributed. In the shaft, compression is minimal on the anterior (−10.9 MPa) and lateral side (−11.7 MPa), whereas higher values are predicted on the posterior (−21.1 MPa) and medial (−33.2 MPa) side. 1st principal stresses are opposite to the compressive stresses (Fig. 2c, d). Values are generally lower with tensile stresses of 10 MPa anterior, 21.1 MPa lateral, 6.6 MPa posterior, and 5 MPa medial. Before optimization of muscle forces but including the iliotibial band and using physiological boundary conditions bending stresses are 24 MPa in the sagittal and 24.9 MPa in the frontal plane. After optimization, bending stresses in the frontal plane decrease by 78% while increase in the frontal plane by 9%. Loading results in axial forces between 200 and 985 N at midshaft with minimal shear loading. Axial loadings peak at the end of loading response and terminal stance. Hip and knee joint resultant is comparable to subject-specific musculoskeletal models in literature [58].Fig. 2 Views of superposition of stresses of all nine load cases illustrate loading of cortical bone: 3rd principal stresses σ3 in MPa in frontal (a) and sagittal (b) views highlighting compressive stresses and 1st principal stresses σ1 in MPa in frontal (c) and sagittal (d) views highlighting tensile stresses in cortical bone. The stresses are greatest at the proximal metaphysis. In the femoral shaft, 3rd principal stresses peak medial and 1st principal stresses lateral. Most parts of the cortical bone exhibit compressive stresses between −6 and −27 MPa
+
+Cross sections show corresponding stresses in the trabecular bone (Fig. 3). In the frontal section, the highest compression is observed in the proximal femur on the medial side, while tension peaks at the lateral side. As in cortical bone, the trabecular bone of the distal femur is more uniformly stressed. Of note, the compression near the distal growth plate is slightly higher anterior and lateral. Other than that, in the sagittal section compressive and tensile stresses are mostly homogeneously distributed.Fig. 3 Sections of superposition of stresses of all nine load cases illustrate loading of trabecular bone: 3rd principal stresses σ3 in MPa in frontal (a) and sagittal (b) sections highlighting compressive stresses and 1st principal stresses σ1 in MPa in frontal (c) and sagittal (d) sections highlighting tensile stresses in cortical bone. At the proximal metaphysis, 3rd principal stresses peak medial and 1st principal stresses lateral. Most parts of the trabecular bone exhibit compressive stresses between −0.25 and −2.25 MPa
+
+Simulation of physiological growth
+
+The predicted growth direction of the proximal femur is highly dependent on Young’s modulus of the growth plate. An increase in the b/a ratio was associated with a greater decrease in the neck–shaft angle, while the decrease in the anteversion angle was smaller at higher values (Fig. 4). Lower values of the Young’s modulus of the epiphyseal plates resulted in a greater reduction in both the anteversion angle and the neck–shaft angle. The LDFA showed with a b/a ratio of 0.3 a decrease for a low Young’s modulus and an increase for higher stiffness. For higher b/a ratios, higher stiffness resulted in a more pronounced decrease of the LDFA. An appositional growth corresponding to radiological data was only achieved at a threshold value for periosteal bone formation of 0 MPa, matching observations in animal models. For the following calculations, a Young’s modulus of 10 MPa, b/a ratio of 0.5, and a threshold for periosteal apposition of 0 MPa are chosen.Fig. 4 Plots of the absolute change in ° per year in NSA (a), anteversion angle (b) and LDFA (c) depending on the Young´s modulus and b/a ratio of 0.3 (blue), 0.5 (orange), 0.7 (yellow), and 1 (purple). As the b/a ratio increased, the reduction in the neck-shaft angle became more pronounced, whereas the decrease in the anteversion angle became smaller. Lower Young’s modulus values were associated with greater reductions in both angles
+
+The growth rate as the sum of the biological baseline and the osteogenic index is calculated for all growth plates (Fig. 5). The growth plate of the proximal femur exhibits a centric distribution of the growth rate. In the growth plate of the distal femur, the growth rate shows a homogeneous distribution.Fig. 5 Top view of the proximal hypertrophic (a) and proliferative (b) zone as well as the distal proximal hypertrophic (c) and proliferative (d) zone showing the growth rate in mm/month
+
+The simulation predicted an increase in both bone length and diameter in accordance with anthropometric data (Table 2). The ATD remains constant. The NSA decreased on average by 0.1° per month, the anteversion angle by 0.2°. The LDFA decreased by 0.1° per month. Table 2 Changes in the morphometries per year as predicted by the in silico model compared to anthropometric data
+
+Measurement	In silico model	Anthropometric data	
+Bone length	 + 23.7 mm	 + 20.8 mm [59]	
+Neck–shaft angle	− 1.4°	−1.1° [60]	
+Articulo-trochanteric distance	0 mm	0 mm [61]	
+Lateral distal femoral angle	− 1.6°	0° [62]	
+Shaft diameter (Anterior–Posterior/Medial–Lateral)	0.7 mm/0.8 mm	1 mm [63]	
+Anteversion angle	− 2.3°	−0.7° [64]	
+
+A second model without modeling the growth of the greater trochanter reduced the decrease of the NSA to 75%. In our model, closure of the apophyseal plate of the greater trochanter results in a higher NSA, matching in vivo data [55, 56].
+
+Compressive stresses are highest at the medial side of the femoral shaft (Fig. 6, a). The bone apposition rate is 20, 40, 20, and 60 µm/month anterior, posterior, lateral and medial. This results in a decrease of bending stresses in the sagittal plane of 9% while bending in the frontal plane is essentially unchanged.Fig. 6 Compressive stresses in transversal section of the femoral shaft (a). Increased density due to inner remodeling in the proximal femur. Darker areas correspond to an increased bone mineral density (b). Periosteal bone formation is predicted posteriormedially and an increase of cancellous bone density medially
+
+Inner remodeling predicted an increase in bone density on the medial side of the proximal femur given by an increase of Young’s modulus (Fig. 6, b). These areas correspond to regions exhibiting higher compression.
+
+Discussion
+
+Several computational models of femoral long bone growth have been presented in the literature [65–70]. These models provide valuable insights into the principles of the mechanobiology of bone growth. Furthermore, the development of various pediatric deformities can be explained [40–44]. However, they are limited to certain aspects of growth. Complex deformities, such as resulting from fractures, are corrected by a combination of altered growth of all growth plates and bony remodeling [71].
+
+This study investigates stresses acting on the juvenile femur during gait using finite element analysis. A well-established mechanobiological model that uses octahedral shear stresses and hydrostatic stresses as the mechanical input values is employed to calculate the endochondral growth of the proximal and distal femur as well as that of the greater trochanter. Appositional growth of the femoral shaft and inner remodeling of the trabecular bone are also included.
+
+The calculated stresses depend to a large extent on the boundary conditions. The question of bending stress on bones has long been the subject of controversial debate in biomechanics. For adults, Sverdlova and Witzel [72] and later Lutz et al. [73] showed that the femoral shaft is primarily subjected to compressive stresses through muscle activation. This allows weight to be saved, which represents an evolutionary advantage [30]. On the other hand, Bertram and Biewener [74] argue that residual bending allows the direction of bending to be predicted. In this study inertia relief, muscle force optimization, and the iliotibial band are combined to model physiological boundary conditions.
+
+The stress analyses of the juvenile femur reveal reduced bending stresses in the sagittal plane. Nevertheless, bending in the frontal plane cannot be compensated for entirely. The highest appositional growth is predicted for the medial site, but the decrease in the NSA and the growth of the femoral neck result in a more eccentric hip joint resultant. In this simulation the functional adaption compensates the additional bending, but is not able to further reduce bending stresses in the frontal plane. It can be assumed that functional adaption and muscle forces mainly reduce bending in the sagittal plane whereas the iliotibial tract is the primary mechanism for reducing bending stresses in the frontal plane.
+
+However, with a modulus of elasticity of 12,000 MPa for cortical bone, the bones in children and adolescents are significantly more elastic than in adults and their elasticity allows greater bending until material failure. Bones become stiffer as they grow. At the same time, the simulation of bone growth predicts functional changes that reduce bending stresses. The changes in bone morphology during growth can therefore be understood as adaptions to mechanical loading.
+
+In the proximal femur, peak compressive stresses are found medially and result in an increase in bone density similar to previous studies [52]. This shifts the center of mass of the neck of the femur medially toward the resulting axial force. In the diaphysis, internal axial loading is between 200 and 985 N during gait, while shear loading is considerably lower. This is in agreement with comparable studies in adults [75], whereas the weight-adapted axial load is higher. They have important implications in the healing processes of pediatric femoral shaft fractures, as axial loading can enhance fracture healing, while shear loading decelerates fracture healing [76].
+
+The values for changes in bone length, diaphyseal diameter, NSA, and anteversion agree well with anthropometric values. However, the decline in the LDFA is not observed during adolescent growth. A possible explanation might be that the ring of LaCroix, which is not modeled, reduces the deformity of the cartilage in the growth plate. The predicted changes are also a mechanism of functional adaptation, as a decline in the NSA is associated with lower loading on the proximal femur [77]. Growth of the greater trochanter and the femoral neck isthmus could preserve the morphology of the metaphysis during longitudinal growth. The highest increase in cortical thickness is predicted on the medial side of the diaphysis. Indeed, the femoral shaft has a higher thickness on the medial compared to the lateral side [78]. However, the highest cortical bone thickness is observed posterior.
+
+Higher impact loads during running or stair climbing are likely to result in higher posterior compression due to bending, contributing in asymmetric periosteal growth and thereby further building a bending-minimized optimized lightweight structure. Motion capture and ground-reaction forces during different activities in children should be analyzed in further research to add more time-weighted load cases to the model. In conclusion, it could thus be shown that the mechanobiological model of bone growth presented here is suitable for reproducing the physiological growth of the femur with some limitations.
+
+Other limitations of the model include the assumption of constant muscle strength. However, as the angle of the femur changes, the lever arms of the muscles also change, and thereby the vector of the muscle force. Furthermore, the increase in weight leads to an increase in ground reaction force and a higher level of muscle strength due to muscle build-up. Secondarily, this also results in altered hip and knee joint forces. Further developments of the model should therefore include a stronger coupling of the calculations of bony and muscular growth. As discussed above, the simulated load only includes the gait cycle and therefore does not include the maximum loads that occur during sport and play. However, frequent loads are particularly relevant for the morphological adaptation of the bones to the stresses placed on them and gait is subject to less inter-individual variation than sporting activities. These reasons support the choice of gait as a functional load. Also, the cartilaginous growth at the surface of the femoral head and the greater trochanter was not included and periosteal growth was only considered for the diaphysis. Material models are simplified as linear elastic and isotropic and the geometry is simplified. Yadav et al. [69] were able to demonstrate that modeling of patient-specific growth plate geometry increased the accuracy of the predictions. Future research using medical images to develop a patient-specific model and compare the in silico results with the respective radiological follow-up may allow a more detailed validation.
+
+Cortical and cancellous bone has orthotropic material parameters, which are of particular interest for the simulation of bone remodeling and the development of the trabecular columns and Ward’s triangle in the proximal femur. Including orthotropic remodeling rules [79] in the model presented here is promising in further simulating and understanding the endochondral ossification at the growth plate of the proximal femur.
+
+Previous studies found more valid results for patient-specific growth plate geometries. The present study used a single femur anatomy. Modeling growth in different patient-specific models could improve the simulation by superior validation as well as more realistic geometry of the apophyseal growth plate. The present study assumes a constant Young’s modulus across all growth plates. As illustrated in Fig. 6, a low Young’s modulus was associated with results that are more realistic for the LDFA. Therefore, one explanation might be local differences in the material parameters of different growth plates. Another possibility is the tension cording of the superficial pes anserinus, which is hypothesized to play a role in the mechanical loading of the growth plates next to the knee [80]. Additionally, including micromotion at the cortical–cancellous bone interface using a frictional contact formulation might result in more realistic local strains compared to the bounded contact used in the present study.
+
+The model contains a constant biological baseline, which in reality is influenced by hormones and cellular senescence. For clinical decision-making, it is often necessary to consider growth till its completion. Further research should aim to simulate a longer period of growth. Including the effects of sex hormones and cellular senescence on the growth plate might allow for modeling fusion of the growth plates. However, in the current model growth is simulated by updating the location of the nodes. This only allows the simulation of growth over a few months; otherwise, element distortions will occur. Manipulating a volume model and remeshing instead of directly manipulating the mesh might be a feasible solution to this problem [46].
+
+Conclusions
+
+Bone growth in children does not only lead to an increase in length and thickness but also to complex three-dimensional changes in shape. The implementation of all growth plates and periosteal growth in computational simulations of bone growth can contribute to a better understanding of the interaction between morphological changes and functional loads. Optimizing muscle strength and functional adaptation together reduce bending stresses in growing bone in this in silico model. Future research should aim to simulate bone growth in complex deformities and might be a tool to predict bone remodeling after fractures.
+
+Materials and methods
+
+An iterative algorithm, based on finite element stress analyses, calculation of local growth rates and updating of the model is established (Fig. 7).Fig. 7 Flow diagram of the mechanobiological model: first, the finite element mesh is established in ANSYS and bending-minimized muscle forces are calculated. Stresses for all load cases are physiologically superimposed and hydrostatic and octahedral shear stresses at the growth plates and 3rd principal stresses in the bone are analyzed. The mechanical stimulus is calculated. The working plane of each growth plate element is aligned with the average deformation during gait. The density of cancellous bone is updated according to Eq. 3 based on 3rd principal stresses. Appositional periosteal growth is modeled by moving the external nodes on a line to the midpoint of the respective transverse plane. Forces are removed and growth rate is applied as temperature, and the model geometry is updated after thermal expansion. Nodes are moved to their final location and the thickness of the growth plates is reset to initial values to model ossification. For the next iteration, forces are applied again to the modified mesh
+
+1. A finite element mesh of the adolescent right femur, made freely available at SimTK by Kainz et al. [65] based on MRI data of a typically developed child (8 years old, weight: 20.4 kg, height: 1.24 m), was imported into ANSYS Mechanical version 19.2 (ANSYS Inc, Canonsburg, PA, USA). The modeling approach has previously been shown to accurately predict growth in 18 out of 20 cases [81]. The mesh has 22,560 elements and consists of 3-D 8-node structural solids (SOLID185). The element thickness is 4 mm at the shaft and as low as 0.2 mm in regions of interest like the growth plate. A mesh sensitivity analysis is performed. Further mesh refinement up to 902,384 elements results in a change of less than 10% in average principal stresses.
+
+The outer shaft diameter was adapted to 15.5 mm matching values for boys of the age of 8 [63]. The model includes the medullary cavity. The diaphysis is composed of cortical bone, and the meta- and epiphyses are composed of cancellous bone covered by a layer of cortical bone. The proximal and distal growth plates with thicknesses of 0.9 mm and 2.1 mm, respectively, are modeled [82]. The widths are in a ratio of approximately 30:70 to simulate the different contributions of the two epiphyseal plates to femoral growth [83] and correspond to the literature values of an 8-year-old male [84, 85]. Additionally, a layer of elements representing the resting zone is included in the model. The growth plate of the apophysis of the trochanter major is modeled with an angle of 50° to the body horizontal [86]. Pozdnikin et al. [61] reported an almost constant articulo-trochanteric distance measured between the tip of the greater trochanter and the upper point of the femoral head in normal hips of children aged 3 to 17 years. Therefore, the growth plate of the greater trochanter is assumed to have the same thickness as the proximal growth plate to map growth at the same rate. The cartilage of the femoral neck isthmus as well as the articular cartilage is modeled as one layer of proliferative chondrocytes. To reduce computation time and like comparable finite element models [37, 65], all materials are assumed to be linearly elastic, isotropic, and homogeneous. The material properties are given in Table 3. Young´s modulus of the growth plate highly affects the deformation and therefore the growth direction. Values in the literature range, starting with 0.49 MPa for the proliferative and hypertrophic zone and 0.99 MPa for the resting zone [87]. Therefore, a sensitivity analysis is performed to investigate the influence of the rigidity of the growth plates on growth tendency. Table 3 Initial material properties
+
+Material	Density in kg/m^3	Young's modulus in MPa	Poisson's ratio	
+Cortical bone	1100 [88]	12,000 [90]	0.3 [93]	
+Cancellous bone	150 [88]	345 [91]	0.25 [9]	
+Cartilage	1100 [89]	0.5 – 10 [37, 65, 87]	0.47 [87]	
+Bone marrow	1000 [89]	0.01 [92]	0.49 [92]	
+
+Rigid boundary conditions with fixed bearings in all directions at the condyles lead to artificially high stresses [94]. Therefore, physiological boundary conditions with a bearing fixed in all directions at the femoral notch, a bearing fixed in the anterior–posterior direction at the lateral epicondyle of the distal femur, and a bearing fixed in the anterior–posterior and medial–lateral directions at the middle of the femoral head were used [72]. To prevent artificial stresses near the bearings and to take into account the inertia forces generated during movement, inertia relief is used. This method can be used to balance the forces when analyzing individual load steps during the gait and achieve physiological stresses [95]. The boundary conditions are thereby only used to prevent rigid body movements, but the bearings themselves do not generate a reaction force. Instead, the applied forces are balanced by the inertial forces that the body experiences in the acceleration field. The acceleration field is defined as the standard gravitational force on the earth in the inferior direction. To model bone growth by thermal expansion, the femur was fixed at both condyles in all directions.
+
+2. Using load cases, a dynamic gait cycle can be represented by a finite number of static simulations. These discrete load cases can be combined as a functional load history to calculate the mechanical stimulus [26]. For this purpose, a physiological superposition of all loading cases is performed by cumulating the highest values of compressive stresses occurring in one of the loading cases [36]. Nine load cases based on a published multibody simulation are identified and used as initial muscle and joint forces [65]. In addition, the force of the iliotibial band is included, which reduces bending stresses in the diaphysis. This force is taken into account with 50% of the amount of the hip joint resultant of the respective load case [86].
+
+Optimization of muscle forces has been shown to reduce bending stresses, and bending minimization can be used as a principle for determining muscle forces [72]. Therefore, the ANSYS subproblem routine is performed with 30 iterations for each load case. The muscle forces are used as design variables and are allowed to vary within a range of 50 to 200% of the initial value. Forces acting on the hip and knee joint are adopted as fixed values. Bending stresses are calculated in the mediolateral and anteroposterior directions by analyzing the absolute highest principal stresses at four points in the middle of the shaft [96]:σbending=±σmedial/anterior-σlateral/posterior2.
+
+The sum of both bending stresses at the midshaft is minimized (objective function). Additionally, both are independently used as state variables with a target value below 10 MPa. Principal stresses are analyzed by superposition of the minimal and maximal principal stresses, respectively. To calculate internal axial loading, a surface perpendicular to the femoral shaft axis is created. Normal stresses on this surface are averaged and multiplied with the cross-sectional area to obtain axial forces. Values are converted to percent body weight.
+
+3. Epiphyseal growth is modeled as thermal expansion. Proliferation increases the overall volume and therefore accounts for the isotropic growth ratio, while hypertrophy enlarges the columns unidirectionally. A combination of biomechanical and histological analyses found a high correlation between the direction of the distortion of the hypertrophic chondrocytes and orientation of the columns of the growth plate, a mechanism by which shear stresses are reduced [22]. Therefore, for every element representing hypertrophic chondrocytes, the average deformation over all nine load cases is aligned with the z-axis of the element’s local coordinate system. To avoid disturbance of adjacent elements, the vector is calculated for each pair of nodes of the elements of the hypertrophic zone. This is achieved by making use of the fact that in the hexagonal mesh, each proximal node has an assigned distal node. The vector is calculated based on the coordinates of the node adjacent to the proliferative zone and the corresponding node adjacent to the bone as the mean of all nine load cases.
+
+The growth rate is the sum of the biological baseline rb0 and a mechanically stimulated growth rate rm and is modeled as temperature difference. The growth of an element of the growth plate g can be calculated by the local thickness of the respective zone l and both growth rates as:g=l∙rb0+rm.
+
+Proliferation and production of extracellular matrix in the proliferative zone account for about 27%, and hypertrophy and production of extracellular matrix in the hypertrophic zone account for 73% [97]. Both growth mechanisms are modeled by the choice of thermal expansion coefficients. rb0 and rm are calculated based on a model developed by Wong and Carter [66], Stevens et al. [67], and Yadav et al. [68–70]. Briefly, based on a reported growth rate of the proximal femur of 9 mm/year [80], an assumed percentage of nonmechanically stimulated growth of 66% [16, 68], and a thickness of the proximal growth plate of 0.9 mm, rb0 is given as 0.55 mm/month. rm is given by the sum of the maximum octahedral shear stress and the minimum hydrostatic stress obtained over all nine loading cases, where the coefficients a and b describe the respective influence of octahedral shear stress and hydrostatic stress on rm [66]:rm=a∙maxσ1-σ22+σ2-σ32+σ3-σ123+b∙minσ1+σ2+σ33.
+
+The ratio of b/a was set at 0.5 in agreement with previous studies [40] and calibrated to correspond to 33% of total growth.
+
+4. Changes in bone density in cancellous bone and thereby changes in Young’s modulus can be described by a differential equation developed by Li et al. [98]. It considers bone resorption due to disuse, bone formation due to physiological overload in a dose-dependent manner, and bone resorption due to microdamage and pathological overload. 2 MPa is used as thresholds for bone formation [30]. Pathological overload is assumed for loading four times higher [31, 34]. Furthermore, it is assumed that the curve is symmetrical. This can be used to solve a system of equations for 3 support points. The maximum bone formation rate per bone volume in trabecular bone is 4% per month [99]. The Young’s modulus of a specific element representing cancellous bone after one month of simulated loading Ei+1 can therefore be expressed as function of the volume at the beginning of the iteration Ei:Ei+1=Ei+0.2916∙e0.77021MPaσ3-0.07721MPa2σ32-1∙0.04MPa.
+
+Physiological loading of cortical bone is around ten times higher than in cancellous bone [30]. In contrast to cancellous bone and the endosteal surface, animal models found no periosteal resorption even without any loading [100]. With a maximal apposition rate of 0.06 mm/month [9], the mechanically stimulated apposition rate per month AR is given by:AR=e0.03465741MPaσ3-0.0004332171MPa2σ32-1∙0.06mm/month.
+
+A parameter sensitivity study is performed for the Young’s modulus of the growth plate (0.5 to 10 MPa) [37, 64, 84], b/a ratio (0.3 to 1) [40], and the threshold of periosteal apposition (0 to 20 MPa). 0 MPa is chosen to simulate a remodeling law where no resorption due to unloading takes place as seen in animal models [100], while 20 MPa is the threshold in adults [30, 31].
+
+5. After calculating all growth rates, the nodes are moved to their updated positions according to the growth rates calculated in the previous steps.
+
+6. In a final step, thickness of the growth plate is adjusted to starting values again. This represents the ossification front and ensures the normalization of the growth rate, which is dependent on the thickness of the growth plate.
+
+The updates mesh serves as an initial model for the next iteration. After simulation of bone growth, the following values were measured and compared to reference values for validation (Fig. 8):•Femur length: the distance between the center of the femoral head and the intercondylar femoral fossa is used here, as these two points are also used to determine the mechanical femoral axis [101].
+
+•Neck–shaft angle (NSA): the projected NSA angle is defined in the frontal plane as the angle between the femoral neck axis and the femoral shaft axis. To determine this, a circle is drawn around the center of the femoral head that intersects the femoral neck medially and laterally. The femoral neck axis can then be constructed by drawing a line through the middle of this line and the center of the head. The femoral shaft axis is the line between the centers of two transverse diameters below the lesser trochanter [102].
+
+•Articulo-trochanteric distance (ATD): the articulo-trochanteric distance is calculated as the distance between two parallel lines orthograde to the femoral shaft axis that are tangential to the maximum points of the femoral head and the greater trochanter [103].
+
+•Lateral distal femoral angle (LDFA): the mechanical lateral distal femoral angle is the lateral angle between the mechanical femoral axis and the knee line as a tangent to the most distal points of both knee condyles. There is also the anatomical lateral distal femoral angle between the femoral shaft axis and the knee line, but this is less commonly used and is therefore not used in this study [104].
+
+•Antetorsion angle (AT): the antetorsion angle describes the rotation of the femoral neck in relation to the shaft. It is measured in the axial plane between the projection of the femoral neck axis and a line tangential to the distal condyles [105].
+
+•Anteroposterior and mediolateral diameter: since the femoral shaft is not cylindrical and shows an eccentric growth behavior, the diameter is determined at the level of the middle of the femur in the axial section between the most anterior and posterior as well as medial and lateral points.
+
+Fig. 8 Anthropometric measurements of the femur used in the present study. a Length between the center of the femoral head and the femoral notch. b Neck–shaft angle (NSA). c Articulo-trochanteric distance (ATD). d Lateral distal femoral angle (LDFA). e Anteversion angle
+
+Acknowledgements
+
+The authors are grateful to Hans Kainz and colleagues for making the mesh of the juvenile femur used in this study publicly available under the MIT Use Agreement at SimTK: https://simtk.org/projects/normal-load/. The authors also want to thank Beate Bender, Product Development, and the Institute of Product and Service Engineering, Ruhr-University Bochum, for the provision of computational equipment.
+
+Author contributions
+
+AL conceptualized the project, developed the model, performed the finite element analysis and wrote the manuscript. RB analyzed, interpreted, and validated the modeling results. MK and SS assisted in computational modeling and were major contributors in writing the manuscript. UW supervised the project and was a major contributor in conceptualization of the project and interpreting the results. All authors read and approved the final manuscript.
+
+Funding
+
+Open Access funding enabled and organized by Projekt DEAL. This research was funded by Deutsche Forschungsgesellschaft (DFG, German Research Foundation), grant number 445465815. The content is solely the responsibility of the authors and does not necessarily represent the official views of the DFG.
+
+Data availability
+
+The data presented in this study are available on request from the corresponding author.
+
+Declarations
+
+Ethics approval and consent to participate
+
+Not applicable.
+
+Consent for publication
+
+Not applicable.
+
+Competing interests
+
+The authors declare no competing interests.
+
+Publisher's Note
+
+Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
+
+
+References
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+Bradney M, Karlsson MK, Duan Y, Stuckey S, Bass S, Seeman E. Heterogeneity in the growth of the axial and appendicular skeleton in boys: implications for the pathogenesis of bone fragility in men. J Bone Miner Res. 2000;15:1871–8.11028438 10.1359/jbmr.2000.15.10.1871
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+Upadhyay SS, Burwell RG, Moulton A, Small PG, Wallace WA. Femoral anteversion in healthy children application of a new method using ultrasound. J Anat. 1990;169:49–61.2200768 PMC1256956
+65. Kainz H Killen BA Wesseling M Perez-Boerema F Pitto L Garcia Aznar JM Shefelbine S Jonkers I A multi-scale modelling framework combining musculoskeletal rigid-body simulations with adaptive finite element analyses, to evaluate the impact of femoral geometry on hip joint contact forces and femoral bone growth PLoS ONE 2020 15 e0235966 10.1371/journal.pone.0235966 32702015 PMC7377390
+Kainz H, Killen BA, Wesseling M, Perez-Boerema F, Pitto L, Garcia Aznar JM, et al. A multi-scale modelling framework combining musculoskeletal rigid-body simulations with adaptive finite element analyses, to evaluate the impact of femoral geometry on hip joint contact forces and femoral bone growth. PLoS ONE. 2020;15:e0235966.32702015 10.1371/journal.pone.0235966 PMC7377390
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+Yadav P, Shefelbine SJ, Pontén E, Gutierrez-Farewik EM. Influence of muscle groups’ activation on proximal femoral growth tendency. Biomech Model Mechanobiol. 2017;16:1869–83.28639152 10.1007/s10237-017-0925-3 PMC5671539
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+Yadav P, Shefelbine SJ, Gutierrez-Farewik EM. Effect of growth plate geometry and growth direction on prediction of proximal femoral morphology. J Biomech. 2016;49:1613–9.27063249 10.1016/j.jbiomech.2016.03.039
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+Yadav P, Peña Fernández M, Gutierrez-Farewik EM. Influence of loading direction due to physical activity on proximal femoral growth tendency. Med Eng Phys. 2021;90:83–91.33781483 10.1016/j.medengphy.2021.02.008
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+Sverdlova NS, Witzel U. Principles of determination and verification of muscle forces in the human musculoskeletal system: muscle forces to minimise bending stress. J Biomech. 2010;43:387–96.19880120 10.1016/j.jbiomech.2009.09.049
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+Lutz F, Mastel R, Runge M, Stief F, Schmidt A, Meurer A, et al. Calculation of muscle forces during normal gait under consideration of femoral bending moments. Med Eng Phys. 2016;38:1008–15.27318439 10.1016/j.medengphy.2016.05.005
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+Duda GN, Schneider E, Chao EY. Internal forces and moments in the femur during walking. J Biomech. 1997;30:933–41.9302616 10.1016/s0021-9290(97)00057-2
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+Augat P, Burger J, Schorlemmer S, Henke T, Peraus M, Claes L. Shear movement at the fracture site delays healing in a diaphyseal fracture model. J Orthop Res. 2003;21:1011–7.14554213 10.1016/S0736-0266(03)00098-6
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+Kainz H, Mindler GT, Kranzl A. Influence of femoral anteversion angle and neck-shaft angle on muscle forces and joint loading during walking. PLoS ONE. 2023;18:e0291458.37824447 10.1371/journal.pone.0291458 PMC10569567
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+Someya K, Mochizuki T, Hokari S, Tanifuji O, Katsumi R, Koga H, et al. Age- and sex-related characteristics in cortical thickness of femoral diaphysis for young and elderly subjects. J Bone Miner Metab. 2020;38:533–43.32002681 10.1007/s00774-019-01079-9
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+Rodríguez DQ, Ho Ba Tho MC, Trabelsi O, Garzón-Alvarado D. Exploring the impact of mechanical stimuli on growth plate morphology and trabecular adaptation: a finite element approach. J Orthop. 2025;63:228–37.40475877 10.1016/j.jor.2025.04.014 PMC12134541
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+Koller W, Svehlik M, Wallnöfer E, Kranzl A, Mindler G, Baca A, et al. Femoral bone growth predictions based on personalized multi-scale simulations: validation and sensitivity analysis of a mechanobiological model. Biomech Model Mechanobiol. 2025;24:879–94.40227492 10.1007/s10237-025-01942-x PMC12162800
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+Abiodun AA, Falana BA, Olatunbosun A. Baseline thickness of proximal femoral epiphysis in the diagnosis of hip diseases in infants and children in Nigeria. Int J Surg Res. 2014;3:22–6.
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+Kim A, Dombi E, Solomon J, Fox E, Balis FM, Widemann BC. Automated volumetric growth plate measurement using magnetic resonance imaging for monitoring skeletal toxicity in children treated on investigational drug trials. Clin Cancer Res. 2011;17:5982–90.21807634 10.1158/1078-0432.CCR-10-2259 PMC3439140
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+Heimkes B, Posel P, Plitz W, Zimmer M. Die altersabhängige Kräfteverteilung am koxalen Femurende des normal wachsenden Kindes. Z Orthop Ihre Grenzgeb. 1997;135:17–23.9199067 10.1055/s-2008-1039549
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+Gao J, Roan E, Williams JL. Regional variations in growth plate chondrocyte deformation as predicted by three-dimensional multi-scale simulations. PLoS ONE. 2015;10:e0124862.25885547 10.1371/journal.pone.0124862 PMC4401775
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+Rauch F, Schoenau E. Changes in bone density during childhood and adolescence: an approach based on bone’s biological organization. J Bone Miner Res. 2001;16:597–604.11315987 10.1359/jbmr.2001.16.4.597
+89. Hasgall PA, Di Gennaro F, Baumgartner C, Neufeld E, Lloyd B, Gosselin MC, Payne D, Klingenböck A, Kuster N, “IT’IS Database for thermal and electromagnetic parameters of biological tissues,” Version 4.1. 2022, 10.13099/VIP21000-04-1. itis.swiss/database
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+Öhman C, Baleani M, Pani C, Taddei F, Alberghini M, Viceconti M, et al. Compressive behaviour of child and adult cortical bone. Bone. 2011;49:769–76.21763479 10.1016/j.bone.2011.06.035
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+Piszczatowski S. Material aspects of growth plate modelling using Carter’s and Stokes’s approaches. Acta Bioeng Biomech. 2011;13:3–14.22097913
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+Jansen LE, Birch NP, Schiffman JD, Crosby AJ, Peyton SR. Mechanics of intact bone marrow. J Mech Behav Biomed Mater. 2015;50:299–307.26189198 10.1016/j.jmbbm.2015.06.023 PMC4554886
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+Lai YS, Chen WC, Huang CH, Cheng CK, Chan KK, Chang TK. The effect of graft strength on knee laxity and graft in-situ forces after posterior cruciate ligament reconstruction. PLoS ONE. 2015;10:e0127293.26001045 10.1371/journal.pone.0127293 PMC4441446
+94. Speirs AD Heller MO Duda GN Taylor WR Physiologically based boundary conditions in finite element modelling J Biomech 2007 40 2318 2323 10.1016/j.jbiomech.2006.10.038 17166504
+Speirs AD, Heller MO, Duda GN, Taylor WR. Physiologically based boundary conditions in finite element modelling. J Biomech. 2007;40:2318–23.17166504 10.1016/j.jbiomech.2006.10.038
+95. Heyland M Trepczynski A Duda GN Zehn M Schaser KD Märdian S Selecting boundary conditions in physiological strain analysis of the femur: balanced loads, inertia relief method and follower load Med Eng Phys 2015 37 1180 1185 10.1016/j.medengphy.2015.10.002 26521092
+Heyland M, Trepczynski A, Duda GN, Zehn M, Schaser KD, Märdian S. Selecting boundary conditions in physiological strain analysis of the femur: balanced loads, inertia relief method and follower load. Med Eng Phys. 2015;37:1180–5.26521092 10.1016/j.medengphy.2015.10.002
+96. Main RP Biewener AA Ontogenetic patterns of limb loading, in vivo bone strains and growth in the goat radius J Exp Biol 2004 207 2577 2588 10.1242/jeb.01065 15201290
+Main RP, Biewener AA. Ontogenetic patterns of limb loading, in vivo bone strains and growth in the goat radius. J Exp Biol. 2004;207:2577–88.15201290 10.1242/jeb.01065
+97. Wilsman NJ Farnum CE Leiferman EM Fry M Barreto C Differential growth by growth plates as a function of multiple parameters of chondrocytic kinetics J Orthop Res 1996 14 927 936 10.1002/jor.1100140613 8982136
+Wilsman NJ, Farnum CE, Leiferman EM, Fry M, Barreto C. Differential growth by growth plates as a function of multiple parameters of chondrocytic kinetics. J Orthop Res. 1996;14:927–36.8982136 10.1002/jor.1100140613
+98. Li J Li H Shi L Fok AS Ucer C Devlin H Horner K Silikas N A mathematical model for simulating the bone remodeling process under mechanical stimulus Dent Mater 2007 23 1073 1078 10.1016/j.dental.2006.10.004 17137621
+Li J, Li H, Shi L, Fok AS, Ucer C, Devlin H, et al. A mathematical model for simulating the bone remodeling process under mechanical stimulus. Dent Mater. 2007;23:1073–8.17137621 10.1016/j.dental.2006.10.004
+99. Glorieux FH Travers R Taylor A Bowen JR Rauch F Norman M Parfitt AM Normative data for iliac bone histomorphometry in growing children Bone 2000 26 103 109 10.1016/S8756-3282(99)00257-4 10678403
+Glorieux FH, Travers R, Taylor A, Bowen JR, Rauch F, Norman M, et al. Normative data for iliac bone histomorphometry in growing children. Bone. 2000;26:103–9.10678403 10.1016/s8756-3282(99)00257-4
+100. Li B Sankaran JS Judex S Trabecular and cortical bone of growing C3H mice is highly responsive to the removal of weightbearing PLoS ONE 2016 11 e0156222 10.1371/journal.pone.0156222 27223115 PMC4880346
+Li B, Sankaran JS, Judex S. Trabecular and cortical bone of growing C3H mice is highly responsive to the removal of weightbearing. PLoS ONE. 2016;11:e0156222.27223115 10.1371/journal.pone.0156222 PMC4880346
+101. Guenoun B Zadegan F Aim F Hannouche D Nizard R Reliability of a new method for lower-extremity measurements based on stereoradiographic three-dimensional reconstruction Orthop Traumatol Surg Res 2012 98 506 513 10.1016/j.otsr.2012.03.014 22858107
+Guenoun B, Zadegan F, Aim F, Hannouche D, Nizard R. Reliability of a new method for lower-extremity measurements based on stereoradiographic three-dimensional reconstruction. Orthop Traumatol Surg Res. 2012;98:506–13.22858107 10.1016/j.otsr.2012.03.014
+102. Fischer CS Kühn JP Völzke H Ittermann T Gümbel D Kasch R Haralambiev L Laqua R Hinz P Lange J The neck-shaft angle: an update on reference values and associated factors Acta Orthop 2020 91 53 57 10.1080/17453674.2019.1690873 31735107 PMC7006743
+Fischer CS, Kühn JP, Völzke H, Ittermann T, Gümbel D, Kasch R, et al. The neck-shaft angle: an update on reference values and associated factors. Acta Orthop. 2020;91:53–7.31735107 10.1080/17453674.2019.1690873 PMC7006743
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+Yoon PW, Shin YH, Yoo JJ, Yoon KS, Kim HJ. Progression of a fracture site impaction as a prognostic indicator of impacted femoral neck fracture treated with multiple pinning. Clin Orthop Surg. 2012;4:66–71.22379557 10.4055/cios.2012.4.1.66 PMC3288496
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+Marques Luís N, Varatojo R. Radiological assessment of lower limb alignment. EFORT Open Rev. 2021;6:487–94.34267938 10.1302/2058-5241.6.210015 PMC8246117
+105. Scorcelletti M Reeves ND Rittweger J Ireland A Femoral anteversion: significance and measurement J Anat 2020 237 811 826 10.1111/joa.13249 32579722 PMC7542196
+Scorcelletti M, Reeves ND, Rittweger J, Ireland A. Femoral anteversion: significance and measurement. J Anat. 2020;237:811–26.32579722 10.1111/joa.13249 PMC7542196
diff --git a/corpus/psychology/text/cee5735464208f02.txt b/corpus/psychology/text/cee5735464208f02.txt
new file mode 100644
index 0000000000000000000000000000000000000000..75de9c5e19ed17bdda6d07d8f405a94774202522
--- /dev/null
+++ b/corpus/psychology/text/cee5735464208f02.txt
@@ -0,0 +1,3 @@
+Binary Path Sort: A Sorting Algorithm to Assess the Ranking Order of a Single Respondent
+
+Preference based sorting is integral to experimental research and applications across various disciplines, including psychology, marketing, and education. Under the transitivity assumption, it is not necessary to compare all objects directly to determine the preferred order. The field of computer science offers a rich literature on comparison-based sorting algorithms, presenting numerous strategies for the adaptive selection of pairwise comparisons. Typically, the focus is on minimizing resource utilization, such as computer memory. However, in many fields, particularly in psychology, comparisons are made by human respondents. Here, the key considerations are a low number of expected pairwise comparisons and a robust performance in worst-case scenarios. This study introduces Binary Path Sort (BPS), a novel and efficient sorting algorithm based on a priority queue. It will be demonstrated that BPS requires fewer pairwise comparisons in the worst-case scenario compared to the currently best priority queue-based sorting algorithm. Moreover, BPS is equivalent in terms of the number of comparison required for best, average, and worst-case scenarios to the non-priority queue algorithm Mergesort. A simulation study is presented to illustrate the avoidance of worst-case scenarios and which elements are compared. Finally, the study discusses the implications of these findings, particularly for forced-choice measurement applications.
diff --git a/corpus/psychology/text/d45e72106c0588ef.txt b/corpus/psychology/text/d45e72106c0588ef.txt
new file mode 100644
index 0000000000000000000000000000000000000000..8fce6c40ca6148454213460d46aa16f1c7905de3
--- /dev/null
+++ b/corpus/psychology/text/d45e72106c0588ef.txt
@@ -0,0 +1,51 @@
+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Cureus
+Journal ID: Cureus
+NLM Journal ID: 101596737
+Journal ID: Cureus
+
+Cureus
+
+EISSN: 2168-8184
+Publisher: Cureus Inc.
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC12714293
+PMID: 41425683
+DOI: 10.7759/cureus.r212
+Article version: 1
+Subjects: Retraction
+
+Retraction: Correlation of FIRE-MADE (Frailty Index in Rural Elderly - Mental Status, Activities of Daily Living, Depression, and Events) With Sarcopenia in Elderly Population of Central Rural India
+
+Retraction
+
+Muacevic Alexander
+Adler John R
+Khan Khalid I 1
+Gaidhane Shilpa A 1
+Kumar Sunil 1
+Acharya Sourya 1
+1 Medicine, Jawaharlal Nehru Medical College, Datta Meghe Institute of Medical Sciences, Wardha, IND
+Khalid I. Khan khalid.khan9t@gmail.com
+Electronic publication date: 2025 Dec 18
+Publication date: 2025 Dec
+Volume: 17
+Issue: 12
+Electronic Location ID: r212
+Copyright: Copyright © 2025, Khan et al.
+Copyright year: 2025
+Copyright holder: Khan et al.
+License: This is an open access article distributed under the terms of the Creative Commons Attribution License CC-BY 4.0., which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Retraction of: Correlation of FIRE-MADE (Frailty Index in Rural Elderly - Mental Status, Activities of Daily Living, Depression, and Events) With Sarcopenia in Elderly Population of Central Rural India. 15 9 9 9 2023 e44942 e44942 Cureus 10.7759/cureus.44942 37818502
+
+Ÿ==============================Ÿ
+This article has been retracted by the Editors-in-Chief due to a copyright violation by the authors concerning the unauthorized use of the Mini-Mental State Examination (MMSE). As a result, this article has been retracted and the article contents have been removed.
+
+No competing interests declared.
+
diff --git a/corpus/psychology/text/d66eb002a5af92f7.txt b/corpus/psychology/text/d66eb002a5af92f7.txt
new file mode 100644
index 0000000000000000000000000000000000000000..e4aeb1492af99951cbbe8e042c911804a437dbed
--- /dev/null
+++ b/corpus/psychology/text/d66eb002a5af92f7.txt
@@ -0,0 +1,10 @@
+Feeling the way to words: Parents' speech and touch cues highlight word-to-world mappings of body parts. Language Learning and Development,
+
+Touch cues might facilitate infants’ early word comprehension and explain why body part words
+emerge so early. Parents were instructed to teach their infants, 4- to 5-month-olds or 10- to 11-
+month-olds, nonce words for body parts and a contrast object but were given no instructions
+about the use of touch. Parents spontaneously touched target body parts in close timing to
+uttering the target nonce words. They did not show this alignment for unrelated touches and
+nonce words. Moreover, when parents used this temporally synchronized speech and touch input,
+infants looked more frequently to the target locations on their bodies and to their parent’s faces
+compared to when the input was mismatched or only speech. Similar to other research on parents' use of speech and gesture input, these results show how parents use multimodal speech-touch input and raise the possibility that infants use touch cues to segment and map early words.
diff --git a/corpus/psychology/text/d77956307d27dd63.txt b/corpus/psychology/text/d77956307d27dd63.txt
new file mode 100644
index 0000000000000000000000000000000000000000..ea42f2fe83f327547e04995b2454431e9ffbd439
--- /dev/null
+++ b/corpus/psychology/text/d77956307d27dd63.txt
@@ -0,0 +1,77 @@
+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Cancer Med
+Journal ID: Cancer Med
+NLM Journal ID: 101595310
+Journal ID: CAM4
+
+Cancer Medicine
+
+EISSN: 2045-7634
+Publisher: Wiley
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC11197028
+PMID: 38923212
+DOI: 10.1002/cam4.7426
+Article ID: CAM47426
+Article version: 1
+Subjects: Correction, Correction
+
+Correction to “Depression and anxiety in cancer patient enrolled in clinical trials with serious adverse events”
+
+Electronic publication date: 2024 Jun 25
+Publication date: 2024 Jun
+Volume: 13
+Issue: 12
+Electronic Location ID: e7426
+Copyright: © 2024 The Author(s). Cancer Medicine published by John Wiley & Sons Ltd.
+License: This is an open access article under the terms of the http://creativecommons.org/licenses/by/4.0/ License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Erratum for: Depression and anxiety in cancer patient enrolled in clinical trials with serious adverse events 12 19 18 9 2023 20015 20026 Cancer Medicine 10.1002/cam4.6556 PMC10587935 37723836
+Figure count: 0
+Table count: 0
+Page count: 1
+
+source-schema-version-number: 2.0
+cover-date: June 2024
+details-of-publishers-convertor: Converter:WILEY_ML3GV2_TO_JATSPMC version:6.4.4 mode:remove_FC converted:25.06.2024
+
+Ÿ==============================Ÿ
+Peng Z, Wang C, Sun Y, et al. Depression and anxiety in cancer patient enrolled in clinical trials with serious adverse events. Cancer Med. 2023;12(19):20015‐20026. doi:10.1002/cam4.6556
+
+In the “Author affiliation” section, the text
+
+“1Division of Life Sciences and Medicine, Drug Clinical Trial Institution, The First Affiliated Hospital of USTC, University of Science and Technology of China, Anhui, Hefei, China
+
+2Division of Life Sciences and Medicine, Department of Oncology, The First Affiliated Hospital of USTC, University of Science and Technology of China, Hefei, Anhui, China
+
+3Division of Life Sciences and Medicine, Department of Rheumatology and Immunology, The First Affiliated Hospital of USTC, University of Science and Technology of China, Hefei, Anhui, China
+
+4Division of Life Sciences and Medicine, Department of Endocrinology, The First Affiliated Hospital of USTC, University of Science and Technology of China, Hefei, Anhui, China
+
+5Division of Life Sciences and Medicine, Department of Pulmonary and Critical Care Medicine, The First Affiliated Hospital of USTC, University of Science and Technology of China, Hefei, Anhui, China
+
+6Division of Life Sciences and Medicine, Department of Scientific Research, The First Affiliated Hospital of USTC, University of Science and Technology of China, Hefei, Anhui, China” was incorrect.
+
+This should be:
+
+“1Drug Clinical Trial Institution, The First Affiliated Hospital of USTC, Division of Life Sciences and Medicine, University of Science and Technology of China, Hefei, Anhui, China.
+
+2Department of Oncology, The First Affiliated Hospital of USTC, Division of Life Sciences and Medicine, University of Science and Technology of China, Hefei, Anhui, China
+
+3Department of Rheumatology and Immunology, The First Affiliated Hospital of USTC, Division of Life Sciences and Medicine, University of Science and Technology of China, Hefei, Anhui, China
+
+4Department of Endocrinology, The First Affiliated Hospital of USTC, Division of Life Sciences and Medicine, University of Science and Technology of China, Hefei, Anhui, China
+
+5Department of Pulmonary and Critical Care Medicine, The First Affiliated Hospital of USTC, Division of Life Sciences and Medicine, University of Science and Technology of China, Hefei, Anhui, China
+
+6Department of Scientific Research, The First Affiliated Hospital of USTC, Division of Life Sciences and Medicine, University of Science and Technology of China, Hefei, Anhui, China.”
+
+In the “Correspondence” section, the text “Division of Life Sciences and Medicine, Department of Scientific Research, The First Affiliated Hospital of USTC, University of Science and Technology of China, Hefei, Anhui, China” was incorrect. This should be: “Department of Scientific Research, The First Affiliated Hospital of USTC, Division of Life Sciences and Medicine, University of Science and Technology of China, Hefei, Anhui, China.”
+
+We apologize for this error.
+
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+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: IEEE Trans Comput Imaging
+Journal ID: IEEE Trans Comput Imaging
+NLM Journal ID: 101660833
+
+IEEE transactions on computational imaging
+
+ISSN: 2573-0436
+EISSN: 2333-9403
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC13251729
+Article ID: NIHMS2181623
+PMID: 42281598
+DOI: 10.1109/tci.2026.3694126
+Article ID: NIHMS2181623
+Article ID: NIHPA2181623
+Article version: 1
+Subjects: Article
+
+2D Ultrasound Elasticity Imaging of Abdominal Aortic Aneurysms Using Deep Neural Networks
+
+http://orcid.org/0009-0002-9744-0098 Tuladhar Utsav Ratna Rochester Institute of Technology, Rochester, NY 14623 USA
+
+Simon Richard Rochester Institute of Technology, Rochester, NY 14623 USA
+
+Mix Doran University of Rochester Medical Center, Rochester, NY 14642 USA
+
+Richards Michael S. Rochester Institute of Technology, Rochester, NY 14623 USA, and also with the University of Rochester Medical Center, Rochester, NY 14642 USA
+
+Corresponding author: Utsav Ratna Tuladhar. ut3320@rit.edu
+Print publication date: 2026
+Electronic publication date: 2026 May 18
+Volume: 12
+First page: 921
+Last page: 934
+Author manuscript; available in PMC: 2026 Jun 11
+License: This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Keywords: Ultrasound, elastography, medical imaging, deep learning, inverse problems
+
+Ÿ==============================Ÿ
+Abdominal aortic aneurysms (AAA) pose a significant clinical risk due to their potential for rupture, which is often asymptomatic but can be fatal. Although maximum diameter is commonly used for risk assessment, diameter alone is insufficient as it does not capture the properties of the underlying material of the vessel wall, which play a critical role in determining the risk of rupture. To overcome this limitation, we propose a deep learning-based framework for elasticity imaging of AAAs with 2D ultrasound. Leveraging finite element simulations, we generate a diverse dataset of displacement fields with their corresponding modulus distributions. We train a model with U-Net architecture and normalized mean squared error (NMSE) to infer the spatial modulus distribution from the axial and lateral components of the displacement fields. This model is evaluated across three experimental domains: digital phantom data from 3D COMSOL simulations, physical phantom experiments using biomechanically distinct vessel models, and clinical ultrasound exams from AAA patients. Our simulated results demonstrate that the proposed deep learning model is able to reconstruct modulus distributions, achieving an NMSE score of 1.6%. Similarly, in phantom data, the predicted modular ratio closely matches the expected values, affirming the model’s ability to generalize to phantom data. We compare our approach with an iterative method which shows comparable performance but higher computation time per reconstruction. In contrast, once trained offline, the deep learning method can provide quick and accurate estimates of tissue stiffness from ultrasound images, so as to provide near real-time predictions of AAA growth.
+
+I. Introduction
+
+Abdominal aortic aneurysms (AAA) are a life-threatening cardiovascular disease characterized by localized enlargement and weakening of the abdominal aorta. Left untreated, the progression of an aneurysm can lead to its rupture, a catastrophic event associated with a high mortality rate [1]. In addition, AAAs are often asymptomatic, highlighting the importance of early detection and continuous monitoring [2]. Most AAAs are identified incidentally through screening programs or diagnostic imaging for unrelated conditions. Individuals with certain risk factors [3], such as old age, male sex, smoking history, or a family history of aneurysms, are at increased risk and therefore are prioritized for screening [4]. For such screening, ultrasound imaging is a particularly reliable and preferred method [5], [6] due to its accurate visualization of the aorta, as demonstrated by Sprouse et al. [7], as well as its non-invasive, safe, and widely accessible nature.
+
+Accurate assessment of the risk of rupture of an aneurysm remains a challenge, although advances in imaging techniques have improved diagnosis and monitoring. Usually, the risk of AAA rupture is assessed by measuring the maximum diameter of the aorta from ultrasound images [8]. However, diameter alone is not a sufficient indicator of rupture risk [9]. Although diameter analysis has been widely adopted in clinical practice, it does not account for the multi-factorial nature of AAA pathogenesis [10]. The risk of progression and rupture of an aneurysm is influenced by various factors beyond the geometry, such as the biomechanical properties of the aortic wall [11], [12], [13]. Among these properties, stiffness is particularly significant as it provides direct insight into the structural integrity of the aortic wall [14], [15]. Since ultrasound is already used to obtain clinical measures of AAA size, our proposed technique could potentially use these same scans to measure the stiffness of the vessel with minimal changes to standard clinical practice.
+
+To address the inadequacy of diameter alone in AAA risk assessment, an adjunct modality to ultrasound imaging, elastographic strain imaging, has emerged as a promising tool for estimating tissue stiffness [16]. Elasticity imaging, an additional step to strain imaging, calculates stiffness by solving an inverse problem using elastography-derived displacement fields measured from ultrasound [17]. This approach helps to estimate the biomechanical behavior of the aortic vessel, providing a better understanding of aneurysms. Traditionally, iterative techniques have been used to solve the inverse problem. However, these methods often suffer from high computational complexity [18]. Recently, with the rapid advancement of deep learning, data-driven approaches have shown great potential to solve inverse problems more efficiently [19].
+
+Early work by Bonnardeaux et al. [20] tracked the physiologic motion of the aortic wall, to calculate the strain, from the B-mode ultrasound images. Similarly, Trachet et al. [21] conducted a comprehensive in-vivo study of AAA in mice comparing various ultrasound modalities for strain estimation. Fromageau et al. [22] demonstrated the feasibility of applying elastography to abdominal aortic aneurysms (AAA) by computing the strain measured from ultrasound data. Mix et al. introduced a pressure-normalized strain imaging approach to detect changes in stiffness. Their method involved measuring maximum principal strain (the spatial derivative of displacement), which serves as a surrogate to estimating the stiffness [23].
+
+Voizard et al. [24] explored shear wave elastography to calculate stiffness in the aortic sac after endovascular aneurysm surgical repair. They also noted that shear wave signals can go undetected in certain regions, particularly in the posterior wall, limiting consistent quantification. Disseldorp et al. used 3D ultrasound to track vessel wall displacements and applied an iterative characterization method to estimate stiffness distributions [25]. This approach relied on sophisticated 3D ultrasound probes, which are not commonly available in standard clinical settings. Long et al. proposed a method to quantify the compliance, the inverse of stiffness, from the US Doppler images of AAA [26]. Our proposed method uses 2D ultrasound to capture stiffness variations, offering greater accessibility and clinically useful mechanical insights with simpler imaging hardware.
+
+In recent years, deep learning techniques have shown promise in the field of medical imaging and in solving complex problems. Deep learning can also make complex mappings between the input and output images [27]. The use of such a technique has also been extended to the field of ultrasound elastography to calculate the properties of the material [28]. Convolutional neural networks (CNNs) in particular have been applied to estimate strain directly from raw radiofrequency (RF) ultrasound data [29], [30]. To solve the inverse problem and infer stiffness, Tuladhar et al. proposed a U-Net-based architecture to reconstruct stiffness maps from US measured displacement fields [31].
+
+The application of deep learning to AAAs is still an emerging field, but its potential has been highlighted in related work. Lu et al. [32] and Hong et al. [33] employed deep neural networks to segment AAAs in computed tomography (CT) scans, enabling more accurate anatomical localization and measurement. Similiarly, Maas et al. proposed a deep learning approach for automatic AAA segmentation in ultrasound images [34]. However, the integration of deep learning with ultrasound elastography for AAAs remains largely unexplored, leaving a key gap in biomechanical assessment.
+
+To address these gaps, we introduce a deep learning framework for elasticity imaging of abdominal aortic aneurysms. We first generate a comprehensive dataset through finite element (FE) forward modeling, which simulates realistic displacement fields resulting from diverse underlying modulus distributions. In this work, we use the shear modulus as our specific quantitative measure of tissue stiffness. For brevity, the term ‘modulus’ and ‘shear modulus’ are used to exclusively refer to the shear modulus throughout the remainder of this paper. We then train a U-net based deep neural network using normalized mean squared error (NMSE) as the loss function to learn the mapping between the displacement field and the corresponding spatial modulus distribution. To validate the model’s generalizability and clinical relevance, we evaluated the trained network on several forms of realistic displacement data measured from simulated, phantom and clinical ultrasound image data. First, we test the trained network on digital phantom data generated via 3D COMSOL simulations. Next, we expand the experimental scope to include physical phantom experiments involving four different types of vessels, designed to mimic varying biomechanical conditions. Finally, we assess the performance of the model on clinical ultrasound exams of human patients with AAA, demonstrating real-world applicability. We evaluated the output of the simulated data using a NMSE comparison of the reconstructed modulus image and the true forward modulus image. In addition, for the simulated data and experimental data, we calculated the ratio of the modulus between regions of the vessel with expected values. Using the same measured displacement fields as inputs, we compared these outcome metrics for our deep learning (DL) based predictions with results obtained from an iterative elasticity reconstruction method (ITR). The ITR algorithm used here is adapted from that used in Richards et al. [18].
+
+In summary, the contributions of this study are: (1) the development of a comprehensive and physiologically relevant dataset for the imaging of elasticity of aortic vessels; (2) the training of a deep learning model to estimate the distribution of the modulus from the displacement field; (3) the application of this model in simulated, experimental phantom and clinical data, highlighting its potential for clinical translation; and (4) comparison with an iterative method. Unlike prior work, where we focused on strain estimation, our approach here directly targets the reconstruction of shear modulus fields, thereby advancing the capability of ultrasound elastography to produce quantitative tissue parameter characterization.
+
+II. Data Generation and Acquisition
+
+A. Simulated Data With Finite Element Modeling
+
+Our deep learning approach leverages a data-driven framework to model the relationship between displacement fields and modulus distributions. Using a 2D, nearly incompressible plane strain finite element (FE) model, we simulated modulus distributions and their corresponding displacement fields to create a dataset to train the DL model. The FE simulations incorporated the various components as depicted in Fig. 1. The inputs included the spatial shear modulus distribution representing the 2D modulus distribution of the aortic vessel and the surrounding tissue domain, the vessel’s geometry discretized into an FE mesh, and boundary conditions applied at the tissue domain boundary and the inner wall of the vessel. The FE mesh was composed of triangular elements with nodes distributed over a grid spanning [0.12, 0.12] m in the x-direction and [0, 0.20] m in the y-direction. The outputs from the model were the displacement fields in the x and y direction, denoted as ux(x,y) and uy(x,y), respectively. To create the spatial modulus distribution, we first constructed an aortic geometry by varying the inner radius of the vessel wall and the wall thickness. We simulated the variability of the inner radius with the following equation: (1) r(θ)=ro+∑i=13Aicos(2πiθ+ψ).
+
+Here, ro is the base radius randomly selected between 1.5cm and 2.5cm. Variations in radius were brought about by adding a sum of harmonic perturbations to the base radius, as seen in (1). In this equation, Ai is the amplitude of the ith perturbation and is randomly chosen between 0 and 1cm. In (1), ψ is a random phase with an offset ensuring non-aligned perturbations, and θ is the angle from 0 to 2π. Thus, the radius varied between 1.5cm to ~4 cm throughout the dataset which is the typical range for aneurysms [35]. We also shifted the center of the geometry randomly between ± 5 mm in X direction and ±1 mm in the Y direction.
+
+Similarly, for the thickness of the aorta, we use the following equation: (2) h(θ)=h0+∑i=12Bi(1+cos(2πiθ+ψ)).
+
+Here, h0 is the base thickness, set as 5 mm, and with similar perturbations applied such that Bi varies between 0 and 5 mm, the vessel thickness is varied between 5 mm to ~ 25 mm throughout the dataset, which is the estimated range for the AAA patients [36].
+
+We also varied the magnitude of the modulus angularly (around the perimeter of the vessel) with the following equation: (3) μn(θ)=μ0+∑i=13Ci(1+cos(2πiθ+ψ)),
+
+where μ0 is the base shear modulus of 1 kPa and Ci is the amplitude of the ith harmonic variations and is randomly selected between 0.75 and 1.5 kPa. Again, ψ is a random phase offset and θ is between 0 to 2π. To simulate regions with more drastic changes in mechanical properties, mimicking the heterogeneity in the vessel wall that could arise from localized tissue remodeling [37], we modified the function of (3) as follows: (4) μ(θ)=μ1(θ),ifθ0<θ<θ0+θ1μ2(θ),otherwise
+
+where θ0 randomly chosen between 0 and 2π and θ1 is randomly chosen between 2π/3 and π. The distribution μ1(θ) was normalized to a range of 1 to 2 kPa, while the distribution μ2(θ) was normalized to a range from 0.25 to 10 kPa. Finally, for half of the generated modulus functions a Gaussian filter, applied angularly, was used to give a smooth transition between regions, thus resulting in modulus distributions with both sharp and smooth transitions in simulated material properties. Ultimately, the values of the shear modulus functions varied between 0.25 kPa to 10 kPa throughout vessel regions in the dataset. In this work, we only modeled variations angularly around the vessels. Radial variations were not modeled. The shear modulus of the background tissue (outside the vessel) in the models, μb, was set at a constant of 5 Pa in all simulations. Variations in the boundary conditions were implemented as follows. The point in the center of the models, as shown in Fig. 1, was fully fixed in both the x and y directions, that is, ux(0.20,0)=uy(0.20,0)=0.0. The remaining displacement magnitudes along the top edge (that is, at x=0.20) were randomly selected to be fixed in the x-direction or traction-free, that is, ux(0.20,y)=0.0 or τx(0.20,y)=0.0. The remaining boundary conditions on this surface were traction-free (i.e. τy(0.20,y)=0.0). Similarly, the bottom point, as shown in Fig. 1, of all models was fixed in the y direction, i.e. uy(0.05,0)=0.0 and the remaining bottom edge was randomly chosen to be fixed in the x direction (i.e. ux(0.05,y)=0.0) or traction-free τx(0.50,y)=0.0. All other outer boundary conditions were traction-free. We used a traction boundary condition on the vessel inner lumen, approximating a hydrostatic pressure normal to the surface of the lumen as follows: (5) τP=Pn,
+
+where, n is the unit vector function normal to the inner lumen wall (see Fig. 1(a)). The magnitude of the pressure (P) was also varied randomly between 1 to 8 kPa.
+
+In this way, by systematically varying the geometry of the vessel, the modulus distributions, and the applied boundary conditions, we generated a comprehensive dataset consisting of paired samples of the spatial modulus distribution and their corresponding displacement fields. To further enhance the variability, we also added random translations to the displacement fields. Furthermore, prior to training our DL model, we normalized the displacement fields by the applied pressure, resulting in pressure-normalized displacement fields that allow quantitative modulus estimation [23]: (6) u~x(x)=ux(x)/P,and
+
+(7) u~y(x)=uy(x)/P.
+
+Lastly, the displacement fields and the modulus fields were interpolated from the FE mesh to a regularly spaced grid, which was the same for all models, of 128 × 128 pixels, with a pixel spacing in x and y of 0.86 mm (see Fig. 4(c)). The pixels in the interpolated images that were located outside the vessel FE mesh elements were set to 0. This provided our deep learning model with an implicit segmentation of the vessel lumen. This dataset, consisting of input images u~ijx and u~ijy and output image μij, forms the basis for training our deep learning model to solve the inverse problem in elastography. Our training set includes 30,000 paired examples of 128 × 128 sized displacement and modulus images. Similarly, we created a validation and test dataset containing 3,000 examples each for a total of 36,000 forward, FE simulated models. The domain characteristics of the training dataset are as follows. The average displacement magnitude is 0.14 ± 0.18 m. The mean modulus is 2.7 ± 2.0 kPa. The average maximum modulus is 4.3 ± 3.2 kPa, while the average minimum modulus is 1.4 ± 1.6 kPa. The mean pressure is 4.47 ± 2.01.
+
+B. COMSOL Data
+
+A central, transverse slice of displacement data was acquired from 3D FE simulations (COMSOL) with known modulus variations of the ventral wall of the aorta to create simulated US images of the deforming aorta using a point spread function approximating a curvilinear transducer.
+
+A 3D finite element (FE) model of the abdominal aorta was constructed in COMSOL Multiphysics software to simulate physiologically relevant deformation under a pressure load. The model geometry consisted of a cylindrical segment with a localized aneurysmal bulge, representing the aneurysm. The aortic wall was modeled as a linearly elastic, nearly incompressible material (with Poisson’s ratio of 0.495) with regionally varying Young’s modulus. Material properties were specified by dividing the wall into two longitudinal zones as shown in Fig. 2, with the lower region assigned a fixed Young’s modulus of 200 kPa and the upper region assigned a varying modulus within values of 100, 200, 400, and 800 kPa to simulate stiffness contrasts. The Young’s modulus of the background tissue, as shown in gray in Fig. 2(b), was set to 10 kPa in all models. The FE mesh was generated using tetrahedral elements. The average size of the mesh was 3.25mm3 inside the vessel and 23.6mm3 outside the vessel. A static internal pressure (PCM) of 5.33 kPa, mimicking pulse pressure of 40 mmHg, was applied to the inner lumen. The outer anterior surface, where the ultrasound transducer would contact the tissue, was fixed to mimic the transducer-tissue interaction. The linear elastic solver computed the full 3D displacement field across the aortic vessel. From this output, a central, transverse 2D slice orthogonal to the vessel’s axis was extracted, capturing the displacement behavior across the aneurysmal region. This 2D displacement field was used to simulate realistic radio-frequency (RF) US images by convolution of a 2-D point spread function (PSF) with point scatterers in an image plane. The PSF was defined to mimic the point response of the Ultrasonix C7–3/50 convex transducer [23]. RF US of deformed tissue were created by deforming the same point scatterers using COMSOL generated displacement fields, within the plane of the image, and repeating the image simulation process.
+
+C. Phantom Data
+
+Aorta mimicking US phantoms were also created, with varying material properties, and imaged with a 5 MHz, curvilinear US transducer [23]. Displacements were tracked and accumulated from diastolic to systolic pressure via registration of the RF image sequences and a novel regularization.
+
+Phantom data were acquired using an experimental setup as described in Mix et al. [23]. The phantoms, previously developed and characterized as shown in Table I, were submerged in a water bath and connected to a hemodynamic pump designed to produce physiologic cyclic blood flow profiles. The pressure profile, measured by a catheter-based pressure sensor (Millar Mikro-Cath, Auckland, New Zealand) proximal to the ultrasound imaging plane, was synchronized with ultrasound frames using a National Instruments USB-6251 DAQ (National Instruments, Austin, TX, USA). The pulse pressure for these phantoms (Pph) was calculated as the difference between the maximum and minimum pressures measured via the catheter during image acquisition. Ultrasound imaging was performed with a Sonix-TOUCH system (Analogic) and a C7–3/50 convex transducer at a center frequency of 5 MHz. Imaging settings included a 60% sector, 12 cm depth, and a single focus at the posterior wall. RF data were collected at a frame rate of 72 Hz over a 10-second interval (720 frames), corresponding to 10 cardiac cycles.
+
+D. Clinical Data
+
+Patients were prospectively recruited from the vascular surgery department at the University of Rochester Medical Center between July 2015 and August 2016. Eligibility was based on clinical need for a standard ultrasound screening exam for a suspected, newly diagnosed, or previously identified non-repaired abdominal aortic aneurysm (infrarenal or suprarenal). Exclusion criteria included individuals unable to provide informed consent, minors, and members of protected populations such as pregnant individuals and prisoners. Written informed consent was obtained from all participants prior to imaging. The study protocol was reviewed and approved by the office of the Research Subjects Review Board of the University of Rochester. For each enrolled patient, raw RF image data was collected using the same ultrasound machine and imaging settings as those used for phantom acquisitions. Systolic and diastolic frames were identified, via visual inspection, using B-mode image sequences. In addition, blood pressure measurements were taken immediately before and after ultrasound examination using a pressure cuff. The patient’s pulse pressure (Pcl) was then calculated as the difference between the recorded systolic and diastolic blood pressures, converted to kPa, averaged between the two measurements. [23]. Further details of the clinical protocol can be found in Zottola et al. [38]. We applied our methods to four patients collected from this clinical study.
+
+The summary of various dataset distribution and splits is described in Table II.
+
+III. Image Processing and Analysis
+
+A. Image Registration for Displacement Estimation
+
+An image registration algorithm was used to measure tissue displacements from RF US images for phantom and clinical data. We calculated the total accumulated displacement field within the vessel wall and surrounding tissue (excluding the blood lumen) from diastole to systole to capture the vessel wall deformation. The details of the registration algorithm can be found in Tuladhar et al. [31]. Briefly, displacements were computed sequentially, frame-to-frame, and accumulated with respect to the diastolic frame as a reference. The optimization functional for the ith frame-to-frame displacement is: (8) πui(x)=12∫ΩIi-1x+ui-1(x)-Iix+ui(x)2dΩ+α∫Ω∇⋅Ai(x)dΩ,
+
+where Ai(x) is the constitutive relation for a linear elastic, homogeneous, incompressible material deforming under plane strain and can be written as: (9) Ai(x)=2ν1-2ν∇⋅ui(x)I+∇ui(x)+∇ui(x)T.
+
+In (8) the first term estimates the displacement field that best captures the deformation of the tissue, as realized by spatial shifts of image intensity, while the second term is a regularization that penalizes deformation patterns that are physically inconsistent with plane strain [39]. In this work, a value of ν=0.45 was used, as the tissue was assumed to be nearly incompressible. The frames corresponding to minimum diastole, where u0(x)=0, and maximum systole were manually identified by a vascular surgeon based on B-mode image sequences [23]. The displacements were measured from only two frames that corresponded to the point of minimum diastolic pressure and the maximum systolic pressure. Segmentation of the boundary between the vessel and blood and the boundary between the vessel and surrounding tissue was manually segmented by a vascular surgeon using the B-mode image at minimum diastole [23]. Fig. 4(a) shows an example B-mode image of a phantom. Displacement fields were measured within the vessel wall and surrounding tissue on a finite element (FE) discretized mesh of quadrilateral elements, created using open-source mesh generation software [40]. The average area of the FE elements were 0.027 ± 0.015 cm2. An example FE mesh is shown in Fig. 4(b).
+
+The output of the image registration algorithm was the axial and lateral components of the displacement field, within the vessel wall and surrounding tissue on the FE mesh. For all displacement field measurements to be input into the deep learning model, the displacement field grid values within the vessel were interpolated onto a regular grid as shown in Fig. 4(c). Again, the gridded values within the surrounding tissue and blood regions were zeroed for both components. Normalized displacement fields, u~ijx and u~ijy, were found by dividing the COMSOL measurements with the forcing pressure BC used in the forward simulation (PCM=5.33kPa), the phantom measurements by the pulse pressure measured independently during the experiments (Pph) and the clinical measurements by the measured pulse pressure (Pcl) found using the blood pressure cuff at the time of clinical scan.
+
+The input to the iterative reconstruction algorithm was the displacement field on the registration mesh, both within the vessel and within the surrounding tissue, and thus no interpolation or normalization was performed for those input data.
+
+B. Iterative Method for Modulus Reconstruction
+
+A model-based optimization algorithm was used to reconstruct the modulus distribution (μitr(x)) from the measured displacement fields of the COMSOL, phantom, and clinically acquired US image data. The algorithm is based on a soft prior reconstruction technique described in Richards et al. [18], previously developed for intravascular ultrasound elastography. First, a 2D finite element model was created, using a constitutive equation for a nearly incompressible material that deforms in plane strain, with two domains, the vessel and the surrounding tissue, as shown in Fig. 4. The Poisson ratio of the entire domain was set to ν=0.45 and the shear modulus values within the vessel domain are the optimized parameters. A 2D traction vector function, τo, is applied to the outermost edge of the domain of this model and a pressure boundary condition, τP with magnitude Pit such that τP(x)=Pitn(x), is applied to the blood lumen wall. Here, n(x) is a unit vector function defined on the inner lumen, ΓP, that is everywhere normal to that boundary.
+
+The iterative algorithm used here consists of two steps. The first step solves for the boundary conditions of the desired domain, keeping the modulus distribution fixed, which minimizes the difference between the total measured displacement field (um(x)), from diastole to max systole, and a model-predicted displacement field up(x), in the least squares sense. The optimization functional for this step is as follows: (10) πBτo,Pit=12∫Ωupτo,Pit-um2dΩ,
+
+where Ω is the modeled domain. Using the same FE discretization as was used in the registration algorithm described in Section III-A, we can rewrite (10) as the following matrix equation: (11) π‾B=u‾p-u‾mTDu‾p-u‾m,
+
+where u‾p is an array of both components (x and y) of the discrete displacement fields, defined at the nodal positions, and u‾m is an array of the same size consisting of the measured values of the displacement fields. Here, D is a matrix that performs the integration of shape functions for the least squares difference of the measured and predicted displacement fields using a 3 × 3 Gauss quadrature integration.
+
+To constrain the displacement fields in (10), we also define a forward FE model for a nearly incompressible material deforming in 2D plane deformation (within Ω) with the following weak form of a static linear elastic material (neglecting body forces) as: (12) ∫Ω∇G(x)Ap(x)⋅w(x)dΩ=0
+
+where Ap(x) is defined in (9) with ν=0.45,G(x) is a scaled version of the modulus distribution, and w(x) are the weighting functions of the displacement field [41]. The tissue is modeled under the assumptions of a linear elastic, isotropic, and nearly incompressible material deforming in plane strain. In this algorithm, we chose to use a unitless modulus function, G(x), where the regularization keeps the mean of G(x) approximately equal to 1 within the vessel domain. We then search for the boundary conditions that result in the best match to our measured displacement field, given that modulus. The modulus is then scaled to a quantitative magnitude in post-processing. With only traction boundary conditions, integration by parts can be used to rearrange (12) as (dropping the explicit dependence on x): (13) ∫Ω∇w⋅GApdΩ=∫Γw⋅tdΓ.
+
+Here, t are the traction boundary conditions that we define to exist on the entire boundary of the domain, Γ. The boundary can also be divided into the inner lumen boundary ΓP and the outer boundary of the background tissue Γo such that Γ=ΓP∪Γo. We then define the traction boundary conditions in 3 parts: the pressure in the inner lumen, Pit, the traction vector function on the outer boundary, τo, and a weak spring-like traction on the outer boundary, necessary to avoid rigid body translations and rotations and to keep the predicted displacements close to the measured values on that boundary. Thus, (13) can be written more explicitly as: (14) ∫Ω∇w⋅GApdΩ=∫Γow⋅τodΓo+⋯ks∫Γow⋅um-updΓo+∫ΓPw⋅τPdΓP.
+
+Here n is a function defining the normal vector to the inner lumen wall as shown in Fig. 1(a). Assuming that μ(x) is known and fixed and using the same FE discretization as above, we can plug (5) into (14) and perform the integrations to find the following matrix equation: (15) Ku‾p=Foτ‾o+ksFou‾m-u‾p+fPPit,
+
+where K is the stiffness matrix representing the integrations of the LHS of (14), performed within quadrilateral elements using a 3 by 3 Gauss quadrature numerical integration with reduced integration of the displacement dilatation term of Ap(x) to avoid mesh locking [41]. Then, τ‾o is an array of both components of the discrete traction on the outer boundary, only nonzero at the nodes on the outer boundary. Fo is a matrix that performs the integration of the first term of the RHS of (14) using a 1D, 3 point Gauss integration method on the edges of the elements along the outer surface of the domain. This matrix is the same size as K and mostly sparse, except for the row/column locations corresponding to nodes on the outer boundary. Lastly, fP is an array the same size as τ‾oT that corresponds to the integration of ∫ΓPw⋅ndΓP, again using a 1D, 3 point Gaussian integration method. Equation (15) can be rearranged to solve for u‾p as follows: (16) u‾p=K+ksFo-1Foτ‾o+fPP+ksFou‾m.
+
+and plugged into (11) to result in a linear equation for the boundary parameters (that is, τo and P), which can be solved directly via linear least squares. In all inversions done in this work, ks=1e-3 was chosen empirically such that ksum-up≪τo but large enough to keep the matrix inversion in (16) well posed.
+
+The second step of the reconstruction method solves for the modulus distribution (G(x)) of the desired domain, keeping the boundary conditions found in the first step, τo and P, fixed. Here, the difference between the total measured displacement field and a model-predicted displacement field is minimized, as in the first step, in the least squares sense. However, the modulus field in the second step is updated iteratively using a quasi-Newton method. The details of the optimization algorithm were published previously in Richards et al. [18]. The algorithm developed there was adapted for use in this paper. As in Richards et al. [18], the second step also uses a priori information for modulus recovery, incorporated into the regularization, to improve the ill-posedness of the inverse problem. The optimization functional utilized here is as follows: (17) πμ[Gˆ(x)]=12∫Ωup[G(x)]-um2dΩ+α∫Ω∇cG(x),G0(x)dΩ.
+
+Here, G(x) is the modulus distribution within the entire solid tissue domain Ω,Gˆ(x) are the modulus values that fall within the wall of the vessel and G0(x) is the nominal function that serves as the prior spatial information to which the modulus is regularized. In this work, the value of G0(x) within the vessel was set to a value of 1 and the value in the surrounding tissue was set to 0.001. Thus, we make the implicit assumption that the segmented surrounding tissue has a shear modulus that is one order of magnitude lower than the logarithmic mean of the modulus within the vessel. These modulus values also served as the initial guess to the modulus field. Note that we only search for, and thus update, the values of the modulus within the vessel. Thus, the modulus values within the surrounding tissue remain constant at 0.1. The function cG,G0 here serves as the logarithmic regularization function, used to remove the dependence of the regularization on the general magnitude of the modulus and the assumed contrast between the modulus of the vessel and the surrounding tissue: (18) cG,G0=lnG/G0.
+
+Thus, the regularization used here is a TVD-type regularization of the logarithmic function cG,G0 [18]. Only the modulus values within the vessel (that is, Gˆ(x)) were allowed to update. The modulus of the background tissue was held fixed. Equation (14) was used, with τo and P fixed, as the constraint equation of the model and an adjoint method was used to calculate the gradient of (17) as described by Richards et al. [18]. Optimization was performed using Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm with 5 update iterations each time the second step was performed.
+
+All reconstruction methods were implemented in MATLAB (The Mathworks Inc., Natick, MA, United States). The stiffness matrix and boundary integration matrices were stored as sparse matrices in MATLAB. We ran 100 total iterations (Step 1 then Step 2) to arrive at the output reconstructed modulus. Furthermore, we scaled the reconstructed modulus field with the independently measured pulse pressure to obtain the quantitative value of the modulus in kPa (i.e., μitr(x)=PP×G(x)/Pit), where PP was equal to PCM,Pph, or Pcl depending on the data source, and interpolated from the FE mesh onto the same uniform spatial grid of 128 × 128 pixels, as described in Section II-A, to arrive at our discrete, quantitative modulus image, μijitr.
+
+C. Deep Learning for Modulus Reconstruction
+
+1) Deep Learning Framework:
+
+In this work, we formulate the problem as an inverse elasticity problem, where the objective is to estimate the spatial distribution of shear modulus from pressure-normalized displacement fields. We used a deep learning framework of convolutional neural networks (CNNs) to learn the mapping between the pressure-normalized displacement fields and the spatial distribution of modulus as shown schematically in Fig. 5. Specifically, both the axial and lateral displacement fields are used as input channels.
+
+Preprocessing:
+
+First, the computational domain was discretized into a uniformly spaced grid of 128 × 128 pixels. Each point in the grid (i,j) corresponded to a spatial location, where u~ijx and u~ijy denote the axial and lateral components of the input displacement fields, respectively, and μij represents the modulus output image. As discussed in Section II-A, only those values of the input and output images that were within the vessel wall had non-zero values. This served to provide our CNNs with an implicit vessel geometry. To ensure a consistent scale for the DL model and stabilize training [42], we further normalize our input displacement fields by the maximum of displacement magnitude, nm, calculated as: (19) nm=maxi,ju~ijx2+u~ijy2,
+
+where ()2 denotes a pixel-wise squaring. Then, we divide the displacement field images: (20) uˆijx=u~ijx/nm;uˆijy=u~ijy/nm,
+
+and normalize the corresponding modulus image by multiplying with the same factor: (21) Gij=μij×nm.
+
+This results in normalized axial (uˆijx) and lateral (uˆijy) displacement field images and a normalized modulus image, Gij, used to train our DL model.
+
+Postprocessing:
+
+All modulus images output from the fully trained model are rescaled to a quantitative modulus such that the values are in units of kPa: (22) μijdl=Gij/nm.
+
+This normalization and rescaling procedure was applied to ensure that displacement fields and modulus fields are within a consistent scale as they pass through our DL model.
+
+2) Network Architecture:
+
+We utilized a U-net based architecture [43], which is well-suited for tasks requiring precise localization and spatial understanding. Specifically, reconstructing the modulus distribution from displacement fields is fundamentally an image-to-image translation problem. The U-Net architecture has skip connections that allow the network to retain the high-resolution information that would otherwise be lost during downsampling. Additionally, we drew inspiration from the Pix-to-Pix framework [27] widely used for image-to-image translation. However, in our implementation, we used the generator component with a loss function as it was more appropriate with our objective of predicting continuous-valued outputs. This neural network consisted of 7 downsampling layers in the encoder and 7 upsampling layers in the decoder, with a latent dimension of 512. Specifically, each downsampling block consists of a 4 × 4 convolutional layer with a stride of 2, followed by batch normalization and a leaky ReLU activation function. Conversely, each upsampling block in the decoder utilizes a 4 × 4 transposed convolution with a stride of 2, followed by batch normalization, and a standard ReLU activation. The skip connections merge the encoder and decoder features via channel-wise concatenation.
+
+3) Loss Function:
+
+To train the model, we employed the normalized mean squared error (NMSE) as the loss function between the ground truth normalized modulus (Gijt) and the predicted normalized modulus (Gijp), defined as: (23) ℒNMSE=NMSEGijt,Gijp,
+
+where, (24) NMSEAij,Bij≔∑i=1128∑j=1128Aij-Bij2∑i=1128∑j=1128Aij2,
+
+and the ()2 operations are applied pixel-wise.
+
+4) Evaluation Metrics:
+
+To evaluate the performance of the DL model on the validation and test sets, we calculated the NMSE loss between the predicted rescaled modulus μijdl, obtained from (22), and the corresponding ground truth modulus (μij) from the dataset, calculated using (24), (i.e., NMSE μij,μijdl).
+
+In addition, to assess the model’s ability to accurately localize the aorta, we calculate the dice score coefficient (DSC) [44]. To calculate DSC, we first created binary masks (Bijt) from ground truth modulus distribution by: (25) Bijt=1,ifμij>00,otherwise.
+
+The binary mask from the predicted modulus distribution (Bijp) was computed similarly. The overlap between Bijt and Bijp was then measured using the DSC: (26) DSC=2∑i=1128∑j=1128Bijt⊙Bijp∑i=1128∑j=1128Bijt+∑i=1128∑j=1128Bijp,
+
+where ⊙ is the element-wise Hadamard product. The DSC score ranges from 0 to 1, where 1 indicates perfect overlap between the predicted and true mask, and 0 indicates no overlap.
+
+5) Training and Validation:
+
+During training, model performance was monitored using the validation set, evaluating the performance at regular intervals. The model checkpoint corresponding to the lowest validation NMSE was selected for further evaluation. We trained our DL model for 500 epochs. We trained our model using TensorFlow. We used a batch size of 32 and an Adam optimizer with a learning rate of 2 × 10−4. Fig. 6 shows the NMSE loss for both the training set (blue) and the validation set (orange) across the training process. The final model was selected at the epoch corresponding to the minimum validation loss, which occurred at epoch 166 with an NMSE of 0.016. After training completion, the model was applied to the displacement data from four domains — simulated test cases, COMSOL-generated digital phantoms, tissue-mimicking phantom experiments, and clinical datasets, to assess generalizability and robustness.
+
+IV. Results
+
+A. Simulated Test Data
+
+We evaluated our DL model on the test dataset to assess its performance. Our DL model achieved a mean NMSE error of 0.016 across the test dataset. A detailed summary of various performance metrics is presented in Table III. We also present two samples from the test set in Fig. 7. The figure shows the two input displacement fields, the ground truth, and the predicted modulus distribution. These inputs and outputs undergo the preprocessing and postprocessing steps described in the earlier section. For example (a), the NMSE is 0.015 and the DSC is 1.0, and similarly for example (b), the NMSE is 0.008 and the DSC is 1.0.
+
+These results demonstrate that the model performs well on the simulated data. The low NMSE values and high DSC score confirm that the predicted outputs closely match the ground truth, both quantitatively and spatially. We further extend the model to the real-world data.
+
+B. COMSOL Data
+
+For our digital phantoms simulated from COMSOL, we first calculated the displacement fields from 3D simulated ultrasound images using the image registration algorithm as described in Section III-A. We then input the displacement fields into both ITR and DL reconstruction techniques to predict the modulus distribution. Our digital phantoms were designed with two distinct regions, upper (anterior) region and a lower (posterior) region, composed of different material property. Hence, we divided the predictions into four quadrants (upper, lower, right, and left) with the two corner-to-corner diagonals of the image, assuming their intersection approximated the vessel center. In our digital phantoms, the stiffened region consistently occupied the upper quadrant of the vessel, while the lower quadrant remained within the nominal background modulus region. We calculated the modular ratio between the upper and lower regions, using the equation: (27) Modular Ratio(η)=Modulus of upper regionModulus of lower region.
+
+Table IV provides the details of the evaluation metrics we used for the COMSOL data for both the DL and ITR methods. It reports the NMSE score for both methods. Additionally, the modulus values for the upper and lower regions of the four different digital phantoms are summarized in this table where we report the mean and standard deviation for the expected modulus of the upper region (∖boldsymbolμup) and it’s predicted modulus with DL (DL-\boldsymbolμˆup) and ITR (ITR-\boldsymbolμˆup) method, expected modulus of the lower region (∖boldsymbolμlow) and it’s predicted modulus with DL (DL-\boldsymbolμˆlow) and ITR (ITR-\boldsymbolμˆlow) method, expected (∖boldsymbolη) and predicted modular ratios from DL (DL-\boldsymbolμˆlow) and ITR (ITR-\boldsymbolμˆlow) method. The images of the displacement fields and the predicted modulus distribution are shown in Fig. 8.
+
+C. Phantom Data
+
+For our experimental phantoms, we first calculate the displacement fields from ultrasound RF images using the image registration algorithm, as described in Section III-A. We then input the pressure-normalized displacement fields into both our ITR algorithm and the DL model and predict the modulus distribution. We divided the predicted image into four quadrants (upper, lower, right, and left) using the two corner-to-corner diagonals of the image. We assumed that the intersecting point of these diagonals coincided approximately with the center of the vessel. The stiffened region of our phantoms always covered the segmented upper quadrant of the vessel image, while the segmented lower quadrant vessel was within the nominal background modulus region. We then calculated the modular ratio between the two regions using (27).
+
+The results for the four different phantoms are summarized in Table V. In this table, we report the mean and standard deviation for the expected modulus of the upper region (\boldmathμup) and it’s predicted modulus with DL (\boldmathDL-μˆup) and ITR (lboldmathITR-μˆup) method, expected modulus of the lower region (lboldmathμlow) and it’s predicted modulus with DL (lboldmathDL-μˆlow) and ITR-(lboldmathITRμˆlow) method, expected (lboldmathη) and predicted modular ratios from DL (lboldmath DL-μˆlow) and ITR (lboldmath ITR-μˆlow) method. The images of the displacement fields and the predicted modulus distribution are shown in Fig. 9
+
+D. Clinical Data
+
+We applied our iterative algorithm and DL model to four patients collected from our previous clinical study. The displacement fields were obtained from US image sequences using the image registration algorithm, as described above. The B-mode images are shown in Fig. 10, which also depict segmented vessels, blood lumen in red, and outer vessel in green, found by an expert surgeon [38]. Upon applying our deep learning and iterative reconstruction method, we obtain the modulus reconstruction as shown in Fig. 11.
+
+V. Discussion
+
+In this study, we created a comprehensive simulated dataset of the 2D aorta that we used to train a DL model, which was then applied to both phantom and clinical data. We used pressure-normalized displacements as input to the DL model, inspired by the use of pressure-normalized strain proposed by Mix et al. [23], to allow quantitative calculation of the modulus. The modulus distributions predicted by our DL model from the axial and lateral displacement fields demonstrate strong performance across key evaluation metrics. The low NMSE in the predicted modulus values in the test set validates the quantitative accuracy of the model. Similarly, the high DSC indicates strong spatial agreement between the predicted and ground truth vessel regions. These results confirm that the chosen architecture is well suited for solving the inverse problem in elastography and effectively captures the underlying mechanical patterns in the data.
+
+For the COMSOL simulated digital phantoms, we obtained modulus values from both the DL model and the ITR algorithm. Overall, both approaches demonstrate consistent performance when applied to 2D cross-sectional data extracted from 3D simulations. When comparing the absolute modulus values from the upper and lower regions for the COMSOL data, both methods consistently overestimate the ground truth magnitudes across all four cases. This global overestimation of absolute stiffness magnitude is, in part, an artifact of applying the 2D plane-strain assumptions to 3D data with convex geometry out of plane. This geometry leads to an smaller overall strain magnitude compared to straight, tubular out of plane geometries. Despite the overestimation of absolute magnitudes, both methods capture the modular ratio with reasonable accuracy. Both methods, however, tend to underestimate the recovered contrast in almost all cases. This underestimation may arise because, even in a forward simulation, when localized modulus contrast is present in a modulus distribution, the differences in the displacement fields as the contrast increases become increasingly small and easily obscured by noise. We hypothesize that both models may err on the side of reduced contrast when faced with such data. In addition, the momentum-based regularization used here effectively penalizes large jumps in functions of the strains, which may also have reduced the apparent contrast in the modulus prior to being input into the DL and ITR methods. It is also likely that the loss of contrast recovery in the ITR technique could have affected the overall magnitude of the modulus. The algorithm may have adjusted the average modulus, rather than the contrast penalized in the regularization, to best match the displacement measurements. Furthermore, for the COMSOL dataset, the vessel geometry was not varied to isolate the effect of material heterogeneity; evaluation under varying geometries was instead performed using an experimental phantom dataset.
+
+Interestingly, for the phantom data, both the DL and ITR methods consistently overestimate the absolute modulus values in all cases, similar to the trend observed in the COMSOL generated data, however to a larger degree. This global offset could be exaggerated by the dynamic experiments that were performed in the phantoms. The viscoelastic nature of PVA phantoms may have led to an overall damping of the phantom motion and thus leas to an apparent stiffening [45]. Additionally, during experimental image collection of the phantom aortas, the aortas were placed in a softer, homogeneous background material, mimicking the vessels surrounding tissue (5% PVA, 2.6 kPa) [23]. The relative stiffenss of the background material is higher than the background modulus material used in both the DL and ITR methods. This model mismatch may also contribute to the overestimation of the reconstructed values. In general, a similar sitation is likely to exist in real clinical data as well as the surrounding tissues modulus is unknown. This is nevertheless consistent with other research in this field that extract only the vessel geometry from medical images for use in mechanical models and assume the outside vessel wall is traction free [46]. Moreover, discrepancies in the magnitude of the recovered modulus, in both techniques, could be attributed to inaccurate segmentation of the vessel wall. Base on inspection of the analytical equation presented in the supplemental material for an axisymmetric geometry, overestimation of the vessel thickness is expected to yield an underestimation of the magnitude of the modulus and vice versa. However, evaluation of the sensitivity of modulus magnitude in the general case is beyond the scope of this study and left to future work. It is also notable that the ITR method yields substantially noisier absolute estimates across all phantoms. This is likely driven by artifacts introduced by the regularization terms in the ITR optimization. In contrast, the DL method remains less susceptible to these specific artifacts, as it is bounded by the training data. For the modular ratio, the DL method generally provides more accurate and stable estimates than the ITR method. For Phantom 1 and 4, both methods overestimate the expected modulus contrast, though the DL method’s prediction remains closer to the expected values. For Phantom 2, the DL method slightly underestimates the ratio while the ITR method overestimates it; conversely, both methods underestimate the contrast in Phantom 3. While the reasons for the global offsets in absolute magnitude require further study, the DL method demonstrates a comparable capability to preserve and quantify the relative contrast between regions in experimental data. However, both approaches capture the contrast ratio with reasonable accuracy, which is itself a valuable biomarker [47].
+
+For ITR reconstructions, a noticeable radial variation was observed in the COMSOL predictions and, more prominently, in the phantom predictions. This artifact could be likely be attributed to the nature of the optimization and the regularization strategy. Clearly, iterative optimization had a bias toward increasing the magnitude of the modulus closer to the vessel lumen. However, such patterns do not appear in the DL reconstruction, likely due to the fact that radial variations were not present in the simulated data used for training.
+
+While the ITR approach is based on explicit regularization terms to ensure stability and converge to an optimized solution, the DL model learns from the large amount of data. Although the foundational approaches differ, one rooted in a physics-based model, while the other is data-driven, both methods yielded similar results. Incorporating physics into the deep learning framework could further enhance its performance, which could be a direction for future research.
+
+For the clinical data, where ground truth modulus values were not available, we performed a strain-based analysis of the measured displacement data. For each clinical case, we calculate the maximum principal strain distribution from the estimated displacement fields. From this we calculate the average maximum principal strain, within the vessel, and normalize to arrive at the pressure normalized maximum principal strain εP+¯, similar to that calculated in Mix et al. [23]. We also calculated the average of predicted modulus (μavg) for each clinical case. Theoretically, εP+¯, which is an estimate of vessel compliance, and μavg are expected to exhibit an inverse relationship between the images. This expected trend is indeed observed in Fig. 12, where both the DL and ITR estimated values show similar average modulus values and are seemingly correlated to 1/εP+¯, supporting the validity of our predictions even in the absence of ground truth values.
+
+To understand the model’s generalization performance across different dataset domains, it is important to consider the characteristics of the test datasets. Prior to using displacement fields as input, we start from raw RF data acquired from an ultrasound image sequence. Then we manually segment the vessel region, using B-mode images created from the RF data, and use the segmented geometry to create the FE mesh. Lastly, we estimate the displacement through image registration with a regularization penalizing deformations inconsistent with 2D plane strain. Thus, the resulting displacement measurements exhibit characteristics that are similar to those of the training data as described in Section II-A. Hence, we believe this alignment contributes to the strong performance observed across other datasets.
+
+In clinical practice, this DL-based framework could potentially be integrated into ultrasound software to provide pseudo real-time maps alongside standard B-mode imaging. Instead of relying solely on maximum diameter measurements, clinicians could examine the modulus magnitude or variations to make diagnostic determinations. This biomechanical assessment could help predict higher aneurysmal growth rates. A metric which incorporates functional information regarding the biomechanics of AAA is far more suggestive of the true disease state, potentially capturing the underlying elastin loss, strain hardening, or collagen turnover more than size alone [48].
+
+The computational efficiency of the DL method demonstrates a clear advantage over the ITR approach. The processing time for the DL prediction was on average 0.058 seconds per example, compared to 1295.1 seconds for 100 iterations (12.95 seconds per iteration) for the ITR method. The image registration took an average of 55.02 seconds per example, likely due to the accumulation process, which could be reduced with more optimized algorithm. This highlights the effectiveness of DL as a powerful tool for modulus reconstruction, with strong potential for real-time application in the future. One of the limitations of this study is that the simulated training data was restricted to 2D. Although it would be possible to generate 3D data, as in the COMSOL simulations, this approach is highly time consuming and computationally expensive. In the future, we plan to investigate simplified 3D models that may simulate a 3D deforming material, but with limited geometries or using simplified BCs such that generating large datasets is computationally tractable. Nevertheless, even with 2D data, the reconstructions obtained here demonstrate strong agreement with the ground truth. Another limitation lies in the nature of the simulated displacement fields used for training, which are noiseless except for minor discretization artifacts. However, displacement fields measured from ultrasound data are affected by multiple sources of error, including discretization inaccuracies, limitations in displacement estimation algorithms, and inherent noise in the raw RF signals. These differences between simulated and real-world data may impact model generalization, particularly in experimental and clinical applications. In future work, we intend to conduct noise and sensitivity studies for these methods. The iterative method utilizes a finite element mesh that conforms precisely to the complex, curved geometry of the vessel wall, preserving high geometric fidelity. In contrast, standard convolutional architectures like the U-Net require data to be formatted on a regular Cartesian grid. Consequently, interpolating the displacement fields and geometry onto a pixel grid could introduce discretization artifacts (i.e., stair-stepping) at the vessel boundaries, which may affect the reconstruction fidelity at the edges compared to the conforming mesh. However, our comparable performance show reasonable reconstruction of modulus distribution even without high-fidelity geometry. The present work primarily demonstrates that a deep learning framework can be applied to this problem and achieve performance comparable to the ITR method. In the future, our goal is to improve the DL model through exploration of various architectures, hyperparameter tuning, and the generation of more realistic simulated ultrasound data. Currently, we require medical experts to select the ROI and appropriate frames from ultrasound sequences manually. We plan to automate this process and incorporate a greater number of US frames during training to reduce the dependency on manual selection. We also expect that the local overall accuracy of our modulus reconstructions will increase by using frames over multiple cardiac cycles to estimate the modulus. Finally, we plan to expand our clinical dataset and perform more extensive in vivo evaluations to rigorously test and validate the practical applicability of the method.
+
+VI. Conclusion
+
+We demonstrate that a deep learning model, trained only on FE simulated data, can be used to predict shear modulus from both simulated and experimental ultrasound elastography displacement estimates. Our study includes model training using simulated displacement fields, followed by validation on digital phantoms, experimental phantoms, and preliminary clinical data. The results show that the model can generalize well across different variations and successfully learn the relationship between displacement fields and modulus distribution. Moreover, we compared the deep learning model with iterative reconstruction methods which shows comparable performance. This suggests that, with sufficiently diverse and representative simulated training data of AAAs, deep learning models can generalize well to real-world experimental conditions for estimating the shear modulus of the aorta. The clinical results provide encouraging evidence for the applicability of our method in practical settings.
+
+Supplementary Material
+
+supp1-3694126
+
+This article has supplementary downloadable material available at https://doi.org/10.1109/TCI.2026.3694126, provided by the authors.
+
+This work was supported by the National Institute of Health SuRE award under Grant R16DC022229. The associate editor coordinating the review of this article and approving it for publication was Prof. Yang Chen.
+
+Fig. 1. FE schematics: (a) illustrates different boundary conditions, (b) depicts variations in the geometry, (c) shows the FE mesh structure, and (d) the interpolated spatial grid.
+
+Fig. 2. COMSOL 3D simulation model. (a) highlights the upper region where the modulus is varied and the lower region where it remains constant, and (b) shows the extracted US image plane.
+
+Fig. 3. Experimental phantom setup and phantom model [23].
+
+Fig. 4. (a) B-mode image of Phantom 1, (b) FE mesh structure used for modeling, and (c) the interpolated spatial grid used as input to the DL method. Note that this interpolation is applied similarly to all four experimental phantom configurations.
+
+Fig. 5. Deep learning U-NET model featuring a NMSE loss function for optimization.
+
+Fig. 6. Training curve for the deep learning model.
+
+Fig. 7. Simulated test examples showing pressure-normalized X and Y displacement fields as inputs to the DL model, along with the corresponding ground truth and predicted modulus distributions.
+
+Fig. 8. COMSOL simulation results for (a) COMSOL model 1, (b) COMSOL model 2, (c) COMSOL model 3, and (d) COMSOL model 4, showing ground truth modulus (μij) and predictions from the DL (μijdl) and ITR (μijitr) reconstruction methods.
+
+Fig. 9. Results for (a) phantom 1, (b) phantom 2, (c) phantom 3, and (d) phantom 4, showing pressure-normalized X and Y measured displacement inputs and the corresponding modulus predictions from the DL (μijdl) and ITR (μijitr) reconstruction methods.
+
+Fig. 10. B-mode images of clinical patients with annotation of the aorta location.
+
+Fig. 11. Results for clinical patient (a) 1, (b) 2, (c) 3, and (d) 4, showing pressure-normalized X and Y measured displacement inputs and the corresponding modulus predictions from the DL μijdl and ITR μijitr reconstruction methods.
+
+Fig. 12. Plot showing the relationship between the average modulus and the inverse of the average pressure normalized maximum principal strain across different clinical patients.
+
+TABLE I Material Properties of the Anterior and Posterior Ends of the Phantoms
+
+Phantom	Anterior End Material (PVA % wt)	μ(kPa)	Posterior End Material (PVA % wt)	μ(kPa)	
+1	10%	17.4±1	10%	17.4±1	
+2	15%	48.3±5.7	10%	17.4±1	
+3	20%	95.1±0.4	10%	17.4±1	
+4	25%	170±4.1	10%	17.4±1	
+
+TABLE II Dataset Distribution
+
+Dataset Type	Purpose	Dataset Size	
+FE Simulated	Training	30,000	
+FE Simulated	Validation	3,000	
+FE Simulated	Testing	3,000	
+Digital Phantom	Testing	4	
+Experimental Phantom	Testing	4	
+Clinical in-vivo	Testing	4	
+
+TABLE III Summary of Mean of Various Evaluation Metics for the Simulated Test Dataset
+
+No. of test images	3, 000	
+Mean NMSE	0.016	
+Mean DSC	0.999	
+
+TABLE IV Summary of Evaluation Metrics and Modulus Values on Different Regions for Various Comsol Simulated Phantoms
+
+Metric	Comsol 1	Comsol 2	Comsol 3	Comsol 4	
+DL NMSE	0.76	0.60	0.43	0.41	
+ITR NMSE	0.69	0.67	0.57	0.37	
+μup(kPa)	33.3	66.7	133.3	266.7	
+DL-μˆup(kPa)	55.4±6.1	102.4±5.6	195.1±9.8	410.1±54.3	
+ITR-μˆup(kPa)	67.3±9.3	114.4±4.4	198.4±12.44	326.12±50.85	
+μlow(kPa)	66.7	66.7	66.7	66.7	
+DL-μˆlow(kPa)	122.4±13	121.6±13.4	122.7±13.5	122.9±15.1	
+ITR-μˆlow(kPa)	166.3±4.6	166.6±2.04	119.4±5.1	119.6±7.6	
+η	0.50	1.00	2.00	4.00	
+DL-ηˆ	0.45	0.84	1.59	3.34	
+ITR-ηˆ	0.58	0.98	1.66	2.73	
+
+TABLE V Summary of Modulus Values on Different Regions for Various Experimental Phantoms
+
+Metric	Phantom 1	Phantom 2	Phantom 3	Phantom 4	
+μup(kPa)	17.4±1	48.3±5.7	95.1±0.4	170±4.1	
+DL-μˆup(kPa)	63.2±17.8	161.8±42.2	231.3±21.9	418.7±33.3	
+ITR-μˆup(kPa)	71±124	166.1±205	167.9±34.7	442.1±181	
+μlow(kPa)	17.4±1	17.4±1	17.4±1	17.4±1	
+DL-μˆlow(kPa)	58.9±5.9	66±5.1	43.4±6.1	36.8±5.5	
+ITR-μˆlow(kPa)	47±47.2	58.1±53.8	40.1±39.4	33.8±39.8	
+η	1.00	2.78	5.47	9.77	
+DL-ηˆ	1.07	2.45	5.33	11.38	
+ITR-ηˆ	1.51	2.86	4.19	13.09	
+
+
+References
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diff --git a/corpus/psychology/text/dffb6f856d4fa958.txt b/corpus/psychology/text/dffb6f856d4fa958.txt
new file mode 100644
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+++ b/corpus/psychology/text/dffb6f856d4fa958.txt
@@ -0,0 +1,73 @@
+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Front Psychol
+Journal ID: Front Psychol
+NLM Journal ID: 101550902
+Journal ID: Front. Psychol.
+
+Frontiers in Psychology
+
+EISSN: 1664-1078
+Publisher: Frontiers Media SA
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC13101653
+PMID: 42027271
+DOI: 10.3389/fpsyg.2026.1823085
+Article version: 1
+Article version:
+Subjects: Correction
+
+Correction: Real-world evidence for clergy well-being: developing a culturally grounded self-screening tool to promote sustainable mental health outcomes
+
+Li Wen-Cheng 1
+Chin Yu-Ting 1
+Wu Li-Hsin 2
+Ling I-Ling 3 *
+Lee Chien-Hung 1 4 5 *
+1 Department of Public Health, College of Health Sciences, Kaohsiung Medical University , Kaohsiung , Taiwan
+2 Department of Psychology, University of Toronto , Toronto , ON , Canada
+3 Department of Marketing & Tourism Management, National Chiayi University , Chiayi , Taiwan
+4 Research Center for Precision Environmental Medicine, Kaohsiung Medical University , Kaohsiung , Taiwan
+5 Department of Medical Research, Kaohsiung Medical University Hospital, Kaohsiung Medical University , Kaohsiung , Taiwan
+* Correspondence: I-Ling Ling, yiling@mail.ncyu.edu.tw; Chien-Hung Lee, cnhung@kmu.edu.tw
+Electronic publication date: 2026 Apr 8
+Publication date: 2026
+Volume: 17
+Electronic Location ID: 1823085
+Received 2026 Mar 4; Accepted 2026 Mar 5
+Copyright: Copyright © 2026 Li, Chin, Wu, Ling and Lee.
+Copyright year: 2026
+Copyright holder: Li, Chin, Wu, Ling and Lee
+License: This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Erratum for: Real-world evidence for clergy well-being: developing a culturally grounded self-screening tool to promote sustainable mental health outcomes 17 3 3 2026 1677071 Frontiers in Psychology 10.3389/fpsyg.2026.1677071 PMC12991992 41853815
+Keywords: Chinese clergy, clergy well-being, psychological well-being, scale development, spiritual well-being, subjective well-being, work-related psychological health
+Figure count: 0
+Table count: 0
+Equation count: 0
+Reference count: 0
+Page count: 1
+
+section-at-acceptance: Cultural Psychology
+
+Ÿ==============================Ÿ
+Affiliation “Department of Public Health, College of Health Sciences, Kaohsiung Medical University, Kaohsiung, Taiwan” was omitted for author Yu-Ting Chin. This affiliation has now been added for author Yu-Ting Chin.
+
+Author Yu-Ting Chin was erroneously assigned to affiliation “Department of Marketing & Tourism Management, National Chiayi University, Chiayi, Taiwan.” This affiliation has now been removed for author Yu-Ting Chin.
+
+A correction has been made to Section “4.2.4 Criterion-related and incremental validities”:
+
+“fatigue (ΔR2 = 0.397, p < 0.01), and burnout (ΔR2 = 0.290, p < 0.01); fatigue (ΔR2 = 0.023, p < 0.01); engagement (ΔR2 = 0.018, p < 0.01); stability (ΔR2 = 0.018, p < 0.01).”
+
+The original version of this article has been updated.
+
+Publisher's note
+
+All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.
+
+Approved by: Frontiers Editorial Office, Frontiers Media SA, Switzerland
+
diff --git a/corpus/psychology/text/e08c58c42dbd412b.txt b/corpus/psychology/text/e08c58c42dbd412b.txt
new file mode 100644
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+++ b/corpus/psychology/text/e08c58c42dbd412b.txt
@@ -0,0 +1,175 @@
+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Materials (Basel)
+Journal ID: Materials (Basel)
+NLM Journal ID: 101555929
+Journal ID: materials
+
+Materials
+
+EISSN: 1996-1944
+Publisher: Multidisciplinary Digital Publishing Institute (MDPI)
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC13303729
+PMID: 42355184
+DOI: 10.3390/ma19122603
+Article ID: materials-19-02603
+Article version: 1
+Subjects: Article
+
+Design of Trabecular Bone-Inspired Mechano-Acoustic Coupling Porous Structures
+
+Lin Yiyan Conceptualization Writing – original draft 1
+Zhang Jundong Project administration Supervision 2
+Zhang Chaolei Supervision Project administration 1
+https://orcid.org/0000-0003-4794-399X Liu Ruiyao Methodology Writing – review & editing 3 *
+Yu Zhenglei Software 1 *
+1 College of Biological and Agricultural Engineering, Jilin University, Changchun 130022, China
+2 Central Research Institute, China Automotive Technology and Research Center Co., Ltd., Tianjin 300300, China
+3 School of Mechanical and Aerospace Engineering, Jilin University, Changchun 130025, China
+* Correspondence: ruiyaoliu@126.com (R.L.); zlyu@jlu.edu.cn (Z.Y.)
+Electronic publication date: 2026 Jun 17
+Publication date: 2026 Jun
+Volume: 19
+Issue: 12
+Electronic Location ID: 2603
+Received 2026 May 10; Revised 2026 Jun 5; Accepted 2026 Jun 13
+Copyright: © 2026 by the authors.
+Copyright year: 2026
+License: Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Keywords: bionic design, additive manufacturing, mechano-acoustic coupling, implicit surface structures
+
+Funding: Postdoctoral Fellowship Program and China Postdoctoral Science Foundation BX20250428 2025 Jilin Provincial Education Department Excellent Young Scholars Program JJKH20261331KJ This research was funded by the Postdoctoral Fellowship Program and China Postdoctoral Science Foundation under Grant Number (BX20250428), and 2025 Jilin Provincial Education Department Excellent Young Scholars Program (JJKH20261331KJ).
+
+Ÿ==============================Ÿ
+Aiming at the technical bottleneck that traditional porous structures can hardly achieve mechanical load-bearing and acoustic regulation simultaneously, this study designs and fabricates three implicit surface porous structures (Gyroid, Diamond, Lidinoid) based on the bionic principle of trabecular bone. Experimental characterization and numerical analysis of their mechano-acoustic coupling performance are systematically carried out. Selective Laser Melting (SLM) technology is employed to realize the integrated forming of 316L bionic structures. Quasi-static compression experiments and finite element simulations are conducted to reveal the progressive deformation mechanism and energy absorption characteristics of different topological configurations. The results indicate that the Diamond structure exhibits the optimal comprehensive performance in terms of load-bearing capacity, specific energy absorption and isotropy. On this basis, the sound absorption and sound insulation performances of the structures are evaluated via an acoustic impedance tube test. The results show that the Diamond structure possesses a remarkably higher sound absorption coefficient and sound insulation value in the high-frequency range than other configurations, demonstrating excellent acoustic energy dissipation and sound wave isolation capability. The research indicates that the synergistic optimization of mechanical and acoustic performances can be achieved by regulating the Triply Periodic Minimal Surface (TPMS) topological configuration. Benefiting from its efficient stress transfer paths and intricate sound wave propagation channels, the Diamond structure realizes the coupling of high load-bearing capacity, superior energy absorption and favorable acoustic performance. This work provides a theoretical basis and technical support for the design of bionic porous structures in multifunctional scenarios such as bone implants and protective noise reduction.
+
+1. Introduction
+
+With the escalating demand for structural performance in aerospace, rail transit, biomedical implants and other fields [1,2,3,4,5], traditional single-function porous materials can hardly meet the multiple requirements of high load-bearing protection, efficient energy absorption and noise control simultaneously. The development of multifunctional structures with excellent mechanical properties and acoustic regulation capability has become an important research direction in the fields of materials science and mechanical engineering [6,7,8,9,10]. Biological tissues such as natural trabecular bone achieve the collaborative optimization of mechanical load-bearing and mass transport through hierarchical and multi-scale porous topology, providing significant bionic inspiration for the design of artificial multifunctional structures [11,12,13,14,15]. Among them, Triply Periodic Minimal Surface (TPMS) structures constructed based on implicit surfaces are regarded as ideal carriers for the synergistic regulation of mechanical and acoustic performances. Featuring continuously smooth pore channel topology, high specific surface area, excellent mechanical designability and uniform stress distribution characteristics, TPMS structures have become a research hotspot in the field of bionic porous structures in recent years [16,17,18,19,20].
+
+In terms of the mechanical properties of TPMS porous structures, scholars have conducted extensive fundamental research. For instance, Wan et al. [21] compared the quasi-static compressive responses of four typical TPMS topologies including Gyroid and Diamond through experimental and numerical methods. The results revealed that the Diamond structure possesses higher load-bearing capacity and energy absorption efficiency due to its highly symmetric truss-like topology. She et al. [22] further investigated the influence of unit morphological characteristics on the mechanical performance of TPMS structures, and established a correlation model between topological morphological parameters and mechanical properties. Moreover, Daynes [23] demonstrated that the continuous surface characteristics of TPMS structures can effectively improve their mechanical functional performance and remarkably enhance structural mechanical stability. These studies have laid an important foundation for understanding the mechanical behavior of TPMS structures. However, most existing studies mainly focus on the characterization of a single mechanical property, while the complex multi-field coupling working conditions faced by structures in practical engineering applications are rarely fully considered. In terms of acoustic performance research, the unique pore channel characteristics of TPMS porous structures have also attracted widespread attention. Sirivuri et al. [24] explored the effects of different TPMS configurations on sound absorption performance, and found that the continuous curved pore channels of TPMS structures can prolong the propagation path of sound waves and strengthen the viscous dissipation effect of air, thereby improving sound absorption efficiency. Chua et al. [25] proposed a novel multi-scale acoustic framework to compare the acoustic performance of TPMS topologies, providing a methodological basis for the design and optimization of structural acoustic properties. In addition, several studies have attempted to realize acoustic regulation in specific frequency bands via topology optimization. Nevertheless, most designs only target a single acoustic performance without integrating the synergistic optimization of mechanical and acoustic properties.
+
+Although existing studies have made certain progress in investigating the mechanical or acoustic properties of TPMS structures separately, most of them only analyze a single mechanical or acoustic performance [26,27]. There is a lack of systematic characterization on the coupled mechano-acoustic properties of the same topology, making it difficult to evaluate the comprehensive performance of TPMS structures in multifunctional application scenarios. Moreover, the majority of current research focuses merely on a single material or a single working condition, and fails to carry out full-process design and verification combined with the manufacturability of additive manufacturing processes, which greatly limits their potential for practical engineering applications [28,29,30].
+
+Based on the above research background, this study designs and fabricates three typical TPMS porous structures, namely Gyroid, Diamond and Lidinoid, inspired by the bionic concept of natural trabecular bone. Selective Laser Melting (SLM) additive manufacturing technology is adopted to realize the integrated forming of 316L bionic structures. Quasi-static compression experiments and finite element simulations are conducted to systematically characterize the load-bearing capacity, energy absorption characteristics and progressive deformation and failure modes of different topological configurations. Meanwhile, sound impedance tube tests are performed to evaluate the sound absorption and sound insulation performances of the structures in a broadband frequency range. This study carries out full-process structural design and performance verification considering the manufacturability of additive manufacturing, and conducts integrated mechano-acoustic experiments and coupled finite element characterization. By exploring the inherent law that TPMS topological configurations dominate the load-bearing, energy absorption and noise reduction performances, this work aims to reveal the mechano-acoustic coupling regulation mechanism of different TPMS bionic porous structures, and further provide a solid theoretical basis and feasible technical support for the optimal design of bionic porous structures applicable to multifunctional scenarios including aerospace protection and biomedical implants.
+
+2. Materials and Methods
+
+2.1. Femur-Inspired Bionic Structural Design and Fabrication
+
+This design takes the porous microstructure of the proximal femoral cancellous bone as the bionic prototype. Proximal femoral cancellous bone is composed of highly ordered three-dimensional trabecular networks, featuring a hierarchical porous structure, high specific strength, excellent stress conduction and energy absorption characteristics, and serving as a naturally efficient lightweight load-bearing structure. Figure 1a clearly shows the macro morphology of the proximal femur and the micro trabecular network in its cancellous bone region, whose porosity, connectivity and topological structure provide dual biomechanical and biological references for the design of porous implants.
+
+Based on the bionic design concept of femoral cancellous bone, three typical TPMS porous structures, namely Gyroid, Diamond and Lidinoid, are constructed using nTopology 5.9.2 software, as shown in Figure 1b–d. TPMS structures possess zero mean curvature, high connectivity, tunable porosity and topological uniformity, and can effectively replicate the mechanical and biological characteristics of trabecular bone. The Gyroid structure exhibits continuously smooth curved features with helically three-dimensionally interconnected pore channels and no sharp corners. The Diamond structure is based on the topological configuration of Diamond crystals and is characterized by high symmetry and uniform pore distribution. The Lidinoid structure integrates high connectivity and complex pore topology with a larger specific surface area and superior potential for graded pore regulation. All three TPMS structures inherit the bionic design philosophy of cancellous bone, and customized design of porosity, pore size and topological morphology can be realized through parametric regulation.
+
+In this study, the Selective Laser Melting (SLM) additive manufacturing process is adopted to realize the integrated forming of bionic TPMS porous structures, and the principle of the forming process is illustrated in Figure 2a. High-precision forming of complex curved topological structures is achieved by precisely controlling the printing parameters, including a laser power of 180 W, a scanning spacing of 100 μm, a scanning speed of 900 mm/s, and a layer thickness of 20 μm. The designed printed structure has a diameter of 29 mm and a height of 10 mm, and the physical specimens of the three configurations are presented in Figure 2b. Quasi-static tensile tests are carried out on 316L bulk specimens, and the corresponding force–displacement curves are shown in Figure 2c, which exhibit typical characteristics of plastic deformation and necking fracture. To clarify the intrinsic mechanical properties of the material, quasi-static compressive tests are performed on solid 316L cylindrical specimens, and their force–displacement curves are displayed in Figure 2d. The curves reflect the elastoplastic deformation and yield hardening behavior of the material under axial compressive loading, providing an accurate material constitutive basis for the subsequent mechanical analysis and numerical simulation of porous structures. This also comprehensively reveals the differences in mechanical behavior of the material under tensile and compressive loads.
+
+2.2. Femur-Inspired Bionic Structural Experimental and Numerical Setup
+
+To evaluate the static load-bearing capacity of porous structures, a universal material testing machine (Model ZDSHPB-4080, Zongde, Taian, Shandong, China) is employed to conduct quasi-static compression tests. The test apparatus and specimen loading configuration are shown in Figure 3a. Axial loading is applied at a constant rate of 4 mm/min to obtain the force–displacement response of the structure under low strain rate conditions, which provides an experimental basis for analyzing its load-bearing and energy absorption characteristics. To investigate the acoustic performance of bionic porous structures, an acoustic impedance tube testing system (Model BSWA SW, BSWA Technology, Beijing, China) is established. The experimental setup and specimen installation scheme are illustrated in Figure 3b. Based on the standing wave method, sound waves are excited inside the impedance tube and sound pressure signals are collected to measure the sound absorption coefficient and sound insulation properties of porous specimens. This study reveals the regulation mechanism of different TPMS topologies on sound wave propagation, and provides performance support for their application in noise reduction scenarios. Furthermore, to guarantee the reliability and accuracy of experimental data, all tests in this study were repeated three times, and the average values were taken as the final experimental results for subsequent analysis.
+
+In this study, quasi-static compression simulation of bionic porous structures was performed using Abaqus2023 software to thoroughly explore the mechanical behaviors of bionic skeleton structures under compressive loading. The boundary conditions were established based on the quasi-static compression experimental scheme. The bottom surface of the bionic skeleton structure was fully constrained to limit all translational and rotational degrees of freedom in the x, y, and z directions, maintaining a fixed boundary state throughout the loading process. A uniform displacement load in the negative y-axis direction was applied to the top surface of the structure, as depicted in Figure 4a. In terms of contact settings, general contact was adopted between the upper and lower surfaces of the structure and the loading plates. This contact configuration accurately defines the interfacial interaction and ensures the effective transmission of normal pressure on the contact surface.
+
+The C3D10M ten-node modified quadratic tetrahedral element, which is compatible with the implicit solving algorithm, was selected for mesh discretization. Considering the high computational cost of full-scale structural simulation and to improve analytical efficiency, a single unit cell of the Diamond structure was adopted as the simulation object. The unit cell model was meshed in HyperMesh 2021 with four element sizes of 0.4 mm, 0.6 mm, 0.8 mm, and 1.0 mm. Taking the simulation results of the 0.4 mm mesh as the benchmark, mesh independence verification was completed by comparing the mechanical responses obtained under different mesh sizes. The corresponding verification results are displayed in Figure 4b.
+
+3. Results and Analysis of Structural Mechanical Properties
+
+The quasi-static compressive mechanical properties of three bionic TPMS porous structures are characterized, and the results are presented in Figure 5. Among them, Figure 5a compares the experimental and simulated force–displacement curves of Gyroid, Diamond and Lidinoid topologies. The results indicate that the simulated curves exhibit a highly consistent variation trend with the experimental curves in both the elastic stage and yield plateau stage, which verifies that the established numerical model can accurately reproduce the mechanical response and deformation behavior of porous structures. In terms of load-bearing capacity, the peak load of the three structures shows obvious differences. The Diamond structure possesses the optimal load-bearing capacity, followed by the Lidinoid structure, while the Gyroid structure exhibits the lowest capacity. Such differences originate from the spatial stress transfer paths of different topological configurations. The Diamond structure achieves efficient stress transfer through a highly symmetric truss-like distribution, whereas the helical curved features of the Gyroid structure easily induce premature local stress concentration, thereby reducing the overall load-bearing capacity.
+
+Further analysis of energy absorption performance shows in Figure 5b that the total energy absorption (EA) value of the Diamond structure reaches 731.49 J, which is significantly higher than 633.86 J of the Lidinoid structure and 503.57 J of the Gyroid structure. The comparison results of specific energy absorption (SEA) in Figure 5c follow the same trend. The SEA value of the Diamond structure is 31.45 J/g, superior to 27.11 J/g of the Lidinoid structure and 25.97 J/g of the Gyroid structure. This demonstrates that the Diamond structure not only has a stronger total energy dissipation capability, but also achieves higher energy absorption efficiency under lightweight conditions, making it more suitable for scenarios requiring both light weight and impact resistance, such as aerospace protection and orthopedic implants. To further evaluate its performance advantages, Figure 5d compares the SEA-relative density performance of the three TPMS structures in this study with various porous materials reported [31,32,33,34,35,36]. The results show that the proposed structures still deliver remarkably higher SEA values than other materials at a relatively high relative density, locating in the superior region of the performance distribution. It is confirmed that the continuously smooth curved surface and uniform stress distribution characteristics of TPMS topologies effectively avoid the stress concentration problem of traditional truss structures and achieve a prominent improvement in energy absorption efficiency. Finally, the elastic anisotropy analysis (Figure 5e1–e3) reveals differences in the elastic modulus distribution among the three structures. The Diamond structure shows the most uniform modulus distribution and presents nearly isotropic characteristics, while the Gyroid and Lidinoid structures exhibit an obvious modulus gradient along different crystallographic directions. Specifically, the modulus is higher in the [001] direction and relatively lower in the [100] and [010] directions. This anisotropy difference provides a direct basis for structural application selection. For scenarios with high requirements on mechanical isotropy such as orthopedic implants, the Diamond structure is more conducive to achieving mechanical matching with natural bone tissue and reducing the stress shielding effect. For protective scenarios without special isotropy requirements, the directional dependence of Gyroid and Lidinoid structures can also be utilized by optimizing the loading direction.
+
+By means of quasi-static compression experiments and finite element simulations, the progressive deformation behavior and stress evolution law of three bionic TPMS porous structures, namely Gyroid, Diamond and Lidinoid, are comparatively analyzed. From left to right, the four groups of images sequentially present the experimental deformation photographs and equivalent stress contours at different compression stages. The results show that all three structures exhibit the typical deformation process of porous materials, including elastic deformation, yield collapse and densification. Nevertheless, topological configuration significantly regulates their failure modes and stress distribution characteristics. As shown in Figure 6a, the Gyroid structure achieves more uniform stress benefiting from its continuously smooth curved topology. No obvious local shear band appears during compression, and the structure undergoes a layer-by-layer progressive collapse failure mode, in which the stress concentration effect is effectively suppressed. In Figure 6b, the highly symmetric truss-like topology of the Diamond structure endows it with superior load-bearing capacity, but also induces more prominent early-stage stress concentration. Local high-stress bands tend to form and further trigger shear-dominated failure. In Figure 6c, the failure behavior of the Lidinoid structure lies between the above two, presenting a mixed characteristic of uniform deformation and local buckling. Meanwhile, the high-stress regions predicted by finite element stress contours are in good agreement with the positions where buckling and collapse occur in experimental specimens. This verifies the accurate prediction capability of the numerical model for structural deformation behavior and failure modes, and further reveals the regulation mechanism of TPMS topological configuration on the mechanical response and energy absorption characteristics of porous structures.
+
+4. Results and Analysis of Structural Acoustic Properties
+
+The acoustic performances of three bionic TPMS porous structures (Gyroid, Diamond, Lidinoid) are systematically characterized, and the results are shown in Figure 7. In terms of sound absorption performance (Figure 7a), the sound absorption coefficients of all three structures increase significantly with the rise in frequency, showing the typical sound absorption characteristics of porous materials. Among them, the Diamond structure exhibits the optimal sound absorption performance, with a peak sound absorption coefficient close to 0.6 in the high-frequency range (approximately 6000 Hz), followed by the Lidinoid structure, while the Gyroid structure performs relatively poorly. This indicates that topological configuration exerts a remarkable regulatory effect on the viscous dissipation and resonance effect of sound waves. The sound insulation test results (Figure 7b) follow a consistent trend with the sound absorption performance. The Diamond structure achieves the highest sound insulation value, reaching approximately 4.3 dB at 6000 Hz, followed by the Lidinoid structure, and the Gyroid structure has the lowest value. It demonstrates that the Diamond topology not only dissipates acoustic energy more effectively, but also improves the sound insulation effect through more complex sound wave reflection and scattering paths. Overall, all three TPMS structures present excellent potential for acoustic regulation in the high-frequency range. Benefiting from its unique pore channel structure and sound wave propagation paths, the Diamond structure shows obvious advantages in both sound absorption and sound insulation performances. Although the specimens achieve optimal sound absorption and insulation at 6 kHz, high-frequency noise commonly exists in aerospace and rail transit equipment, which provides performance support for their engineering application in noise reduction scenarios. The comparative analysis of mechanical and acoustic properties of the bionic porous structures is presented in Table 1.
+
+5. Conclusions
+
+Based on the bionic concept of trabecular bone, three implicit surface TPMS porous structures are designed and fabricated. The regulation law of topological configuration on their mechano-acoustic coupling performance is systematically revealed, and the multifunctional collaborative optimization of mechanical and acoustic properties is realized. The main conclusions are drawn as follows:(1) Topological configuration significantly regulates the quasi-static mechanical behavior and failure modes of TPMS porous structures. All three structures exhibit typical compressive response characteristics of porous materials. Among them, the Diamond structure possesses the highest load-bearing capacity, with the optimal total energy absorption (731.49 J) and specific energy absorption (31.45 J/g), as well as the highest degree of mechanical isotropy. The Gyroid structure shows uniform stress distribution and presents a stable progressive layer-by-layer collapse failure mode. The mechanical properties and failure characteristics of the Lidinoid structure lie between the above two structures. The simulation results are in good agreement with the experimental data, which verifies the prediction capability of the numerical model for deformation and failure behaviors.
+
+(2) The pore characteristics of different TPMS topologies exert a significant influence on acoustic performance, showing a consistent variation trend with mechanical properties. The sound absorption coefficient and sound insulation value of all three structures increase with rising frequency. The Diamond structure achieves a peak sound absorption coefficient close to 0.6 and a sound insulation value of approximately 4.3 dB in the high-frequency range, which are remarkably superior to those of the Lidinoid and Gyroid structures. This is closely related to its complex internal pore channel structure and efficient viscous dissipation mechanism of sound waves.
+
+(3) Synergistic optimization of the mechano-acoustic performance of TPMS porous structures can be realized through topological regulation. Under identical fabrication conditions, the Diamond TPMS with highly symmetrical skeletal distribution achieves superior comprehensive performance balancing high load-bearing, excellent energy absorption and prominent high-frequency noise reduction compared with Gyroid and Lidinoid. Its uniform truss layout enables homogeneous stress dispersion to avoid local stress concentration for improved mechanical reliability, while the regularly distributed interconnected pores lengthen sound transmission paths and strengthen air viscous dissipation, jointly contributing to its outstanding mechano-acoustic coupling property.
+
+This study provides theoretical references and technical support for the development of biomimetic porous structures applied in multifunctional fields including bone implants, aerospace and rail transit noise reduction protection. However, the present work is restricted to a fixed porosity and single 316L material, which constitutes certain limitations. Future research will adjust porosity, develop composite-material TPMS and optimize geometric parameters to improve low-frequency noise reduction performance.
+
+Author Contributions
+
+Conceptualization, R.L.; software, J.Z. and C.Z.; writing—original draft preparation, Y.L.; writing—review and editing, Y.L., J.Z., C.Z., R.L. and Z.Y.; Visualization, Y.L.; Data curation, J.Z. and C.Z.; Validation, J.Z. and C.Z.; Funding acquisition, R.L. and Z.Y.; Project administration, R.L.; Resources, Z.Y.; Supervision, Z.Y. All authors have read and agreed to the published version of the manuscript.
+
+Data Availability Statement
+
+The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding authors.
+
+Conflicts of Interest
+
+Jundong Zhang was employed by the Central Research Institute, China Automotive Technology and Research Center Co., Ltd., Tianjin, China. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as potential conflicts of interest.
+
+Figure 1 Design of TPMS porous structures inspired by femoral cancellous bone. (a) Macro morphology of the proximal human femur and the micro trabecular network of its cancellous bone; (b) Gyroid-type TPMS porous structure; (c) Diamond-type TPMS porous structure; (d) Lidinoid-type TPMS porous structure.
+
+Figure 2 Fabrication and mechanical property testing of 316L bionic porous structures. (a) Schematic diagram of the Selective Laser Melting (SLM) additive manufacturing process for bionic porous structures; (b) physical photographs of bionic porous specimens with different topological configurations fabricated by SLM process; (c) quasi-static tensile force–displacement curve of 316L bulk material; (d) quasi-static compressive force–displacement curve of solid 316L cylindrical specimen.
+
+Figure 3 Performance test apparatus for bionic TPMS porous structures. (a) Universal material testing machine and schematic diagram of specimen loading; (b) acoustic impedance tube experimental setup and schematic diagram of specimen installation.
+
+Figure 4 Mesh independence verification of bionic TPMS porous structures. (a) Simulation settings of Diamond-type unit cell structure; (b) error vs. time for different mesh sizes.
+
+Figure 5 Quasi-static compressive mechanical properties of bionic TPMS porous structures. (a) Comparison of experimental and simulated force–displacement curves; (b) comparison of energy absorption (EA) performance; (c) comparison of specific energy absorption (SEA) performance; (d) Ashby chart of SEA versus relative density for the proposed structures and several typical lattice structures; (e1–e3) polar diagrams of elastic anisotropy for unit cells of the three structures.
+
+Figure 6 Deformation and stress evolution of bionic TPMS porous structures under quasi-static compression. (a) Experimental deformation and equivalent stress contour cloud of Gyroid structure at compressive displacements ranging from 0 to 5 mm; (b) experimental deformation and equivalent stress contour cloud of Diamond structure at compressive displacements ranging from 0 to 5 mm; (c) experimental deformation and equivalent stress contour cloud of Lidinoid structure at compressive displacements ranging from 0 to 5 mm.
+
+Figure 7 Acoustic performance of bionic TPMS porous structures. (a) Variation curves of sound absorption coefficient with frequency for different topological structures; (b) variation curves of sound insulation loss with frequency for different topological structures.
+
+materials-19-02603-t001_Table 1 Table 1 Comparative analysis of mechanical and acoustic properties of bionic porous structures.
+
+Structure	EA (J)	SEA (J/g)	Sound Absorption Coefficient at 6000 Hz	Sound Transmission Loss at 6000 Hz (dB)	
+Gyroid	503.57	25.97	0.462	3.196	
+Diamond	731.49	31.45	0.584	4.169	
+Lidinoid	633.86	27.11	0.499	3.649	
+
+Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.
+
+
+References
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diff --git a/corpus/psychology/text/e1bd276046289585.txt b/corpus/psychology/text/e1bd276046289585.txt
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+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Mol Brain
+Journal ID: Mol Brain
+NLM Journal ID: 101468876
+
+Molecular Brain
+
+EISSN: 1756-6606
+Publisher: BMC
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC13307405
+PMID: 42321855
+DOI: 10.1186/s13041-026-01323-0
+Article ID: 1323
+Article version: 1
+Subjects: Review
+
+Therapeutic potential of AdipoRon in cognitive, depressive, and anxiety disorders: a systematic review and meta-analysis
+
+Gheibi Fatemeh Sadat 1
+http://orcid.org/0000-0002-4203-4618 Hosseini Leila leilahosseini337@gmail.com
+1
+Kalejahi Parinaz 1
+Dastgiri Saeed 2
+Shafiee-Kandjani Ali Reza 1
+http://orcid.org/0000-0002-1985-1986 Noorazar Seyed Gholamreza s.gh.noorazar@gmail.com
+1
+1 https://ror.org/04krpx645 grid.412888.f 0000 0001 2174 8913 Research Center of Psychiatry and Behavioral Sciences, Tabriz University of Medical Sciences, Tabriz, Iran
+2 https://ror.org/04krpx645 grid.412888.f 0000 0001 2174 8913 Department of Community Medicine, Tabriz University of Medical Sciences, Tabriz, Iran
+Electronic publication date: 2026 Jun 19
+Publication date: 2026
+Volume: 19
+Electronic Location ID: 50
+Received 2026 Jan 30; Accepted 2026 Jun 11
+Copyright: © The Author(s) 2026
+Copyright year: 2026
+License: Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated in a credit line to the data.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Keywords: AdipoRon, Cognition, Alzheimer, Depression, Anxiety, Meta-analysis
+issue-copyright-statement: © Min Zhuo, Bong-Kiun Kaang and BioMed central Ltd. 2026
+
+Ÿ==============================Ÿ
+Rising cases of cognitive disorders, depression, and anxiety underscore the need for new treatments, given the limited effectiveness and side effects of current options. AdipoRon targets adiponectin receptors and shows promise for protecting the brain, reducing inflammation, and supporting metabolism. This review examines preclinical data to determine whether AdipoRon consistently improves mood and cognitive function and to identify the underlying neurobiological pathways. We conducted a comprehensive literature search using PubMed, Embase, Web of Science, and Scopus, with no time limit, up to August 30, 2025. The quality of the selected studies was evaluated using the Collaborative Approach to Meta-Analysis and Review of Animal Studies (CAMARADES) checklists and the SYRCLE risk of bias tool. The studies found that AdipoRon treatment significantly reduced immobility in the forced swim test and had a significant anxiolytic effect in the open field test, especially in chronic unpredictable mild stress models. It also improved recognition memory in the novel object recognition test in models of Alzheimer’s and Parkinson’s diseases. Additionally, AdipoRon increased the expression of synaptic proteins, such as synaptophysin and PSD-95, in rodent models of these diseases. It also modulated the production of inflammatory cytokines. This review establishes AdipoRon’s capacity to resolve depressive, anxious, and cognitive deficits in rodent models. Because the meta-analyses were based on a limited number of studies and substantial heterogeneity was observed across studies, the findings should be interpreted with caution. However, further well-designed preclinical and clinical investigations are essential to confirm these findings.
+
+Introduction
+
+Cognitive impairments, depression, and anxiety are three interlinked domains that can negatively affect an individual’s mental state and functional capacity in day-to-day activities [1]. Cognitive impairment is a common feature of neurological disorders, including dementia and traumatic brain injury, and of psychiatric disorders, including schizophrenia, depression, and anxiety [2]. In these patients, cognitive impairment varies across attention, processing speed, and difficulties with decision-making, problem-solving, or completing daily tasks. Some cognitive impairments are more visible in daily life and arise from complex interactions among discriminative and causal factors and independent neurocognitive models [3, 4].
+
+Depression is characterized by symptoms such as a loss of interest in activities, feelings of sadness, and cognitive deficits, including difficulties with concentration and decision-making [1]. On the other hand, anxiety disorders often manifest as excessive and irrational worry, restlessness, psychomotor agitation, and increased physiological arousal, which can also lead to cognitive difficulties [2–4].
+
+Adiponectin is a hormone produced by adipose tissue, and its relevance has become a major subject of medical interest owing to its diverse functions in human health [5]. This hormone has been linked to regulating various bodily processes, such as glucose regulation in the bloodstream, fatty acid metabolism, and other intricate cellular processes [5]. Adiponectin influences cellular functions through its interaction with two receptors: adiponectin receptor 1 (AdipoR1) and adiponectin receptor 2 (AdipoR2), which are central regulators of essential cellular function [6, 7]. These receptors are abundantly expressed in several brain regions, such as the hippocampus, cortex, brainstem, and hypothalamus [8]. Activation of AdipoR1 and AdipoR2 regulates several intracellular signaling cascades, primarily the AMP-activated protein kinase (AMPK)/Sirtuin 1 (SIRT1) and peroxisome proliferator-activated receptor-α (PPAR-α) pathways, which play critical roles in cellular energy homeostasis, mitochondrial function, inflammation inhibition, oxidative stress reduction, neuronal survival, and vasodilatory properties [9–11]. AdipoRon can traverse the blood-brain barrier and activate adiponectin-related pathways by interacting with both AdipoR1 and AdipoR2 [12]. As an orally active small-molecule AdipoR agonist, AdipoRon exerts various biological properties in peripheral and neural tissues, such as pro-neurogenic, insulin-sensitizing, anti-atherosclerotic, anti-depressant, anti-oxidant, and anti-inflammatory activities [12, 13]. Studies investigating the effects of AdipoRon on Alzheimer’s disease (AD) indicate that it exerts neuroprotective actions [13–15]. It could decrease neuroinflammation and tau hyperphosphorylation, and improve mitochondrial function [16, 17]. Moreover, research has shown that long-term administration of AdipoRon reverses cognitive deficits and attenuates pathological features in experimental models, including cell lines and transgenic mice [18]. It also promotes the expansion of hippocampal stem cell populations and enhances synaptic function through the AdipoR1/AMPK signaling pathway [19]. Overall, this body of evidence supports AdipoRon as a new treatment option that may address multiple harmful processes related to AD, thus improving cognition and slowing down progression [17]. Furthermore, studies have demonstrated that AdipoRon effectively alleviates anxiety and depression-like behaviors in animal models, highlighting its broader therapeutic potential in addressing psychiatric conditions [20].
+
+A study examined the therapeutic effects of AdipoRon, a synthetic adiponectin receptor agonist, on anxiety and depression symptoms caused by chronic sleep restriction (SR) in mice. Chronic SR, defined as sleep of 6 h or less per night, is an increasing problem associated with mood disorders. The researchers used a mouse model subjected to 21 days of SR and provided daily intranasal treatment with AdipoRon, comparing it with melatonin and a control group. Behavioral tests (open field, elevated plus maze, forced swim, sucrose splash tests) showed that SR resulted in anxiety-like and depression-like behaviors. Intranasal AdipoRon notably decreased anxiety behaviors and depressive symptoms [21].
+
+AdipoRon treatment effectively lowered corticosterone levels, suppressed microglial activation, and reduced inflammatory cytokine expression, indicating its anti-inflammatory properties are mediated by the suppression of the NF-κB signaling pathway. The study suggests that AdipoRon mediates its anxiolytic and antidepressant effects by regulating the hypothalamic-pituitary-adrenal (HPA) axis and neuroinflammation [22]. Based on the available evidence, AdipoRon appears to contribute to improved cognitive performance and to the reduction of depressive- and anxiety-like behaviors [18]. These findings suggest that AdipoRon may represent a promising candidate for future therapeutic strategies targeting cognitive disorders, depression, and anxiety. Accordingly, the present review examines and synthesizes the existing literature in this area.
+
+Method
+
+Search strategy
+
+The search strategy carried out in this systematic review followed the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines. The protocols used in this systematic review and meta-analysis have been registered in PROSPERO (CRD420251164652). The Ethics Committee of Tabriz University of Medical Sciences (IR.TBZMED.VCR. REC.1404.115) approved the research.
+
+Two researchers independently searched PubMed, Embase, Web of Science, and Scopus for articles without a time limit until August 30, 2025. The relevant database, Open gray, will also be used to evaluate gray literature. The Search keywords based on MeSH terms were as follows:
+
+(((((cognitive[Title/Abstract]) OR (cognitive impairment[Title/Abstract])) OR (“Cognitive Dysfunction“[Mesh])) OR (cognition[Title/Abstract])) OR (“Cognition“[Mesh]))) AND ((AdipoRon[Title/Abstract]) OR (Adiponectin receptor agonist[Title/Abstract]))) OR (((AdipoRon[Title/Abstract]) OR (Adiponectin receptor agonist[Title/Abstract])) AND (((Anxiety[Title/Abstract]) OR (“Anxiety“[Mesh])) OR (anxiolytic[Title/Abstract])))) OR (((AdipoRon[Title/Abstract]) OR (Adiponectin receptor agonist[Title/Abstract])) AND ((depression[Title/Abstract]) OR (“Depression“[Mesh]))). The PICO framework guiding our study was as follows:
+
+(P)The population consists of preclinical models of depression, anxiety, and cognitive disorders, including animal studies.
+
+(I)The intervention focuses on AdipoRon-based adiponectin replacement therapies for addressing depression, anxiety, or cognitive impairment.
+
+(C) The comparison involves control groups, such as untreated models or those administered a placebo.
+
+(O)The outcomes evaluated include depression-like or anxiety behaviors, neuroinflammation, cognitive function, molecular pathways, and the systemic therapeutic impact of AdipoRon.
+
+Inclusion criteria
+
+In light of the lack of clinical trials, our study focused on preclinical research. We included studies employing animal models to investigate depression, anxiety, and cognitive impairments, in which experimental groups were treated with AdipoRon. Furthermore, inclusion was restricted to studies published in English to ensure consistency and accessibility of the data.
+
+Exclusion criteria
+
+Exclusion criteria included: articles that did not meet the required quality, letters to the editor or proposals, case reports, studies, reprints that used the same sample data, conference abstracts, and narrative reviews.
+
+Data extraction
+
+Data extraction was performed using a standardized template to gather key details: the first author, publication year, experimental models, behavioural tests, AdipoRon treatment specifics (including dosage and duration), and outcomes. Means, sample sizes, and standard deviation (SD) were obtained from studies. In some studies, multi-arm treatments were used, including different dosing regimens. We assumed each dose was an independent study. When data were only shown graphically, the GetData Graph Digitizer software (version 2.26) was used to extract numerical data. If SD was not reported, it was calculated as √N × SEM, where N is the sample size.
+
+Quality assessment
+
+The CAMARADES (Collaborative Approach to Meta-Analysis and Review of Animal Data from Experimental Studies) quality checklist was employed in this systematic review. It provides a standardized framework for assessing methodological rigor and reproducibility. The checklist consists of ten essential items: (1) publication in a peer-reviewed journal, (2) statement regarding temperature control, (3) randomization of treatment or control, (4) allocation concealment, (5) blinded assessment of outcomes, (6) avoidance of anesthetics with significant intrinsic properties, (7) animal model description, (8) calculation of sample size, (9) compliance with animal welfare regulations, and (10) disclosure of potential conflicts of interest.
+
+Also, we employed SYRCLE’s (Systematic Review Centre for Laboratory Animal Experimentation) tool to conduct a comprehensive bias risk assessment. This tool has 10 items covering common bias types. These include adaptations of five Cochrane domains (sequence generation, allocation concealment, incomplete data, selective reporting, other bias) plus five items tailored to animal studies (baseline characteristics, random housing, blinding of caregivers, random outcome selection, blinding of outcome assessment). Quality assessment was conducted independently by two authors (LH and FG), and differences were resolved through discussion by the third author (PK).
+
+Statistical analysis
+
+The meta-analysis was conducted using RevMan version 5.4.1 (version 5.4; The Nordic Cochrane Centre, Copenhagen, Denmark). Effect sizes were reported as weighted mean differences (WMD) with 95% confidence intervals (CI) for comparisons between the treatment and control groups. Study heterogeneity was evaluated using the chi-square distribution and the I² statistic. A random effects model was implemented when I2 > 50%; otherwise, a fixed effects model was applied. Subgroup analyses were performed based on route of injection and disease. In all tests, p-values less than 0.05 were considered statistically significant.
+
+Results
+
+Study selection
+
+A comprehensive literature search identified 139 articles. We excluded 84 articles that contained duplicate content. Fifty-five full-text articles were then assessed using inclusion and exclusion criteria. Of these, 17 studies met the inclusion criteria and were incorporated into this review. Figure 1 presents a PRISMA flow diagram outlining the study selection process.
+
+Fig. 1 Flow diagram of the study identification and selection process according to PRISMA guidelines
+
+Characteristics of included studies
+
+This systematic review and meta-analysis include a total of 17 studies published up to 2025, with their key characteristics summarized in Table 1. C57BL/6 mice were used in 10 studies [12, 18, 22–29], Wistar rats were used in 2 studies [20, 30], Swiss albino mice were used in only one study [21], P301S mice were used in only one study [31], APP/PS1 mice were used in 2 studies [13, 32], and 5xFAD mice were used in only one study [23]. The AdipoRon dosage ranged from 1 µg/kg to 50 mg/kg. Four studies administered AdipoRon via gavage [13, 23, 27, 31], seven via intraperitoneal injection [12, 18, 22, 23, 25, 26, 28], three via intranasal injection [20, 21, 30], and the remaining via intracerebroventricular (ICV) [24, 29, 32]. The duration of AdipoRon ranged from 7 days to 4 months. All studies used male animals.Table 1 Characteristics of the included studies
+
+Author and year	Type of study	Species	Sex age (months)	Duration, dose, and route of treatment	Anxiety	Depression	Cognitive	Main findings in ivivo	
+Douglas A. Formolo et al. 2023	Invivo	C57BL/6J and CamKIIα-Cre mice	Male, Eight-week-old	7-day, 20 mg/kg, i.p	Novelty-suppressed feeding test and Light–Dark Box	SPT and FST		Reduced immobility time in the FST, anxiolytic-like effects, no change in adult hippocampal neurogenesis, reduced protein levels of BDNF and PSD-95	
+Thomas H Lee et al. 2021	Invivo and invitro, T2DM	C57BL/6J Mice	Male, Five-week-old	20 mg/kg, i.p,14 days	OFT		Y-Maze test	Improved spatial memory, restored hippocampal adult neurogenesis, activated AMPK/PPAR-γ/PGC-1α signaling, ameliorated spine loss, restored LTP deficits in the dentate gyrus, promoted BDNF Levels, and increased serum adiponectin	
+Thomas H. Lee et al. 2021	In vivo, Memory	C57BL/6J Mice	Male, Five-week-old	20 or 50 mg/kg i.p., continuously
+
+for 14 days
+
+	OFT		Y-Maze test	20 mg/kg promoted hippocampal cell proliferation, increased serum levels of adiponectin and BDNF, no effects on spatial recognition memory and locomotor activity. At a dose of 50 mg/kg, impaired spatial recognition memory, inhibited cell proliferation, and neuronal differentiation	
+Bin Liu et al. 2020	In vivo, AD	C57BL/6 mice, APP/PS1	Male ,7 months	1 µg in 2 µl vehicle, lateral ventricle			OFT, NOR, Y-maze, and MWM	Suppressed the Aβ deposition and inhibited BACE1 expression in both the cortex and hippocampus, reversed the dissipation of the ΔΨm, escape latency decreased, and improved cognitive	
+Wenyan Zhao et al. 2025	In vivo, T2DM	C57BL/6 mice	Male, Seven-week-old	20 mg/kg and a vehicle
+
+i.p, 14 days
+
+	OFT	SPT and FST		Improved depression-like behavior, anti-apoptotic effect in the hippocampus, and increased the number of synapses in the prefrontal cortex and hippocampus, increased the density of dendritic spines in the CA1 region, decreased NLRP3, ASC, and IL-1β protein levels in the PFC and hippocampus, and increased the ratio of LC3II/ LC3I and beclin1 in the hippocampus, activated the AMPK/mTOR autophagy pathway, and increased AdipoR1	
+Mayuri Khandelwal et al. 2022	Invivo and invitro, AD	APP/PS1 mice	Male, Seven-week-old	50 mg/kg, gavage, 30 days			MWM and Y- maze	Potentiated insulin sensitivity, reversed cognitive deficits, reduced Aβ amyloid burden, and induced AMPK activation, reduced GFAB and promoted GLUTs expression, increased PSD-95 and synaptophysin, and BACE	
+Roy Chun-Laam Ng et al. 2021	Invivo and invitro, AD	5xFAD mice and wild-type
+
+C57BL/6 N
+
+	Male, Seven-week-old	50 mg/kg, gavage, 3 months	OFT		MWM, NOR
+
+, and the Fear-conditioning test
+
+	Improved cognitive functions and restored neuronal and synaptic densities, rescued neuronal loss, and restored reduction of dendritic spine density, decreased Aβ deposition, and ameliorated amyloid pathology, diminished microgliosis, astrogliosis, and inflammatory responses (IL1β and TNFα, GFAB)	
+Beriwan Malaei et al. 2025	In vivo, Sleep	Swiss albino mice	Male, 3 months old	10 µg/mouse in 10 µL, Intranasal, 21 days	OFT and
+
+EPM
+
+	FST and SPT		Attenuated depressive-like symptoms, decreased serum corticosterone, suppressed microgliosis in the PFC (Iba-1), inhibited inflammatory responses (IL-1β, p-NF-κB)	
+Sarah Nicolas et al. 2018	In vivo, Depression	C57BL/6J mice	Male, five-week-old	1 mg/kg, i.p, 3 weeks	NSF test	Light and dark test, SPT, social interaction test, learned helplessness test, FST		Ameliorated corticosterone, induced excess weight and dyslipidemia, reversed the anxiety and depressive-like behavior, restored BDNF, VEGFα, IGF1, and NGF	
+Fengjiao Sun et al. 2024	In vivo and in vitro, AD	APP/PS1 transgenic mice	Male, 8 months	1 µg per mouse, ICV, 7 days			NOR test, Y-maze, and MWM	Facilitated Aβ clearance, activated autophagy (LC3II, P62), AdipoR1/AMPK, and SIRT1, alleviated the cognitive impairment	
+Soraya Alimohammadi et al. 2025	Invivo, PD	Wistar Rat	Male, 2 months	0.1, 1, 10 µg in 10 µl/rat, Intranasal, 21 days			NOR and Barnes-Maze test	Improved recognition memory and motor function, spatial memory, decreased ROS levels, enhanced the antioxidant system (SOD, GPX, TAC), upregulated BDNF and PSD-95	
+Negin Azizifar et al. 2024	Invivo, PD	Wistar Rat	Male, 2 months	0.1, 1, and 10 µg, Intranasal, 21
+
+days
+
+	OFT and EPM	SPT and FST		Reduced corticosterone, decreased inflammasome components (NLRP3, caspase 1, and IL-1β), and increased Sirt-1 protein levels in the prefrontal cortex	
+Yaqi Liu et al. 2024	In vitro and in vivo, Depression	C57BL/6J mice	Male,7–8 weeks old	10,20,40 mg/kg, i.p, 14 days	OFT	SPT, TST, and FST		Ameliorated depressive-like behaviors, alleviated neuronal damage and inflammation (IL-1β, IL-6, TNF-α, and IL-18), inhibited Iba-1, and NLRP3/caspase 1/IL-1β	
+Guangyang Bai et al. 2024	Invivo, Septic	C57BL/6J mice	Male, 8 weeks	50 mg/kg, gavage, 7 days			MWM	Improved memory deficits, ameliorated synapse damage and neuronal loss, promoted the phosphorylation of adenosine 5 ’-monophosphate activated protein kinase (pAMPK)	
+Wenyan Zhao et al. 2024	Invivo, T2DM, AD	C57BL/6 mice	Male, 8 weeks	50 mg/kg, i.p, 14 days			MWM	Restored the cognitive deficits, up-regulated PSD95, SYN, GAP43, and SYP, increased the number of hippocampal synapses, attenuated synaptic damage and Tau phosphorylation, decreased the activity of GSK-3β, increased AdipoR1&2, p-AMPK, AMPK, Reduced p-mTOR/mTOR	
+Cailin Wang et al. 2023	In vitro and in vivo, AD	SH-SY5Y cells, P301S mice	Male, 6 months old	20 µM in vitro, 50 mg/kg
+
+in vivo, gavage, 4 months
+
+			NOR and MWM	Improve synaptic function, enhanced mitochondrial fusion, and mitigated hyperphosphorylated tau accumulation, rescued memory deficits	
+Jingjing You et al. 2021	Depression	C57BL/6J mice	Male, 12-month-
+
+old
+
+	1 µl/1 mM, ICV	OFT, light-dark
+
+test, and EPM
+
+	FST, SPT, and TST	NOR, MWM, and Y-maze	Promoted hippocampal neurogenesis and improved cognitive dysfunction, increased the number of Ki67- and DCX-positive cells, increased expression of NICD, ADAM10, Hes1, Hes5, Hey1, and Heyl and upregulated Notch1 signaling	
+
+Quality and risk of bias of included studies
+
+Of the studies reviewed, all were published in peer-reviewed journals and included statements on temperature control. A conflict of interest disclosure and mention of random allocation were provided in 100% of the articles. Three studies mentioned allocation concealment. All studies stated compliance with animal welfare regulations. Random allocation to treatment or control was reported in 100% of the publications. However, one article reported a sample size calculation. Blinded outcome assessment was described in 56.25% of the papers. Additionally, avoidance of anesthetics with significant intrinsic properties was reported in 25% of studies (Fig. 2).
+
+Fig. 2 Evaluation of the included studies using the modified CAMARADES quality checklist
+
+Risk of bias
+
+The assessment of bias risk in the included studies indicated that the majority had either a low or moderate risk of bias across most domains. Sequence generation was deemed to be of low risk of bias in 52.94% of the studies. There was an unclear risk of bias regarding allocation concealment (88.23%), Selective outcome reporting (64.70%), other biases (58.82%), and Random housing (70.58%). High risk of bias was identified for investigator blinding in 17.65% of articles. Blinding of outcome assessment was low risk in 52.94% of the studies, and incomplete outcome data were low risk in 58.82% of the studies. Moreover, baseline characteristics (58.82%) and random outcome assessment (47.05%) were low risk in the studies (Fig. 3A and B).
+
+Fig. 3 A Methodological quality graph: review authors’ judgments about each methodological quality item presented as percentages across all included studies. B Diagram of risk of bias in the included studies. + = low risk of bias, – = high risk of bias, ? = unclear risk of bias
+
+Behavioral tests
+
+Depressive
+
+Forced swim test (FST)
+
+A total of three studies (7 arms) involving 66 animals in the AdipoRon group and 66 in the control group were included in FST [12, 20, 26]. The effects of AdipoRon were analyzed separately for Parkinson’s disease (PD) and depression models. In the subgroup analysis of PD models, three arms were included. AdipoRon administration resulted in a reduced immobility time versus controls (WMD = − 17.37, 95% CI [− 26.64,−8.10]; p = 0.0002). Heterogeneity among these studies was negligible (I2 = 0%), indicating a consistent effect across the included PD models.
+
+Two studies (4 arms) were included in the depression model. AdipoRon significantly improved depressive-like behaviors (WMD = − 76.45, 95% CI [− 108.11, − 44.78]; p < 0.00001). Substantial heterogeneity was observed (I² = 88%), indicating marked variability across depression models. These findings are summarized in the forest plot shown in Fig. 4, which illustrates the effect of AdipoRon on FST.
+
+Fig. 4 Forest plot of studies on the effect of AdipoRon on FST
+
+Sucrose preference test (SPT)
+
+Regarding SPT, four studies (six arms) comprising 54 animals in the AdipoRon group and 54 animals in the control group were included in the meta-analysis of SPT [22, 25–27]. The results indicated that AdipoRon treatment significantly increased sucrose preference versus the control group (WMD = 10.19; 95% CI [6.44, 13.94]; p < 0.0001; I2 = 55%). Figure 5 presents the forest plot that demonstrates the effect of AdipoRon on SPT.
+
+Fig. 5 Forest plot of studies on the effect of AdipoRon on SPT
+
+Anxiety
+
+Open field test (OFT)
+
+A random-effects meta-analysis was carried out to investigate the effect of AdipoRon on anxiety-like behavior in animal models, as measured by the OFT (Fig. 6). Eight arms of four studies from diabetes [23, 25], PD [20], and chronic unpredictable mild stress (CUMS) models [26] were included. In diabetic models, AdipoRon had a non-significant effect on anxiety-like behavior (WMD = 2.97, 95% CI [–3.03, 8.97], p = 0.33; I2 = 79%). In PD models, a non-significant trend was observed (WMD = 59.46, 95% CI [–4.80, 123.73], p = 0.07; I² = 88%). Conversely, in CUMS models, AdipoRon significantly reduced anxiety-like behavior (WMD = 5.32, 95% CI [2.50, 8.14], p = 0.0002; I² = 49%).
+
+Fig. 6 Forest plot of subgroup analyses for anxiety by spent center time in the OFT test
+
+Cognition
+
+Novel object recognition (NOR) test
+
+A random-effects meta-analysis was conducted to assess the impact of AdipoRon on recognition memory in animal models of neurodegenerative disorders (Fig. 7). In the AD model (4 studies) [8, 24, 31, 32], AdipoRon significantly improved NOR test performance compared with control groups (WMD = 20.23, 95% CI [10.85, 29.61], p < 0.0001; I2 = 61%). Similarly, in the PD subgroup, AdipoRon treatment could significantly improve (WMD = 20.12, 95% CI [16.13,18.26], p < 0.0001; I2 = 87%).
+
+Fig. 7 Forest plot of subgroup analyses for exploration time in the novel object in the NOR test
+
+Effect of administration routes of AdipoRon on NOR performance
+
+To investigate whether the route of administration influences the cognitive effects of AdipoRon, a subgroup meta-analysis was performed based on delivery methods (ICV, gavage, and intranasal). As seen in Fig. 8, for ICV injection, AdipoRon significantly increased exploration time for novel objects (WMD = 16.72, 95% CI [8.79,24.66], p < 0.0001; I2 = 0%).
+
+Fig. 8 Forest plot of subgroup analyses for exploration time in the novel object in the NOR test. Grouped by route of AdipoRon injection
+
+Gavage AdipoRon administration also resulted in a significant positive effect (WMD = 22.55, 95% CI [2.66, 42.44], p = 0.03; I2 = 74%). Intranasal delivery of AdipoRon also showed improvement in recognition memory (WMD = 12.20, 95% CI [6.13, 18.26], p < 0.0001; I2 = 87%). Overall, AdipoRon treatment significantly improved recognition memory impairments compared with control groups.
+
+Morris water maze (MWM) test
+
+Five studies were included in the meta-analysis of time spent in the target quadrant in the MWM test (n = 104: 52 treated animals and 52 control animals) [8, 13, 24, 31, 32]. Heterogeneity was moderate (I2 = 34%). AdipoRon-treated animals spent significantly more time in the target quadrant than controls (WMD = 2.60, 95% CI [1.81, 3.40], p < 0.00001). These results indicate that AdipoRon improves spatial learning in AD animal models (Fig. 9).
+
+Fig. 9 Forest plot of studies on the effect of AdipoRon on time spent in the target quadrant in the MWM test
+
+Neuroprotective mechanisms
+
+Synaptophysin expression
+
+For synaptophysin (SYP) expression levels, 3 studies were incorporated into the meta-analysis [13, 28, 31]. As seen in Fig. 10A, a significant increase in SYP expression levels was observed in animals treated with AdipoRon compared to the control group (15 treated animals, 15 control animals; WMD = 0.17, 95% CI [0.11, 0.23], p < 0.00001; I2 = 0%).
+
+Fig. 10 Forest plot of studies on the effect of AdipoRon on expression of A synaptophysin, B PSD-95, C P-mTOR /mTOR, and D P-AMPK/AMPK
+
+PSD-95 expression
+
+We identified three studies that measured PSD-95 expression [13, 28, 31]. The pooled results showed a significant increase in PSD-95 levels in the treated group compared with the control group (15 treated animals and 15 control animals; WMD = 0.31, 95% CI [0.22, 0.40], p < 0.00001; I2 = 0%; Fig. 10B).
+
+P-mTOR /mTOR expression
+
+As seen in Fig. 10C, the analysis showed that AdipoRon treatment significantly reduced P-mTOR/mTOR expression versus the control group (7 treated animals, 7 control animals; WMD = − 0.61; 95% CI = [− 1.10, − 0.12]; p = 0.02; I2 = 0% ) [25, 28].
+
+P-AMPK/AMPK expression
+
+As shown in Fig. 10D, a meta-analysis of 4 studies [13, 25, 28, 31] showed that administration of AdipoRon could upregulate the expression of P-AMPK/AMPK ratio compared to the control group (18 treated animals, 18 control animals; WMD = 0.54; 95% CI = [0.29, 0.80]; p < 0.0001; I2 = 89%).
+
+The effects of AdipoRon on memory in the Y-maze test
+
+Of all included studies, six articles used the Y-maze test to evaluate hippocampal-dependent spatial recognition memory. Lee et al. [23] showed that administration of AdipoRon for 14 days restored the memory deficits in diabetic mice. In another study, treatment with 20 mg/kg of AdipoRon did not adversely affect spatial recognition memory; however, administration of 50 mg/kg resulted in a significant impairment of spatial memory, as evidenced by a marked reduction in the exploration index. These findings indicate that high-dose AdipoRon treatment may negatively influence spatial recognition memory [18]. According to Khandelwal et al. [13], AdipoRon treatment for 1 month could improve behavioral performance in the Y maze test by the percentage of time spent in the novel arm among AD mice. Moreover, APP/PS1 transgenic mice exhibited memory deficits that were ameliorated by intracerebroventricular injection of AdipoRon [24]. In the Y maze test, the APP/PS1 group demonstrated a reduced percentage of spontaneous alternation (SA%) compared to the wild-type group. Nevertheless, AdipoRon significantly enhanced the SA% in APP/PS1 transgenic mice [32].In a study, ICV injection of AdipoRon could not significantly affect SA% in depressed mice [29].
+
+The effects of AdipoRon on anxiety in the elevated plus maze test (EPM)
+
+Among the retrieved articles, two investigated the effect of AdipoRon on anxiety in the EPM test. A study by Malaei and colleagues revealed that the intranasal delivery of AdipoRon resulted in a significant both the time spent and entries into open arms compared with the control group in sleep-restricted mice [21]. Similarly, in PD animals, intranasal administration of AdipoRon (1 and 10 µg) increased open arm time and the number of open arm entrances in the EPM test [20]. Together, these findings suggest that intranasal AdipoRon effectively alleviates anxiety-related behavioral deficits.
+
+The effects of AdipoRon on inflammation
+
+Among the included studies, six articles evaluate the anti-inflammatory effect of AdipoRon. Nag et al. [8] provided evidence that AdipoRon reduced Iba-1 and activated astrocytes (GFAP) in both the cortex and hippocampus regions, and normalized the levels of pro-inflammatory factors, including interleukin (IL)-1β and tumor necrosis factor (TNF)-α, in AD mice. Similarly, Malaei et al. [21] found that treatment with AdipoRon attenuated the number of Iba-1-positive cells and decreased levels of TNF-α and IL-1β in the prefrontal cortex of sleep-restricted mice. Another study showed that AdipoRon reduced the density of GFAP-positive cells and Iba-1 1levels in the brain of transgenic APP/PS1 mice [13]. AdipoRon treatment was also shown to suppress the inflammasome pathway (NLRP3, caspase 1, and IL-1β) and reduce the levels of IL-6, TNF-α, and IL-18 in the hippocampus [12, 20, 26].
+
+Effects of AdipoRon on corticosterone levels
+
+Three studies also investigated the effects of AdipoRon on the corticosterone levels. The study by Nicolas et al. revealed that a three-week administration of AdipoRon reduced corticosterone levels in depressed mice [12]. Consistent findings have also been obtained from other studies [20, 21].
+
+Discussion
+
+The current systematic review and meta-analysis support the beneficial effects of AdipoRon on behavioral and neuroprotective outcomes in rodent models. Based on the included studies, these improvements appear to be mediated primarily by upregulation of synaptic proteins, reduction of oxidative stress, and modulation of neuroinflammation. This study synthesized findings from preclinical research examining the antidepressant- and anxiolytic-like effects of AdipoRon, as well as its impact on cognitive function, across a range of behavioral and biochemical measures. The findings demonstrated that AdipoRon had a significant impact on behavioral domains, including immobility time in the FST, time spent in the central area in the OFT, and sucrose preference in the SPT, suggesting its efficacy in relieving depressive and anxiety symptoms in animal studies. Moreover, the administration of AdipoRon improves cognitive impairments in CNS diseases, such as AD, PD, and depression, as assessed by the MWM, NOR, and Y-maze tests.
+
+AdipoRon: depression and anxiety
+
+The majority of the included studies that conducted depression assessment tests discovered that AdipoRon alleviates depression-like behaviors in PD and depression models in both mice and rats [12, 20, 22, 25, 26]. The pooled results of the current meta-analysis were consistent with most of these studies’ findings. A meta-analysis of FST results from studies revealed that AdipoRon reduced immobility time across experimental models [12, 20, 26]. In the PD model, AdipoRon could significantly decrease immobility time in the FST, with negligible heterogeneity (I2 = 0%). In contrast, the depression subgroup showed considerable heterogeneity (I2 = 88%), indicating substantial variability across studies. Several factors may explain this heterogeneity. First, different depression induction paradigms, including chronic unpredictable stress and corticosterone exposure, likely engage distinct neurobiological pathways. Second, variations in AdipoRon dosage and treatment duration may contribute to inconsistent outcomes. Despite this variability, the direction of effect remained consistently favorable, reinforcing the potential antidepressant properties of AdipoRon. Moreover, the findings of the SPT further support the antidepressant-like effects of AdipoRon in preclinical models. AdipoRon treatment significantly increased sucrose preference compared with controls, indicating attenuation of anhedonia, which is considered one of the core behavioral manifestations of depression [33].
+
+D. A. Formolo et al. have demonstrated antidepressant- and anxiolytic-like effects after just 7 days of subchronic AdipoRon treatment, independent of hippocampal structural changes and synaptic function [22]. As Nicolas reported, mice under long-term corticosterone treatment showed increased immobility in the FST, reflecting reduced depressive-like states in mice [12]. The antidepressant effects of AdipoRon appear to be mediated through the modulation of neuroinflammation, as evidenced by alterations in IL-1β, IL-6, and TNF-α levels, as well as the normalization of indoleamine 2,3-dioxygenase and kynurenine aminotransferase expression. Furthermore, AdipoRon restored levels of brain-derived neurotrophic factor (BDNF), vascular endothelial growth factor-α, insulin-like growth factor-1, and nerve growth factor, while also increasing serotonin release and turnover [12].
+
+Neuroinflammation is a key factor in the pathophysiology of depression. Specifically, inflammation mediated by microglia activation is believed to be closely associated with the onset and progression of depressive disorders [34]. Microglia-dependent activation of the inflammasome is crucial in the brain, and the NLRP3 inflammasome is identified as a pivotal molecular platform that regulates the release of pro-inflammatory cytokines. Activation of NLRP3 by repeated stress recruits ASC, which in turn activates caspase-1, which in turn promotes the cleavage of pro-IL-1β and pro-IL-18 into their mature forms [35]. Consequently, this process triggers an inflammatory response that can harm neurons and worsen disease progression [36]. Moreover, increasing evidence suggests that the NLRP3 inflammasome is hyperactivated in both patients with depression and in animal models of the condition [37, 38]. It has been reported that AdipoRon attenuated anxiety- and depression-like related behaviors in the PD rat model through inhibition of NLRP3 activation and modulating downstream inflammatory cascades [20]. You and colleagues examined the impact of intraventricular cannulation and ICV administration of AdipoRon in mice with depression. The findings indicated that AdipoRon enhances hippocampal neurogenesis and ameliorates depression-related cognitive deficits, primarily through the upregulation of Notch signaling and the expression of key regulatory genes [29].
+
+Malaei et al. [21] found that intranasal AdipoRon treatment increased time spent in the open arms during the EPM test, diminished immobility time, and improved grooming behavior during the FST in mice exposed to chronic sleep deprivation, reducing anxiety and depressive symptoms.
+
+A recent study by Li et al. [39] demonstrated that AdipoRon ameliorates anxiety- and depression-like behaviors in chronically stressed mice through modulation of the AMPK-PPAR2-BDNF-TrkB signaling pathway in the hippocampus. Although this study was not included in our meta-analysis due to its recent publication, it provides converging support for a critical role of the AdipoR2 signaling pathway in stress-related depression models. This mechanistic understanding of reported associations enhances the biological viability and translational significance of the outcomes from our review.
+
+AdipoRon and cognitive
+
+The meta-analysis revealed that treatment with AdipoRon improves cognitive and behavioral performance. This is evidenced by increased time spent in the target quadrant in the MWM test and enhanced recognition memory in the NOR test. Accumulating evidence from in vivo models of AD, PD, and diabetes has investigated the efficacy of AdipoRon on cognitive function. They found that AdipoRon exerts beneficial effects on cognitive function via diverse molecular pathways. A study by Wang et al. [31] reported that AdipoRon treatment in SH-SY5Y cells and P301S transgenic male mice attenuated tau hyperphosphorylation and improved cognitive performance, synaptic function, and mitochondrial fusion, primarily through activation of the AMPK/GSK3β signaling cascade and upregulation of mitochondrial fusion proteins. A key limitation of the study is the four-month duration of AdipoRon treatment in mice, which may not be readily applicable to human clinical protocols and raises concerns regarding clinical feasibility and long-term safety.
+
+The findings of Liu et al. [26] indicate that AdipoRon improves cognitive performance and reduces amyloid-β (Aβ) deposition in NE-4 C cells and APP/PS1 mice via the AMPK/CREB signaling pathway. Clinically, these results suggest that AdipoRon may promote neuronal survival and improve cognitive performance in AD by supporting neuroplasticity and mitigating amyloid-induced toxicity. Limitations on the clinical translatability of these findings include limited in vivo investigation time (7 days) and the methodology of administration via lateral ventricle injection, which may not be representative of longer-term human therapeutic dosing. Future studies should evaluate longer treatment durations and develop more suitable delivery strategies. Ng and colleagues [8] evaluated the effects of AdipoRonin in 5xFAD transgenic mice. They found that AdipoRon improved spatial memory and synaptic function and attenuated inflammation. These neuroprotective effects were mechanistically mediated through AMPK activation and the inhibition of Beta-Secretase 1 and NF-κB signaling.
+
+The hippocampus plays a crucial role in regulating learning and memory processes, synaptic plasticity, and neuronal survival, mainly through high levels of BDNF expression. BDNF provides protection against neurotoxic damage, promotes the secretion and recycling of presynaptic dopamine, and addresses mitochondrial dysfunction in dopaminergic neurons of the substantia nigra [40]. Conversely, in individuals with PD and in animal models, there is a notable down-regulation of both the BDNF gene and its protein in the brain and blood. This reduction results in insufficient neurotrophic support, contributing to motor impairments as well as cognitive and psychiatric disorders [41, 42]. Research indicates that the accumulation of α-synuclein in the hippocampus reduces BDNF expression and synaptic proteins, including PSD-95(postsynaptic marker). This decline contributes to synaptic dysfunction and subsequent memory impairment. Alimohammadi et al. reported that adiporon at a dose of 10 mg/kg increases BDNF and PSD-95 levels [30]. Age-related decreases in the levels of PSD-95 are indicative of neuronal and synaptic loss in AD, which is associated with elevated amyloid burden and tau hyperphosphorylation. Additionally, a reduction in the SYP ( presynaptic marker) further exacerbates memory deficits in AD [43]. Several studies have demonstrated that AdipoRon administration increases PSD-95 and SYP levels in AD animals [13, 28, 31]. Moreover, AdipoRon treatment in diabetic mice restored hippocampal neurogenesis, increased spine density, facilitated hippocampal long-term potentiation, and increased serum and BDNF levels in the hippocampus [23].
+
+A study by Lee et al. [18] demonstrated that while low-dose AdipoRon (20 mg/kg) enhanced hippocampal neurogenesis and spatial memory, a higher dose (50 mg/kg) unexpectedly impaired spatial memory, suggesting dose-dependent biphasic effects on hippocampal signaling. The high dose reduced serum adiponectin levels and BDNF, and the number of Ki67-, DCX-, and BrdU-positive cells, indicating impaired neurogenesis. Because BDNF plays a critical role in neuronal survival, synaptic plasticity, and memory formation, its reduction may contribute to the observed cognitive deficits [44]. One possible mechanism involves overactivation of the AdipoR1/AMPK signaling pathway at high doses of AdipoRon. Although AMPK activation is generally considered neuroprotective, AMPK hyperactivation may suppress mTOR signaling, reduce BDNF levels, and so impair hippocampal neurogenesis under physiological conditions. Furthermore, elevated corticosterone levels induced by high-dose AdipoRon may further contribute to reduced neurogenesis and memory impairment [45].
+
+Recent evidence supports the beneficial effects of adiponectin signaling on cognitive function. Hui GG et al. [46] showed that three weeks of physical exercise (voluntary wheel running) increases adiponectin to increase Protein phosphatase 2 A (PP2A) activity, leading to reduced Tau protein phosphorylation levels in the hippocampus and improved cognitive deficits and neuroplasticity in chronic stress exposure mice.
+
+AdipoRon has potential therapeutic implications for the treatment of AD, PD, and depression based on current scientific evidence; however, current limitations in our knowledge of the interactions between AdipoRon and various pathophysiological mechanisms of these diseases could prevent accurate translation from animal models to humans. Also, very few studies have employed long-term administration of AdipoRon, which hampers our ability to assess its long-term effects as a therapeutic agent for these diseases, given the need for consistent therapeutic intervention in chronic, progressive diseases. Future research should focus on conducting prolonged, longitudinal in vivo experiments using various model systems and populations to determine the safety, efficacy, and durability of AdipoRon as a therapeutic agent in humans.
+
+In addition, this review is limited by the predominance of studies conducted in male rodents, which may constrain the external validity of the findings. Given the increased prevalence of depression in females and the potential for sex-specific mechanisms that contribute to depression in females, this imbalance reduces the translational applicability of the evidence. Future preclinical research should examine both sexes and systematically evaluate sex as a biological variable to enhance the robustness and clinical relevance of the findings.
+
+Conclusion
+
+In this preclinical systematic review, AdipoRon demonstrated beneficial effects on depressive- and anxiety-like behaviors and improved cognitive performance in rodent model studies. These effects appear to be mediated through multiple mechanisms, including anti-inflammatory actions, modulation of neurotransmitter systems, and improvement of mitochondrial function. However, due to the lack of human studies available, the clinical applicability of adipoRon remains uncertain. Future research is needed to evaluate these findings through translational research designs and to develop agonists of adiponectin receptors with more favourable pharmacokinetic and safety profiles for future use as clinical therapeutic agents.
+
+Abbreviations
+
+AdipoR1 Adiponectin receptor 1
+
+AdipoR2 Adiponectin receptor 2
+
+AD Alzheimer's disease
+
+BDNF Brain-derived neurotrophic factor
+
+CAMARADES Collaborative approach to meta-analysis and review of animal studies
+
+CI Confidence intervals
+
+CUMS Chronic unpredictable mild stress
+
+EPM Elevated plus maze test
+
+FST Forced swim test
+
+HPA Hypothalamic-pituitary-adrenal
+
+MWM Morris water maze
+
+NOR Novel object recognition
+
+OFT Open field test
+
+PD Parkinson’s disease
+
+PRISMA Preferred reporting items for systematic reviews and meta-analyses
+
+SPT Sucrose preference test
+
+SR Sleep restriction
+
+SYP Synaptophysin
+
+TNF Tumor necrosis factor
+
+WMD Weighted mean differences
+
+Acknowledgements
+
+The authors gratefully acknowledge the “Clinical Research Development Unit of Razi Educational, Research and Treatment Center”, Tabriz University of Medical Sciences, for its consulting services.
+
+Author contributions
+
+Leila Hosseini and Seyed Gholamreza Noorazar designed the study. Saeed Dastgiri, Parinaz Kalejahi, and Leila Hosseini conducted a systematic search. Fatemeh Sadat Gheibi and Ali Reza Shafiee-Kandjani performed the study screening. Leila Hosseini and Fatemeh Sadat Gheibi performed the data extraction and risk of bias assessment. Fatemeh Sadat Gheibi, Parinaz Kalejahi, and Leila Hosseini wrote the original manuscript draft. All authors significantly contributed to the study and approved the final submitted version.
+
+Funding
+
+This is a report of an MD thesis registered in the Research Center of Psychiatry and Behavioral Sciences, Tabriz University of Medical Sciences, Tabriz, Iran (Grant number 75671).
+
+Data availability
+
+No datasets were generated or analysed during the current study.
+
+Declarations
+
+Ethics approval and consent to participate
+
+This study was approved by Tabriz University of Medical Sciences, IRAN. (Ethics No. IR.TBZMED.VCR.REC.1404.115)
+
+Consent for publication
+
+Not applicable.
+
+Competing interests
+
+The authors declare no competing interests.
+
+Publisher’s note
+
+Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
+
+
+References
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+Miranda M, Morici JF, Zanoni MB, Bekinschtein P. Brain-derived neurotrophic factor: a key molecule for memory in the healthy and the pathological brain. Front Cell Neurosci. 2019;13:472800.10.3389/fncel.2019.00363 PMC6692714 31440144
+41. Palasz E Wysocka A Gasiorowska A Chalimoniuk M Niewiadomski W Niewiadomska G BDNF as a promising therapeutic agent in Parkinson’s disease Int J Mol Sci 2020 21 3 1170 10.3390/ijms21031170 32050617 PMC7037114
+Palasz E, Wysocka A, Gasiorowska A, Chalimoniuk M, Niewiadomski W, Niewiadomska G. BDNF as a promising therapeutic agent in Parkinson’s disease. Int J Mol Sci. 2020;21(3):1170.32050617 10.3390/ijms21031170 PMC7037114
+42. Rahmani F Saghazadeh A Rahmani M Teixeira AL Rezaei N Aghamollaii V Plasma levels of brain-derived neurotrophic factor in patients with Parkinson disease: a systematic review and meta-analysis Brain Res 2019 1704 127 36 10.1016/j.brainres.2018.10.006 30296429
+Rahmani F, Saghazadeh A, Rahmani M, Teixeira AL, Rezaei N, Aghamollaii V, et al. Plasma levels of brain-derived neurotrophic factor in patients with Parkinson disease: a systematic review and meta-analysis. Brain Res. 2019;1704:127–36.30296429 10.1016/j.brainres.2018.10.006
+43. Shao CY Mirra SS Sait HB Sacktor TC Sigurdsson EM Postsynaptic degeneration as revealed by PSD-95 reduction occurs after advanced Aβ and tau pathology in transgenic mouse models of Alzheimer’s disease Acta Neuropathol 2011 122 3 285 92 10.1007/s00401-011-0843-x 21630115 PMC3437675
+Shao CY, Mirra SS, Sait HB, Sacktor TC, Sigurdsson EM. Postsynaptic degeneration as revealed by PSD-95 reduction occurs after advanced Aβ and tau pathology in transgenic mouse models of Alzheimer’s disease. Acta Neuropathol. 2011;122(3):285–92.21630115 10.1007/s00401-011-0843-x PMC3437675
+44. Yang T Nie Z Shu H Kuang Y Chen X Cheng J The role of BDNF on neural plasticity in depression Front Cell Neurosci 2020 14 82 10.3389/fncel.2020.00082 32351365 PMC7174655
+Yang T, Nie Z, Shu H, Kuang Y, Chen X, Cheng J, et al. The role of BDNF on neural plasticity in depression. Front Cell Neurosci. 2020;14:82.32351365 10.3389/fncel.2020.00082 PMC7174655
+45. Brummelte S Galea LA Chronic high corticosterone reduces neurogenesis in the dentate gyrus of adult male and female rats Neuroscience 2010 168 3 680 90 10.1016/j.neuroscience.2010.04.023 20406669
+Brummelte S, Galea LA. Chronic high corticosterone reduces neurogenesis in the dentate gyrus of adult male and female rats. Neuroscience. 2010;168(3):680–90.20406669 10.1016/j.neuroscience.2010.04.023
+46. Guo HH Ou HN Yu JS Luo ZR Yau SY Tsang HW The Adiponectin-PP2A Pathway Confers Cognitive Benefits of Physical Exercise Against Chronic Stress-Induced Tau Hyperphosphorylation in the Hippocampus Aging Cell 2026 25 3 e70447 10.1111/acel.70447 41841751 PMC13093838
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+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Nat Commun
+Journal ID: Nat Commun
+NLM Journal ID: 101528555
+
+Nature Communications
+
+EISSN: 2041-1723
+Publisher: Nature Publishing Group
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC13522352
+PMID: 42660917
+DOI: 10.1038/s41467-026-76050-0
+Article ID: 76050
+Article version: 1
+Subjects: Article
+
+A physics-informed eikonal model for simulating arrhythmias in the human heart in real-time
+
+http://orcid.org/0009-0002-6852-4604 Schrotter Thomas G. 1 2
+http://orcid.org/0000-0001-7742-8193 Gsell Matthias A. F. 1
+http://orcid.org/0000-0002-0608-1636 Zappon Elena 1 3
+http://orcid.org/0000-0001-6341-4014 Augustin Christoph M. 1 2 3
+Neic Aurel 2
+http://orcid.org/0000-0002-7432-0424 Pezzuto Simone 4 5
+http://orcid.org/0000-0002-7380-6908 Plank Gernot gernot.plank@medunigraz.at
+1 2 3
+1 https://ror.org/02n0bts35 grid.11598.34 0000 0000 8988 2476 Gottfried Schatz Research Center, Division of Medical Physics and Biophysics, Medical University of Graz, Neue Stiftingtalstraße 6, Graz, Austria
+2 grid.518790.2 NumeriCor GmbH, Conrad-von-Hötzendorfstraße 26/2, Graz, Austria
+3 https://ror.org/02jfbm483 grid.452216.6 BioTechMed-Graz, Mozartgasse 12/II, Graz, Austria
+4 https://ror.org/05trd4x28 grid.11696.39 0000 0004 1937 0351 Department of Mathematics, University of Trento, Via Sommarive 14, Trento, Italy
+5 https://ror.org/03c4atk17 grid.29078.34 0000 0001 2203 2861 Euler Institute, Universitá della Svizzera italiana, Via Buffi 13, Lugano, Switzerland
+Electronic publication date: 2026 Jul 29
+Publication date: 2026
+Volume: 17
+Electronic Location ID: 9209
+Received 2025 Oct 1; Accepted 2026 Jul 20
+Copyright: © The Author(s) 2026
+Copyright year: 2026
+License: Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Keywords: Cardiovascular biology, Computational science
+
+Funding: Austria Science Fund (FWF), number 10.55776/I6476
+
+Funding: Austrian Research Promotion Agency (FFG) grant no. FO999891133
+
+Funding: European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie grant TwinCare-AF (grant agreement no. 101148636)
+
+Funding: Austria Science Fund (FWF), number 10.55776/P37063
+
+Funding: European Union’s Horizon research and innovation program (grant agreement no. 101230597)
+issue-copyright-statement: © Springer Nature Limited 2026
+
+Ÿ==============================Ÿ
+Personalized computational models of cardiac electrophysiology, referred to as cardiac digital twins, are considered a key technology for realizing precision cardiology by tailoring therapies to individual patients. However, the high computational demands of physically detailed simulations prohibit broader adoption of cardiac digital twins in practical applications. Here, we aim to address this challenge with a lightweight Physics-Informed Eikonal model that replicates the biophysical phenomena embedded within cardiac electrophysiology models along with clinical electrograms in near real-time, including arrhythmia scenarios. Validity of the proposed model is shown against a gold-standard cardiac electrophysiology model in complex arrhythmia simulations, including a scar-mediated ventricular tachycardia in a human whole-heart model. In this work, we show that the Physics-Informed Eikonal model delivers near-real time performance and retains high physical fidelity as required for the calibration of cardiac digital twins, thus providing a fundamental core technology to be leveraged in industrial and clinical applications.
+
+The authors present a model for real-time simulation of whole-heart electrophysiology and associated electrocardiograms with high physical fidelity, providing a technology for leveraging cardiac digital twins in clinical practice.
+
+Introduction
+
+Computational models of cardiac electrophysiology (CEP) provide a mechanistic framework capable of precisely predicting real-world behavior of the heart. Their application scope is determined by the fidelity achieved through calibration procedures that aim to minimize the discrepancy between behaviors in real and virtual space. If the gap is small and the response of a heart to a perturbation is predictable in silico, with sufficient certainty, such models can be used to evaluate the efficacy and safety of device1 or drug2 therapies. Thus, they offer vast potential to reduce economic costs and improve patient outcomes3. A most advanced realization of such a predictive CEP model is the concept of a cardiac digital twin (CDT)4–a virtual replica of a real-world human heart that is synchronized with real-time data to provide a holistic view on a heart’s function.
+
+However, realizing such high-fidelity CDTs remains a major challenge. First, the computational costs of numerically evaluating a mechanistically complete high-fidelity description of human CEP, such as the gold-standard cardiac bidomain model5, are prohibitively expensive6. Secondly, the process of calibrating a CDT by matching model predictions to observed data, referred to as functional twinning, constitutes a many-query application that requires a large number of model evaluations to perform parameter inference, sensitivity analysis and uncertainty quantification. Thus, realizing CDTs with current simulation technologies becomes unfeasible as the evaluation of a single patient takes days7 on high performance computing resources6,8,9 which prohibits broader adoption of CDTs.
+
+Attempts to enhance computational efficiency focused on optimizing implementations by exploiting parallelization on Central Processing Units (CPUs)6, Graphics Processing Units (GPUs)8–10 or through spatio-temporal adaptivity10,11. However, none of these approaches achieved sufficient performance for leveraging feasible CDT applications due to the spatio-temporal discretization constraints imposed by reaction-diffusion (RD)-based CEP models. Relaxing constraints by coarsening the spatial resolution reduces computational costs, but yields increasingly lower fidelity solutions6 or even numerical artifacts that produce emergent phenomena which would not occur with adequate discretization12. Realizing CDTs therefore requires alternative methods that are fast to evaluate and retain the key CEP mechanisms necessary to maintain predictive capabilities. Recent developments in data-driven surrogate CEP modeling based on machine learning have shown promise, but are so far limited to simplified toy applications13–18. With regard to physiologically complex CDTs, evidence of feasibility is lacking and projections on applicability appear overly optimistic19.
+
+An alternative approach is to recast the RD model into a traveling wave front problem that lifts the spatio-temporal discretization constraints20 to facilitate simulations of organ-scale CEP robustly at coarse resolutions in near real-time. Such methods employ an Eikonal-based wave propagation mechanism that can be coupled to RD models to support physiological wave front propagation at coarse spatial resolutions21–23, or directly recover a RD solution from a prescribed traveling wave front solution space24. However, the application scope of these approaches is limited as these yield solutions only for stable limit-cycle behaviors, but cannot account for dynamic history-dependence of CEP under irregular repetitive activations occurring under cardiac rhythm disturbances such as arrhythmias. Recent attempts to incorporate history-dependent physiology have been presented23,25–27, but limitations persist due to their incomplete physiological scope.
+
+In this work, we present a Physics-Informed Eikonal (PIE) model that is capable of accurately reproducing the spectrum of biophysical phenomena–including arrhythmias–embedded in RD-based CEP models in near real-time, thus overcoming the limitations of state-of-the-art RD, data-driven or Eikonal-based approaches. High computational performance is achieved by enabling lightweight modeling on coarser anatomical grids, whereas physical fidelity is retained by measuring dynamic system properties in small-scale high-fidelity RD models, and encoding these in lookup maps that govern finite state transitions controlling physical behaviors. The PIE model is able to simulate CEP and associated clinically observable signals such electrocardiograms (ECGs) with high physical fidelity in near real-time, rendering like-for-like comparisons to clinical data feasible. Our model delivers the sought-after performance and fidelity required for the calibration of CDTs, providing the core technology for leveraging CDTs in industrial and clinical applications.
+
+Results
+
+Overview
+
+The PIE framework aims to facilitate real-time cardiac electrophysiology (EP) simulation while retaining high physical fidelity comparable to the computationally expensive gold-standard RD-based bidomain model of CEP5. Crucially, setup and calibration of the PIE model is flexible and does not require expensive training associated with machine learning-based EP models. A high-level overview of the PIE framework is shown in Fig. 1A-D. The PIE model encodes physics by measuring dynamic system properties in small-scale high-fidelity reference RD models through a fully automated, standardized and low-cost calibration stage28 (Fig. 1B). The calibration procedure captures key CEP properties governing emergent physiological behaviors that dictate activation and repolarization patterns in the human heart under normal and diseased conditions, including complex irregular repetitive activation patterns as they occur during arrhythmias. Activation and repolarization patterns critically depend on the velocity and duration of propagating action potentials (APs). Their dynamics are governed by history-dependent factors referred to as cardiac restitution properties which entail a reduction in velocity, a change in shape of the AP and a shortening of action potential duration (APD) as a function of the time elapsed between the end of a previous AP and the onset of a new AP, a time period referred to as diastolic interval (DI). These effects are mediated by the intrinsic factors excitability–the ability of a cardiac cell in resting state to respond to an electrical stimulus by eliciting an AP, and refractoriness–a cellular state immediately following activation during which no further AP can be elicited until the cell recovers excitability when returning close to its resting state. In addition, all properties are modulated by diffusive electrotonic currents which act to smooth out wave backs by either shortening or prolonging the AP, and thus altering the instant of recovery from refractoriness over a spatial area of influence governed by the electrotonic space constant. The propagation of wave fronts and their conduction velocity (CV) is also influenced by diffusive currents by an altered source-sink ratio along curved wave fronts which accelerates or slows down CV for concave or convex wave fronts, respectively. Measurement of these properties and their encoding in feature maps used to steer the physiological behavior of the PIE model is illustrated in Fig. 1B.Fig. 1 Physics-Informed Eikonal (PIE) simulation framework.
+
+A Example of a reference high-fidelity, high-cost RD model for simulating an infarct-mediated ventricular tachycardia (VT)and associated characteristic ECG. B The PIE model attains physiological fidelity during calibration from a reference RD model by measuring physiological properties efficiently in small-scale high-fidelity cell- and tissue-level experiments. For each type of excitable tissue in the simulation domain, history-dependent excitability, APD and CV restitution, as well as CV dependence on electrotonic curvature and diffusion effects are measured and encoded in feature maps. C The PIE model comprises an Eikonal wave propagation model coupled to a Finite State Machine (FSM) which controls AP phases according to the feature maps. Cardiac source distributions are recovered from the traveling wave solution by means of AP lookup in the measured feature map. D Lightweight ECG reconstruction using a lead-field approach.
+
+Conceptually, the PIE model incorporates an Eikonal-based wave propagation mechanism operating over a short moving time horizon where all factors affecting propagation are dictated by a Finite State Machine (FSM) that imposes the measured history-dependent dynamics of cellular AP phase transitions and the impact upon propagation, as encoded in feature maps during calibration (Fig. 1C). The moving time horizon combined with the dynamic tracking of the tissue state facilitates repetitive activation, either driven by multiple stimuli or by reentrant wave fronts. Owing to this robust propagation mechanisms embedded in the PIE model, the strict spatio-temporal discretization constraints imposed by RD models are lifted. Thus, the PIE model is able to represent cardiac sources with high-fidelity at coarse spatial resolutions which yields, combined with lightweight lookup-based physics evaluations, large computational speedups to attain simulations with close to real-time performance. Importantly, all observable clinical signals such as the ECG can be recovered from the spatio-temporal distributions of cardiac sources efficiently with high physical fidelity (Fig. 1D) by leveraging a lead-field approach24,29,30 (Supplementary Sec. A.5). Thus, the PIE framework facilitates like-for-like comparison to clinical data in real-time, offering the performance needed for realizing CDTs.
+
+Evaluation
+
+An established high-fidelity RD model of infarcted human ventricles served as a reference for validating the PIE model7 (Supplementary Sec. A.1 and A.2). Cell and tissue EP properties were set to characterize three different myocardial regions: normal ventricular tissue exhibiting healthy EP, electrically viable border-zone tissue adjacent to infarct scars with impaired EP, and, non-conductive infarct scar tissue. Within regions of healthy and border-zone tissue, cellular dynamics were represented by myocytes of epicardial phenotypes according to the Tusscher-Noble-Noble- Panfilov (TNNP) model31. For border-zone tissue, the peak sodium current, INa, L-type calcium current, ICal, and the potassium currents, IKr and IKs, were reduced by 62%, 69%, 70% and 80%, respectively, resulting in a prolonged APD duration, a decreased upstroke velocity and a decreased AP amplitude. For each electrically viable tissue type, the reference RD model was calibrated for a prescribed target CV at a high spatial resolution of 250 μm28. The calibrated reference RD model parameters are summarized in the Supplementary Sec. A.3.
+
+For normal and border-zone tissue, EP properties of the RD model were measured according to the ForCEPSS standard28. The restitution of AP shapes and APD was recorded in single-cell experiments, whereas CV restitution curves, electrotonic space constants, and the curvature dependence of CV were measured in thin 3D strand or slab preparations. The calibration of the PIE model was carried out once for each considered tissue type, and were used then in all experiments.
+
+The ability of the PIE model to replicate the biophysical behavior captured by the calibration stage was validated in three dedicated experiments, depicted in Fig. 2A–C. These involve isolated testing of the history-dependent excitability of cardiac cells, APD and CV restitution, the CV dependence on wave front curvature, and the electrotonic diffusion effect. By comparing against reference RD model simulations, the fidelity of the calibrated PIE model was assessed based on the spatio-temporal transmembrane voltage maps, Vm (t, x), and on measures of activation and repolarization sequences. These are characterized by local activation time (LAT) maps, tax and CV maps, vx, as well as local repolarization time (LRT) maps, trx, respectively. LAT and LRT in the RD model were determined as the instants in time when Vm crosses a threshold of Vth = − 75 mV or of repolarization to 90% of the action potential amplitude with a positive or negative slope, respectively. CVs maps vx were derived by inverting the delay vector computed as the gradient of the activation map, ∇tax, that is vx=∥∇tax∥2−1. The error maps were computed as signed differences between corresponding LAT, CV, and LRT maps per AP cycle.Fig. 2 Experimental setups for evaluating physiological predictions.
+
+A evaluates APD and CV restitution behaviors by pacing the left face of the strip following a dynamic restitution protocol. B assesses wave front curvature effects by simultaneous pacing tissue on the left-hand side of an isthmus to produce concave, planar and convex wave fronts when approaching, traversing and exiting the isthmus, respectively. C analyzes diffusion effects across an interface between normal and border-zone tissue differing in CV and APD. Pace-induction and maintenance of arrhythmias are simulated with both RD reference and PIE model in setups of increasing complexity comprising (D) an infarct-mediated anatomical reentry, E a functional reentry in tissue slab models, and (F) an infarct-mediated VT in a human whole-heart model.
+
+The validity of the PIE model during reentrant scenarios was investigated by carrying out arrhythmia induction and maintenance experiments, described in Fig. 2D–F, with both the PIE and RD model. Model predictions were compared based on the spatio-temporal patterns of transmembrane voltages, Vm (x, t), the trajectories of rotor cores for functional reentry, and the ECG associated with the transmembrane voltage patterns for human whole heart simulations. In all validation experiments PIE and RD model were solved at mean spatial resolutions, h, of  ≈ 1000 μm and  ≈ 250 μm, respectively, over a 5 s simulation time window to assess long-term deviations during sustained reentrant activity between both models. All tissue models were initialized at a stable limit cycle equivalent to delivering a pacing train of 100 stimuli at a cycle length of 600 ms28. Stimuli to initiate propagation were delivered by clamping Vm at the stimulus location to 0 mV for a duration of 2 ms.
+
+Experiment A - restitution effects
+
+The ability of the PIE model to account for the dependency of the AP shape, APD, and CV upon the rate of activation was investigated using the setup in Fig. 2A. Planar wave front propagation was initiated by stimulating the left-hand face of a strip of tissue with healthy EP. A dynamic pacing protocol was used where the pacing cycle length (PCL) was gradually shortened down from 600 ms in decrements of 25 ms until loss of capture occurred after 12 cycles at a critical PCL of 250 ms. Four different configurations of the PIE model were employed: (i) without APD and CV restitution, (ii) with APD restitution only, (iii) with CV restitution only, and (iv) with both APD and CV restitution. The PIE model (iv) accounting for both APD and CV restitution was able to replicate the reference RD model, yielding virtually indiscernible solutions (Fig. 3A). Very minor errors in LAT, CV, and LRT were reported (Fig. 4A), with root mean square errors (RMSEs) of 0.450 ms, 0.005 m/s and 0.769 ms respectively. Only a sparse number of underestimated CV outliers were measured, located around the stimulation site and the sealed end where propagation terminates. All other PIE models (i)–(iii) ignoring APD or CV restitution led to major discrepancies in terms of wave front and back positions, wave length and spatial extent of the excitable gap, or to loss of capture at short PCLs ≤ 300 ms (Fig. 3A) .Fig. 3 Model validation across electrophysiological restitution and wave dynamics.
+
+The ability of the PIE model to replicate electrophysiology of the RD model in terms of APD and CV restitution behavior, wave front curvature, and diffusion was evaluated. A Snapshots of the transmembrane voltage, Vm, at longer and shorter PCLs are shown for the reference RD model relative to PIE models with four different restitution configurations: (i) no restitution, (ii) APD restitution only, (iii) CV restitution only, and (iv) with both APD and CV restitution. B Impact of concave (left) and convex (right) wave front curvature upon propagation. C Effect of diffusion upon spatio-temporally shifted wave fronts (left) and wavebacks (right) in RD (top) and PIE (bottom) model.
+
+Fig. 4 Quantitative analysis of restitution and wave dynamics experiments.
+
+Signed error maps, error density histograms and outlier plots of LATs, CVs and LRTs measured between the RD and the PIE model during (A) restitution conditions, (B) curved wavefronts and (C) diffusion conditions are shown. Each error map informs about the spatial error distribution for a single slice of nodal data. The corresponding error density histograms, computed from each error map, inform about error frequency across all data slices. Error maps and histograms feature shared color maps where a value smaller than zero (blue) corresponds to an underestimation, while a value larger than zero (red) corresponds to an overestimation of the PIE model. The black dotted line in each error density histogram marks the mean value over the distribution. Quantitative mean, standard deviation and RMSE values are given in red boxes for each distribution. Outliers are visualized as 2D hexagonal binning plots that compare the measurements from the RD model, aligned along the x-axis, against measurements from the PIE model, aligned along the y-axis. Hexagonal markers represent bins of nodal measurements from the PIE model that are colored based on their bin count. Bins are vertically compared against the gray identity line which represents matching values between both models. High measurement counts (red) located on or near the identity line indicate that outliers are scarce.
+
+Experiment B - curvature dependency
+
+The ability of the PIE model to replicate the dependency of CV upon wave front curvature was evaluated using the setup in Fig. 2B where wave fronts were initiated at the left-hand side corners. This forms a concave wave front when approaching the entrance into an isthmus, a planar wave front of zero curvature when traversing the isthmus, and a convex wave front of decreasing curvature when exiting the isthmus. Qualitatively, discrepancy between RD and PIE model were marginal, yielding the same wave front CV over the entire domain for both positive and negative curvature (Fig. 3B). Visual differences along the wave front are due to the coarser resolution of the PIE model, that is insufficient to smoothly resolve the steep wave front. Quantitatively, the density map in Fig. 4B showing the spatial distribution of errors reveal slightly more pronounced errors around stimulation sites, at locations of source-sink mismatch at the isthmus entrance and exit, and at sites where wave fronts collide with domain boundaries. These observations are mirrored by the outliers relating to the underestimation of high CV during the collision of concave wavefronts. LRT outliers were slightly overestimated near domain boundaries where wavefront propagation terminated, but underestimated near stimulation sites. Global RMSEs in LAT, CV and LRT were minor, with 1.241 ms, 0.063 m/s and 2.153 ms respectively.
+
+Experiment C - influence of diffusion
+
+In experiment described by Fig. 2C, the effect of electrotonic diffusion across the interface between tissue domains of different electrophysiological properties was assessed. Planar wave front propagation was initiated along the interface between healthy and border-zone tissue, characterized by faster/slower CV and shorter/longer APD, respectively. Faster CV in healthy tissue leads to a dragged activation between tissue interfaces, limited in space by the transverse space constant λt (Fig. 3C, left panels). Similarly, diffusion in the electrotonic vicinity of the interface acts to smooth dispersion of repolarization, mediated by the combined effect of differences in wave front arrival times and intrinsic APD gradients (Fig. 3C, right panels). Quantitatively, both spatial distribution as well as global differences in terms of LAT, CV, and LRT are shown in Fig. 4C, with RMSEs of 1.117 ms, 0.052 m/s and 8.615 ms, respectively. More pronounced CV and APD outliers were witnessed, predominately emerging from the difference in asymptotic wavefront profile between the interface of healthy and border-zone tissue32. A detailed discussion on the sources of observed discrepancies is provided in the Supplementary Sec. C.1.
+
+Experiment D - anatomical reentry
+
+The capability of the PIE model for capturing arrhythmia induction mechanisms in response to an S1-S2 arrhythmia induction protocol was investigated in a geometrically simplified 3D slab model of a ventricular wall with an anatomical substrate assumed to underlie monomorphic ventricular tachycardia (VT) in the human heart (Fig. 2D). The substrate is composed of a non-excitable infarct scar surrounded by border-zone tissue that is traversed by an electrically viable isthmus. The repetitive stimulation with a pulse train delivered at a location close to the entrance into the isthmus followed by a premature S2 stimulus delivered at 340 ms led to a unidirectional conduction block at the border-zone tissue which exhibited a longer APD of  ~ 360 ms. The S2 wave fronts traversed the outer loop around the scar at a slower CV due to CV restitution, providing sufficient time for the tissue at the opposite entrance to recover excitability into the isthmus. As the VT path length comprising outer loop and isthmus was long enough, an anatomical reentrant circuit was established that was maintained for the entire simulated period of 5 s (Fig. 5A).
+
+The PIE model correctly recapitulated both induction and maintenance mechanism as observed in the RD model. Discrepancies in terms of transmembrane voltages Vm(t, x) were marginal, with only modest differences in wave front and wave back dynamics. After 5 s of simulated VT activity wave fronts and wave back were located at virtually identical locations (Fig. 5A, bottom), indicating that the PIE model accurately represented the EP behavior of the high-fidelity RD model.
+
+Experiment E - functional reentry
+
+The ability to induce a functional reentry by applying a S1-S2 protocol was investigated in a 3D slab model of healthy tissue representing a portion of ventricular myocardium (Fig. 2E). In both RD and PIE model the S2 stimulus delivered prematurely at t = 340 ms led to an intersection of the critical stimulus strength isoline with the critical refractory isoline of the preceding S1 cycle’s wave back. This created a filament–a 3D line of phase singularities–around which a functional reentry in the form of a 3D scroll wave started to evolve with clockwise chirality. Agreement between RD and PIE model is analyzed qualitatively in Fig. 5B by visually comparing snapshots of transmembrane voltage maps Vm (t, x), as well as by tracking the motion of the filament at the surface over the whole simulated period of 5 s. For a quantitative comparison, the dominant frequency maps based on the power spectral density (PSD), the Euclidean distance in phase singularity location and the phase map correlation based on the Pearson correlation coefficient (PCC) were computed between both models and reported in Fig. 6.
+
+The qualitative behavior of the PIE and RD model (Fig. 5B, left) was comparable, with wave fronts and wave backs remaining spatio-temporally correlated as they traversed the domain. The filament tracked at the surface followed comparable trajectories, covering a similar area and exhibiting a morphology consistent with previous reports33. The frequency analysis shown in Fig. 6A indicates that the PIE and RD models exhibit closely correlated dominant frequencies. However, the PIE model does not fully capture all frequency components of the RD reentrant activity, resulting in more irregular dynamics compared to the RD model. Frequency-related differences in reentrant behavior are also evident in the dominant frequency maps, where regions of elevated frequency are similarly localized in both PIE and RD simulations, yet differ markedly in their spatial distribution and amplitude.Fig. 5 Induction and maintenance of anatomical and functional arrhythmia scenarios.
+
+In simplified 3D slabs of tissue, the spatio-temporal distribution of transmembrane voltages, Vm, generated by the RD and PIE model is shown at selected snapshots in time. A The anatomy-mediated VT is induced by a premature S2 stimulus initiating a wave front that is blocked at the entrance into the isthmus at t = 350 ms to propagate along the outer loop around the scar at t = 500 ms, and reenters into the opposite entrance of the by now recovered isthmus at the at t = 650 ms. Wave fronts and wave backs move synchronously between the models over the entire simulated VT episode. B Functional reentrant activity is initiated in RD and PIE models. Owing to the sensitive non-linear behavior discrepancies in wave front and wave back dynamics emerge over time, but wave fronts remain spatio-temporally correlated and the phase singularity driving the spiral wave follow comparable trajectories covering the same areas.
+
+Fig. 6 Quantitative analysis of the functional reentry experiment.
+
+A The PSD was computed for each nodal Vm trace to show the average PSD across all nodes over time (left) and corresponding dominant frequency maps in the RD (center) and the PIE model (right). The dominant frequency was selected as the frequency with the highest power peak in each nodal PSD. B The difference in phase singularity location between the RD and the PIE model was assessed based on the Euclidean distance error over the 5 s simulation window. C Phase maps between the RD and the PIE model were computed based on the Hilbert transform of Vm60, ranging between [ − π, π]. The phase correlation map contains PCCs computed from each nodal phase trace and visualizes correlation between  − 1 (anti correlation) and 1 (correlation).
+
+The rotor in the PIE model appears less stable compared to the RD model (Fig. 5B, right), consistent with the temporal evolution of the phase singularity location error between the two models (Fig. 6B). The phase evolution of the reentrant activity (Fig. 6C) is qualitatively similar between both models. However, the PIE solution exhibits slightly reduced smoothness in phase definition near the wavefront and waveback. These differences are further reflected in the temporal evolution of phase correlation, which quantifies divergence between the two solutions over time. Phase map correlation analysis indicates that agreement is lowest in the vicinity of the rotor core, while remaining comparable in regions distal to the core.
+
+Owing to the high sensitivity of non-linear functional reentrant behavior to initial conditions and parameter perturbations, identical dynamical behavior between two models that represent physics in fundamentally different form and are discretized with vastly different spatial resolutions cannot be achieved. This is not even the case for the high fidelity RD model where similar discrepancies emerge under minor parameter perturbations. This scenario was demonstrated in Supplementary Sec. C.2 by applying perturbed initial conditions for the RD and the PIE model during this experiment. Considering the similarity over a long observation period involving 19 activation cycles, the PIE model captures the reentrant dynamics of the RD model at a level of fidelity sufficient for most applications, at a small fraction of the computational costs (1.45%).
+
+Experiment F - whole-heart VT
+
+The accuracy of the PIE model in predicting arrhythmic patterns and associated clinical signals, as required for generating CDTs, was investigated. In a most comprehensive experiment (Fig. 2F), an infarct-mediated VT with corresponding clinical 12-lead ECG was simulated in an image-based anatomically accurate human whole-heart torso model that incorporated a structurally accurate infarct scar of isthmus and outer loop topology. Monomorphic VTs in such substrates produce characteristic signatures in the ECG that are used clinically for identifying targets for ablation therapy34.
+
+In both PIE and RD models, a VT was initiated by delivering a depolarizing stimulus at the apical exit of the isthmus adjacent to a hyperpolarizing stimulus that imposed a transient block to impede propagation into the isthmus. The emerging dynamics were qualitatively assessed based on the spatio-temporal evolution of Vm (t, x) by comparing the position of wave front and wave back at various snapshots in time (Fig. 7A). Discrepancies in the predicted clinical ECGs were assessed visually in Fig. 7B and quantitatively in Table 1. Morphological similarity and correlation of predicted ECGs were assessed based on the dynamic time warping (DTW) distance measure35,36 and the PCC37,38, respectively. Long term temporal coherence between both models was assessed by comparing R-R intervals in each lead.Fig. 7 Whole-heart electrophysiology and ECG.
+
+A comparison of activation pattern and associated 12-lead ECG between RD and PIE model during an induced VT in an anatomically accurate human whole-heart torso model. A Snapshots taken at times ti of the distribution of the transmembrane voltage, Vm(x, ti), during 5 s of VT activity. B Clinical 12-lead ECG associated with VT pattern. Dotted lines refer to snapshots in time ti shown in Vm(x, ti).
+
+Table 1 Whole-heart ECG evaluation metrics
+
+Metric	Δx[μm]	I	II	III	maVR	aVL	aVF	V1	V2	V3	V4	V5	V6	MEAN ± STD	
+DTW [mV]	1000	0.608	1.556	0.601	0.797	0.402	0.772	1.566	3.238	0.937	0.876	1.474	1.679	1.209 ± 0.741	
+PCC [-]	1000	0.925	0.707	0.911	0.925	0.919	0.893	0.899	0.839	0.846	0.863	0.917	0.932	0.881 ± 0.061	
+R-R [ms]	250	327	333	333	327	327	333	333	332	331	328	327	327	330 ± 2	
+	1000	326	335	335	327	326	335	337	334	334	326	327	328	331 ± 4	
+A quantitative comparison between ECG lead signals computed by the reference RD, and the PIE, model based on the non-normalized DTW, distance measure37,38, the PCC,35,36 and measured R-R intervals during the whole-heart experiment (F). Lower DTW distance measures indicate a close match in morphology between signals, while the PCC describes the correlation of signals between  − 1 (anti correlation) and 1 (correlation). Bold entries mark the best and worst DTW and PCC results per row. The R-R intervals were measured as the interval between consecutive R-peaks, from which mean and standard deviation were computed across all leads.
+
+Visual discrepancies in the spatio-temporal distribution of Vm (t, x) were negligible between PIE and RD model. A close correspondence in time of arrival of wave front and wave back was maintained over the entire 5 s of simulated activity, indicating that all physiological features affecting CV and APD and, thus, the wave length and excitable gap corresponding to the AP and DI in space, are captured by the PIE model with high-fidelity.
+
+The agreement between models depended on calibration choices, such as the protocol used to measure restitution properties, as well as on numerical parameters such as mesh resolution and coarsening strategy. Because the latter factors influence both model fidelity and computational performance, we conducted a comprehensive quantitative analysis (Supplementary Sec. C.3).
+
+The VT signature in the ECG corresponded very closely between both models. Differences were minor overall, with slightly more pronounced morphological and temporal deviations in limb lead II and precordial lead V2 (Fig. 7B). These discrepancies are mirrored by the quantitative DTW and PCC measures reported for those leads in Table 1. Across all leads, the reported average DTW and PCC measures of 1.209 mV and 0.881, respectively, indicate high similarity between the ECGs. The average R-R interval across all ECG leads of the PIE model (331 ± 4 ms) resides within the variance of those witnessed for the RD model (330 ± 2 ms), confirming high temporal coherence between both models over the 5 s simulation window.
+
+Performance benchmarks
+
+For both the PIE and RD model, computational performance and CPU time scaling as a function of mesh size were investigated based on the slab of tissue used in the functional reentry experiment (Fig. 2E) and the whole-heart experiment (Fig. 2F). The performance evaluation was conducted on either a workstation employing 32 CPU cores or on a high performance computing (HPC) cluster employing 192 cores, with detailed specifications provided in Supplementary Sec. C.4. Computational load was scaled up by increasing the transmural depth, from 250 μm up to 7000 μm (Fig. 8A). Compatibility with the RD model was preserved by keeping the mesh resolution constant at 250 μm. The complexity of the PIE model was increased by incrementing the number of physiological features that are taken into account. This led to six distinct configurations of increasing physical fidelity that (a) ignore physiological adaptations, or consider (b) APD restitution, (c) CV restitution, (d) APD and CV restitution, (e) APD and CV restitution and curvature, and, (f) the full-physics PIE model with APD and CV restitution, curvature and diffusion effects. Only the S1 stimulus was delivered at a cycle length of 500 ms to initiate a planar wave front traversing the domain, to ascertain the same activation and repolarization pattern in all configurations. Activity was simulated over a time window of 1 s at a temporal output rate at 1 ms on the 32 core workstation for both models.Fig. 8 Computational performance and scaling benchmark.
+
+The computational performance of PIE models with varying physiological fidelity is compared to the reference RD model. A S1 stimuli were delivered to the left-hand face of a tissue slab to initiate planar wave front propagation. The transmural depth of the slab was increased from 250 μm to 7000 μm to increase the problem size. B Run time was measured for the RD model (blue) and for six configurations of increasing physical fidelity of the PIE model accounting for effects of APD restitution APD(DI), CV restitution CV(DI), curvature, κ and diffusion, Δ.
+
+Scaling results are shown in Fig. 8B. Accounting for physiological features increased computational cost which reduced performance gains obtained with the PIE over the RD model, from a factor of 409 with (a) down to 46 with (f). Specifically, accounting for curvature and diffusion effects led to a marked increase in compute costs due to slower convergence rate and limited CPU-related parallel computing capabilities of the PIE solver. The ratio between PIE and RD solver execution time remained constant, indicating that scaling with problem size was comparable.
+
+Runtime performance was quantitatively compared between the RD and the PIE, taking into account the time required for calibration, initialization and simulation of the whole-heart VT induction experiment. Simulating the RD model at 250 μm required execution on the HPC cluster, while the PIE model was solved on the workstation at a resolution of 1000 μm.
+
+Performance measurements of simulating VT and associated ECG in a human whole-heart torso model are given in Supplementary Sec. C.4. Simulating 5 s of VT with the RD model required  ~ 17 h in total using 192 cores on the HPC cluster. The same simulation with the PIE model on the 1000 μm mesh was executed within  ~ 4 min on the workstation using 32 cores. This corresponds to an effective speedup of  ~ 275 × while utilizing only 16% of the CPU cores with the PIE model.
+
+Despite the vast speedup obtained, the performance achieved in the whole heart simulation at a discretization of 1000 μm lagged real-time by a factor of  ~ 44 × when using the most accurate numerical settings. A further coarsening of mesh resolution led to a reduction in real-time lag by a factor of  ~ 7 × . When mesh coarsening preserved domain boundaries, ECG fidelity remained essentially unchanged (see Supplementary Sec. C.4). True real-time performance could readily be achieved with the PIE model by optimizing either numerical settings, e.g. increasing the time step of the Eikonal solver, or utilizing GPU acceleration. Overall, the computational performance of the PIE model enables high fidelity EP simulation on desktop machines within feasible time frames.
+
+Discussion
+
+Our PIE modeling framework provides a lightweight approach for accurately simulating human CEP at the organ scale under a broad range of conditions in near real-time, with physical fidelity comparable to RD models, the gold-standard in CEP modeling. After a lightweight initial calibration where CEP key properties of the RD model are measured in small test setups and encoded in feature maps, the PIE model is able to replicate the most important emergent phenomena as predicted by a RD model such as wave front propagation dynamics and conduction blocks under varying heart rates as well as the induction and maintenance of both anatomical and functional reentrant arrhythmias, with high quantitative accuracy, at a fraction of the compute costs. The potential of the PIE model for clinical CDT applications was demonstrated by simulating a VT circuit, mediated by an infarct scar with isthmus and outer-loop topology as typically seen in VT patients39, in an anatomically accurate human whole-heart torso model.
+
+The PIE model was shown to accurately match both the spatio-temporal dynamics of cardiac sources as well as the most prevalent clinically observable signal–the 12-lead ECG, which features a characteristic signal morphology linked to the discrete topological pathways of a VT circuit through the scar. The agreement between models was shown to be robust with respect to important numerical parameter choices such as mesh resolution. Our analyses showed that discrepancies remain small up to a mesh resolution of 3000 μm, given that coarser meshes preserve the interface boundaries between domains of different EP properties of the higher resolution mesh used for RD simulations. Global coarsening not preserving interface boundaries induces topological changes that alter the VT circuit path length, and thus affect VT cycle and maintenance. For instance, even at the highest average resolution of 1000 μm used for the PIE solver, the VT cycle length was affected, leading to a notable error accumulation over time. At a coarser resolution of 3000 μm the VT was not sustained over the observation period (Supplementary Sec. C.3). For boundary-preserving mesh coarsening, discrepancies in predicted ECGs remained marginal in terms of morphology, magnitude and periodicity up to the coarsest resolution tested at 3000μm. Overall, the observed model discrepancies can be considered marginal, particularly when viewed in the context of the significant overall uncertainty all model parameters of the high-dimensional RD model are afflicted with.
+
+Based on its mechanistic completeness, accuracy, and computational speed, the PIE model is able to replace expensive high-fidelity RD models under a broad range of conditions, including arrhythmias. Combined with accurate predictions of observable signals, the PIE model provides the fundamental key technology for leveraging CDT applications for precision cardiology. A CDT for tailoring therapies relies on accurate calibration to ascertain that models operate within a tight physiological envelope matching a given patient40,41, and on physically complete models for correctly predicting the cardiac response to a variety of perturbations. Both calibration and predictive interrogation of a CDT constitute a many query problem, requiring a large number of forward simulation runs to constrain and sample the high dimensional physical parameter space. Due to the vast computational costs of RD models, requiring days to compute even with high performance computing resources, current clinical modeling studies based on RD models refrain from any patient-specific calibration7,42, and do not compute clinically observable signals to facilitate like-for-like comparisons between model and patient. Moreover, to keep simulations tractable, studies using RD models resort to coarse spatial discretization, which renders simulated arrhythmic behavior stochastic12.
+
+The combined biophysical fidelity and real-time capability render the PIE model a competitive technology for realizing patient-specific predictive CEP models in time-critical clinical CDT applications geared toward tailoring therapies. Full-order RD models43 remain the gold-standard in terms of physiological fidelity, but even with optimized implementations using parallelization6 or hardware acceleration8 computational costs remain intractable, hindering their adoption in many-query CDT applications. Data-driven approaches emerging within the field of scientific machine learning have shown promise for generating lightweight surrogate CEP models that are sufficiently fast and accurate for many-query CDT applications. Model-order reduction or operator learning techniques13,15,16,18 may offer, in principle, the computational performance for solving CEP problems in near real-time. However, practicality and generalizability beyond toy problems remain to be investigated. Performance for generating solutions with sufficient spatio-temporal resolution with anatomically accurate organ models, as well as the reconstruction fidelity of observable signals, has not been shown yet. Moreover, the computational resources required for the generation of suitable training data are orders of magnitude more expensive compared to the time needed for calibrating the PIE model, which lasts only on the order of seconds. Further, unlike with the PIE model, where the initial calibration is universal, covering the full parameter space, with data-driven models, the parameter space to be interrogated must be narrowed down to keep off-line training tractable, which limits the flexibility for patient-specific CDT applications. The potential of real-time CEP modeling based on low-cost state-of-the-art Eikonal-based methods24,27 has been investigated, but these lacked physiological completeness to accurately replicate behaviors of full-order RD models under more general conditions, which limits their application scope.
+
+While the PIE model covers a broad range of applications, it cannot be considered a universally applicable replacement of a RD model due to a number of important limitations. A major source of discrepancies between RD and PIE model relates to the mechanism used for approximating the effect of diffusion. Most pronounced differences were noted in simulations of functional reentry, where the PIE model was not able to accurately replicate the repolarization behavior around the phase singularity, which led to differences in the trajectory and shape of the rotor core. However, considering the highly non-linear and sensitive nature of functional reentrant activation, the overall emergent behavior was very comparable, and discrepancies were bounded within reasonable limits, even within the vicinity of the driving phase singularity. Moreover, it is important to note that an exact replication of functional arrhythmia simulations is currently also not feasible with RD models. Due to the highly non-linear nature, minor perturbations in model parameters, solver scheme and numerical settings such as solver tolerances or parallelization, discrepancies will inevitably emerge and grow over time. While such simulations are useful for the mechanistic interpretation of experimental data, caution is warranted in patient-specific modeling applications due to the vast model parameter uncertainty and the inherent stochasticity of model predictions. As functional reentry in the human heart is not directly observable clinically and model parameters are not constrained by measured data, evidence linking model predictions to patient physiology is lacking. In current clinical modeling studies that consider functional reentry, no attempts were undertaken to calibrate models to patient data, not even under baseline conditions44. Nevertheless, the broadly comparable behavior and the substantial computational advantage of the PIE may enable patient-specific assessments based on statistical analysis of large ensembles of representative simulations, acknowledging that individual simulations do not constitute one-to-one representations of a given patient.
+
+Further discrepancies were attributable to stimulation and domain boundary effects on CV and APD. For instance, CV is reduced near initiation sites, increases during propagating toward a tissue boundaries, and wave fronts propagate perpendicular to boundaries due to no-flux boundary conditions. Boundary effects on electrotonic current influence repolarization and APD. These mechanisms are not captured in the PIE model.
+
+Furthermore, no universally applicable formulation exists to prescribe restitution behavior solely as a function of the preceding diastolic interval, due to history dependence commonly referred to as cardiac memory45. The phenomenological representation of CV and APD restitution used by the PIE solver is based on measurements using the RD model under a chosen protocol. However, the choice of protocol captures different aspects of restitution dynamics. The dynamic protocol characterizes restitution at constant cycle length, whereas the S1-S2 protocol captures the immediate response to a DI perturbation from a steady-state limit cycle. The subsequent slow accommodation is described by constant-cycle restitution46. Thus, depending on the protocol used, predictions of APD and CV for the same DI differ31. As the sequence of DIs does not correspond to those observed in tissue-scale simulations, predictions of CV and APD differ between the PIE and RD models. However, the impact of these differences was marginal, as evidenced by the whole-heart VT simulations in which predictions of CV and APD remained in close agreement over a prolonged observation period.
+
+A fundamental limitation of the current PIE model lies in its representation of cardiac tissue as a fully deterministic system characterized by static physiological properties measured only once during calibration (Fig. 1B). Consequently, inherently stochastic phenomena–such as the onset of alternans or spontaneous triggered activity arising from early or late afterdepolarizations, which can initiate arrhythmias–are not captured by the PIE model.
+
+Further development is required to account for such phenomena. Several adaptation strategies are conceivable. For example, cellular dynamics models could be evaluated directly on-the-fly. However, this approach would incur substantial computational costs, resulting in markedly lower performance comparable to that of previous reaction-eikonal-type models22,23.
+
+A more efficient approach could leverage higher-dimensional parameter-phenotype mappings that encode AP, APD, and CV dependence on parameters beyond DI, for example, using logistic regression to predict ectopic event probability47. Such extensions can be incorporated into the PIE framework, albeit with increased finite-state machine complexity and calibration cost. An alternative strategy is to employ surrogate reduced-order models to approximate cellular dynamics on-the-fly using Gaussian processes48 or machine learning49. This latter approach is particularly promising and the focus of ongoing and future investigations.
+
+Independent of stochastic events at the cellular level, additional metrics of spatial coherence must be considered, as ectopy at the tissue scale is determined by the liminal length rather than by cellular triggering alone. Specifically, a sufficiently large population of cells must undergo spontaneous depolarization with adequate temporal synchrony to overcome the repolarizing influence of adjacent subthreshold tissue and initiate an ectopic activation50.
+
+Finally, because the PIE model is statically calibrated under limit-cycle conditions, it does not readily generalize to non-equilibrium dynamics in which physiological properties evolve over time, such as transient responses following drug administration. These effects could be incorporated by periodically recalibrating the PIE model to update system properties (Fig. 1B), an approach that remains efficient since calibration is performed in single-cell or 1D strand models that are computationally inexpensive. Alternatively, a parameter-phenotype map could be employed to explicitly encode temporal evolution, at the cost of an increase in finite-state machine complexity.
+
+Departing from this initial PIE implementation, further improvements in representing diffusion, in accounting for heterogeneity in cellular dynamics and its modulation by drugs, combined with technological advances to further enhance computational performance, are feasible and will be the topic of future research. Ultimately, the PIE strives to deliver full physical fidelity CDTs simulations with true real-time performance to support a broad spectrum of applications in precision cardiology, including intraprocedural online simulation.
+
+Methods
+
+The PIE model builds upon three computational components: (i) a FSM encoding local cellular states, (ii) a wave propagation mechanism supporting repetitive activation, and (iii) an AP voltage recovery. The reconstruction of clinical signals is based on a lead-field approach and is described in Supplementary Sec. A.5. An overview of the functionality of each component of the PIE model and how each component attains physiological fidelity through calibration is given in Fig. 1. The complete algorithmic description of the PIE model is provided in Supplementary Sec. B.
+
+Encoding cellular states
+
+In the heart domain ΩH, the traversal of wave fronts is dictated by the local electrical state of the tissue (Fig. 9A). Whether a wave front arriving at a site x ∈ ΩH is propagated depends on the cellular state at x. If tissue at x ∈ ΩH is in an excitable state and sufficient electrotonic current is provided, either by electrical stimulation or by an approaching wave front, to depolarize Vm (t, x) above the threshold Vth, an active response is elicited in the form of an AP. This behavior is referred to as excitability. Once an AP has been elicited, the cell is in an excited but refractory state in which no new AP can be elicited over a refractory period, lasting until a cell recovers excitability. The states excitable and refractory can be considered mutually exclusive.Fig. 9 Detailed description of the PIE approximation methods.
+
+A Encoding cellular states using a FSM. B Reentrant Eikonal-based wave propagation mechanism. C Voltage recovery depending on diffusion. D Calibration of the PIE model using ForCEPSS by performing high-fidelity but low-cost cell- and tissue-level experiments. E Obtained PIE model calibration data, including AP shapes, APD and CV restitution curves, electrotonic curvature and space constant measurements employed by the diffusion mechanism.
+
+To control the excitability of cardiac cells within the domain ΩH, the PIE model employs a lightweight FSM that represents cardiac AP phases and the transitions between these. Similar to25, each AP cycle is divided into four phases indicated by a state variable, s, that represents the following physiological conditions:ACTIVATING: The short time interval of cellular depolarization comprising subthreshold capacitive loading, referred to as the foot of the AP, and the supra-threshold response manifesting in the fast upstroke of the AP.
+
+EXCITED: After activation, the cell transitions to an excited refractory state, during which the main depolarizing ion channels are inactivated, impeding the elicitation of an AP.
+
+RECOVERING: The cell is sufficiently repolarized to recover excitability, but a stronger stimulus is required for eliciting an AP.
+
+EXCITABLE: The cell is fully repolarized and depolarizing ion channels are recovered from inactivation, rendering cells excitable again.
+
+Phase transitions of a cell located at x ∈ ΩH within the n-th cardiac cycle are described based on the following notation:The LAT, tan(x), represents the instant of depolarization and marks the start of the n-th cycle.
+
+The PCL represents the interval between two supra-threshold stimuli, either delivered by a stimulus or by an approaching depolarization wave front. The PCL is determined at the end of a cycle terminated by a new activation tan, as 1 PCLn−1x=tanx−tan−1x.
+
+The refractory period of the n-th cycle denotes the time elapsed between complete activation until the instant at which the cell starts recovering excitability. The onset of the recovering phase, which depends on the state of ion channels, can be measured in any model of cellular dynamics. As this is closely linked to the repolarization of the AP to a given voltage level, it can be approximated by an AP-dependent surrogate marker, APD90, the instant at which the AP is repolarized to 90% of the AP amplitude. The end of the recovering phase, where excitability has been fully restored, is linearly approximated by APD100 = APD90/0.9. The onset of the recovering state of cycle n at location x ∈ ΩH is denoted as LRT trn(x), given by 2 trnx=tanx+APD90nx.
+
+The DI refers to the interval between an instant of repolarization and the next activation: 3 DIn−1x=tanx−trn−1x.
+
+To identify the current state of a cell located at x ∈ ΩH at a given time t≥taNx, where N = N(x) is a generic index referring to the current cycle, we introduce the relative cycle time τ:[taN,∞)→[0,TAP] as 4 τt,x=minAPD90reft−taN(x)APD90N(x),TAP,
+
+that maps the current solver time t to an cycle time τ defined for a prescribed one-dimensional AP template function fAP:[0,TAP]→R with a basic cycle length of TAP and a corresponding reference APD90ref. The cycle time is scaled by the ratio of the APD from the reference AP and the actual APD90, since the APD is altered over time due to physiological effects. Then, the cell state s(t, x) can be derived from τ(t, x) by 5 st,x=ACTIVATINGifτt,x=0,EXCITEDifτt,x∈(0,APD90ref],RECOVERINGifτt,x∈(APD90ref,APD90ref0.9],EXCITABLEifτt,x∈(APD90ref0.9,TAP]
+
+for t≥taNx (see right panel of Fig. 9A). State transitions depend on relative cycle time τ and APD90N which, in turn, is modulated by the preceding DI and diffusion, both dictated by wave front dynamics. The dependency APD90N(DIN−1), referred to as action potential restitution, must be quantitatively measured in a full-order system during a calibration step, and can be used then to encode state transitions.
+
+Reentrant wave propagation model
+
+Wave front propagation in the myocardium ΩH, as described by the bidomain model, can be expressed as a traveling wave front problem20. Given stimulation sites xs ∈ ΩS ⊂ ΩH where wave propagation is initiated at instances ts(xs), a traveling wave front solution can be obtained by solving the anisotropic Eikonal equation 6 ∇ta⋅V∇ta=1inx∈ΩH\ΩS
+
+7 ta=tsinxs∈ΩS
+
+which yields the wave front arrival times ta(x) in ΩH. The Eikonal model is coupled to the FSM, which dynamically restricts the solution domain ΩH to areas where tissue is in an excitable state25. Eq. (6) is incrementally solved over a short moving time horizon δt over the restricted domain (Fig. 9B). As tissue at x may transition from an excited to an excitable state, as dictated by the physiology of cellular dynamics encoded in the FSM, cells in ΩH can be re-excited multiple times, thus providing the fundamental mechanism for supporting repetitive activation and self-sustained reentrant wave front propagation.
+
+Propagation velocity of the wave front is controlled by the symmetric squared velocity tensor V∈R3×3, defined by 8 V=vf2f⊗f+vs2s⊗s+vn2n⊗n,
+
+where vf, vs, and vn represent orthotropic CVs along the eigenaxes of tissue, referred to as fiber, f(x), sheet, s(x), and sheet-normal, n(x), direction, respectively. The intrinsic CV of wave fronts may be altered by the rate of activation and by wave front curvature. With faster activation rates CV reduces as sodium channels are increasingly less recovered from inactivation at short DIs. This behavior is referred to as CV restitution which can be characterized by measuring the function CVN(DIN−1). At the tissue scales wave front curvature modulates CV by altering the diffusive source-sink ratio21,51 which increases/reduces CV for concave/convex wave fronts, respectively.
+
+To account for both effects, we assume that each factor acts independently, allowing to approximate the resulting CV of a wave front in propagation direction nWF, arriving at x ∈ ΩH at the instant of local activation, t=taN(x), in the current cycle N = N(x) by modifying the CV vζ along each anisotropy axis ζ ∈ {f, s, n} as 9 vζ=v0,ζ⋅fCVCκ⋅fCVR,ζDIN−1,
+
+where v0,ζ represents the nominal CV of a planar wave front measured at long DIs along the direction ζ. fCVR,ζ is a relative normalized representation of the CV restitution function measured for planar wave fronts propagating in direction ζ at variable DIs, and fCVC is a function quantifying the CV dependence on anisotropic curvature κ. Specifically, following20,21,52 we model the linear dependency of the CV on the anisotropic curvature as 10 fCVCκ=1−κρβCmwithκ=∇⋅σmnWFnWF⋅σmnWF
+
+where the wave front normal pointing in the direction of the propagation is given by nWF=∇taN∥∇taN∥
+
+and ρ being the proportionality constant between CV of a planar wave front traveling along nWF and the tissue conductivity along the same axis (Supplementary Sec. A.4). For a negative κ, which is associated with concave wave fronts, CV increases, while for a positive κ, which is associated with convex wave fronts, CV decreases relative to the velocity of a planar wave front with κ = 0. At a critical positive curvature κζ,crit wave front propagation cannot be maintained and breaks down due to an unfavorable source-sink mismatch.
+
+CV restitution curves as measured in reference RD models with suitable protocols28 feature a non-linear monotonically decreasing function with increasingly pronounced reduction at shorter DIs, until propagation failure occurs at a critically short DI. The relative normalized CV restitution function fCVR,ζ:R→[0,1] is determined by measuring CV(DI), and scaling with the reference CV measured at a resting pacing cycle length. For slower pacing cycle lengths leading to increasingly larger DI it is assumed that fCVR follows 11 limDI→∞fCVR,ζDI=1.
+
+Voltage recovery
+
+The time course and duration of the AP at any x ∈ ΩH are governed by the intrinsic cellular properties, the preceding diastolic interval DIN−1, and, electrotonic currents acting during repolarization to shorten or prolong APD. These functional relations AP(t, DIN−1) and APDN(DIN−1) can be measured in a reference RD model and, combined with known activation time ta and anisotropic curvature κ of a wave front arriving at x, used to dictate state transitions in the FSM. Thus, with known instants of state transitions, ta and tr, the temporal history-dependent evolution of Vm (t, x) at any x ∈ ΩH can be recovered (Fig. 9C).
+
+The implemented voltage recovery procedure assumes that the restitution and diffusion influence the AP independently. The restitution effect on the AP at location x ∈ ΩH in the current cycle N = N(x) alters AP shape, Vm(t), and duration, APD, as a function of the preceding DIN−1. This dependency is measured for each domain of differing EP properties by pacing a single cell according to a restitution protocol which is readily achieved, at low cost, by solving the system of ordinary differential equations (ODEs) given by Supplementary Eq. (A14). The measured restitution curve is stored then as a function 12 APD90ref=fAPDDIN−1
+
+and the precomputed AP wave profiles, fAP, with a cycle length, TAP, are stored as a two-dimensional table 13 Vm(τ)=fAPτ,APD90ref,
+
+where each APD obtained from the restitution function fAPD corresponds to a specific AP profile Vm(τ) within the table fAP:[0,TAP]×R+→R. The voltage at site x within cycle N(x) at cycle time τ(t, x) as per Eq. (4), is recovered then by determining first APD90ref(x) from DIN−1(x), and looking up the current value of Vm in Eq. (13). If diffusive effects are deemed negligible, Eq. (13) can be used to recover Vm as APD is fully determined at the moment of activation due to the linear progression of the cycle time τ (Fig. 9C, upper panels). In this case, the procedure of voltage recovery is a post-processing step, that is entirely independent of the FSM and the Eikonal-driven wave front propagation within the PIE implementation. Since the solution of the system of ODEs which is expensive at the tissue scale, is avoided, and only a comparably cheap solution at a single cell level is required, carried out only once in a pre-processing step, the computational costs incurring with voltage recovery are negligible.
+
+Diffusive electrotonic currents act (i) during depolarization of the AP to mediate propagation of the wave front, and (ii) during repolarization to shorten or prolong APD, associated with changes in the AP wave form (Fig. 9C, bottom panels). The role of diffusion in propagation (i) does not require further attention as its physical effect is already accounted for by the Eikonal equation, Eq. (6), which is able to approximate the propagation of wave front propagation on much coarser computational grids than feasible with a RD model. Diffusion during repolarization (ii) is taken into account by phenomenologically approximating the main effect observed in RD models – an anisotropic smoothing of the repolarizing wave back. Thus, diffusion strongly influences clinically observable extracellular signals such as the ECG by attenuating transmembrane voltage gradients  ∇ Vm(x) as seen in Supplementary Eq. (A18). In the PIE model these effects are approximated by evaluating the AP template function during voltage recovery in Eq. (13) with locally smoothed state variables, that is 14 Vm(t,x)=fAPτ~t,x,APD~90(t,x),
+
+where τ~(t,x) is a smoothed cycle time, suitably averaged over the volume influenced by electronic currents.
+
+To keep the diffusion mechanism within the PIE model lightweight, we approximate global diffusion of RD models with local diffusion53 based on the observation that any local perturbation decays exponentially in space where the rate of decay along a direction ζ is governed by the electrotonic space constant, λζ. The volume of electrotonic influence is therefore bounded by an elliptic subdomain EΛ,δx⊂ΩH around x ∈ ΩH defined by 15 EΛ,δx=y∈ΩHx−y⊤Λ−1x−y≤δ,
+
+with the space constant tensor defined as Λ=λff⊗f+λss⊗s+λnn⊗n, where λζ are the orthotropic space constants along each eigenaxis ζ. The smoothed action potential duration APD~90N and smoothed cycle time τ~ are solutions to local anisotropic diffusion problems, given by 16 APD~90(t,x)=∫EΛ,δxK(t−taN(x),x−y)APD90ref(y)dy
+
+and 17 τ~(t,x)=min∫taN(x)t∫EΛ,δxK(t−s,x−y)APD90ref(y)APD~90(s,y)dyds,TAP
+
+for x ∈ ΩH and t>taN(x). Diffusivity within the subdomain is controlled by the anisotropic heat kernel 18 K(t,x)=14πt3∣detD∣exp−x⊤D−1x4t.
+
+using a locally constant, symmetric, and invertible diffusion tensor D∈R3×3 with its eigenvalues given by 19 Dζ=σm,ζβCm,
+
+derived from the harmonic-mean conductivity tensor of the RD model in Supplementary Eq. (A16). Without diffusion, δ = 0, the Eqs. (16) and (17) reduce to the previous Eqs. (12) and (4).
+
+Model calibration
+
+The calibration stage of the PIE model measures individual EP properties for each electrically viable tissue type in the reference RD model (Fig. 9D), and maps these onto the PIE model as prescribed functions and constants (Fig. 9E). Specifically, AP shapes, APD and CV restitution curves, as well as diffusive space constants, were quantitatively measured in cellular and tissue-level experiments using the ForCEPSS28 framework:APD restitution curves fAPD were measured in single cells following a S1-S2 protocol where a stable limit cycle was approximated using a train of 20 stimuli, delivered at a S1 cycle length of 600 ms (Fig. 9D). At premature S2 cycles, APDN, and preceding DIN−1 were measured to construct fAPD according to Eq. (12). Premature S2 AP shapes were stored in a two-dimensional lookup table (Fig. 9E, leftmost panel), as given in Eq. (13).
+
+CV restitution was measured in 3D strand models along each eigenaxis ζ using a dynamic pacing protocol28. Starting at a PCL of 600 ms, the PCL was gradually shortened in decrements of 25 ms until loss of capture occurred. CV was determined by measuring the difference in wave front arrival times, Δt, between two reference location along the strand, placed at a distance Δζ, yielding the eigenvelocities vζ = Δζ/Δt (Fig. 9D). The diastolic interval DIN−1 was measured at the center of the strand to construct CV restitution curves fCV R,ζ (Fig. 9E), as given in Eq. (11).
+
+The dependency of the CV on the anisotropic curvature, described by the function fCVC given in Eq. (10), was determined by deriving ρ from the proportional relationship between the harmonic mean conductivities and the measured planar wavefront velocities in each axis (described in Supplementary Sec. A.4). The conduction properties, the surface-to-volume ratio β and the membrane capacitance Cm were provided by the calibrated reference RD model.
+
+The strength of local diffusion, described by the diffusion coefficients along each tissue eigenaxes Dζ according to Eq. (18), were derived from the relationship given in Eq. (19) with the parameters of the calibrated reference RD model. Eigenvalues λζ of the space constant tensor Λ bounding the volume of local diffusion in Eq. (15) were determined in 3D strand models under subthreshold conditions, without triggering wave front propagation, by applying a  + 5 mV voltage clamp. After arriving at a steady state, λζ was estimated as the exponential decay rate in space of Vm(x) (Fig. 9E, rightmost panel).
+
+Error metrics
+
+The similarity between obtained multichannel ECGs was measured using the PCC37,38 and the DTW distance measure35,36. Since the ECG simulations featured the same start time, end time and time step, all measured ECG signals were aligned and of equal length. Given two discrete time series of equal length N, A and B, the PCC between both time series is computed by PCCA,B=1N−1∑i=1NAi−μAσABi−μBσB,
+
+where each time series is normalized with respect to their means, μA and μB, and standard deviations, σA and σB.
+
+The DTW distance measure between the two given time series represents the solution to the optimization problem DTWA,B=minp∈P(A,B) ∑(i,j)∈pdAi,Bj2,
+
+where p∈P represents all possible alignments described as paths spanned by the two time series A and B. A path represents a sequence of index pairs where the cost to reach each index pair is given by the recursive distance function dAi,Bj2=Ai−Bj22+mindAi−1,Bj−12,dAi,Bj−12,dAi−1,Bj2.
+
+Furthermore, valid paths of length K must satisfy the start- and endpoint condition, p0 = (0, 0) and pK−1 = (N − 1, N − 1), and the initial condition d0 = 0. Following36, we accumulated the DTW distance measures over each subsequence of each ECG lead signal, where subsequences were extracted based on local peak detection. In our specific case, we decided to omit the z-normalization of each subsequence in order to quantify and compare DTW distance measures in mV.
+
+For the analysis of dominant frequency maps in the functional reentry experiment (E), the PSD was computed over each discrete nodal transmembrane voltage trace using Welch’s method54,55. Given the m-th windowed, zero-padded frame from a signal x of length N, where xm[n] = w[n] × [n + mR] with window size M and hop size R, the periodogram for each frame k ∈ K, given by 20 Pxm,Mωk=1MFFTN,kxm2,
+
+is averaged over time to estimate the PSD, given by 21 S^xωk=1K∑m=0K−1Pxm,Mωk.
+
+Mesh generation and solvers
+
+The meshes employed in the experiments simulating anatomical and the functional reentry in 3D slab models and the detailed validation experiments in Supplementary Sec. C were generated using mesher and processed using MeshTool56, as provided in ref. 43. Coarse- and fine-resolution whole heart models were carried over from our previous study41. Utilizing universal ventricular coordinates57, the scar region was mapped from a pig heart58 into the left ventricle of the coarse whole heart model. Since the fine and coarse models almost superimpose spatially, elements in the fine model that lie within the scar area of the coarse model were simply retagged.
+
+All RD simulations were solved using the finite element solver framework openCARP43, configured with an implicit-explicit Crank-Nicolson scheme with operator-splitting and mass-lumping turned off, and solved iteratively8 using a time step of dt = 25 μs (see openCARP user’s manual, pp. 135). The complete parameter set is deposited in the GitHub database under https://github.com/medunigraz/PIE-Model-Experiments and in the Zenodo database59 under accession code (https://doi.org/10.5281/zenodo.17198150).
+
+Whole-heart model acquisition and ethical statement
+
+This study involved only computational modeling using a previously developed anatomical model41 and did not involve the recruitment of participants or the collection of new human data. Consequently, participant demographic characteristics, including race and ethnicity, were not relevant to this study. The study complies with applicable research ethics requirements.
+
+Statistics and reproducibility
+
+This study presents a computational methodology based on an anatomical model of a single male subject. As no biological or experimental samples were analyzed and no statistical comparisons were performed, no statistical methods were used to predetermine sample size. No data were excluded from the analyses and the experiments were not randomized.
+
+The software for reproducing all experimental results is publicly available in the GitHub database under https://github.com/medunigraz/PIE-Model-Experiments and in the Zenodo database59 under accession code (https://doi.org/10.5281/zenodo.17198150). All reference results can be reproduced with open source simulation software openCARP. For details we refer to the Data and Code Availability sections.
+
+Reporting summary
+
+Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.
+
+Supplementary information
+
+Supplementary Information
+
+Reporting Summary
+
+Transparent Peer Review file
+
+Supplementary information
+
+The online version contains supplementary material available at https://doi.org/10.1038/s41467-026-76050-0.
+
+Author contributions
+
+G.P., A.N., and M.A.F.G. conceived this project. T.G.S. performed the implementation, numerical simulations and analysis. T.G.S., M.A.F.G., E.Z. and G.P. drafted and wrote the manuscript. A.N., M.A.F.G. and C.M.A. provided the implementation framework. S.P. and C.M.A. provided theoretical and conceptual input. All authors discussed the results and reviewed the manuscript.
+
+Peer review
+
+Peer review information
+
+Nature Communications thanks Diana Cruz De Oliveira and the other anonymous reviewer for their contribution to the peer review of this work. A peer review file is available.
+
+Funding
+
+This research received support from the Austrian Science Fund (FWF) (grant no. 10.55776/I6476 and 10.55776/I6540 to G.P. and grant no. 10.55776/P37063 to C.M.A.), the Austrian Research Promotion Agency (FFG) (grant no. FO999891133 to M.A.F.G.) and from the European Research Council (ERC) under the European Union’s Horizon Europe research and innovation programme (grant agreement no. 101230597 awarded to S.P.) and the Marie Sklodowska-Curie grant TwinCare-AF (grant agreement no. 101148636 to E.Z.). S.P. also acknowledges support from the Swiss National Supercomputing Centre (CSCS) (project no. lp157) and the SNSF project CardioTwin (no. 214817). The simulation of the whole-heart model was carried out on the Austrian Scientific Cluster (ASC) infrastructure, which is maintained by the ASC Research Center together with the Campus IT of the Technical University Vienna (project no. 71138). Open access funding was provided by the Medical University of Graz.
+
+Data availability
+
+The whole-heart model used in this study was carried over from a previous study41 which is publicly accessible under https://doi.org/10.1016/j.media.2021.102080. All experimental setups employed in this study and its supplementary material, the calibration data of the RD and the PIE model, the generated ECGs and rendered videos of each experiment are publicly available in the GitHub database under (https://github.com/medunigraz/PIE-Model-Experiments). A complete dataset including the calibration data, the generated meshes, the anonymized human whole-heart model and respective lead-field data, computed simulation data and rendered videos of each experiment have been deposited in the Zenodo database59 under accession code (https://doi.org/10.5281/zenodo.17198150).
+
+Code availability
+
+All reference experiments using the RD model were simulated with the openCARP framework (version 18.0), which includes the software for the finite element solver, mesh generation, manipulation and the measurement of physiological features encoded in ForCEPSS28. All codes for replication of RD simulations are freely available through (https://opencarp.org/download/). The code for the evaluation of the experiments is publicly available in the GitHub database under https://github.com/medunigraz/PIE-Model-Experiments and in the Zenodo database59 under accession code (https://doi.org/10.5281/zenodo.17198150). The implementation of the PIE solver (version 1.0) requires proprietary libraries which cannot be publicly disclosed. Binary executables compiled for the major platforms (Linux, macOS or Windows) can be provided upon request within a complete Docker image for replicating the results of this study.
+
+Competing interests
+
+The authors declare no competing interests.
+
+Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
+
+
+References
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+41. Gillette K A framework for the generation of digital twins of cardiac electrophysiology from clinical 12-leads ECGs Med. Imag. Anal. 2021 71 102080 10.1016/j.media.2021.102080 33975097
+Gillette, K. et al. A framework for the generation of digital twins of cardiac electrophysiology from clinical 12-leads ECGs. Med. Imag. Anal. 71, 102080 (2021).10.1016/j.media.2021.102080 33975097
+42. Prakosa A Personalized virtual-heart technology for guiding the ablation of infarct-related ventricular tachycardia Nat. Biomed. Eng. 2018 2 732 10.1038/s41551-018-0282-2 30847259 PMC6400313
+Prakosa, A. et al. Personalized virtual-heart technology for guiding the ablation of infarct-related ventricular tachycardia. Nat. Biomed. Eng. 2, 732 (2018).30847259 10.1038/s41551-018-0282-2 PMC6400313
+43. Plank G The openCARP simulation environment for cardiac electrophysiology Comput. Methods Programs Biomed. 2021 208 106223 10.1016/j.cmpb.2021.106223 34171774
+Plank, G. et al. The openCARP simulation environment for cardiac electrophysiology. Comput. Methods Programs Biomed. 208, 106223 (2021).34171774 10.1016/j.cmpb.2021.106223
+44. Sung E Personalized digital-heart technology for ventricular tachycardia ablation targeting in hearts with infiltrating adiposity Circ. Arrhythm. Electrophysiol. 2020 13 008912 10.1161/CIRCEP.120.008912 PMC7738410 33198484
+Sung, E. et al. Personalized digital-heart technology for ventricular tachycardia ablation targeting in hearts with infiltrating adiposity. Circ. Arrhythm. Electrophysiol. 13, 008912 (2020).10.1161/CIRCEP.120.008912 PMC7738410 33198484
+45. Bueno-Orovio A Cherry EM Fenton FH Minimal model for human ventricular action potentials in tissue J. Theor. Biol. 2008 253 544 10.1016/j.jtbi.2008.03.029 18495166
+Bueno-Orovio, A., Cherry, E. M. & Fenton, F. H. Minimal model for human ventricular action potentials in tissue. J. Theor. Biol. 253, 544 (2008).18495166 10.1016/j.jtbi.2008.03.029
+46. Kalb SS The restitution portrait: a new method for investigating rate-dependent restitution J Cardiovasc Electrophysiol. 2004 15 698 10.1046/j.1540-8167.2004.03550.x 15175067
+Kalb, S. S. et al. The restitution portrait: a new method for investigating rate-dependent restitution. J Cardiovasc Electrophysiol. 15, 698 (2004).15175067 10.1046/j.1540-8167.2004.03550.x
+47. Jin Q Greenstein JL Winslow RL Estimating the probability of early afterdepolarizations and predicting arrhythmic risk associated with long qt syndrome type 1 mutations Biophys. J. 2023 122 4042 10.1016/j.bpj.2023.09.001 37705243 PMC10598291
+Jin, Q., Greenstein, J. L. & Winslow, R. L. Estimating the probability of early afterdepolarizations and predicting arrhythmic risk associated with long qt syndrome type 1 mutations. Biophys. J. 122, 4042 (2023).37705243 10.1016/j.bpj.2023.09.001 PMC10598291
+48. Mohammadi H Challenor P Goodfellow M Emulating dynamic non-linear simulators using Gaussian processes Comput. Stat. Data Anal. 2019 139 178 10.1016/j.csda.2019.05.006
+Mohammadi, H., Challenor, P. & Goodfellow, M. Emulating dynamic non-linear simulators using Gaussian processes. Comput. Stat. Data Anal. 139, 178 (2019).
+49. Grandits T Neural network emulation of the human ventricular cardiomyocyte action potential: a promising tool for more efficient computations in quantitative systems pharmacology studies J. Pharmacol. Toxicol. Methods 2025 135 107850 10.1016/j.vascn.2025.107850
+Grandits, T. et al. Neural network emulation of the human ventricular cardiomyocyte action potential: a promising tool for more efficient computations in quantitative systems pharmacology studies. J. Pharmacol. Toxicol. Methods 135, 107850 (2025).
+50. Campos FO Stochastic spontaneous calcium release events trigger premature ventricular complexes by overcoming electrotonic load Cardiovasc. Res. 2015 107 175 10.1093/cvr/cvv149 25969391 PMC4560047
+Campos, F. O. et al. Stochastic spontaneous calcium release events trigger premature ventricular complexes by overcoming electrotonic load. Cardiovasc. Res. 107, 175 (2015).25969391 10.1093/cvr/cvv149 PMC4560047
+51. Buenzli PR Simpson MJ Curvature dependences of wave propagation in reaction–diffusion models Proc. R. Soc. A. 2022 478 20220582 10.1098/rspa.2022.0582
+Buenzli, P. R. & Simpson, M. J. Curvature dependences of wave propagation in reaction–diffusion models. Proc. R. Soc. A. 478, 20220582 (2022).
+52. Colli Franzone P Guerri L Rovida S Wavefront propagation in an activation model of the anisotropic cardiac tissue: asymptotic analysis and numerical simulations J. Math. Biol. 1990 28 121 10.1007/BF00163143 2319210
+Colli Franzone, P., Guerri, L. & Rovida, S. Wavefront propagation in an activation model of the anisotropic cardiac tissue: asymptotic analysis and numerical simulations. J. Math. Biol. 28, 121 (1990).2319210 10.1007/BF00163143
+53. Tschumperlé D Fast anisotropic smoothing of multi-valued images using curvature-preserving PDE’s Int. J. Comput. Vis. 2006 68 65 10.1007/s11263-006-5631-z
+Tschumperlé, D. Fast anisotropic smoothing of multi-valued images using curvature-preserving PDE’s. Int. J. Comput. Vis. 68, 65 (2006).
+54. Welch PD The use of fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms IEEE Trans. Signal Process. 1967 15 70
+Welch, P. D. The use of fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms. IEEE Trans. Signal Process. 15, 70 (1967).
+55. Julius, O. S. et al. Spectral Audio Signal Processing. http://ccrma.stanford.edu/jos/sasp/, Stanford University (2026).
+56. Neic A Gsell MAF Karabelas E Prassl AJ Plank G Automating image-based mesh generation and manipulation tasks in cardiac modeling workflows using Meshtool SoftwareX 2020 11 100454 10.1016/j.softx.2020.100454 32607406 PMC7326605
+Neic, A., Gsell, M. A. F., Karabelas, E., Prassl, A. J. & Plank, G. Automating image-based mesh generation and manipulation tasks in cardiac modeling workflows using Meshtool. SoftwareX 11, 100454 (2020).32607406 10.1016/j.softx.2020.100454 PMC7326605
+57. Bayer J Universal ventricular coordinates: a generic framework for describing position within the heart and transferring data Med. Image Anal. 2018 45 83 10.1016/j.media.2018.01.005 29414438
+Bayer, J. et al. Universal ventricular coordinates: a generic framework for describing position within the heart and transferring data. Med. Image Anal. 45, 83 (2018).29414438 10.1016/j.media.2018.01.005
+58. Costa CM Determining anatomical and electrophysiological detail requirements for computational ventricular models of porcine myocardial infarction Comput. Biol. Med. 2022 141 105061 10.1016/j.compbiomed.2021.105061 34915331 PMC8819160
+Costa, C. M. et al. Determining anatomical and electrophysiological detail requirements for computational ventricular models of porcine myocardial infarction. Comput. Biol. Med. 141, 105061 (2022).34915331 10.1016/j.compbiomed.2021.105061 PMC8819160
+59. Schrotter, T.G. et al. PIE-Experiments. Zenodo. 10.5281/zenodo.17198150 (2026).
+60. Rodrigo M Technical considerations on phase mapping for identification of atrial reentrant activity in direct-and inverse-computed electrograms Circ. Arrhythm. Electrophysiol. 2017 10 005008 10.1161/CIRCEP.117.005008 28887361
+Rodrigo, M. et al. Technical considerations on phase mapping for identification of atrial reentrant activity in direct-and inverse-computed electrograms. Circ. Arrhythm. Electrophysiol. 10, 005008 (2017).10.1161/CIRCEP.117.005008 28887361
diff --git a/corpus/psychology/text/e8fc5d953f43d160.txt b/corpus/psychology/text/e8fc5d953f43d160.txt
new file mode 100644
index 0000000000000000000000000000000000000000..7821821c12bd7acc579c635594a6e4de6f12300f
--- /dev/null
+++ b/corpus/psychology/text/e8fc5d953f43d160.txt
@@ -0,0 +1,54 @@
+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Front Psychol
+Journal ID: Front Psychol
+NLM Journal ID: 101550902
+Journal ID: Front. Psychol.
+
+Frontiers in Psychology
+
+EISSN: 1664-1078
+Publisher: Frontiers Media SA
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC10507393
+PMID: 37731875
+DOI: 10.3389/fpsyg.2023.1285158
+Article version: 1
+Subjects: Psychology, Retraction
+
+Retraction: The COVID-19 fear, anxiety, and resilience among emergency nurses
+
+Frontiers Editorial Office *
+Approved by: Gianluca Castelnuovo, Catholic University of the Sacred Heart, Italy
+
+*Correspondence: Frontiers Editorial Office research.integrity@frontiersin.org
+Electronic publication date: 2023 Sep 4
+Publication date: 2023
+Volume: 14
+Electronic Location ID: 1285158
+Received 2023 Aug 29; Accepted 2023 Aug 29
+Copyright: Copyright © 2023 Frontiers Editorial Office.
+Copyright year: 2023
+Copyright holder: Frontiers Editorial Office
+License: This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Retraction of: The COVID-19 fear, anxiety, and resilience among emergency nurses 13 2 9 2022 999111 Frontiers in Psychology 10.3389/fpsyg.2022.999111 PMC9479324 36118421
+Figure count: 0
+Table count: 0
+Equation count: 0
+Reference count: 0
+Page count: 1
+
+section-at-acceptance: Psychology for Clinical Settings
+
+Ÿ==============================Ÿ
+The journal retracts the 2022 article cited above.
+
+Following publication, concerns were raised regarding the contributions of the authors of the article. Our investigation, conducted in accordance with Frontiers policies, confirmed a serious breach of our authorship policies and of publication ethics; the article is therefore retracted.
+
+This retraction was approved by the Chief Editors of Frontiers in Psychology and the Chief Executive Editor of Frontiers. The authors responded to the concerns raised, but did not provide a satisfactory explanation. The authors do not agree to this retraction.
+
diff --git a/corpus/psychology/text/eec251db57f562c1.txt b/corpus/psychology/text/eec251db57f562c1.txt
new file mode 100644
index 0000000000000000000000000000000000000000..3d4620e4623aae48e2942a296e2ee062d60f85d3
--- /dev/null
+++ b/corpus/psychology/text/eec251db57f562c1.txt
@@ -0,0 +1,3 @@
+What Pilot Studies Can (and Cannot) Do for Validity in Psychological Research
+
+Recent debates about psychology’s credibility have renewed attention to validity threats. We argue that pilot studies can function as methodological due diligence by improving early decisions about design, measurement, manipulation, sampling, and analysis prior to a main study. We examine four types of validity: construct, internal, external, and statistical-conclusion validity. Across these domains, we show how piloting can help researchers assess whether materials and procedures function as intended, identify potential validity threats, and provide key design parameters for planning and model choice. However, we also caution that piloting can harm validity when treated as a consequence-free space in which design or analytic choices are made without disclosing the pilot evidence behind them, or when small, noisy pilots are used to justify overconfident inferences. We therefore argue that when pilots are used to justify substantive design or analytic choices, they should be treated as part of the evidential record and reported transparently. Greater transparency would enable readers to evaluate how pilot evidence shaped the final design of a study and, consequently, better assess the validity of its findings.
diff --git a/corpus/psychology/text/f2c036bc42d8e809.txt b/corpus/psychology/text/f2c036bc42d8e809.txt
new file mode 100644
index 0000000000000000000000000000000000000000..a48702600f5eafbed75e0a34b5ee78dd3167ed7a
--- /dev/null
+++ b/corpus/psychology/text/f2c036bc42d8e809.txt
@@ -0,0 +1,780 @@
+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Cureus
+Journal ID: Cureus
+NLM Journal ID: 101596737
+
+Cureus
+
+EISSN: 2168-8184
+Publisher: Cureus Inc.
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC12905630
+PMID: 41694909
+DOI: 10.7759/cureus.101581
+Article version: 1
+Subjects: Neurology, Epidemiology/Public Health
+
+A Systematic Literature Review of the Epidemiological, Diagnostic Workup, Humanistic, and Economic Burden of Alzheimer’s Disease in Spain
+
+Muacevic Alexander
+Adler John R
+Altuna Miren 1 2 3
+Rodríguez Eloy 4 5 6 7
+Núñez Mercedes 8
+Trueba-Saiz Ángel 8
+Lizan Luis 9
+Díaz-Cerezo Silvia 8
+1 Center for Research and Memory Clinic, Centro de Investigación y Terapias Avanzadas (CITA)Alzheimer Foundation, San Sebastián, ESP
+2 Department of Neurology, Bioaraba Health Research Institute, Araba University Hospital-Txagorritxu, Vitoria-Gasteiz, ESP
+3 Department of Medicine, Faculty of Health Sciences, University of Deusto, Bilbao, ESP
+4 Department of Neurology, Marqués de Valdecilla University Hospital, Santander, ESP
+5 Department of Neurodegenerative Diseases, Institute for Research Marqués de Valdecilla (IDIVAL), Santander, ESP
+6 Department of Medicine and Psychiatry, University of Cantabria, Santander, ESP
+7 Department of Research, Network Center for Biomedical Research in Neurodegenerative Diseases, National Institute of Health Carlos III, Madrid, ESP
+8 Department of Medical Affairs, Eli Lilly and Company, Madrid, ESP
+9 Department of Outcomes Research, Outcomes’10 a Product-Life Group Company, Castellon de la Plana, ESP
+Mercedes Núñez nunez_mercedes@lilly.com
+Electronic publication date: 2026 Jan 15
+Publication date: 2026 Jan
+Volume: 18
+Issue: 1
+Electronic Location ID: e101581
+Accepted 2026 Jan 9
+Copyright: Copyright © 2026, Altuna et al.
+Copyright year: 2026
+Copyright holder: Altuna et al.
+License: This is an open access article distributed under the terms of the Creative Commons Attribution License CC-BY 4.0., which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+This article is available from https://cureus.com/articles/436521-a-systematic-literature-review-of-the-epidemiological-diagnostic-workup-humanistic-and-economic-burden-of-alzheimers-disease-in-spain
+Keywords: alzheimer’s disease, caregiver burden, costs, early diagnosis, epidemiology
+
+Funding: The study has been funded by Lilly Spain, which provided funding to Outcomes'10 for methodological assistance and medical writing services.
+
+Ÿ==============================Ÿ
+Introduction: Alzheimer’s disease (AD), the leading cause of dementia, affects over 700,000 individuals in Spain, with prevalence expected to rise due to population aging and improved diagnostic accuracy. Around 40,000 new cases are diagnosed annually, yet early-stage AD dementia remains underdiagnosed, limiting understanding of its full epidemiological, clinical, humanistic, and economic burden in Spain.
+
+Methods: A systematic literature review (SLR) was conducted on the burden of AD dementia in Spain, focusing on observational studies published from January 2019 to January 2024. Searches were performed in PubMed/Medical Literature Analysis and Retrieval System Online (MEDLINE), Medicina en Español (MEDES), and Índice Bibliográfico Español en Ciencias de la Salud (IBECS), following Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines.
+
+Results: Twenty-six publications were included, mainly addressing moderate-to-severe AD dementia, with limited evidence on mild cognitive impairment (MCI) due to AD. Commonly used tools included the Mini-Mental State Examination (MMSE), Barthel Index, and Global Deterioration Scale (GDS). Neurologists were the primary clinicians involved in diagnosis (78.6%), though etiological diagnosis often lacked core AD biomarkers. Most caregivers were informal (mainly women), experiencing significant declines in health-related quality of life (HRQoL). Non-healthcare costs accounted for 84.6%-90.7% of total expenditures, followed by direct healthcare (6.1%-10.0%) and social care costs (2.8%-4.6%). Indirect costs, mostly from reduced working hours, represented 0.5%-0.8%.
+
+Conclusions: This study highlights the need to improve early diagnosis of AD dementia and to establish reliable health registries to measure its burden. The lack of evidence on practice heterogeneity hinders standardized care strategies. Addressing these gaps is essential to improve patient management, ensure equitable access to timely and accurate diagnosis, and facilitate access to emerging disease-modifying treatments for AD dementia.
+
+Introduction and background
+
+Alzheimer’s disease (AD) is the leading cause of dementia, accounting for 60%-80% of all cases [1, 2]. It is a neurodegenerative disorder marked by progressive cognitive decline, mostly with amnesic symptoms [3], and its neuropathological signs include accumulation of beta-amyloid plaques and tau neurofibrillary tangles (NFT) in the brain [1, 2]. Over 90% of AD cases have a late onset, where symptoms develop at or after the age of 65 [4]. Consequently, AD is a leading cause of disability and dependence among the elderly [1], accounting for 11.9% of the years lived with disability due to chronic diseases [1]. The disease progresses over decades through several stages: preclinical (asymptomatic) stage, mild cognitive impairment (MCI), and mild, moderate, and severe dementia [1, 5]. Symptoms worsen over time, leading to a gradual decline in daily functionality and independence. Simple tasks, such as dressing or eating, become increasingly challenging until individuals with severe dementia often require full-time care and assistance [1].
+
+In Spain, there are over 700,000 people affected by AD among a population of 49 million (of which 9.62 million are aged over 65 years) [6], with 40,000 new cases diagnosed annually [7]. However, reliable records on the epidemiology of AD stages are lacking. AD is estimated to be underdiagnosed in 50%-70% of cases and is often diagnosed at relatively advanced stages [1], with loss of functional autonomy. Unfortunately, there is no universal access to core AD biomarkers or a standardized neuropsychological assessment able to diagnose AD at the MCI stage, which is optimal according to clinical recommendations [8].
+
+Early diagnosis of AD during initial symptomatic stages is crucial for patients, families, caregivers, and healthcare professionals. This allows for effective planning of patient care, appropriate referral to healthcare services, access to new therapeutic options, and involvement of patients in decision-making processes, including potential inclusion in clinical trials [1, 9, 10]. Currently, early symptoms, such as mild memory loss, are often misattributed to normal aging, delaying accurate diagnosis [1]. Addressing this misconception could heighten awareness of the development of diseases such as AD. Another key aspect is improving the diagnostic process, starting with brief cognitive screening tests, which currently show suboptimal performance in detecting MCI, particularly in younger individuals and/or those with higher levels of education [11]. Current diagnostic methods involve a comprehensive clinical evaluation, including brief cognitive tests and a neurological examination, followed by blood tests to rule out treatable causes of cognitive decline [12]. Additional assessments may include neuropsychological evaluation, structural and functional brain imaging, and cerebrospinal fluid (CSF) core biomarker analysis to support diagnosis [12]. There is inequitable access to diagnostic workup due to its ongoing advancements, the lack of universal access to approved diagnostic resources, limitations in healthcare infrastructure, cost, and the invasive nature of certain tests [13]. In addition, according to the updated National Institute on Aging-Alzheimer’s Association (NIA-AA) research framework, AD is defined biologically through the AT(N) system, which classifies biomarkers into three categories: amyloid (A), tau (T), and neurodegeneration (N) [14]. This framework provides a standardized approach for the diagnosis of MCI due to AD and improves diagnostic accuracy, a critical aspect of the diagnostic workup for AD. Diagnosing AD without AT(N) biomarkers reduces diagnostic reliability and hinders a comprehensive, patient-centered therapeutic approach [15, 16].
+
+Most of the available therapies for AD alleviate the symptoms but do not address disease progression; however, new disease-modifying therapies (DMTs) have been shown to slow disease progression in early symptomatic stages [3, 5, 17]. This underscores the importance of earlier and accurate core biomarker-based diagnosis at initial symptomatic stages, such as MCI or mild dementia.
+
+The cost of AD management significantly impacts overall healthcare costs. In southern Europe, the average annual cost per patient with dementia is €35,866, varying by disease stage and increasing with symptomatic progression [18]. Notably, 85% of the AD-related economic burden is covered by the patient and their family [1], even in countries such as Spain, where there is a universal healthcare system. This is associated with considerable emotional and physical strain, mainly anxiety and depression, faced by caregivers and direct family members [19-21].
+
+Despite the substantial public health burden of AD in Spain, significant gaps remain in understanding the current epidemiological landscape, diagnostic practices, and the humanistic and economic impacts of the disease. Addressing these gaps is crucial to fully understanding the true impact of AD. Given the high prevalence and burden of AD among the elderly, more population-based data are essential to develop effective resource allocation and efficient healthcare management strategies. This study reviews recent literature (2019-2024) to capture the latest advancements in AD research, particularly in relation to new DMTs and updates to diagnostic criteria, aiming to support informed decision-making in policy and clinical practice.
+
+Review
+
+Methods
+
+A systematic literature review (SLR) was conducted to evaluate 1) epidemiology, 2) diagnostic workup, 3) patient journey, 4) humanistic burden (functionality and cognitive impairment in patients with AD, as well as health-related quality of life (HRQoL) of their caregivers), and 5) economic burden (resource utilization and direct and indirect costs) of AD in Spain. The recommendations included in the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) were followed [22]. This SRL followed a standardized and unpublished protocol.
+
+Data Sources and Search Strategy
+
+The international databases PubMed/Medical Literature Analysis and Retrieval System Online (MEDLINE), Medicina en Español (MEDES), and Índice Bibliográfico Español en Ciencias de la Salud (IBECS) were searched using standardized search filters to identify relevant publications. Because this review aimed to characterize the epidemiological, diagnostic, humanistic, and economic burden of AD specifically within the Spanish healthcare context, databases with extensive coverage of Spanish biomedical literature were prioritized. In particular, MEDES and IBECS were included to capture studies published in Spanish-language journals that may be underrepresented in broader international databases.
+
+Both Medical Subject Headings (MeSH) and free-text terms were used and combined with the Boolean connectors OR and AND to search the databases. The MeSH and free-text terms used are detailed in Table 1.
+
+Table 1 Search strategy for PubMed/Medical Literature Analysis and Retrieval System Online (MEDLINE), Medicina en Español (MEDES), and Índice Bibliográfico Español en Ciencias de la Salud (IBECS)
+
+Search strategy for PubMed/MedLine	 	
+Disease	 	
+1.	Alzheimer Disease [MeSH]	 	
+2.	Alzheimer [tiab]	 	
+Country	 	
+3.	Spain [tw]	 	
+4.	Spanish [tw]	 	
+5.	Andalucia [tw]	 	
+6.	Andalusía [tw]	 	
+7.	Aragon [tw]	 	
+8.	Asturias [tw]	 	
+9.	Balear* [tw]	 	
+10.	Canar* [tw]	 	
+11.	Cantabria [tw]	 	
+12.	Castilla [tw]	 	
+13.	Cataluña [tw]	 	
+14.	Catalunya [tw]	 	
+15.	Catalonia [tw]	 	
+16.	Ceuta [tw]	 	
+17.	Valenciana [tw]	 	
+18.	Valencian [tw]	 	
+19.	Extremadura [tw]	 	
+20.	Galicia [tw]	 	
+21.	Madrid [tw]	 	
+22.	Murcia [tw]	 	
+23.	Melilla [tw]	 	
+24.	Navarr* [tw]	 	
+25.	Vasco [tw]	 	
+26.	Euskadi [tw]	 	
+27.	Basque [tw]	 	
+28.	Rioja [tw]	 	
+Clinical Burden	 	
+29.	Epidemiologic factor [MeSH]	 	
+30.	Incidence [MeSH]	 	
+31.	Prevalence [MeSH]	 	
+32.	Age of Onset [MeSH]	 	
+33.	Mortality [MeSH]	 	
+34.	Epidemiologic factors [tiab]	 	
+35.	Incidence [tiab]	 	
+36.	Prevalence [tiab]	 	
+37.	Age of Onset [tiab]	 	
+38.	Mortality [tiab]	 	
+Diagnosis	 	
+39.	Diagnosis [MeSH]	 	
+40.	Risk factors [MeSH]	 	
+41.	Cognitive Dysfunction [MeSH]	 	
+42.	Dementia [MeSH]	 	
+43.	Biomarkers [MeSH]	 	
+44.	Diagnos* [tiab]	 	
+45.	Diagnostic technique* [tiab]	 	
+46.	Cognitive dysfunction [tiab]	 	
+47.	Cognitive impairment [tiab]	 	
+48.	Dementia [tiab]	 	
+49.	Risk factors [tiab]	 	
+50.	Biomarker [tiab]	 	
+51.	Subjective cognitive complaint [tiab]	 	
+52.	Self-reported memory complaint [tiab]	 	
+Humanistic burden	 	
+53.	Quality of life [MeSH]	 	
+54.	Patient-Reported Outcome Measures [MeSH]	 	
+55.	Quality of life [tiab]	 	
+56.	Patient-Reported Outcome Measures [tiab]	 	
+57.	Health-related quality of life [tiab]	 	
+58.	Health status [tiab]	 	
+Economic burden	 	
+59.	Global Burden of Disease [MeSH]	 	
+60.	Cost of Illness [MeSH]	 	
+61.	Cost of Illness [tiab]	 	
+62.	Costs and cost analysis [MeSH]	 	
+63.	Economic burden [tiab]	 	
+64.	Burden [tiab]	 	
+65.	Cost [tiab]	 	
+66.	Absenteeism [tiab]	 	
+67.	Presenteeism [tiab]	 	
+68.	Productivity [tiab]	 	
+69.	Activity impairment [tiab]	 	
+70.	Disability [tiab]	 	
+71.	Economics [tiab]	 	
+Disease management	 	
+72.	Standard of care [MeSH]	 	
+73.	Treatment patterns [tiab]	 	
+74.	Standard of care [tiab]	 	
+75.	Patient care management [MeSH]	 	
+76.	Disease management [tiab]	 	
+77.	Patient journey [tiab]	 	
+((OR 1-2) AND (OR 3-28)) AND (OR 29-77)	 	
+Search strategy for Medicina en Español (MEDES)	 	
+Disease	 	
+1.	Alzheimer [título/resumen/palabras_clave]	
+Country	
+2.	España [Todos los campos]	
+3.	Andalucia [Todos los campos]	
+4.	Aragon [Todos los campos]	
+5.	Asturias [Todos los campos]	
+6.	Balear* [Todos los campos]	
+7.	Canar* [Todos los campos]	
+8.	Cantabria [Todos los campos]	
+9.	Castilla [Todos los campos]	
+10.	Cataluña [Todos los campos]	
+11.	Ceuta [Todos los campos]	
+12.	Valenciana [Todos los campos]	
+13.	Extremadura [Todos los campos]	
+14.	Galicia [Todos los campos]	
+15.	Madrid [Todos los campos]	
+16.	Murcia [Todos los campos]	
+17.	Melilla [Todos los campos]	
+18.	Navarra [Todos los campos]	
+19.	Vasco [Todos los campos]	
+20.	Euskadi [Todos los campos]	
+21.	Rioja [Todos los campos]	
+Clinical Burden	
+22.	Epidemiologi* [título/resumen/palabras_clave]	
+23.	Incidencia [título/resumen/palabras_clave]	
+24.	Prevalencia [título/resumen/palabras_clave]	
+25.	Edad de inicio [título/resumen/palabras_clave]	
+26.	Mortalidad [título/resumen/palabras_clave]	
+Diagnosis	
+27.	Diagnóstico [título/resumen/palabras_clave]	
+28.	Factores de riesgo [título/resumen/palabras_clave]	
+29.	Deterioro cognitivo[título/resumen/palabras_clave]	
+30.	Demencia [título/resumen/palabras_clave]	
+31.	Biomarcadores [título/resumen/palabras_clave]	
+32.	Queja subjetiva de memoria [título/resumen/palabras_clave]	
+33.	Pérdida subjetiva de memoria [título/resumen/palabras_clave]	
+Humanistic burden	
+34.	Calidad de vida [título/resumen/palabras_clave]	
+35.	Resultados percibidos por el paciente [título/resumen/palabras_clave]	
+Economic burden	
+36.	Carga de la enfermedad [título/resumen/palabras_clave]	
+37.	Coste de la enfermedad [título/resumen/palabras_clave]	
+38.	Carga económica[título/resumen/palabras_clave]	
+39.	Absentismo [título/resumen/palabras_clave]	
+40.	Presencialismo [título/resumen/palabras_clave]	
+41.	Productividad [título/resumen/palabras_clave]	
+42.	Discapacidad [título/resumen/palabras_clave]	
+43.	Económico [título/resumen/palabras_clave]	
+44.	Economía [título/resumen/palabras_clave]	
+Disease management	
+45.	Calidad asistencial [título/resumen/palabras_clave]	
+46.	Manejo [título/resumen/palabras_clave]	
+47.	Estándar de calidad [título/resumen/palabras_clave]	
+48.	Viaje del paciente [título/resumen/palabras_clave]	
+49.	Flujo asistencial [título/resumen/palabras_clave]	
+50.	Proceso asistencial [título/resumen/palabras_clave]	
+51.	Indicador de calidad [título/resumen/palabras_clave]	
+(1 AND (OR 2-21)) AND (OR 22-51)	
+Search strategy for Índice Bibliográfico Español en Ciencias de la Salud (IBECS)	
+Disease	
+1.	Alzheimer [palabras del resumen]	 	
+Country	 	
+2.	España [Palabras]	 	
+3.	Andalucia [Palabras]	 	
+4.	Aragon [Palabras]	 	
+5.	Asturias [Palabras]	 	
+6.	Balear* [Palabras]	 	
+7.	Canar* [Palabras]	 	
+8.	Cantabria [Palabras]	 	
+9.	Castilla [Palabras]	 	
+10.	Cataluña [Palabras]	 	
+11.	Ceuta [Palabras]	 	
+12.	Valenciana [Palabras]	 	
+13.	Extremadura [Palabras]	 	
+14.	Galicia [Palabras]	 	
+15.	Madrid [Palabras]	 	
+16.	Murcia [Palabras]	 	
+17.	Melilla [Palabras]	 	
+18.	Navarra [Palabras]	 	
+19.	Vasco [Palabras]	 	
+20.	Euskadi [Palabras]	 	
+21.	Rioja [Palabras]	 	
+Clinical Burden	 	
+22.	Epidemiologia* [Palabras del resumen]	 	
+23.	Incidencia [Palabras del resumen]	 	
+24.	Prevalencia [Palabras del resumen]	 	
+25.	Edad de inicio [Palabras del resumen]	 	
+26.	Mortalidad [Palabras del resumen]	 	
+Diagnosis	 	
+27.	Diagnóstico [Palabras del resumen]	 	
+28.	Factores de riesgo [Palabras del resumen]	 	
+29.	Deterioro cognitivo [Palabras del resumen]	 	
+30.	Demencia [Palabras del resumen]	 	
+31.	Biomarcadores [Palabras del resumen]	 	
+32.	Queja subjetiva de memoria [Palabras del resumen]	 	
+33.	Pérdida subjetiva de memoria [Palabras del resumen]	 	
+Humanistic burden	 	
+34.	Calidad de vida [Palabras del resumen]	 	
+35.	Resultados percibidos por el paciente [Palabras del resumen]	 	
+Economic burden	 	
+36.	Carga de la enfermedad [Palabras del resumen]	 	
+37.	Coste de la enfermedad [Palabras del resumen]	 	
+38.	Carga económica [Palabras del resumen]	 	
+39.	Absentismo [Palabras del resumen]	 	
+40.	Presencialismo [Palabras del resumen]	 	
+41.	Productividad [Palabras del resumen]	 	
+42.	Discapacidad [Palabras del resumen]	 	
+43.	Económico [Palabras del resumen]	 	
+44.	Economía [Palabras del resumen]	 	
+Disease management	 	
+45.	Calidad asistencial [Palabras del resumen]	 	
+46.	Manejo [Palabras del resumen]	 	
+47.	Estándar de calidad [Palabras del resumen]	 	
+48.	Viaje del paciente [Palabras del resumen]	 	
+49.	Flujo asistencial [Palabras del resumen]	 	
+50.	Proceso asistencial [Palabras del resumen]	 	
+51.	Indicador de calidad [Palabras del resumen]	 	
+(1 AND (OR 2-21)) AND (OR 22-51)	 	
+
+Grey literature was reviewed as part of the search process. However, these findings referred to dementia in general and did not specify AD as the underlying etiology; therefore, they were excluded from the review.
+
+Eligibility Criteria
+
+The search included only cohort, case-control, and cross-sectional observational studies published from January 2019 to January 2024, in Spanish or English, involving a Spanish population of adults with AD diagnosis, MCI, or mild dementia due to AD (Table 2).
+
+Table 2 Eligibility criteria
+
+HRQoL: health-related quality of life; AD: Alzheimer's disease; NA: not applicable
+
+Study Characteristics	Eligible	Ineligible	
+Patient population	At least one of the following is required to be eligible: Adults with an AD diagnosis, Adults with mild cognitive impairment due to AD, Adults with mild dementia due to AD, Adults with subjective memory complaints related to AD	Non-Alzheimer’s dementias	
+Intervention - Treatment	NA	NA	
+Intervention - Comparison	NA	NA	
+Outcomes–	Epidemiology: Incidence, prevalence, mortality; Population characteristics: age, sex, risk factors, disease severity, age of onset; Clinical management: diagnostic techniques, biomarkers, patient journey, HRQoL of patients and caregivers; Resource utilization and costs: resource use, direct cost, pharmacological cost, productivity of patients and caregivers, absenteeism/presenteeism of patients and caregivers	NA	
+Study design	Observational studies (including cost studies)	Narrative reviews, Systematic reviews, and meta-analysis, Clinical trials, Opinion articles, Editorial, Pharmacoeconomic evaluations  	
+Country	Spanish studies, Multi-country studies with the Spanish population (if disaggregated data are available)	Non-Spanish studies, Multi-country studies without Spanish population, Multi-country studies with no disaggregated data	
+Time Frame	Articles published: January 2019 to January 2024	Publications prior to 2019	
+Language	English, Spanish	Non-English, Non-Spanish	
+
+The search excluded narrative reviews, systematic reviews, meta-analyses, conference abstracts, clinical trials, opinion articles, editorials, pharmacoeconomic evaluations, studies including adults with a non-Alzheimer's dementia diagnosis, and studies without a Spanish population.
+
+Study Selection
+
+Two independent researchers selected eligible publications. Firstly, the investigators screened by title and abstract, discarding publications outside the scope of the review. Then, the full text of the selected publications was reviewed to ascertain the final eligibility for this SRL. Discrepancies were resolved by consensus or by involving a third team member. Only full-text articles were included.
+
+Data Extraction and Quality Assessment
+
+Data extracted included the author, the publication year, the objective of the study, the type of study, characteristics of the study population, epidemiology, diagnosis, patient journey, HRQoL of patients and caregivers, resource utilization, and costs. No formal statistical analysis was performed. The methodological quality and risk of bias of the included studies were assessed using the Newcastle-Ottawa Scale (NOS) [23]. This instrument was selected because the included studies were non-interventional observational designs, for which the NOS provides the most appropriate framework to evaluate both methodological quality and potential sources of bias. Two independent reviewers extracted the data and assessed the quality of the studies, and the discrepancies were solved by consensus.
+
+Ethical Approval
+
+This article is based on published studies and, therefore, does not involve studies with human participants or animals performed by the authors. Accordingly, as a systematic review of published literature, this study did not require evaluation by an ethics committee.
+
+Results
+
+Out of the 429 articles initially identified, 26 publications were finally included in the SLR (Figure 1). The NOS quality assessment indicated a medium-to-high quality rating in most of the selected publications (score ≥5 out of a maximum of 9). Lower scores observed in some studies reflected the inclusion of descriptive cross-sectional or other non-comparative designs that did not fully align with the NOS framework, originally developed for cohort and case-control studies (Table 3). The characteristics of each publication are described in Table 4. Most of the publications included combined information about several variables of interest, such as epidemiology, diagnostic workup, patient journey, information about the caregivers and their HRQoL, resource utilization, and costs.
+
+Figure 1 PRISMA flow diagram
+
+PRISMA: Preferred Reporting Items for Systematic Reviews and Meta-Analyses; MEDES: Medicina en Español; IBECS: Índice Bibliográfico Español en Ciencias de la Salud; AD: Alzheimer’s disease; SLR: systematic literature review
+
+Table 3 Newcastle–Ottawa scale (NOS) assessment of methodological quality and risk of bias of included studies
+
+NA: Not aplicable/Not available; * descriptive cross-sectional studies or other types of studies (not cohort or case control studies) were analyzed according to the NOS method most similar to the specific study. #: “Item” refers to each criterion evaluated within the NOS domains (Selection, Comparability, and Outcome/Exposure). The presence of 0 or 1 indicates that the study fulfilled the criterion and was awarded one point.
+
+Study	Study design analysis	Item	Total score	
+1	2	3	4	5	6	7	8	
+Andreu-Reinón (2020) [24]	Cohort	  1	  NA	  1	  1	  1	  1	  1	  1	  7	
+Cámara-Calmaestra (2023) [25]*	Case control	1	0	1	1	1	1	1	NA	6	
+Cantón-Habas (2020) [26]	Case control	1	1	1	1	1	1	1	0	7	
+Casal Rodríguez (2019) [19]*	Cohort	0	0	1	0	NA	1	1	1	4	
+Darbà (2021) [27]	Cohort	1	0	1	0	NA	1	1	1	5	
+Durán-Gómez (2020) [20]*	Cohort	0	0	1	1	NA	1	1	1	5	
+Fernández Rubio (2023) [28]*	Cohort	1	0	1	0	NA	1	1	1	5	
+García-Escobar (2023) [29]*	Case control	1	0	0	1	2	1	1	1	7	
+Garcia-Ribas (2020) [30]*	Case control	1	0	1	1	1	1	1	0	6	
+Gomez-Gallego (2021) [31]*	Case control	1	1	0	0	1	1	0	0	4	
+Gómez Maldonado (2023) [32]*	Cohort	0	0	1	1	NA	1	1	1	5	
+Hernández-Padilla (2021) [33]*	Cohort	0	0	1	0	NA	1	1	1	4	
+Khandker (2020) [34]*	Cohort	1	0	1	0	NA	1	1	1	5	
+Kishita (2023) [35]*	Cohort	1	0	1	0	NA	1	1	1	5	
+Luque-Carrillo (2020) [36]*	Cohort	0	0	1	0	NA	1	0	1	3	
+Macedo (2021) [37]	Cohort	1	1	1	0	2	1	1	1	8	
+Mariezcurrena (2020) [38]*	Cohort	1	0	1	0	NA	1	1	0	4	
+Martínez Arrechea (2021) [39]*	Case control	1	1	0	1	1	1	1	1	7	
+Ponjoan (2020) [40]	Cohort	1	1	1	0	2	1	1	1	8	
+Poudevida (2022) [41]	Case control	1	1	1	1	2	1	1	0	8	
+Puig-Pijoan (2022) [42]	Cohort	1	1	1	0	2	1	1	1	8	
+Rosende-Roca (2022) [21]*	Cohort	0	0	1	0	NA	1	1	1	4	
+Roth (2023) [43]*	Cohort	1	0	1	0	NA	0	1	1	4	
+Ruiz-Fernández (2019) [44]*	Cohort	0	0	1	0	NA	1	1	1	4	
+Tortajada-Soler (2020) [45]*	Case control	1	0	1	1	1	1	1	1	7	
+Turró-Garriga (2020) [46]*	Cohort	0	0	1	0	NA	1	1	1	4	
+
+Table 4 Main characteristics of the selected studies
+
+* Descriptive cross-sectional studies for which no specific New Castle Ottawa Scale (NOS) evaluation method exist that were analyzed using the NOS methodology, classifying them as either case-control or cohort studies, depending on which study design they most closely resembled. Cross-sectional studies were considered retrospective if data were obtained from prior records, and prospective if data were collected during the study.
+
+AD: Alzheimer’s disease; aMCI: amnestic mild cognitive impairment; BDU® : Unified database (Base de datos unificados in Spanish); CU: cognitively unimpairedt; EPIC: European Prospective Investigation into Cancer and Nutrition cohort; HRQoL: Health-related quality of life; MCI: mild cognitive impairment; NA: not available; PCP: primary care physician; SIDIAP database: Information System for Research in Primary Care.
+
+Author (year)	Geographical area	Recruitment year	Follow-up time	Type of study and study design	Population	Population size	Data source	Healthcare setting	Recovered variables	
+Andreu-Reinón (2020) [24]	National	1992–1996	20 years	Cohort study: longitudinal, prospective	General population (outpatient and hospital records)	774	EPIC cohort	Primary care, hospital	Demographic characteristics, epidemiology	
+Cámara-Calmaestra (2023) [25]	Regional (Andalusia)	2021–2022	NA	Case-control* study: Cross-sectional prospective	Geriatric population (nursing homes and living at home)	Total: 194 ≥ 65 yr AD patients: 114 ≥ 65 yr non-AD: 80	Study Survey	Nursing homes	Demographic characteristics, clinical management, resource utilization and costs, patient journey	
+Cantón-Habas (2020) [26]	National	2018–2019	NA	Case control study: cross-sectional, retrospective	Geriatric population (nursing homes and dementia-specific facilities)	221	Clinical history	Nursing homes and dementia-specific facilities	Demographic characteristics, epidemiology, clinical management, and HRQoL of patients	
+Casal Rodríguez (2019) [19]	Regional (Galicia)  	2007–2008	NA	Cohort* study: cross-sectional, retrospective	Caregivers of patients with AD	175	Survey	Patient's home	Caregiver burden	
+Darbà (2021) [27]	National	2011–2016	NA	Cohort study: longitudinal, retrospective	General population (hospital records)	83	Spanish National Hospital Discharge Database	Hospital	Demographic characteristics, epidemiology, resource utilization, and costs	
+Durán-Gómez (2020) [20]	Regional (Extremadura)	2018–2019	NA	Cohort* study: cross-sectional, retrospective	General population (outpatient; patients and caregivers)	120	Survey	Patient's home	HRQoL of patients and caregivers	
+Fernández Rubio (2023) [28]	Regional (Andalusia)  	2021	NA	Cohort* study: cross-sectional, retrospective	General population (on active therapies)	Total: 408,788, Patients with AD: NA	BDU® study database	Health management area	Demographic characteristics, resource utilization, and costs	
+García-Escobar (2023) [29]	Regional (Catalonia)	NA	NA	Case-control* study: cross-sectional, prospective	General population (hospital records)	Total: 112 CU: 42 MCI: 35 Mild AD: 35	CORCOBIA study database	Hospital	Demographic characteristics Clinical management	
+Garcia-Ribas (2020) [30]	National	2019–2020	NA	Case-control* study: cross-sectional, Prospective	General population (caregivers and non-caregivers)	Total: 447; AD caregivers: 42; Non- Non-caregivers: 405	Survey	Same dwelling caregiver home, other relatives' home, nursing home	Demographic characteristics, patient journey, and caregivers	
+Gomez-Gallego (2021) [31]	NA	NA	NA	Case-control* study: cross-sectional, Prospective	General population (outpatient)	196	Clinical data and validated questionnaires	Primary health centers and dementia day centers	Demographic characteristics, clinical management, HRQoL of patients and caregivers	
+Gómez Maldonado (2023) [32]	National	2021–2022	NA	Cohort* study: cross-sectional, retrospective	Caregivers of patients with AD	171	Survey	Same dwelling, own home, nursing home  	Demographic characteristics, resource utilization and costs, patient journey, and caregivers	
+Hernández-Padilla (2021) [33]	Regional (Andalusia)  	2015–2015	NA	Cohort* study: cross-sectional, retrospective	Caregivers of patients with AD	255	Survey	Health management area	Demographic characteristics of caregivers	
+Khandker (2020) [34]	National	2015–2016	NA	Cohort* study: cross-sectional, retrospective	General population, including patients with cognitive impairment	Total: 846; MCI: 48; Mild AD: 334; moderate AD: 386; severe AD: 78	Survey	Primary care, hospitalization, and institutionalized	Demographic characteristics, epidemiology, resource utilization, and costs	
+Kishita (2023) [35]	National	NA	NA	Cohort* study: longitudinal, retrospective	Caregivers (family) of patients with AD	Caregivers: 322; patients: 322	Clinical history	NA	Demographic characteristics, epidemiology	
+Luque-Carrillo (2020) [36]	Regional (Andalusia)  	NA	NA	Cohort* study: cross-sectional, retrospective	Patients with AD and their caregivers	69	Survey	Day care center	Demographic characteristics, HRQoL of patients and caregivers	
+Macedo (2021) [37]	Regional (Castile and Leon)  	NA	NA	Cohort study: cross-sectional, prospective	Geriatric population	111	Clinical history	NA	Demographic characteristics, epidemiology, and clinical management	
+Mariezcurrena (2020) [38]	Regional (Navarra)  	2019–2019	NA	Cohort* study: cross-sectional, prospective	Caregivers and families of patients with patients	76	Survey, clinical data, and validated questionnaires	NA	Demographic characteristics of caregivers	
+Martínez Arrechea (2021) [39]	Regional (Andalusia)  	Phase 1: 2017; Phase 2: 2019–2019	NA	Case-control* study: cross-sectional, Retrospective	Geriatric population (institutionalized)	Total: 178; AD: 114 (64%)	Clinical history	Nursing homes	Resource utilization and costs	
+Ponjoan (2020) [40]	Regional (Catalonia)  	2016–2016	NA	Cohort study: cross-sectional, retrospective	General population (>65 yr)	Total: 1,048,956; AD: 39,448; other: 1,009,508	SIDIAP database	Primary care	Demographic characteristics, epidemiology, and clinical management	
+Poudevida (2022) [41]	National	2013–2014	NA	Case-control study: longitudinal, prospective	Caregivers of patients with AD	221	Clinical data and validated questionnaires	Hospital and outpatient  	Demographic characteristics, clinical management, and caregivers	
+Puig-Pijoan (2022) [42]	Regional (Catalonia)  	2014–2019	19 months	Cohort study: cross-sectional, prospective	Patients with AD and unimpaired individuals (60-85 yr)	Total: 125; CU: 42; aMCI: 35; mild AD: 48  	Clinical data and validated questionnaires	Hospital and outpatient  	Demographic characteristics, clinical management	
+Rosende-Roca (2022) [21]	Regional (Catalonia)	2011–2020	NA	Cohort study: cross-sectional, prospective	Patients with AD and their caregivers	1065	Ace Alzheimer Barcelona center database	Alzheimer Care Center  	Demographic characteristics, clinical management, patient journey, and caregivers	
+Roth (2023) [43]	National	2021–2021	NA	Cohort* study: cross-sectional, prospective	Healthcare providers	241	Survey	Healthcare System	Epidemiology, clinical management. resource utilization and costs, patient journey	
+Ruiz-Fernández (2019) [44]	Regional (Andalusia)	2015–2015	NA	Cohort* study: cross-sectional, prospective	General population (healthcare records)	255	Case manager nurses’ caregiver database	Health Management Area  	Demographic characteristics, HRQoL of patients and caregivers	
+Tortajada-Soler (2020) [45]	Regional (Castile and Leon)	2019	NA	Case-control* study: cross-sectional, retrospective	Patients with AD and controls (>65)	Total: 200; AD: 100; Non-AD: 100	Clinical history	Alzheimer Care Center	Demographic characteristics, resource utilization, and costs	
+Turró-Garriga (2020) [46]	Regional (Catalonia)	2018–2019	24 months	Cohort* study: cross-sectional, prospective	Caregivers of patients with AD (clinical registries)	147	Survey	Healthcare System (memory clinics)  	Demographic characteristics, clinical management, HRQoL of patients, resource utilization and costs, patient journey, and caregivers	
+
+Population Characteristics
+
+Demographic characteristics: The studies included in this SLR were highly variable in terms of the contexts in which they were conducted (e.g., general population, nursing homes, daycare centers, hospital records), study design, and AD disease stage evaluated. However, in general, the AD population included in these studies had a higher proportion of women (60%-70%) than men [19-21, 24-27, 29, 31-37, 40, 42, 44, 46], and the mean age of patients with AD ranged from 70 to 82 years [19, 20, 26, 29, 31, 32, 35, 36, 42, 46]. Patients with AD were more likely to have low and middle socioeconomic status, while non-AD patients predominantly fell into middle status [19, 25]. Patients with AD generally had a lower education level (39.8-93.8% primary education or lower, 6.2-60.2% secondary or higher education) (Table 5) [21, 25].
+
+Table 5 Main demographic characteristics of the study population on reporting publications
+
+Population age is represented as the mean (years). Disease severity is represented as N (%): Percentages are calculated out of the total number of patients with AD except in García-Escobar (2023) [29] and Puig-Pijoan (2022) ) [38], which included cognitively unimpaired (CU) individuals and population with mild-stage AD or amnestic mild cognitive impairment (aMCI), and percentages are 100% for each specific disease population or * are calculated considering the total number of participants in the study (CU+MCI+Mild AD). Sex and place of residence are represented as N (%).  
+
+AD: Alzheimer’s disease; CU: cognitively unimpaired; MCI: mild cognitive impairment; NA: not applicable/not available; n.d: not defined; SD: standard deviation.
+
+Author (year)	Sex (female, %)	Population age (years ± SD)	Population	Disease severity	Place of residence	Monthly income	Education level	
+Andreu-Reinón (2020) [24]	453 (58.5%)	Age at recruitment (N, %) <65: 751, 97.7% ≥ 65: 23, 2.3%	General population (outpatient and hospital records)	NA	NA	NA	NA	
+Cámara-Calmaestra (2023) [25]	Overall: 131 (67.5%), AD: 86 (75.4%), CU: 45 (56.3%)	Overall: 79.0 ± 8.6 AD: 82.9 ± 7.2 CU: 73.5 ± 7.2	Geriatric population (nursing homes and living at home)	NA	AD: 114 (100 %) nursing homes CU: 80 (100%) home	AD: Low 26 (22.8%), medium 77 (67.5%), high 11 (9.7%). CU: Low 5 (6.3%), medium 72 (90%), high 3 (3.8%)	AD: No studies: 42 (36.8%), Primary education: 65 (57.0%), Secondary education: 6 (5.3%), University: 1 (0.9%), CU: No studies: 5 (6.2%), Primary education: 635 (43.8%), Secondary education: 18 (22.5%), University: 22 (27.5%)	
+Cantón-Habas (2020) [26]	168 (76%)	79.1 ± 8.6	Geriatric population (nursing homes and dementia-specific facilities)	NA	Nursing homes: 107 (48.4%)	NA	NA	
+Casal Rodríguez (2019) [19]	AD: 136 (77.7%), Caregivers: 124 (70.9%)	AD: 78.3 ± 8.2 Caregivers: 58.1 ± 14.2	Caregivers of AD patients	Mild AD: 62 (35.8%) Moderate AD: 66 (37.7%) Severe AD: 47 (26.7%)	NA	AD: < 900€: 127 (75.6%) 900–2,400€: 40 (22.9%) > 2,400€: 4 (2.3%) n.d.: 4 (2.3%), Caregivers: < 900€: 95 (54.3%) 900–2,400€: 66 (37.7%) > 2,400€: 10 (5.7%) n.d.: 4 (2.3%)	AD: NA, Caregivers: No studies: 6 (3.4%), Primary education: 57 (32.6%), Secondary education: 67 (38.3%), University: 45 (25.7%)	
+Darbà (2021) [27]	(62.0%)	80.4 ± 8.3	General population (hospital records)	NA	NA	NA	NA	
+Durán-Gómez (2020) [20]	AD: 78 (65%), Caregivers: 104 (86.7%)	AD: 73.2 ± 5.6, Caregivers: 50.5 ± 4.2	General population (not institutionalized)	NA	NA	NA	AD: NA, Caregivers: No studies: 7 (5.8%) Primary education: 48 (40%), Secondary education: 42 (35%)m University: 23 (19.2%)	
+García-Escobar (2023) [29]	CU: 21 (50%), MCI: 19 (54.3%), Mild AD: 24 (68.6%)	CU: 71.3 ± 5.5, MCI: 74.5 ± 4.3, Mild AD: 74.3 ± 6.3	General population (Hospital records)	MCI: 35 (100%); 35 (*31.3) Mild AD: 35 (100%); 35 (*31.3) Moderate AD: NA Severe AD: NA	NA	NA	NA	
+Garcia-Ribas (2020) [30]	Caregivers: 30 (71.4%)	Caregivers: ≤30 years: 1 (2.9%) 31–40 years: 5 (11.9%) 41–50 years: 20 (47.6%) 51–60 years: 16 (38.1%) >60 years: 0 (0%)	General population (caregivers and non-caregivers)	AD: MCI: NA, Mild AD: 11 (26.2%), Moderate AD: 8 (19.1%), Severe AD: 23 (54.8%)	AD: Own home: 27 (64.3%), Caregiver home: 1 (2.4%), Other relatives home: 4 (9.5%), Nursing home: 10 (23.8%)	NA	AD: NA, Caregivers: Secondary education: 3 (7.1%), Vocational training: 3 (7.1%), University: 36 (85.8%)	
+Gomez-Gallego (2021) [31]	119 (60.7%)  	Female: 78.1 ± 9.2  	General population (not institutionalized)	NA	NA	NA	NA	
+Gómez Maldonado (2023) [32]	117 (68.8%)	79.1 ± 7.4	Caregivers of AD patients	MCI: NA Mild AD: 24 (14.0%) Moderate AD: 75 (43.9%) Severe AD: 72 (42.1%)	Same dwelling: 144 (84.2%), Own home: 19 (11.1%), Nursing home: 8 (4.7%)	NA	NA	
+Hernández-Padilla (2021) [33]	AD: 149 (58.4%), Caregivers: 218 (85.5%)	AD: Age at recruitment (N, %) ≤ 70 years: 29 (11.4%) 71–80 years: 114 (44.7%) ≥81 years: 112 (43.9%)   Caregivers: 55.35 ± 12.35	Caregivers of patients with AD	NA	NA	NA	AD: NA, Caregivers: No studies: 46 (16.5%), Primary studies: 107 (42%), Secondary studies: 71 (27.8%), University: 36 (13.7%)	
+Khandker (2020) [34]	Overall: 3291 (53.7%), Very mild AD: 312 (47.3%), Mild AD: 1308 (53.0%), Moderate AD: 1426 (54.8%), Severe AD: 245 (60.0%)	Overall: 76.3 ± 8.8, Very mild AD: 71.8 ± 9.4, Mild AD: 75.1 ± 8.7, Moderate AD: 78.1 ± 8.1, Severe AD: 80.2 ± 8.6	General population, including patients with cognitive impairment	MCI: NA, Mild AD: 334 (41.9%), Moderate AD: 386 (48.4%), Severe AD: 78 (9.8%)	Institutionalized Mild AD: 8 (2.4%), Moderate AD: 57 (14.8%), Severe AD: 22 (28.6%)	NA	NA	
+Kishita (2023) [35]	AD: 209 (64.9%), Caregivers: 223 (69.3%)  	AD: 79.9 ± 8.9, Caregivers: 62.28 ± 12.77	Caregivers (family) of patients with AD	NA	NA	NA	NA	
+Luque-Carrillo (2020) [36]	AD: 48 (69.6%), Caregivers: 49 (71%)	AD: 79. 8 ± 7.9, Caregivers: 58.77 ± 11.23	Patients with AD and their caregivers	NA	NA	NA	AD: NA, Caregivers: No studies: 9 (13%), Primary studies: 15 (21.7%), Secondary studies: 14 (20.3%), University studies: 20 (29%), Incomplete studies (secondary or university studies): 11 (15.9%)	
+Macedo (2021) [37]	Overall: 74 (66.6%), CU: 12 (50%), MCI: 15 (68.2%), Mild AD: 12 (50%), Moderate AD: 18 (81.8%), Severe AD: 17 (89.5%)	NA	Geriatric population	MCI: 23 (20.7%), Mild AD: 24 (21.6%), Moderate AD: 22 (19.8%), Severe AD: 19 (17.1%)	NA	NA	NA	
+Ponjoan (2020) [40]	Overall: 599,942 (57.2%), AD: 28,360 (71.9%), Other: 571,582 (56.6%)	Overall: 75.9 ± 7.9, AD: 83.1 ± 6.6, Other: 75.6 ± 7.8	General population (>65 yr)	NA	NA	NA	NA	
+Puig-Pijoan (2022) [42]	CU: 21 (50%), aMCI: NA, Mild AD: 35 (72.9%)	CU: 71.3 ± 5.5, aMCI: NA, Mild AD: 73.7± 6.1	Patients with AD and unimpaired individuals (60-85 yr)	MCI: 35 (100%); 35 (*28%), Mild AD: 48 (100%); 35 (*38.4%) Moderate AD: NA, Severe AD: NA	NA	NA	NA	
+Rosende-Roca (2022) [21]	AD patients: 648 (60.8%), Caregivers: 670 (62.9%)	AD patients: 80.1 ± 7.9   Caregivers: 69.0 ± 12.0	Patients with AD and their caregivers	NA	NA	NA	AD: Primary or lower: 424 (39.8%), Secondary or higher: 641 (60.2%), Caregivers: Primary or lower: 654 (61.4%), Secondary or higher: 411 (38.6%)	
+Ruiz-Fernández (2019) [44]	AD: Early-stage: 60 (55.6%), Middle-stage: 89 (60.5%). Caregivers of patients with early-stage AD: 88 (81.5%), Caregivers of Middle-stage AD patients: 130 (88.4%)  	AD: Early-stage patients: 76.6 ± 8.2, Middle-stage patients: 80.0 ± 6.3,   Caregivers: NA	General population (healthcare records). Patients with AD and their caregivers	MCI: NA, Mild AD: 108 (42.4%), Moderate AD: 147 (57.6%), Severe AD: NA	NA	NA	AD: NA, Caregivers of patients with early-stage AD: No studies: 21.3 (23%), Primary studies: 42 (38.9%), Secondary studies: 30 (27.8%), University: 13 (12%), Caregivers of patients with middle-stage AD: No studies: 12.9 (19%), Primary studies: 65 (44.2%), Secondary studies: 41 (27.9%), University: 22 (15%)  	
+Tortajada-Soler (2020) [45]	Overall: (61%), Non-AD: (53%), AD: (69%)	NA	Patients with AD and controls (>65)	NA	NA	NA	NA	
+Turró-Garriga (2020) [46]	AD: 92 (62.6%), Caregivers: 90 (61.2%)	AD: 78.4 ± 5.9, Caregivers: 65.0 ± 12.9	Caregivers of patients with patients (clinical registries)	NA	Own home: 91.2 %	Household income > 25,000€ per year: 43 (29.5%)	Caregivers: Primary school or lower: 81 (55.1%)	
+
+Disease severity: Disease severity, from MCI to dementia (mild, moderate, and severe), was described in eight publications (Table 5). The distribution of subpopulations varied between studies, with the moderate and severe forms of AD dementia being the most commonly represented (19.1%-57.6% moderate AD; 9.8-54.8% severe AD) [19, 29, 30, 32, 34, 37, 42, 44]. Only two studies included patients with MCI due to AD [29, 42]. One study showed that institutionalization of patients with AD increased as the severity of the disease progressed (2.4% for mild AD, 14.8% for moderate AD, and 28.6% for severe AD) (Table 5) [34].
+
+Epidemiology
+
+Incidence: Three publications reported data on the incidence of AD dementia, two of them at the national level (Spain) [24, 27], and one at a regional level (Catalonia) [40]. The European Prospective Investigation into Cancer and Nutrition (EPIC) Spain Dementia Cohort study included data from the general population aged 30-70 years, recruited between 1992 and 1996, with 20 years of follow-up, including in-hospital or primary care registries. The study specifically comprises data from centers in three provinces of Spain (Gipuzkoa and Navarra in the North and the Region of Murcia in the South), for which there was available information on the incidence of dementia (Figure 2) [24]. This study found that the incidence of AD dementia in people ≥65 was 2.8 per 1,000 inhabitants (5.5 per 1,000 inhabitants after age-standardized rate adjustment), 3.26 per 1,000 person-years (6.20 after age-standardized rate adjustment) in women, and 2.36 (4.59 after adjustment) in men [24]. Another study performed in 2016 in Catalonia with data from the general population primary care registry showed a slightly higher incidence of dementia among people ≥65, estimated as 4.2 per 1,000 inhabitants, 5.6 per 1,000 inhabitants (4.9 after age-sex standardization) in women, and 3.5 per 1,000 inhabitants (3.5 after age-sex standardization) in men [40]. A third study based on records of inpatient and outpatient admissions from a database of hospital discharges in Spain reported a mean national in-hospital incidence of AD dementia of 0.37 per 1,000 inhabitants (mean age: 80.4 years, SD: 8.1) between 2011 and 2016 [27]. This study also provided mean incidence rates by sex: 0.436 per 1,000 inhabitants in women (62.0% of the patients) and 0.294 per 1,000 inhabitants in men [27].
+
+Figure 2 Incidence rates of AD per 1,000 person-years, stratified by age and sex
+
+Incidence of AD in Catalonia in 2016 (red; Ponjoan et al. [40]) and in EPIC-Spain Dementia Cohort between 1992 and 1996 (blue; Andreu-Reinón et al. [24]).
+
+AD: Alzheimer's disease; EPIC: European Prospective Investigation into Cancer and Nutrition
+
+Prevalence: Four publications reported data on the prevalence of AD dementia in people aged ≥65 years (Table 6); one did so in the general population in a region of Spain, while the other three reported it in patients with dementia, with varying inclusion criteria [26, 35, 43]. Ponjoan and colleagues reported an estimated 3.8% (3.3% age-standardized and 3.6% sex-standardized) prevalence of AD dementia in the general population using the Information System for Research in Primary Care (SIDIAP) database [40]. The other three studies evaluated data collected from nursing homes [26] or reported by either healthcare providers [43] or caregivers of patients with dementia [35]; overall, the prevalence of AD dementia ranged from 33.5% to 55.6% [26, 35, 43]. Two articles reported differences by sex, with a higher prevalence in women (3.8%-35.7%) than men (2.4%-26.4%) [26, 40].
+
+Table 6 Prevalence of AD dementia in the specific populations analyzed
+
+AD: Alzheimer's disease; HCP: health care professional; MCI, mild cognitive impairment; NA, not applicable. Data are presented as % (N). *AD% % is not specified.
+
+Author (year)	Geographical area and study population	Setting	Inclusion criteria	Prevalence of AD dementia in the general population	Prevalence of AD dementia in the study population	
+Ponjoan (2020) [40]	Regional: 1,048,956 people registered in SIDIAP*	General population (≥65 years)	AD cases identified by diagnosis code or dementia drug use, excluding cases with other dementia types, recent cerebrovascular disease, or Parkinson’s in individuals aged ≥ 65	Overall: 3.8% (3.1% after age-sex-standardization) (N = 39,448), Women: 4.7% (3.8% after age-sex-standardization), Men: 2.5% (2.4% after age-sex-standardization)	NA	
+Cantón-Habas (2020) [26]	National: 221 125 people without dementia, 96 participants with dementia (of whom 74 subjects had AD)	Geriatric population (nursing homes and one dementia-specific facility)  	People without dementia/AD: Person ≥ 65 years not presenting with a diagnosis of dementia or AD Dementia/AD: Person ≥ 65 years with dementia and/or AD and a score of 5–7 on the Global Deterioration Scale (GDS)	NA  	33.5% (N = 74) Women: 35.7% Men: 26.4%	
+Roth (2023) [43]	National: 449 AD: 187 Vascular dementia: 107 Lewy body dementia: 35 Dementia linked to Parkinson’s disease: 34 Non-etiologic diagnoses of symptoms: 73 Other: 13	Survey of healthcare providers  	Patients with dementia (most of them ≥66 years)	NA  	41.6% (N = 187)	
+Kishita (2023) [35]	National: 322 (attended by caregivers), AD: 179, Other type of dementia: 92	Survey to caregivers (family) of patients with AD	Patients with dementia or related disorders ≥70 years attended by caregivers	NA  	55.6 % (N = 179)	
+
+Mortality: Only one publication reported AD-associated mortality data [27]; specifically, the mean in-hospital AD-associated mortality rate was 9.5% (between 2011 and 2016, at the national level), mainly due to respiratory complications or heart failure [27].
+
+Diagnosis
+
+Clinical assessment instruments. Information about the cognitive tests used for diagnosing AD was reported in eleven publications, which evaluated people with AD and dementia, with data extracted from primary care and hospital registries (Figure 3). The variability in the data was attributed to the heterogeneity in study design. Most of the studied populations presented data of moderate AD dementia and mainly evaluated cognitive status with brief cognitive tests, the most common being the Mini-Mental State Examination (MMSE). This test is a standardized tool, commonly used to grade AD severity, that assesses global cognitive function (score range 0-30), with lower scores indicating greater cognitive impairment. The average MMSE score ranged from 13.9 to 19.4 [21, 29, 31, 36, 37, 40, 43, 46], suggesting that the mild AD population is underrepresented in these studies. The presence and severity of neuropsychiatric symptoms, very common in AD, were mainly evaluated with the Neuropsychiatric Inventory Questionnaire (NPI-Q) and the Psychosocial Support Questionnaire (PSQ); the studies using these questionnaires evaluated only people with mild-to-moderate AD dementia [31, 44, 46]. Several studies showed that the presence of neuropsychiatric symptoms and/or their severity increases with disease progression. Specifically, Ruiz-Fernández and colleagues reported a mean ± SD NPI-Q of 6.9 ± 2.3 and 8.0 ± 2.3 in patients with mild and moderate AD dementia, respectively [44]; Turró-Garriga reported a mean ± SD NPI-Q score of 4.0 ± 3.7 in patients with mild-to-moderate AD [46]; and Gómez-Gallego et al. showed a mean ± SD PSQ score of 16.0 ± 3.5 and 16.8 ± 3.2 in women and men, respectively, in patients with moderate AD [31]. Moreover, seven publications also evaluated the functional impairment associated with cognitive decline in people with AD dementia (Figure 4) using different tests such as the Barthel Index, which assesses the autonomy of patients with AD in activities of daily living [23, 26, 36, 44]. The percentage of patients with total dependency ranged between 40.6% and 61.5% and correlated with disease severity [26, 36]. According to the Barthel Index, only 1.4% of patients had low dependence [36], while 7.3%-49.4% had moderate dependency [26, 36, 44], and 31.3%-74.8% were highly dependent [26, 44]. The most frequently used tool to assess disease severity was the Global Deterioration Scale (GDS), with scores ranging from 4 to 7 [20, 26, 29, 41, 42, 46].
+
+Figure 3 Number of publications reporting cognitive test use with (orange) and without score data (blue).
+
+* Not specified
+
+MMSE: Mini-Mental State Examination; CDR: clinical dementia rating; BDRS: Blessed Dementia Rating Scale; ADAS-cog: Alzheimer’s Disease Assessment Scale–Cognitive Subscale; GPCOG: General Practitioner Assessment of Cognition; CANTAB mobile device test: Cambridge Neuropsychological Test Automated Battery; ANAM: Automated Neuropsychological Assessment Metrics; BEHAVE-AD: Behavioural Pathology in Alzheimer’s Disease Rating Scale
+
+Figure 4 Number of publications reporting functionality and cognitive test use with (orange) and without score data (blue).
+
+AD: Alzheimer’s disease; BDI-II: Beck Depression Inventory; CIRS-G: Cumulative Illness Rating Scale–Geriatric; DS: Dependence scale; GADS: Goldberg Anxiety and Depression Scale; IADL: Katz’s Instrumental Activities of Daily Living Index; MMSE: Mini-Mental State Examination; NPI-Q: Neuropsychiatric Inventory Questionnaire; PHQ-15: Patient Health Questionnaire; PSQ: Psychosocial Support Questionnaire.
+
+Medical exams for differential diagnosis: Two studies reported information about general diagnostic evaluation: one focused on patients with AD attending memory clinics, and the other consisted of a survey examining usual practices of physicians [43, 46]. The most frequently reported clinical assessments were anamnesis and neurological physical examinations (82.8%-89.1%), highlighting the importance of interviews as a first step in the diagnostic workup to evaluate cognitive, neuropsychiatric, and functional symptoms. Other examinations used to a lesser extent during AD diagnostic workup were computed tomography (57.5%-62.6%) or magnetic resonance imaging (MRI) (36.1%-59.4%), as well as laboratory tests for differential diagnosis and detection of treatable/modifiable causes of cognitive impairment (58.5%-71.3%) [43, 46].
+
+AD biomarkers: Only one study reported the use of specific AD biomarkers (amyloid positron emission tomography (PET)) in clinical practice (28.3%), as reported by specialists participating in a survey [43]. This study also reported that 27.3% of specialists used CSF biomarkers in their clinical practice [43]. Other studies examined CSF biomarkers, based on the AT(N) framework, in a research context [29, 36].
+
+Patient journey
+
+Six publications reported data related to the patient journey [21, 25, 30, 32, 43, 46]. The time to final diagnosis of AD dementia from the onset of symptoms was described in two studies as under six months (26.2% of the patients), one to two years (38.1%), and more than two years (28.6%) [30, 32]. The diagnosis was carried out mainly by neurologists (78.6%) [25, 30], followed by geriatricians (9.5%) and psychiatrists (2.4%) [30, 43]. Moreover, the follow-up appointments for patients with AD attending memory clinics were conducted by primary care physicians (70.1%) and neurologists (91.8%), with 63.3% of the cases involving additional neuropsychological assessments [46]. One publication indicated that the first medical consultation for symptoms of cognitive impairment or cognitive complaints was made by the patients or their families (62.4%), followed by healthcare professionals (36.3%) (Table 7) [43]. As a result of the medical consultation, 43.9% of patients received a diagnosis, and 25.1% were referred to another specialist for further testing or diagnosis (Table 7) [43].
+
+Table 7 Patient journey during AD in Spain
+
+NA: not applicable/not available; AD: Alzheimer's disease; PCP: primary care physician; Unless specified, data are presented as N (%).
+
+Author (year)	Time to first reported symptoms to diagnosis	Specialty for diagnosis; N (%)	Specialty for follow-up	
+Cámara-Calmaestra (2023) [25]	NA	Neurologists	NA	
+Garcia-Ribas (2020) [30]	6 months–1 year: 11 (26.2%), 1–2 years: 16 (38.1%), ˃2 years: 12 (28.6%), Unknown: 3 (7.1%)  	PCPs: 4 (9.5%), Neurologist: 33 (78.6%), Geriatrician: 4 (9.5%), Psychiatrist: 1 (2.4%)	NA	
+Gómez Maldonado (2023) [32]	Years (Mean ± SD) 1.8 ± 2.3	NA	NA	
+Roth (2023) [43]	NA	PCP: 53 (35.8%), Other specialist: 134 (44.5%)	NA	
+Turró-Garriga (2020) [46]	NA	NA	70.1% primary care, average 1.8 visits. 91.8% other specialist appointments: neurologist. Neuropsychological assessments were conducted in 63.3% of these visits.	
+
+Comorbidities: Nine publications described the presence of comorbidities in the AD population [19, 20, 24-27, 34, 40, 45]. Interestingly, the prevalence of comorbid conditions increased with the severity of the disease [34]. The mean number of concomitant conditions suffered by AD patients varied between 1.88 and 3.11 [19, 20]. The most frequent comorbidities were hypertension (32.5%-69.7%) [24, 40], heart diseases (including myocardial infarction: 0.5%-11.8% [24, 34], cardiac dysrhythmias: 13.89% [27], congestive heart failure: 3.07%-11.8% [27, 34, 40], and coronary artery disease: 10.1% [40]), other cardiovascular diseases (6.9%-61.4%) [25, 34, 45], and cerebrovascular disease (1%-16.9%) [24, 25, 40, 45]. Hyperlipidemia (25.0%-56.1%) [27, 35], diabetes mellitus (11.5-31.6%) [24, 25], and depression (8.6%-28.5%) [27, 40] were also reported. Table 8 includes two studies that examine comorbidities in populations with and without AD and one study that shows comorbidities according to AD severity; hyperlipidemia, hypertension, and heart disease are the most frequent comorbidities among patients with AD [25, 34, 45].
+
+Table 8 Comorbidities
+
+Comorbidities presented as N (%)
+
+AD: Alzheimer’s disease, MCI: mild cognitive impairment, NA: not applicable/not available; TIAs: transient ischemic attacks
+
+      Author (year)	Disease severity	Cardiometabolic diseases	Others	
+Diabetes mellitus	Hyperlipidemia	Hypertension	Cerebrovascular disease	Heart disease	Other cardiovascular diseases	Depression	
+Cámara-Calmaestra (2023) [25]	Total	46 (23.7%)	NA	NA	NA	NA	108 (55.7%)	28 (14.4%)	
+AD	36 (31.6%)	NA	70 (61.4%)	21 (18.4%)	
+Non-AD	10 (12.5%)	NA	38 (47.5%)	7 (8.8%)	
+Khandker (2020) [34]	Total	249 (29.7%)	NA	517 (61.8%)	Stroke 72 (8.6%), TIAs 52 (6.2%), Cerebrovascular disease: 76 (9.1%)	Myocardial infarction: 63 (7.5%), Congestive heart failure: 56 (6.7%)	Peripheral vascular disease: 71 (8.5%)	226 (27.0%)	
+MCI	9 (18.8%)	20 (41.7%)	Stroke 5 (10.4%), TIAs 2 (4.2%), Cerebrovascular disease: 3 (6.3%)	Myocardial infarction: 3 (6.3%), Congestive heart failure: 2 (4.2%)	Peripheral vascular disease: 6 (12.5%)	11 (22.9%)	
+Mild AD	89 (26.9%)	182 (55.0%)	Stroke 22 (6.6%), TIAs 16 (4.8%), Cerebrovascular disease: 22 (6.6%)	Myocardial infarction: 17 (5.1%), Congestive heart failure: 17 (5.1%)	Peripheral vascular disease: 23 (6.9%)	82 (24.8%)	
+Moderate AD	123 (32.2%)	261 (68.3%)	Stroke 37 (9.7%), TIAs 29 (7.6%), Cerebrovascular disease 43 (11.3%)	Myocardial infarction: 34 (8.9%), Congestive heart failure: 28 (7.3%)	Peripheral vascular disease: 32 (8.4%)	107 (28.0%)	
+Severe AD	28 (36.8%)  	54 (71.1%)	Stroke 8 (10.5%), TIAs 5 (6.6%), Cerebrovascular disease: 8 (10.5%)	Myocardial infarction: 9 (11.8%), Congestive heart failure: 9 (11.8%)	Peripheral vascular disease: 10 (13.2%)	26 (34.2%)	
+Tortajada-Soler (2020) [45]	AD group	19%	45%	NA	1%	31%	Peripheral vascular disease: 21%, Atrial fibrillation: 7%	27%	
+Non-AD	20%	39%	5%	26%	Peripheral vascular disease: 34%, Atrial fibrillation: 11%	26%	
+
+Caregivers
+
+Ten publications included information about caregivers [19-21, 30, 32, 33, 36, 41, 44, 46]. In all the studies, caregivers were informal, mainly (69.05%-93.5%) immediate family members, 61.2%-88.4% were women, 56%-70.1% were daughters/sons, and 26.7%-55.1% were partners [19, 32, 33, 36, 44, 46]. In many cases, the caregivers cohabited with the patients (56.7%-86.9%) [19, 20]. The education level of caregivers varied widely, with most having primary or secondary education (49.2%-75%), a smaller proportion having university studies (12%-29%; except one study reporting 85.8%), and a few having no formal education (3.4%-23%). Moreover, the reported percentage of caregivers with active employment was 21.8%-32.5% [19, 20, 41], except in one study conducted among employees of a pharmaceutical company [30].
+
+Caregiver burden: Information about the caregiver burden was collected from six studies [19, 20, 30, 32, 36, 46]; five reported the time spent by the caregiver attending to the patient, ranging from 71.4 to 94.4 hours/week [19, 20, 30, 32, 46]. One article reported that most caregivers did full-time caring for the patient with AD [19], and three studies showed that the duration of caring varied between 40.9 and 79.1 months [19, 20, 36]. The caregiver's work/social life was partially or very affected in 42.9% and 14.3% of the cases, respectively [30]. Other data were only reported in individual studies, such as the treatment needed to cope with care (required by 33.7% of caregivers) [19], the use of medication due to caring tasks (in 50.3% of caregivers) [32], the mean free available time (10.7 ± 6.8 hours) [20], and the mean subjective burden (61.7% of caregivers reporting a heavy care burden score) [20]. None of the studies classify the caregiver burden according to AD severity.
+
+Caregivers’ HRQoL: Caregivers’ mental health and ability to manage care situations were reported in twelve publications [19-21, 30-33, 36, 38, 41, 44, 46] (Table 9). Different HRQoL questionnaires showed that caregivers were in a below-average health status (30.3-49.5 Short Form-36 Health Survey Questionnaire (SF-36)) [19, 20, 41]. Indeed, questionnaires used to evaluate neuropsychiatric symptoms, mental health, and ability to manage care revealed an impact of caregiving in terms of anxiety or depression (40%-75%) [19-21], sleeping problems (28%-96%), and pain/discomfort (56%-95%) (Table 10).
+
+Table 9 Caregiver HRQoL, mental health, and ability to manage care
+
+AD: Alzheimer’s disease; HRQoL: health-related quality of life; Alzheimer’s Disease Knowledge Scale (ADKS) is expressed as mean ± SD; the Beck Anxiety Inventory (BAI) score is expressed as N; the Beck Depression Inventory-Fast Screen (BDI-FS) score is expressed as N (%); The caregivers’ reaction scale is expressed as mean ± SD; the caregivers’ strain index score is expressed as mean ± SD; CASP-19 (quality of life questionnaire in older adults) is expressed as mean ± SD; The Connor-Davidson Resilience Scale (CD-RISC) is expressed as a mean ± SD; the CD-RISC-10 is expressed as a mean ± SD; CI 95%; The Coping Orientations to Problems Experienced (COPE28) Questionnaire is expressed as a mean ± SD; DUKE UNC-11 (Perceived Social Support Questionnaire) is as mean ± SD; EuroQol-5 Dimension (EQ-5D) is presented as a mean; The ESTE-II Scale is expressed as mean ± SD; the Goldberg Anxiety and Depression Scale (GADS) is expressed as mean ± SD; GC: accompanying control group; Goldberg's General Health Questionnaire (GHQ28) is expressed as mean ± SD; GI: psychotherapeutic group without active post-intervention follow-up; GIS: psychotherapeutic group with active post-intervention follow-up; Min-Max; MOS Social Support Survey (MOS-SSS) is expressed as a mean ± SD; Neuropsychiatric Inventory Questionnaire (NPI-Q) is expressed as mean (female-male) and N (%); The Orientation to Life Questionnaire (OQL-13) is expressed as a number of points; QoL: quality of life; the Revised Memory and Behavior Checklist (RMBC) is expressed as mean ± SD; the Rosenberg Self-Esteem Scale (RSES); the Short Form-36 Health Survey Questionnaire (SF-36) is expressed as mean ± SD; the Satisfaction Life Scale (SWLS) is expressed as mean ± SD; and the Zarit Burden Inventory (ZBI).
+
+Author (year)	HRQoL questionnaire	Score	
+Casal Rodríguez (2019) [19]	EQ-SD	0.75	
+Durán-Gómez (2020) [20]	SF-36	30.3 ± 5.4 (Mean ± SD)	
+ZBI	60.7 ± 13.7 (Mean ± SD)	
+CD-RISC	69.2 ± 14.1 (Mean ± SD)	
+MOS-SSS	74.3 ± 15.3 (Mean ± SD)	
+Garcia-Ribas (2020) [30]	SWLS	26.8 ± 5.6 (Mean ± SD)	
+BDI-FS	1.6 (2.6) (N (%))	
+ADKS	22.1 ± 2.9 (Mean ± SD)	
+Caregivers’ reactions scale	26.8 ± 20.2; 0–74 (Mean ± SD; CI 95%)	
+RMBPC	36.4 ± 25.7; 0–92 (Mean ± SD, CI95%)	
+Gomez-Gallego (2021) [31]	NPI symptoms	Delusions: 1.1–0.57, Hallucinations: 0.78–0.29, Agitation: 0.67–0.29, Depression: 1.11–0.57, Anxiety: 1.00–0.29, Elation: 0.44–0.29, Apathy: 0.43–0.43, Disinhibition: 0.56–0.86, Liability: 0.78–0.29  (Mean Female–Mean Male)	
+NPI subscales	Mood: 2.89–1.14, Agitation: 2.67–1.43, Psychosis: 1.89–0.84, Frontal: 2.22–1.85 (Mean Female–Mean Male)	
+Gómez Maldonado (2023) [32]	Caregiver Strain Index	8.9 ± 3.1 (Mean ± SD)	
+Hernández-Padilla (2021) [33]	GHQ-28	30.8 ± 5.8 (Mean ± SD)	
+Caregiver Strain Index	7.6 ± 3.2 (Mean ± SD)	
+DUKE-UNC-11	35.7 ± 10.0 (Mean ± SD)	
+Luque-Carrillo (2020) [36]	ESTE-II scale	8.4 (4.3)	
+BAI	11.1 (9.5) [N (%)]	
+BDI-FS	8.3 (7.3) [N (%)]	
+ZBI	29.2 (14.0) [N (%)]	
+Mariezcurrena (2020) [38]	COPE28	34.2 (8.0) [N (%)]	
+ZBI	39.4 ± 14.2; 36.1–42.7 (Mean ± SD; CI95%)	
+CD-RISC-10	 24.7 ± 7.3; 23.0–26.3 (Mean ± SD, CI95%)	
+Poudevida (2022) [41]	SF-36	QoL, physical health (Mean ± SD): GI + GIS 52.4 ± 7.7 GC 50.9 ± 7.32 QoL, mental health (Mean ± SD): GI + GIS 49.5 ± 10.0 GC 48.7 ± 9.5 GI +GIS 52.4 ± 7.7 GC 50.9 ± 7.32	
+CASP-19	GI + GIS: 38.2 ± 8.4 (Mean ± SD) GC: 37.9 ± 8.0 (Mean ± SD)	
+GADS	GI + GIS: 3.3± 3.7 (Mean ± SD) GC: 2.3 ± 2.71 (Mean ± SD)	
+ZBI	GI + GIS: 54.6 ± 14.0 (Mean ± SD) GC: 50.2 ± 13.0 (Mean ± SD)	
+CD-RISC	GI + GIS 68.5 ± 13.6 (Mean ± SD) GC 67.3 ± 11.6 (Mean ± SD)	
+DUKE-UNC-11	GI + GIS 39.3 ± 10 (Mean ± SD) GC 40.3 ± 8.6 (Mean ± SD)	
+Rosende-Roca (2022) [21]	NPI-Q score	Agitation/aggression: 122 (11.5%), Hallucinations: 95 (8.9%), Anxiety: 528 (49.6%), Apathy/indifference: 677 (63.6%), Aberrant motor behavior: 73 (6.9%), Delusions: 197 (18.5%), Depression/dysphoria: 429 (40.3%), Disinhibition: 72 (6.8%), Elation/euphoria, 14 (1.3%), Appetite and eating disorders: 154 (14.5%), Irritability/lability: 565 (53.1%), Sleep and night-time behaviors: 303 (28.5%) (N (%))	
+ZBI	51.9 (Mean)	
+Ruiz-Fernández (2019) [44]	DUKE-UNC-11	AD-Early-Stage: 36.7 ± 10.0* (Mean ± SD) AD-Middle-Stage: 35.06 ± 10.0** (Mean ± SD) *p value <0.05 **p value <0.01	
+Turró-Garriga (2020) [46]	OQL-13	73.3 (Mean)	
+
+Table 10 Impact of caregiving for a patient with AD
+
+NA: not applicable/not available; AD: Alzheimer's disease
+
+Author (year)	Symptoms reported by caregivers	
+Sleeping problems	Pain and related symptoms	Psychological	
+Behavioral	Emotional	
+Casal Rodríguez (2019) [19]	NA	Pain/discomfort: 56.8%	NA	Anxiety, depression: 72.8%	
+Durán-Gómez (2020) [20]	Sleep disorders: 95.8%	Pain: arms, legs, and joints: 95%, Back pain: 73.3%, Headaches: 72.5%, Fatigue: 90.9%, Gastrointestinal symptoms: Constipation or diarrhea: 68.4% Stomach pain: 57.5%	NA	Anxiety: 63.3%, Depression: 62.5%	
+Rosende-Roca (2022) [21]	Sleep and night-time behaviors: 28.5%	NA	Psychotic symptoms: Hallucinations: 8.9%, Delusions: 18.5%, Behavioral symptoms: Agitation/aggression: 11.5%, Disinhibition: 6.8%, Elation/euphoria: 1.3%, Irritability: 53.1%, Others: Appetite and eating disorders: 14.5%, Aberrant motor behavior: 6.9%	Apathy: 63.6%, Anxiety: 49.6%, Depression: 40.3%	
+
+Resource Utilization and Costs
+
+Healthcare resource use: Eight publications reported data about the use of resources by patients with AD [25, 27, 28, 32, 34, 39, 43, 45, 46]. Most of the information regarding hospital resource use concerned admission rates [27, 34, 46], which increased as the disease progressed, as shown by Khandker et al. (regression analysis: mild AD: 0.2; moderate AD: 0.3; severe AD: 0.5) [34], and was independent of age and the presence of comorbidities. Additionally, Darbà and colleagues noted that 10.5% of all hospital admissions were due to dementia. The medical specialties accessed were internal medicine, neurology, geriatrics, and psychiatric services (46.2%, 19.1%, 10.8%, and 10.6%, respectively) [27]. Furthermore, Turró-Garriga and colleagues found that 19.1% of patients with AD sought emergency care, and 6.8% were hospitalized, with 70.1% attending outpatient consultations and 100% seeking specialist care over one year [46]. Finally, as reported by only one study evaluating patients with mild-to-moderate AD (GDS score of 4-6) who attended memory clinics, 15% and 14.9% of participants used domiciliary care and daycare centers, respectively [46]. No data were reported on the use of hospice care, palliative care, or other end-of-life services in the included studies, indicating a lack of evidence regarding service utilization at later disease stages. Regarding treatments and medical procedures for patients with AD, the mean number of prescribed medicines ranged from 5.8 to 7 [25, 39, 45] Two studies reported the prevalence of prescribed medication for AD: 52.6% of patients were prescribed acetylcholinesterase inhibitors in one study with patients with dementia institutionalized in residential care facilities [39]; in the other study, conducted in a regional healthcare area, 3.8% of patients aged 75-79 years and 7.9% of those aged ≥85 years received treatment [28].
+
+Total costs: One recent national study estimated the total cost of direct healthcare, non-healthcare, and social care costs, as well as indirect costs, between December 2021 and February 2022, as €42,336.4-€70,445.1 per patient/year, depending on the method used to estimate non-healthcare costs. This study also reported that the direct cost per patient/year increased with AD severity. Using the proxy good method with the price per hour of a home employee (HE), the direct non-healthcare costs (mean ± SD) (including informal care cost) were: mild AD: €25,725.8 ± €26,116.8; moderate AD: €42,315.9 ± €24,329.3; and severe AD: €47,894.6 ± €34,896.7 [32]. However, the direct non-healthcare costs (mean ± SD) estimated using the price per hour of home help service (HHS) were higher: mild AD: €42,014.2 ± €42,677.1; moderate AD: €72,676.9 ± €45,683.4; and severe AD: €77,597.2 ± €59,260.2 [32]. There was no cost estimation for patients with MCI. This study reported that direct non-healthcare costs accounted for 84.6%-90.7% of total costs, followed by direct healthcare costs of 6.1%-10.0% and social care costs of 2.8%-4.6%. Indirect costs represented 0.5%-0.8% of total costs due to labor productivity losses resulting from reduced working hours or workdays because of the disease.
+
+Direct healthcare costs: Two studies estimated the total direct cost per patient as €3,647.1-€4,969/year, evaluating data from 2011-2016 [27] and from December 2021 to February 2022 [32]; costs increased with disease progression (mean ± SD) (mild AD: €3,253.6 ± €7,349.8; moderate AD: €2,836.0 ± €2,840.4; severe AD: €4,623.2 ± €7,815.0) [32]. The main components of direct costs were hospitalizations, medical tests, visits to specialists, and emergency services. Extended hospital stays increased healthcare expenses from €1,040.7 [32] to €5,051 [27] per patient and year. Additionally, two studies showed that prolonged hospitalization also elevated costs in tests, specialist visits (mainly internal medicine services, €2,107.2 [46] to €5,531 [27] per patient and year), emergency services (€1,276.8 [46] to €5,057 [27] per patient and year), scheduled admissions, and readmissions (Table 11). Furthermore, one study reported increased direct healthcare costs mainly related to pharmacological costs (€862.7 per patient and year), outpatient visits (€644.3 per patient and year), palliative care (€489.2 per patient and year), and emergency services (€429.3 per patient and year) [32].
+
+Table 11 Direct healthcare costs
+
+NA: not applicable/not available; €: Euros; Emergency services, scheduled admission, and readmission are expressed as mean (€). ‡Calculated data from the reported €/month and patient value in Turró-Garriga (2020) [47].
+
+Direct healthcare costs	National: Darbà (2021) [27]	National: Gómez Maldonado (2023) [32]	Regional: Turró-Garriga (2020) [46]	
+Total direct healthcare costs (€ per patient and year)	4,818–5,393 (mean for study period: 4,969)	3,647.1 ± 6,086.3	NA	
+Outpatient visits (€ per patient and year)	NA	644.3 ± 598.6	NA	
+Patients deceased during the admission (€)	5,580 (≤ 7 days of hospital stay), 6,197 (> 7 days of hospital stay)	NA	NA	
+Medical care (€ per patient and year)	18,074 (≤ 7 days of hospital stay) 58,686 (> 7 days of hospital stay)	93.1 ± 234.5	NA	
+Pharmacological costs (€ per patient and year)	NA	862.7 ± 702.5	NA	
+Specialists	€ per patient and year: 17,895 (≤ 7 days of hospital stay), 19,175 (> 7 days of hospital stay)	NA	€ per patient and month: 175.6 (‡€ per patient and year: 2,107.2)	
+Emergency services	€ per patient and year: 4,653 (≤ 7 days of hospital stay), 5,057 (>7 days of hospital stay)	€ per patient and year: 429.3 ± 635.6	€ per patient and month: 106.4 (‡€ per patient and year: 1,276.8)	
+Hospitalizations	€ per patient and year: 4,626 (≤ 7 days of hospital stay), 5,051 (> 7 days of hospital stay)	€ per patient and year: 1,040.7 ± 3714.7	€ per patient and month: 2,067.7 (‡€ per patient and year: 24,812.4)  	
+Palliative care (€ per patient and year)	NA	489.2 ± 2979.7	NA	
+
+Direct social care and non-healthcare costs. Social care, understood as non-medical support services that assist people with AD in daily living and maintaining independence, and non-healthcare costs are summarized in Table 12. The direct social care costs (mean ± SD) were estimated at €1,957.1 ± €2,815.5 per patient and year. These costs were associated with dependence and the psychological symptoms of patients with AD and ranged from €791.9 ± €1,444.7 per patient and year in mild AD to €2,372.8 ± €3,208.5 per patient and year in severe AD [32]. Direct non-healthcare costs (mean ± SD), presumably assumed by patient and family, were €36,364.8 ± €27,241.8 per patient and year (HE) and €64,473.5 ± €49,954.3 per patient and year (HHS). Direct non-healthcare costs also depended on AD progression and ranged from €21,680.0 ± €21,339.2 in mild AD to €40,026.2 ± €31,420.1 per patient and year in severe AD [32]. Most of the direct non-healthcare costs were due to informal care (€29,231.5 ± €24,350 per patient and year (HE), and €57,340 ± €47,765.4 per patient and year (HHS)), professional care, costs related to housing adaptation, and out-of-pocket expenses [32]. Additionally, two studies reported data about day centers, where costs ranged €1,758.9-€4,845.6 per patient and year [32, 46].
+
+Table 12 Direct non-healthcare and social care costs per patient
+
+HE: When direct non-healthcare costs include informal care costs estimated with the proxy good method, using the price per hour of a HE as a proxy; HHS: when direct non-healthcare costs include informal care costs estimated with the proxy good method, using the price per hour of HHS. ‡ Calculated data from the reported €/month value in Turró-Garriga (2020) [47]. 
+
+HE: home employee; HHS: home help service, NA: not applicable/not available; €: euros
+
+Direct non-healthcare and social care costs	National: Gómez Maldonado (2023) [32]	Regional: Turró-Garriga (2020) [46]	
+Direct social care costs	Total direct social care costs (€/year)	1,957.1 ± 2,815.5	NA	
+Nursing homes (€/year)	198.2 ± 1,245.4	NA	
+Day-care centers (€/year)	1,758.9 ± 2,660.3	4,845.6	
+Domiciliary care (€/month)	NA	322.5	
+Other social care resources (€/month)	NA	164.4	
+Direct non-healthcare costs	Total Direct NON-healthcare costs (€/year)	36,364.8 ± 27,241.8HE 64,473.5 ± 49,954.3HHS	NA	
+Informal care (€/year)	29,231.5 ± 24,350.4HE 57,340.1 ± 47,765.4HHS	NA	
+Professional care (€/year)	3,450.5 ± 6,888.5HE, HHS	NA	
+Caregiving time (€/month)	NA	842.8	
+Housing adaptations (€/year)	1,653.5 ± 4,280.2HE, HHS	NA	
+Orthopedic devices (€/year)	525.1 ± 1,288.6 HE, HHS	NA	
+Out-of-pocket expenses (€/year)	1,278.9 ± 1,668.2 HE, HHS	NA	
+Transportation (€/year)	225.3 ± 495.3 HE, HHS	NA	
+Basic activities of daily living (€/month)	NA	420.5	
+Instrumental activities of daily living (€/month)	NA	642.5	
+
+Indirect costs: Indirect costs (mean ± SD) at the national level related to labor productivity losses of patients with AD were estimated to be €367.4 ± €3386.8 (per patient and year) from a questionnaire aimed at informal caregivers [32]. This study included information on labor productivity losses due to the disease, as well as informal caregivers’ labor productivity losses due to caring for patients with AD. Patients cared for in this study had an average age of 79 years, with stages ranging from mild to severe AD dementia; MCI and early-onset AD were not included. Caregivers had an average age of 54-61 years. The earnings lost by the working patients due to sick leave or disease-related work absence were estimated as €15.32 and €17.08 per regular working hour for the women’s and men’s average wages, respectively. Indirect costs due to labor productivity loss also increased with disease severity and were €872.5 ± €5197.8 per patient per year in patients with severe AD [32]. Moreover, the earnings lost by the working patients because of reduced working hours or recurrent days of absence associated with AD were estimated using the national average hourly wage, by sex, employment type, and reduced or lost working hours. These losses were higher in men than women (average wage per year of €31,408.56 vs. €24,934.54, respectively). Additionally, the mean number of effective work hours per week was 43.0 and 38.0 hours/week for the self-employed men and women, respectively, and 37.7 and 33.3 hours/week for employed men and women, respectively.
+
+Discussion
+
+This systematic review provides a comprehensive overview of the epidemiology, diagnosis, patient journey, humanistic and caregiver’s burden, resource utilization, and costs of AD in Spain based on evidence published between January 2019 and January 2024. We included 26 studies with variable designs, disease stages, healthcare settings, and temporal and geographic scopes. Patients and caregivers included in these studies ranged from 69 to over 1,000,000 people, with a median size of approximately 150.
+
+Incidence and Prevalence
+
+Results suggest that current studies are insufficient to accurately determine the prevalence and incidence of AD in Spain. Evidence suggested significant underdiagnosis of MCI due to AD, particularly in primary care. In our SRL, the incidence of AD varies. This variability may be attributed to the period of analysis (1992-1996 vs. 2011-2016), the healthcare setting (medical reports or in-hospital incidence), and the geographical scope (national or regional). Increased life expectancy and changes in the diagnostic work-up could also explain this variability. The incidence reported from the SIDIAP database might be lower [40], as it was estimated in the general population with generic syndromic diagnoses. In contrast, other national studies included an older, institutionalized population presenting cognitive symptoms and multiple diseases [24, 27]. The observed incidence in the SIDIAP database (4.2 per 1,000 inhabitants in the population aged over 65) [40] contrasts with the average European incidence (11.08 per 1,000 inhabitants) [47]. This discrepancy may stem from an underdiagnosis of AD in Spain. Additionally, in individuals aged 80 and older, although cognitive impaired cases may be higher, etiological diagnosis often remains incomplete, which may be a result of few referrals to specialists for a definitive diagnosis, leading to a lack of clarity regarding the underlying cause of cognitive decline.
+
+This review also highlights variability in AD prevalence reported in the included studies. The variability observed between prevalence estimates derived from large population-based databases and those reported by specialist-based registries suggests that epidemiological figures for AD are strongly shaped by the underlying data source and the diagnostic pathways used to identify cases [40, 47-49]. Population-based databases, particularly those drawing on administrative or primary care records, are useful for describing the overall burden of AD at the population level, but they are less likely to capture early-stage or etiologically defined cases. Specialist registries, by contrast, usually reflect more selected patient groups, most often assessed in memory clinics, where broader diagnostic workups are available and diagnostic certainty is consequently higher. These differences do not arise solely from methodological choices. They are also influenced by contextual factors such as socioeconomic status, educational level, and differences between rural and urban settings, as well as by unequal access to specialized services capable of completing full etiological assessments. Taken together, these factors affect both the timing of diagnosis and subsequent care pathways, including the use of residential facilities or day care services, which in turn increases the likelihood that individuals with AD are identified and recorded in healthcare databases [50-53].
+
+The Spanish Society of Neurology (SEN) has highlighted the lack of adequate national records of cognitive impaired and AD cases and determined the epidemiology of AD and MCI due to AD in Spain, based on prevalence rates previously estimated by Gustavsson et al. (2023) [54]. According to these estimates, prevalence rates were 2.7% for ages 60-64, 3.8% for ages 65-69, and 5.2% for ages 70-74 [2]. In contrast, a recent study in the Basque Country, which focused on the validation of brief cognitive tests to diagnose MCI, reported a 23.10% prevalence of different CI stages, from MCI to dementia of any etiology, among individuals over 60. This finding reflects data from the general population rather than a specific cohort [55] and is much higher than the prevalence reported by the SEN [2]. Specifically, this population was assessed using the Cardiovascular Risk Factors, Aging, and Dementia (CAIDE) index ≥ 9, which reached 33.46%. Therefore, the information of this study reflects a population-level prevalence within a sample with an increased risk of cognitive impairment.
+
+Most studies that were reviewed here included populations aged over 65. The mean age of patients with AD dementia is 70-80 years. The time to diagnosis ranges from six months to two years, and women are more affected than men [25, 30]. It should be noted that the first symptoms of MCI are often underrecognized, frequently misattributed to normal aging. Furthermore, there is a lack of data on the mean age at diagnosis, which would be valuable for understanding disease progression and early detection. The SEN has pointed out that progressive aging of the population and increased life expectancy will impact the number of cases of MCI and AD in the coming decades [7]. The development of better diagnostic practices and tools, including the refinement of brief cognitive screening tests, as well as the potential application of digital biomarkers, will also improve the detection of AD [56]. Currently, population-based studies on AD are limited and mainly conducted in geriatric centers, where advanced stages are more prevalent [25, 26, 34, 46]. This limits our understanding of the true prevalence of AD in Spain, particularly in its early stages. The scarce information makes it harder to study the early stages of the disease, which in turn delays progress in early diagnosis and the development of treatment strategies.
+
+Mortality
+
+In 2023, the Spanish National Statistics Institute estimated 21,084 deaths due to dementia (representing the fourth most common cause of death) and 13,172 deaths due to AD in Spain (3.03% of the total number of deaths, the seventh cause of death) [57]. These figures likely underestimate the true mortality, as AD and dementia are often not recorded as the primary cause of death. Mortality data were very scarce in the studies analyzed in this review; only one study reported the mortality rate (9.5%), which was related to hospitalizations [27]. In this study, Darbà and colleagues observed that mortality was mainly due to respiratory problems and heart failure [27]. However, determining the immediate cause of death may be subject to bias, as respiratory infections are common in clinical contexts, and heart failure is often an outcome induced by other underlying factors. Moreover, the studies included in this SRL suggest that AD usually coexists with other comorbidities, such as cardiovascular risk factors and cerebrovascular diseases [19, 20, 24-27, 34, 40, 45], which may directly impact survival and/or worsen dependency.
+
+Diagnosis
+
+The predominance of moderate-to-severe AD dementia suggests a delayed diagnosis, which results in a lower detection of MCI. The variability in the study settings, mainly conducted in residential care facilities, does not capture the full spectrum of AD dementia, which highlights the lack of an adequate national registry for such data. Currently, the diagnosis of AD dementia is a sequential process, from syndromic diagnosis, based on semiology and findings in neurological-neuropsychological examination, to the determination of the specific biological fingerprint of some diseases such as AD [2]. However, in Spain, there is considerable variability in diagnostic and treatment processes across regions, and diagnostic tests are not uniformly available [58]. This SLR reveals that the MMSE test is the most frequently used diagnostic tool despite its suboptimal performance in detecting MCI and identifying atypical presentations of AD dementia in initial dementia stages [59]. The techniques most frequently used for etiological diagnosis were structural neuroimaging techniques, such as computed tomography and MRI, along with general blood tests [43, 46].
+
+The low use of CSF biomarkers and PET in the studies included in this SRL may be due to the inclusion of subjects at more advanced stages, where these approaches are not clinically indicated in routine care [2, 58, 60]. This underscores the need for better diagnostic processes, transitioning from syndromic to etiological diagnosis, especially in early stages. Early diagnosis and monitoring with these tests could help slow AD by detecting molecular changes and targeting disrupted pathways [61]. In this context, the future applicability of plasma biomarkers offers a promising alternative that will facilitate the early diagnosis of AD [2, 62, 63]. In this regard, p-Tau217 has demonstrated a high diagnostic accuracy with precise individual prediction in a real-world clinic cohort [29, 42]. Additionally, once DMTs become available, APOE genotyping will be necessary for eligible individuals, despite not currently being recommended in routine clinical practice [64].
+
+Patient Journey
+
+Information about the patient journey is also scarce. Neurologists are the specialists primarily responsible for the diagnosis of AD, which spans several months to more than two years from symptom onset [30, 32]. However, most of the studies have included populations in late stages of dementia, and early dementia symptoms may have been misattributed to age-related cognitive decline. Other specialists involved in AD diagnosis included primary care physicians, geriatricians, and psychiatrists [30, 43]. A systematic review found barriers along the patient journey, such as resistance to seeking care among patients with AD [65]. Thus, promoting studies focusing on the outcomes and experiences reported by patients with AD in Spain could be valuable in helping improve the patient journey.
+
+Caregivers
+
+Most caregivers of patients with AD are informal, primarily women (more than 50%) [21], immediate family members, and cohabit with the patients [19, 20]. The burden of caregiving impacts multiple health dimensions. Caregivers face considerable emotional and physical strain, mainly anxiety and depression [19-21]. Disrupted sleep, highlighted in several studies, directly impacts caregivers' quality of life and is a modifiable risk factor for multiple diseases [20, 21]. A recent systematic review evaluated the interventions that could reduce caregiver burden in various dementia diseases; the study suggested that individual therapy ameliorates caregivers’ stress, which can be further improved in group therapy by enabling interactions with others in the same situation [66]. Therefore, there is a need to improve support systems for caregivers, including advisory services and psychological support [58].
+
+Healthcare Resources and Costs
+
+Most information on healthcare resource utilization indicates that service utilization, particularly hospital admissions, increases as AD progresses, reflecting increasing clinical complexity at older ages [27, 34, 46]. Across studies, non-healthcare and social care needs emerged as major drivers of overall costs, largely due to the burden of dependence, behavioral symptoms, and the extensive reliance on informal caregiving [32]. Healthcare costs were mainly associated with hospital care, diagnostic procedures, specialist visits, and emergency services [27, 32, 46], while additional support, such as domiciliary or day care services, was used by only a subset of patients [46]. Indirect costs related to lost productivity for both patients and caregivers also contributed meaningfully to the overall economic burden [32]. This is in line with recent data showing that 80% of the total direct non-healthcare costs and total costs of AD are due to informal care and non-medical direct costs, and are significantly higher in moderate-to-severe AD dementia [67]. Additionally, approximately 3%-4% of adults aged ≥65 years in Spain remain employed according to the National Institute of Statistics, reflecting the limited contribution to the socioeconomic burden of the disease [68]. Thus, early diagnosis and treatment could contribute to a better organization of resources and optimization of care, which could reduce the economic impact on the healthcare system, patients, and their families/caregivers. Additionally, multimodal non-pharmacological interventions, supported by the Dependency Law [69] or the FINGER program [70], which focus on lifestyle-based interventions to reduce the risk of CI or dementia, may contribute to slowing cognitive decline. These interventions could be integrated into the universal healthcare system so that patients can access DMTs and improve their outcomes.
+
+Limitations
+
+Our review has some limitations. First, although the search strategy was designed to identify studies most relevant to the Spanish context, the exclusion of some international databases such as the Excerpta Medica database (Embase) or Scopus may have limited the retrieval of additional publications indexed exclusively in broader bibliographic sources. In addition, there is considerable heterogeneity in the studies included in this SLR in terms of population characteristics and study designs, which hinders the synthesis of the results and their interpretation. Most studies evaluated populations aged 65 and older from nursing and geriatric centers, or cohorts already diagnosed with dementia, revealing a gap in the real epidemiology of AD in Spain and the disease’s onset in younger individuals.
+
+Furthermore, the heterogeneity of study designs, populations, and outcome measures limited the feasibility of a quantitative synthesis, and findings were therefore integrated using a structured narrative approach.
+
+Evidence presented as abstracts has been omitted from our review and may have resulted in the omission of potentially relevant data. Future research should focus on pre-dementia stages; studies that include all forms of late-onset, sporadic, or genetically determined AD; caregiver support; and optimization of healthcare resources to address the growing impact of AD in Spain effectively.
+
+Part of the study period coincided with the COVID-19 pandemic, which may have affected healthcare delivery, access to diagnostic services, and reporting practices in some of the included studies. At the same time, the data reflect routine clinical practice under constrained healthcare conditions and offer insight into how diagnostic pathways and care processes for AD were maintained during a period of substantial system-level disruption.
+
+Conclusions
+
+This SLR underscores the urgent need to advance early diagnosis of AD dementia and to establish reliable health registries to accurately determine its true extent in Spain. The lack of national strategies for a comprehensive understanding of the continuum of AD hinders effective management and planning of care for individuals with different stages of the disease. Reliable health registries are essential for better resource allocation and informed decision-making, especially given the growing number of cases, driven by an aging population.
+
+The study underscores the existing heterogeneity in access to early and accurate diagnosis across Spain. Variability in diagnostic practices, tools, and regional resources contributes to delays in AD diagnosis, particularly in its early stages, when timely intervention could have the most significant impact. Addressing these disparities is crucial to ensuring that all individuals, regardless of their location, can access early and effective care, especially with the advent of DMTs. Although the Spanish National Healthcare System provides universal coverage, the economic burden of diagnosing and managing AD dementia remains substantial, placing considerable financial strain on both the healthcare system and families/caregivers of patients with AD. This burden is further exacerbated by the increasing emotional and social challenges faced by caregivers. Addressing these issues is vital for improving the management of patients with AD in Spain, enhancing their HRQoL, and ensuring that families/caregivers receive the necessary support, while also mitigating the significant economic impact on both families/caregivers and the healthcare system.
+
+The authors would like to thank Outcomes’10 for its methodological assistance and medical writing services, especially Paloma Gonzalez and Irene Huerga.
+
+Disclosures
+
+Author Contributions
+
+Conflicts of interest: In compliance with the ICMJE uniform disclosure form, all authors declare the following:
+
+Payment/services info: The study has been funded by Lilly Spain, which provided funding to Outcomes'10 for methodological assistance and medical writing services.
+
+Financial relationships: All authors have declared that they have no financial relationships at present or within the previous three years with any organizations that might have an interest in the submitted work.
+
+Other relationships: All authors have declared that there are no other relationships or activities that could appear to have influenced the submitted work.
+
+Concept and design:  Mercedes Núñez, Miren Altuna, Eloy Rodríguez, Ángel Trueba-Saiz, Silvia Díaz-Cerezo, Luis Lizan
+
+Acquisition, analysis, or interpretation of data:  Mercedes Núñez, Miren Altuna, Eloy Rodríguez, Ángel Trueba-Saiz, Silvia Díaz-Cerezo, Luis Lizan
+
+Drafting of the manuscript:  Mercedes Núñez, Miren Altuna, Eloy Rodríguez, Ángel Trueba-Saiz, Silvia Díaz-Cerezo, Luis Lizan
+
+Critical review of the manuscript for important intellectual content:  Mercedes Núñez, Miren Altuna, Eloy Rodríguez, Ángel Trueba-Saiz, Silvia Díaz-Cerezo, Luis Lizan
+
+Supervision:  Mercedes Núñez, Silvia Díaz-Cerezo
+
+
+References
+
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+2 Sociedad española de neurología. Impacto sociosanitario de las enfermedades neurológicas en españa Socioeconomic and Healthcare Impact of Neurological Diseases in Spain (Book in Spanish) Sociedad Española de Neurología 2025 Barcelona, Spain Sociedad Española de Neurología 23 2024 https://www.sen.es/pdf/2024/Informe_sociosanitario_2024.pdf
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+5 Alzheimer's disease: treatment strategies and their limitations Int J Mol Sci Passeri E Elkhoury K Morsink M 13954 23 2022 36430432 10.3390/ijms232213954 PMC9697769
+6 Resident population by date, sex, age group and nationality 5 2024 2024 https://www.ine.es/jaxiT3/Datos.htm?t=56936#_tabs-tabla
+7 Thirty-five percent of Alzheimer’s cases can be attributed to nine modifiable risk factors 21 de septiembre: Día mundial de la enfermedad de alzheimer 2023 5 2024 Sociedad española de neurología Spain Sociedad española de neurología 2024 https://www.sen.es/saladeprensa/pdf/Link280.pdf
+8 Diagnosis of early Alzheimer's disease: clinical practice in J Prev Alzheimers Dis Porsteinsson AP Isaacson RS Knox S Sabbagh MN Rubino I 371 386 8 2021 34101796 10.14283/jpad.2021.23 PMC12280795
+9 Diagnostic performance and clinical applicability of blood-based biomarkers in a prospective memory clinic cohort Neurology Sarto J Ruiz-García R Guillén N 0 73 100 2023 10.1212/WNL.0000000000201597 PMC9984216 36450604
+10 Diagnostic performance of plasma pTau(217), pTau(181), Aβ(1-42) and Aβ(1-40) in the LUMIPULSE automated platform for the detection of Alzheimer disease Alzheimers Res Ther Arranz J Zhu N Rubio-Guerra S 139 16 2024 38926773 10.1186/s13195-024-01513-9 PMC11200993
+11 Systematic review of brief cognitive screening tools for identifying dementia and mild cognitive impairment in illiterate and low‐educated populations Alzheimers Dement Zegarra‐Valdivia JA Chino‐Vilca BN Tituana KA 0 20 2025 10.3390/bs15020207 PMC11851668 40001837
+12 Diagnosis and treatment of Alzheimer's disease: an update Dela J Public Health Bomasang-Layno E Bronsther R 74 85 7 2021 34604768 10.32481/djph.2021.09.009 PMC8482985
+13 Innovative diagnostic tools for early detection of Alzheimer's disease Alzheimers Dement Laske C Sohrabi HR Frost SM 561 578 11 2015 https://doi.org/10.1016/j.jalz.2014.06.004 25443858 10.1016/j.jalz.2014.06.004
+14 NIA-AA research framework: toward a biological definition of Alzheimer's disease Alzheimers Dement Jack CR Jr Bennett DA Blennow K 535 562 14 2018 29653606 10.1016/j.jalz.2018.02.018 PMC5958625
+15 Alzheimer’s disease diagnosis based on the amyloid, tau, and neurodegeneration scheme (ATN) in a real-life multicenter cohort of general neurological centers J Alzheimers Dis Baldeiras I Silva-Spínola A Lima M 419 432 90 2022 36120784 10.3233/JAD-220587
+16 Diagnostic accuracy of biomarker combinations in the A/T/N classification for Alzheimer’s disease (P4.182) Neurol J Mendez P Calandri I Demey I 182 90 2018
+17 Erratum: Alzheimer's disease drug development pipeline: 2023 Alzheimers Dement (N Y) 0 9 2023 10.1002/trc2.12407 PMC10301697 37388760
+18 The costs of dementia in Europe: an updated review and meta-analysis Pharmacoeconomics Jönsson L Tate A Frisell O Wimo A 59 75 41 2023 36376775 10.1007/s40273-022-01212-z PMC9813179
+19 Alzheimer's disease and the quality of life of the informal caregiver (Article in Spanish) Rev Esp Geriatr Gerontol Casal Rodríguez B Rivera Castiñeira B Currais Nunes L 81 87 54 2019 30792138 10.1016/j.regg.2018.10.008
+20 Understanding resilience factors among caregivers of people with Alzheimer's disease in Spain Psychol Res Behav Manag Durán-Gómez N Guerrero-Martín J Pérez-Civantos D López Jurado CF Palomo-López P Cáceres MC 1011 1025 13 2020 33262666 10.2147/PRBM.S274758 PMC7700077
+21 Sex, neuropsychiatric profiles, and caregiver burden in Alzheimer's disease dementia: a latent class analysis J Alzheimers Dis Rosende-Roca M Cañabate P Moreno M 993 1002 89 2022 35964175 10.3233/JAD-215648 PMC9535594
+22 Preferred reporting items for systematic reviews and meta-analyses: the PRISMA statement BMJ Moher D Liberati A Tetzlaff J Altman DG 0 339 2009 PMC3090117 21603045
+23 The Newcastle-Ottawa Scale (NOS) for assessing the quality of nonrandomised studies in meta-analyses 5 2024 Wells GA Shea B O’Connell D 2012 https://www.ohri.ca/programs/clinical_epidemiology/oxford.asp
+24 Incidence of dementia and associated factors in the EPIC-Spain dementia cohort J Alzheimers Dis Andreu-Reinón ME Huerta JM Gavrila D 543 555 78 2020 33016917 10.3233/JAD-200774
+25 Falls and sleep disorders in Spanish Alzheimer's disease in nursing homes: an observational study Healthcare (Basel) Cámara-Calmaestra R Martínez-Amat A Aibar-Almazán A 2852 11 2023 37957998 10.3390/healthcare11212852 PMC10649919
+26 Depression as a risk factor for dementia and Alzheimer's disease Biomedicines Cantón-Habas V Rich-Ruiz M Romero-Saldaña M Carrera-González MD 457 8 2020 33126696 10.3390/biomedicines8110457 PMC7693751
+27 Hospital incidence, mortality and costs of Alzheimer's disease in Spain: a retrospective multicenter study Expert Rev Pharmacoecon Outcomes Res Darbà J Marsà A 1101 1106 21 2021 32928002 10.1080/14737167.2020.1820328
+28 Prevalence of drug prescription in Alzheimer's disease and use of combination therapy (Article in Spanish) Rev OFIL·ILAPHAR Fernández-Rubio B Saborido-Cansino C 79 82 33 2023 https://scielo.isciii.es/scielo.php?script=sci_arttext&pid=S1699-714X2023000100014
+29 NEURONORMA cognitive battery associations with cerebrospinal fluid amyloid-β and tau levels in the continuum of Alzheimer's disease J Alzheimers Dis García-Escobar G Puig-Pijoan A Puente-Periz V 1303 1321 92 2023 37038810 10.3233/JAD-220930
+30 Assessing knowledge and perceptions of Alzheimer's disease among employees of a pharmaceutical company in Spain: a comparison between caregivers and non-caregivers Patient Prefer Adherence Garcia-Ribas G García-Arcelay E Montoya A Maurino J 2357 2364 14 2020 33293798 10.2147/PPA.S282147 PMC7718989
+31 Sex moderates the relationship of stress and perceived social support with neuropsychological symptoms among community-dwelling persons with Alzheimer disease in Spain Alzheimer Dis Assoc Disord Gomez-Gallego M Gallego-Mellado M Gómez-Gallego JC Gómez-García JG 353 355 35 2021 33009040 10.1097/WAD.0000000000000416
+32 Cost of patients with Alzheimer's disease in Spain according to disease severity Pharmacoecon Open Gómez Maldonado L de Mora-Figueroa R López-Angarita A Maravilla-Herrera P Merino M 103 114 8 2024 37966711 10.1007/s41669-023-00451-w PMC10781927
+33 Perceived health, caregiver overload and perceived social support in family caregivers of patients with Alzheimer's: gender differences Health Soc Care Community Hernández-Padilla JM Ruiz-Fernández MD Granero-Molina J Ortíz-Amo R López Rodríguez MM Fernández-Sola C 1001 1009 29 2021 32783241 10.1111/hsc.13134
+34 Multi-national, cross-sectional survey of healthcare resource utilization in patients with all stages of cognitive impairment, analyzed by disease severity, country, and geographical region J Alzheimers Dis Khandker RK Ritchie CW Black CM Wood R Jones E Hu X Ambegaonkar BM 1141 1152 75 2020 32390613 10.3233/JAD-190760
+35 Family carers of people with dementia in Japan, Spain, and the UK: a cross-cultural comparison of the relationships between experiential avoidance, cognitive fusion, and carer depression J Geriatr Psychiatry Neurol Kishita N Morimoto H Márquez-González M 254 264 36 2023 36261123 10.1177/08919887221130269 PMC10114255
+36 Women with a high level of education, victims of caregiving for people with Alzheimer’s disease (Article in Spanish) Enfermería Global Luque-Carrillo P Morales-Cané I Carmona-Torres JM Manfredini R Rodríguez-Borrego MA López-Soto P 390 420 19 2020 https://scielo.isciii.es/scielo.php?script=sci_arttext&pid=S1695-61412020000200013
+37 Risk variants in three Alzheimer's disease genes show association with EEG endophenotypes J Alzheimers Dis Macedo A Gómez C Rebelo MÂ 209 223 80 2021 33522999 10.3233/JAD-200963 PMC8075394
+38 Resilience and burden in family caregivers of patients with dementias in Navarre (Article in Spanish) Gerokomos Mariezcurrena-Fernández A Lorea-González I Remirez de Ganuza A Ijalba-Pérez P Barea-Ullate V Jiménez-Acosta A 88 94 33 2022 https://scielo.isciii.es/scielo.php?script=sci_arttext&pid=S1134-928X2022000200005
+39 Prevalence of prescription of anticholinergic/sedative burden drugs among older people with dementia living in nursing homes (Article in Spanish) Rev Esp Geriatr Gerontol Martínez Arrechea S Ferro Uriguen A Beobide Telleria I González Bueno J Alaba Trueba J Sevilla Sánchez D 11 17 56 2021 33309422 10.1016/j.regg.2020.09.008
+40 Is it time to use real-world data from primary care in Alzheimer's disease? Alzheimers Res Ther Ponjoan A Garre-Olmo J Blanch J 60 12 2020 32423489 10.1186/s13195-020-00625-2 PMC7236302
+41 Effectiveness of a psychotherapeutic intervention group program in the improvement of caregiver well-being in Alzheimer's disease patients' family caregivers: the CuiDem study (Article in Spanish) Rev Neurol Poudevida S de Sola S Brugulat-Serrat A 203 211 75 2022 36218251 10.33588/rn.7508.2022180 PMC10280724
+42 The CORCOBIA study: cut-off points of Alzheimer's disease CSF biomarkers in a clinical cohort Neurologia (Engl Ed) Puig-Pijoan A García-Escobar G Fernández-Lebrero A 756 765 39 2024 35961506 10.1016/j.nrleng.2022.05.002
+43 Current diagnostic pathways for Alzheimer's disease: a cross-sectional real-world study across six countries J Alzheimers Dis Rep Roth S Burnie N Suridjan I Yan JT Carboni M 659 674 7 2023 37483324 10.3233/ADR230007 PMC10357118
+44 Predictor factors of perceived health in family caregivers of people diagnosed with mild or moderate Alzheimer's disease Int J Environ Res Public Health Ruiz-Fernández MD Hernández-Padilla JM Ortiz-Amo R Fernández-Sola C Fernández-Medina IM Granero-Molina J 3762 16 2019 31591314 10.3390/ijerph16193762 PMC6801649
+45 Prevalence of comorbidities in individuals diagnosed and undiagnosed with Alzheimer’s disease in León, Spain and a proposal for contingency procedures to follow in the case of emergencies involving people with Alzheimer’s disease Int J Environ Res Public Health Tortajada-Soler M Sánchez-Valdeón L Blanco-Nistal M Benítez-Andrades JA Liébana-Presa C Bayón-Darkistade E 3398 17 2020 32414124 10.3390/ijerph17103398 PMC7277451
+46 Caregivers' sense of coherence: implications on direct and indirect costs of dementia care J Alzheimers Dis Turró-Garriga O Viñas-Díez V Conde-Sala JL 117 126 78 2020 32925037 10.3233/JAD-200350
+47 Prevalence and incidence of Alzheimer's disease in Europe: a meta-analysis Neurología (English Edition) Niu H Álvarez-Álvarez I Guillén-Grima F Aguinaga-Ontoso I 523 532 32 2017 10.1016/j.nrl.2016.02.016 27130306
+48 Junta de anadalucía. Plan integral de alzheimer y otras demencias en andalucía Comprehensive Plan for Alzheimer’s Disease and Other Dementias in Andalusia (Book in Spanish) Regional Government of Andalusia 2025 Seville, Spain Regional Government of Andalusia 23 2023 https://www.juntadeandalucia.es/sites/default/files/inline-files/2023/10/PIAD_septiembre2023_final.pdf
+49 Catalan early onset dementia network 2021 report Alzheimer's Dement Guillén N Balasa M Boada M 0 19 2023
+50 Diagnosis of cognitive decline and dementia in rural areas - a scoping review Int J Geriatr Psychiatry Barth J Nickel F Kolominsky-Rabas PL 459 474 33 2018 29314221 10.1002/gps.4841
+51 Inequitable access to dementia diagnosis and care in low-resource settings - a global perspective Clin Gerontol Seeher K Cataldi R Dua T Kestel D 133 137 46 2023 35672953 10.1080/07317115.2022.2054391
+52 Dementia-related education and support service availability, accessibility, and use in rural areas: barriers and solutions Can J Aging Bayly M Morgan D Froehlich Chow A Kosteniuk J Elliot V 545 585 39 2020 31975685 10.1017/S0714980819000564
+53 Socioeconomic status and risks of cognitive impairment and dementia: a systematic review and meta-analysis of 39 prospective studies J Prev Alzheimers Dis Wang AY Hu HY Ou YN Wang ZT Ma YH Tan L Yu JT 83 94 10 2023 36641612 10.14283/jpad.2022.81
+54 Global estimates on the number of persons across the Alzheimer's disease continuum Alzheimers Dement Gustavsson A Norton N Fast T 658 670 19 2023 35652476 10.1002/alz.12694
+55 Brief cognitive tests as a decision-making tool in primary care. A population and validation study Neurologia (Engl Ed) Tainta M Iriondo A Ecay-Torres M 781 791 39 2024 35963538 10.1016/j.nrleng.2022.08.001
+56 Development and assessment of algorithms for predicting brain amyloid positivity in a population without dementia Alzheimers Res Ther Le Scouarnec L Bouteloup V van der Veere PJ 219 16 2024 39394180 10.1186/s13195-024-01595-5 PMC11468062
+57 Monthly deaths by cause (chapters) by sex 4 2024 2023 https://www.ine.es/jaxi/Tabla.htm?tpx=73575
+58 Map of Alzheimer's disease and other dementias in Spain. MapEA Project (Article in Spanish) Rev Esp Geriatr Gerontol Martínez-Lage P Martín-Carrasco M Arrieta E Rodrigo J Formiga F 26 37 53 2018 29107401 10.1016/j.regg.2017.07.006
+59 Mini-Mental State Examination (MMSE) for the detection of Alzheimer's disease and other dementias in people with mild cognitive impairment (MCI) Cochrane Database Syst Rev Arevalo-Rodriguez I Smailagic N Roqué I Figuls M 0 2015 2015 10.1002/14651858.CD010783.pub2 PMC6464748 25740785
+60 Acceptable performance of blood biomarker tests of amyloid pathology - recommendations from the Global CEO Initiative on Alzheimer's Disease Nat Rev Neurol Schindler SE Galasko D Pereira AC 426 439 20 2024 38866966 10.1038/s41582-024-00977-5
+61 Novel techniques for early diagnosis and monitoring of Alzheimer's disease Expert Rev Neurother Parul Parul Singh A Shukla S 29 42 25 2025 39435792 10.1080/14737175.2024.2415985
+62 The Alzheimer's Association appropriate use recommendations for blood biomarkers in Alzheimer's disease Alzheimers Dement Hansson O Edelmayer RM Boxer AL 2669 2686 18 2022 35908251 10.1002/alz.12756 PMC10087669
+63 Alzheimer disease blood biomarkers: considerations for population-level use Nat Rev Neurol Mielke MM Fowler NR 495 504 20 2024 38862788 10.1038/s41582-024-00989-1 PMC11347965
+64 Benefits and risks of FDA-approved amyloid-targeting antibodies for treatment of early Alzheimer's disease: navigating clinician-patient engagement Alzheimers Dement Rentz DM Aisen PS Atri A 8162 8171 20 2024 39306695 10.1002/alz.14199 PMC11567834
+65 Understanding barriers along the patient journey in Alzheimer's disease using social media data Neurol Ther Tahami Monfared AA Stern Y Doogan S Irizarry M Zhang Q 899 918 12 2023 37060417 10.1007/s40120-023-00472-x PMC10195971
+66 Interventions effective in decreasing burden in caregivers of persons with dementia: a meta-analysis Nurs Rep Rodríguez-Alcázar FJ Juárez-Vela R Sánchez-González JL Martín-Vallejo J 931 945 14 2024 38651483 10.3390/nursrep14020071 PMC11036232
+67 Modelling the pan-European economic burden of Alzheimer's disease JAR Life Martins R Urbich M Brännvall K Gianinazzi M Ching JE Khoury CP El-Hayek YH 38 46 11 2022 36923231 10.14283/jarlife.2022.7 PMC10002890
+68 Assets by sex and age group. Absolute values ​​and percentages relative to the total for each sex 12 2025 2025 https://www.ine.es/jaxiT3/Tabla.htm?t=65080&L=0
+69 Law 39/2006, of December 14, on the promotion of personal autonomy and care for people in situations of dependency Law 39/2006, of december 14, on the promotion of personal autonomy and care for people in a situation of dependency. Official State Gazette (BOE) 3 2025 Gobierno de España 15 Spain Gobierno de España 299 2025 https://www.boe.es/buscar/doc.php?id=BOE-A-2006-21990
+70 The World Wide FINGERS 3 2025 2025 https://www.alz.org/wwfingers/overview.asp
diff --git a/corpus/psychology/text/f3d50f5c45852292.txt b/corpus/psychology/text/f3d50f5c45852292.txt
new file mode 100644
index 0000000000000000000000000000000000000000..77083427a8c98ad579b9abc51fe0788b7c5bb287
--- /dev/null
+++ b/corpus/psychology/text/f3d50f5c45852292.txt
@@ -0,0 +1,3 @@
+The Chaos-State Space Dream Model: Integrating Phenomenology and Neurodynamics in Dream Consciousness
+
+We propose the Chaos-State Space Dream Model (CSSDM): a candidate neural correlate of dream consciousness. CSSDM treats dreaming as the brain's exploration of hierarchically organized attractor landscapes when sensory anchoring lifts and prefrontal control attenuates during REM sleep. The proposal combines two published frameworks. From chaos-theoretic accounts of dream phenomenology, we take the observation that dreams have dynamical structure: attractor-like coherence, bifurcation-like transitions, sensitivity to subtle influence. From an embedding-theoretic account of consciousness, we take a candidate substrate: delay coordinate embedding via generalized synchronization in recurrent cortical networks. The synthesis maps dream phenomenology to specific dynamical properties: narrative coherence to attractor occupation, scene transitions to bifurcations, emotional intensity to limbic modulation of control parameters, bizarreness to access to normally inaccessible state-space regions, immersion to attenuated metacognition. Three predictions follow. First, bifurcation signatures in EEG should precede reported scene transitions. Second, cross-regional REM coherence should predict post-sleep insight. Third, nightmare episodes should show attractor entrapment signatures that normalize with successful therapy. The model generates falsifiable predictions about the neural dynamics of dreaming.
diff --git a/corpus/psychology/text/f6a1058a99a03ee1.txt b/corpus/psychology/text/f6a1058a99a03ee1.txt
new file mode 100644
index 0000000000000000000000000000000000000000..c0e512c3e6a98d267663455557a16972931f2a6b
--- /dev/null
+++ b/corpus/psychology/text/f6a1058a99a03ee1.txt
@@ -0,0 +1,3 @@
+Burning facts: thick and thin causatives
+
+Lexical causative verbs are traditionally assumed to pattern uniformly: they specify only a result state, leaving the manner of causing unarticulated, like the overt cause. We argue that this view obscures a fundamental division within English causative verbs. Building on Rose et al. (2021), we show that a substantial subset of causatives – thick causatives such as burn, melt, break, bury – encode information about the way a change is brought about, and that this specification yields systematic semantic and pragmatic restrictions. Thick causatives in their physical sense resist subjects that denote absences, facts, degrees, or events that fail to instantiate the appropriate productive (force- transmitting) mechanism, in contrast to thin causatives like kill, destroy, and change, which readily combine with such subjects. Using corpus evidence from a representative sample of 37 frequent English causatives, we demonstrate (i) that most thick causatives pattern like Embick’s 2009 break-causatives – compatible with strong adjectival resultatives and requiring production-based causation – while (ii) some thick causatives (e.g., bury) encode the relevant manner information via the state they lexicalize rather than via an event predicate. We develop a pragmatic competition account linking the production constraint to the directness constraint, yielding a unified explanation for the distribution of thick vs. thin causatives in English.
diff --git a/corpus/psychology/text/f6ffd5e5326ebefb.txt b/corpus/psychology/text/f6ffd5e5326ebefb.txt
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index 0000000000000000000000000000000000000000..0c80d5bc7ecb356b1f28bae2192d864e2be3eee3
--- /dev/null
+++ b/corpus/psychology/text/f6ffd5e5326ebefb.txt
@@ -0,0 +1,58 @@
+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Behav Sci (Basel)
+Journal ID: Behav Sci (Basel)
+NLM Journal ID: 101576826
+Journal ID: behavsci
+
+Behavioral Sciences
+
+EISSN: 2076-328X
+Publisher: Multidisciplinary Digital Publishing Institute (MDPI)
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC12561387
+PMID: 41153221
+DOI: 10.3390/bs15101335
+Article ID: behavsci-15-01335
+Article version: 1
+Subjects: Correction
+
+Correction: Pohlman et al. (2025). Interconnecting District and Community Partners to Improve School-Level Social, Emotional, and Behavioral Health. Behavioral Sciences, 15(9), 1225
+
+Pohlman Kathryn B. 1 *
+Jones Kayla 2
+Lira Juan R. 1
+Norton Jennifer 1
+Perales Kelly 1
+1 Midwest PBIS Network, Naperville, IL 60563, USA; juan.lira@midwestpbis.org (J.R.L.); jennifer.norton@midwestpbis.org (J.N.); kelly.perales@midwestpbis.org (K.P.)
+2 West Kentucky Educational Cooperative, Murray, KY 42071, USA; kayla.jones@wkec.org
+* Correspondence: katie.pohlman@midwestpbis.org
+Electronic publication date: 2025 Sep 29
+Publication date: 2025 Oct
+Volume: 15
+Issue: 10
+Electronic Location ID: 1335
+Received 2025 Sep 23; Accepted 2025 Sep 25
+Copyright: © 2025 by the authors.
+Copyright year: 2025
+License: Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Erratum for: Interconnecting District and Community Partners to Improve School-Level Social, Emotional, and Behavioral Health 15 9 9 9 2025 1225 Behavioral Sciences 10.3390/bs15091225 PMC12466477 41009255
+
+Ÿ==============================Ÿ
+In the original publication (Pohlman et al., 2025), the Data Availability Statement was missing. The Data Availability Statement has now been inserted as follows:
+
+“Data Availability Statement: The data presented in this study are available upon request from the corresponding author.”
+
+The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.
+
+Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.
+
+
+Reference
+
+Pohlman K. B. Jones K. Lira J. R. Norton J. Perales K. Interconnecting district and community partners to improve school-level social, emotional, and behavioral health Behavioral Sciences 2025 15 9 1225 10.3390/bs15091225 41009255 PMC12466477
diff --git a/corpus/psychology/text/f9ad7e65c1b23423.txt b/corpus/psychology/text/f9ad7e65c1b23423.txt
new file mode 100644
index 0000000000000000000000000000000000000000..fc7c9549dbb1d51fbdb66f9d34b5eab6624eca8d
--- /dev/null
+++ b/corpus/psychology/text/f9ad7e65c1b23423.txt
@@ -0,0 +1,3 @@
+Empirically derived phenotypes can reduce diagnostic heterogeneity
+
+Diagnostic heterogeneity is a longstanding challenge for the classification of mental illness because people who receive the same diagnosis can differ markedly in their symptom presentations as well as in the mechanisms underlying those symptoms. High heterogeneity undermines both the clinical utility of diagnostic labels and the scientific accuracy of research that treats disorders as coherent constructs. In this study, we examined heterogeneity across six internalizing disorders (specific phobia, social anxiety disorder, agoraphobia, generalized anxiety disorder [GAD], major depressive disorder [MDD], and posttraumatic stress disorder [PTSD]) using three complementary approaches to quantifying heterogeneity: 1) descriptive heterogeneity (how many symptom profiles can theoretically satisfy the diagnostic criteria, and how many are observed in practice), 2) person-focused heterogeneity (whether diagnostic labels capture people with similar symptom presentations), and 3) construct-focused heterogeneity (whether diagnostic labels group symptoms with similar patterns of association with external validators). Analyses drew on subsamples from a large convenience sample with elevated psychopathology, predominantly from Australia and the USA (n = 14,762, mean [SD] age = 38.0 [18.0]; 55% women). Results showed that specific phobia was consistently the least heterogeneous; social anxiety disorder, agoraphobia, and GAD had mixed results; and MDD and PTSD were highly heterogeneous across all metrics. Notably, empirically derived phenotypes nested within each disorder substantively reduced heterogeneity relative to the DSM diagnoses. The study provides both a systematic multi-method approach to characterising different types of diagnostic heterogeneity, and a practical path toward more precise and informative constructs that can be implemented by rescoring existing data.
diff --git a/corpus/psychology/text/fc7d2945920446ca.txt b/corpus/psychology/text/fc7d2945920446ca.txt
new file mode 100644
index 0000000000000000000000000000000000000000..9d58515cf10d6a7f3912028d25f4f02b7193c983
--- /dev/null
+++ b/corpus/psychology/text/fc7d2945920446ca.txt
@@ -0,0 +1,570 @@
+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: BMC Psychiatry
+Journal ID: BMC Psychiatry
+NLM Journal ID: 100968559
+
+BMC Psychiatry
+
+EISSN: 1471-244X
+Publisher: BMC
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC13390239
+PMID: 42157226
+DOI: 10.1186/s12888-026-08154-2
+Article ID: 8154
+Article version: 1
+Subjects: Systematic Review
+
+Meta-analysis of neural correlates of working memory, reward, and emotion processing in major depressive disorder using AES-SDM
+
+Ding Hui 1
+Lu Ying 2
+Hou Yongzhe tedyong@163.com
+3
+Chen Xin 1
+Peng Ji 1
+Chen Xizhao 1
+Li Jing 1
+Zhang Qin 1402974053@qq.com
+1
+1 https://ror.org/042g3qa69 grid.440299.2 Department of Radiology, The Second People’s Hospital of Guizhou Province, Guizhou Guiyang, 550004 China
+2 https://ror.org/02wmsc916 grid.443382.a 0000 0004 1804 268X School of Basic Medical Sciences, Guizhou University of Traditional Chinese Medicine, Guizhou Guiyang, 550025 China
+3 https://ror.org/042g3qa69 grid.440299.2 Department of Women’s and Children’s Psychiatry, Guizhou Second People’s Hospital, Guizhou Guiyang, 550004 China
+Electronic publication date: 2026 May 19
+Publication date: 2026
+Volume: 26
+Electronic Location ID: 543
+Received 2025 Jul 10; Accepted 2026 Apr 29
+Copyright: © The Author(s) 2026
+Copyright year: 2026
+License: Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Keywords: Major depressive disorder, Working memory, Emotion, Reward processing, fMRI, AES-SDM meta-analysis
+
+Funding: 2025 Health Commission of Guizhou Province Project gzwkj2025-045 gzwkj2025-488 Hou Yongzhe Zhang Qin
+
+Funding: 2024 Health Commission of Guizhou Province Project gzwkj2024-475 Zhang Qin
+
+Funding: Scientific and Technological Research Project of Traditional Chinese Medicine and Ethnic Medicine, Guizhou Administration of Traditional Chinese Medicine QZYY-2025-048 Zhang Qin
+
+Funding: Key Advantageous Discipline Construction Project of Guizhou Provincial Health Commission in 2025
+issue-copyright-statement: © BioMed Central Ltd., part of Springer Nature 2026
+
+Ÿ==============================Ÿ
+Objective
+
+We conducted coordinate-based anisotropy effect size signed differential mapping (AES-SDM) meta-analyses to identify task-general and domain-specific (working memory, reward, and emotion processing) activation abnormalities in patients with major depressive disorder (MDD).
+
+Materials and methods
+
+We systematically searched the PubMed, Embase, Web of Science, ScienceDirect, and China National Knowledge Infrastructure databases for functional magnetic resonance imaging (fMRI) studies that compared patients with MDD with healthy controls (HCs) up to December 3, 2024. Differences in brain activity were evaluated using AES-SDM software across all task types, including emotion-processing, working memory, and reward-processing domains, to compare MDD patients with HCs.
+
+Results
+
+Forty-six studies (11 on working memory, 12 on reward processing, and 23 on emotion processing) involving 1,558 patients with MDD and 1,468 HCs were included. Across all task types, patients with MDD showed greater activation in the left lenticular nucleus/putamen, right rolandic operculum, left anterior cingulate/paracingulate gyri, and right inferior frontal gyrus. In the emotion-processing domains, MDD was associated with hyperactivation in the right amygdala and left striatum. No clusters survived the primary corrected threshold in the working memory or reward-processing domains. Jackknife analyses supported the robustness of the main clusters, and Egger’s test did not indicate significant publication bias (all p > 0.05). Meta-regression did not reveal significant effects of age or illness duration on the results.
+
+Conclusions
+
+This meta-analysis demonstrated task-general hyperactivation across salience/control-related regions in patients with MDD and domain-specific hyperactivation in the amygdala–striatal circuitry during emotion processing. The absence of corrected findings in working memory and reward processing highlights the need for more standardized paradigms and larger datasets to clarify domain-specific abnormalities.
+
+Clinical trial number
+
+Not applicable.
+
+Supplementary Information
+
+The online version contains supplementary material available at 10.1186/s12888-026-08154-2.
+
+Background
+
+Major depressive disorder (MDD) is among the most prevalent and disabling psychiatric conditions. It is characterized by persistent low mood, anhedonia, and suicidal ideation, which significantly impair patients’ social functioning and quality of life. This disorder often recurs, contributing to increased morbidity and mortality rates [1]. Although the prevalence of MDD varies across countries and regions [2], its global incidence continues to increase annually, highlighting the urgent need for improved understanding and intervention [3]. Furthermore, owing to the substantial heterogeneity of psychiatric symptoms and the lack of objective diagnostic biomarkers, individualized and precise treatment for specific MDD subtypes or individuals remains a major challenge [4]. Therefore, identifying the neural correlates of working memory, reward, and emotional processing prior to treatment is highly important.
+
+A growing body of functional magnetic resonance imaging (fMRI) data has revealed abnormal brain activity in patients with MDD during key neurocognitive processes such as emotional regulation [5], reward processing [6], and working memory [7], suggesting widespread impairments in both affective and cognitive domains. In working memory tasks, particularly n-back paradigms, patients with MDD frequently exhibit dysfunction in the prefrontal cortex, particularly the dorsolateral prefrontal cortex (dlPFC), with findings ranging from hypoactivation, indicating deficits in cognitive control, to hyperactivation, which possibly reflects compensatory mechanisms [8]. Pharmacological interventions such as vortioxetine have been shown to modulate activity in the right dlPFC and left hippocampus, suggesting a potential role in restoring cognitive network function [9]. In the reward-processing domain, patients with MDD demonstrate heterogeneous patterns of neural activation across different reward stages. Some studies have reported hyperactivation in regions such as the anterior cingulate cortex, middle frontal gyrus, cerebellum, and nucleus accumbens during reward anticipation or reception [10], whereas others have observed hypoactivation in areas such as the superior frontal gyrus during expected loss or reward feedback processing, indicating impairments in reinforced learning and affective regulation [11]. Meta-analyses have further suggested that, in addition to classical reward-related regions such as the striatum and anterior cingulate cortex, the insula, posterior cingulate cortex, and supplementary motor area are involved, reflecting widespread abnormalities in the reward-processing network [12, 13]. Notably, blunted activation in the anterior cingulate cortex and subgenual cortex during reward anticipation has been reported, which may underlie motivational deficits and anhedonia in MDD [14]. With respect to emotional processing, patients with MDD consistently exhibit exaggerated responses to negative emotional stimuli. Regions such as the parahippocampal gyrus, insula, and caudate nucleus show heightened activation when negative facial expressions or affective images are processed, reflecting disrupted emotion-related memory and regulatory mechanisms [15–17]. Similar hyperactivation patterns have been observed in the amygdala, middle temporal gyrus, and superior temporal gyrus, suggesting increased emotional sensitivity and biased negative appraisal [18]. Conversely, diminished responses to positive stimuli have been reported in areas such as the anterior cingulate cortex, lateral occipital cortex, and fusiform gyrus [19, 20], indicating impaired positive emotion processing. Furthermore, during emotional conflict tasks, patients with MDD exhibit decreased behavioral accuracy and reduced activation in brain regions associated with facial recognition and emotional evaluation, supporting the notion of impaired emotional regulation and emotion–cognition integration.
+
+Although an increasing number of fMRI studies have reported abnormal neural activity during emotional processing, reward processing, and working memory in patients with MDD, the findings remain highly inconsistent across studies. Such discrepancies may be driven by substantial heterogeneity in sample characteristics (e.g., symptom severity, illness course, and medication status), task paradigms (e.g., cognitive load, reward stage, and stimulus valence), and imaging/analysis parameters. This variability not only underscores the complexity of MDD pathophysiology but also limits the interpretability and reproducibility of individual reports, highlighting the need for quantitative synthesis using standardized and transparent meta-analytic procedures. In addition, while previous meta-analyses have summarized aberrant neural responses within specific functional domains of MDD [12, 13], the existing evidence remains largely fragmented because most prior work has focused on a single domain or a particular task component in isolation. Consequently, it remains unclear whether reported abnormalities primarily reflect domain-specific dysfunction (e.g., emotion-related circuitry) or, more general, task-related neural alterations that are shared across cognitive–affective domains.
+
+To address these gaps, the present study applied anisotropic effect-size signed differential mapping (AES-SDM) in a unified whole-brain, coordinate-based meta-analytic framework to examine task-based fMRI differences between adults with MDD and healthy controls (HCs). AES-SDM is a validated coordinate-based meta-analytic approach that reconstructs voxel-wise effect-size maps from reported peak coordinates and corresponding statistics, enabling quantitative whole-brain synthesis while accounting for spatial uncertainty and between-study variability [21].
+
+Notably, rather than synthesizing each domain in separate meta-analyses with potentially different inclusion criteria and analytic decisions, we simultaneously conducted (i) a task-general meta-analysis pooling all eligible task types and (ii) parallel domain-specific meta-analyses for three major task domains—emotion processing, working memory, and reward processing—within the same analytical design. By integrating task-general and domain-specific perspectives in a single study, this approach enables a more direct comparison of shared versus domain-dependent neural abnormalities, clarifies whether neural alterations in MDD converge across tasks or are selectively expressed in particular domains, and aims to identify more robust and reproducible patterns of task-evoked brain activation abnormalities in MDD.
+
+Materials and methods
+
+Literature search
+
+This review was registered with PROSPERO (ID: CRD420251101693). A systematic search was conducted for relevant studies in the PubMed, Embase, Web of Science, ScienceDirect and CNKI databases up to December 3, 2024. We used the following key words (using both free-text and MeSH search): ((“fMRI” [tw] OR “fmri”[tw] OR fmr imag* [tw] OR functional magnetic* [tw] OR “functional magnetic resonance imaging” [tw] OR “functional mri” [tw] OR “functional mr” [tw]) OR (“Magnetic Resonance Imaging”[mesh] AND “functional” [tw]) OR ((“Magnetic Resonance Imaging”[mesh] OR MR imag* [tw] OR “MRI”[tw] OR “magnetic resonance”[tw]) AND (“Functional Neuroimaging”[Mesh: noexp] OR functional imag*[tw] OR functional neuroimag* [tw]))) AND (“depression” [Mesh] OR “Depressive Disorder”[Mesh] OR “depression”[tw] OR “Depressive Disorder”[tw] OR “major depressive disorder”[tw] OR “major depression”[tw] OR “depressive”[tw] OR “depressezd” [tw] OR “depression neurosis” [tw] OR “melancholia” [tw] OR Depressive disorder* [tw] OR depress* [tw] OR depression disease* [tw] OR depressive disease* [tw] OR “Depression Disease” [tw] OR depressive Disease* [tw]) NOT (“Animals” [mesh] NOT “Humans” [mesh]).
+
+Manual screening of all potentially relevant results was also conducted. Studies were considered eligible on the basis of the following criteria: (1) task-based fMRI studies involving individuals with MDD; (2) reported whole-brain analysis results in a standard stereotaxic space (Montreal Neurological Institute [MNI] or Talairach coordinates); (3) included participants aged 18 years or older; (4) incorporated a task assessing at least one of the following domains: working memory, reward processing, or emotion processing; and (5) compared adults with MDD and HCs.
+
+The exclusion criteria were as follows: (1) conditions that might influence brain function or any contraindications for MRI scanning; (2) literature reviews, systematic reviews, meta-analyses, methodological papers, case reports, letters, conference abstracts, and editorials; (3) studies employing only regions of interest (ROIs) or seed voxel-based analyses; and (4) studies that did not report activation coordinates or associated statistical values (e.g., T values).
+
+Two physicians independently conducted the literature search, and any disagreements were resolved through discussion to reach consensus. Finally, the included studies were categorized into one or more of the three domains. Study selection was performed in accordance with the PRISMA guidelines.
+
+AES-SDM analysis
+
+AES-SDM software was used to analyze differences between patients with MDD and HCs across all task types, including the emotion processing, working memory, and reward-processing domains [22]. Peak coordinates reported in Talairach space were converted to MNI space by using an online tool (http://www.brainmap.org/icbm-2tal/). When the results were presented as z values, they were converted to t values for analysis (www.sdmproject.com/utilities/?show=Statistics). AES-SDM reconstructed effect size and statistical parameter maps reflecting increased and decreased brain region activation across individual studies. The Monte Carlo random-effects model implemented in AES-SDM integrated these statistical maps, with the significance threshold set at FWHM = 20 mm, 1000 permutations, TFCE-corrected p < 0.05, and a cluster extent threshold ≥ 50 voxels. Cluster coordinate reconstruction involved converting peak t-values to Hedges’ g, followed by the application of a Gaussian kernel to perform nonuniform smoothing of adjacent peak coordinate voxels. Volume rendering of cortical clusters showing significant differences was conducted in MNI standard space using MRIcron software.
+
+Egger’s regression test, integrated within the AES-SDM software, was used to evaluate publication bias on the basis of effect sizes of peak voxels within significant clusters. Heterogeneity among studies was calculated to identify brain regions contributing to between-study variance. Jackknife sensitivity analysis was performed to assess the robustness of the results by iteratively repeating the meta-analysis, each time excluding one study across 11 working memory studies, 12 reward-processing studies, and 23 emotion-processing studies. Additionally, meta-regression analysis was performed using SDM-PSI 6.21 to assess whether study-level covariates—including age, sex distribution, medication status, and depression severity—significantly contributed to the variability of the observed effects.
+
+Results
+
+Literature search results
+
+A total of 46 studies met the inclusion criteria and were included in the final meta-analysis [7–11, 14, 15, 17, 19, 20, 23–57]. These studies were categorized into three task domains (Fig. 1). Specifically, the working memory domain included 11 studies, comprising 380 patients with MDD and 343 HCs; the reward-processing domain included 12 studies, comprising 270 patients with MDD and 239 HCs; and the emotion-processing domain included 23 studies, comprising 908 patients with MDD and 886 HCs (Table 1).
+
+Table 1 Descriptives of included fMRI studies of three domains of working memory, reward processing and emotion processing in the meta-analysis using a whole‐brain approach
+
+	Sample size	Age (X ± S)	Medication	Depression Assessment Tools(MADRS/HAMD/BDI/IDS/HDRS/HRSD/DASS-21/CES-D /PHQ-9)and Scoring Results	Task	Corrective methods	
+Author, year	Patient (n) (female,%)	HCs (n) (female,%)	Patient	HCs	Unknowns (n) Antidepressants (n) Unmedicated (n)	
+Working Memory Tasks									
+Matsuo K, 2007 [7]	15, 67%	15, 60%	34.37 (11.5)	37.77 (12.1)	Unmedicated (8)
+
+Antidepressants (7)
+
+	HAMD 20.3 ± 5.3	n-back task	p < 0.05	
+Smith J, 2018 [9]	48, 56%	48, 54%	20–53	20–53	Antidepressants (48)	BDI-II 7.8 ± 6.7	n-back task	p < 0.05	
+Harvey PO, 2005 [23]	10, 42%	10,50%	19–45	18–42	Unknown (10)	MADRS 26.7 ± 4.6	n-back task	p <0.001	
+Vasic N,2009 [24]	14, 57%	14, 50%	37.0 (8.6)	32.6 (9.0)	Antidepressants (14)	MADRS 23.0 ± 4.0	a positive delay-related component	FDR p < 0.05	
+Lee TW,2013 [25]	14, 21%	14, 36%	65.1 (4.9)	64.8 (4.2)	Unknown (14)	HDRS 16.1 ± 5.8	one-back working memory task:	p < 0.05	
+Le TM, 2017 [26]	18, 67%	21, 57%	22.0 (3.09)	22.19 (3.38)	Unmedicated (18)	IDS 40.79 ± 8.70	delayed recognition task	FDR p < 0.05	
+Goodin P, 2019 [27]	14, 57%	13, 77%	29.79 (9.62)	30.62 (9.99)	Unknown (14)	DASS-21 28.62 ± 6.99	n-back task	TFCE p < 0.05	
+Cao W, 2021 [28]	40, 70%	47, 60%	19.98 (4.70)	20.98 (2.34)	Unknown (40)	CES-D 62.30 ± 9.35	n-back task	FWE p < 0.05	
+Ma M. 2021 [29]	37, 62%	54, 54%	25.89 (4.75)	23.94 (3.05)	Unmedicated (10)
+
+Antidepressants (27)
+
+	HAMD-17 24.35 ± 5.60	“number calculation working memory” task	FWE p < 0.05	
+Schwefel MK, 2023 [30]	110, 48%	55, 62%	36.4 (10.0)	30.5 (7.3)	Unknown (110)	BDI-II 27.3 ± 7.7	n-back paradigm with numerical stimuli	FWE p < 0.05	
+Hempel M, 2024 [31]	60, 43%	52, 44%	39.5 (10.6)	37.6 (10.8)	Antidepressants (60)	BDI-II 31.8 ± 8.5	using the emotion back-task	GRF p < 0.05	
+Reward Tasks									
+Dichter GS, 2012 [10]	19, 79%	19, 63%	24.5 ± 5.4	27.9 ± 6.3	Unmedicated (14)
+
+Antipsychotics (5)
+
+	BDI-II 2.6 ± 4.9	monetary incentive delay task	p < 0.05	
+Smoski MJ, 2011 [11]	9 (-)	13 (-)	34.4 ± 15.0	26.2 ± 6.3	Unmedicated (5)
+
+Antidepressants (4)
+
+	BDI 16.7 ± 4.9	monetary incentive delay task	p < 0.05	
+Smoski MJ,2009 [14]	14, 50%	15, 60%	34.8 (14.3)	30.8 ± 9.7	Unknown (40)	HAMD 18.5–28.5	wheel of fortune task	p < 0.005	
+Schiller CE, 2013 [32]	19, 79%	19, 63%	23.6 (4.1)	27.9 (6.3)	Unknown (19)	BDI-II 2.6 ± 4.9	monetary incentive delay task	p < 0.05	
+Dillon DG,2014 [33]	21, 52%	21, 43%	34.33 (12.16)	36.62 (13.32)	Unmedicated (21)	BDI-II 23.62 ± 7.17	reward tokens	FWE p < 0.05	
+Hall GB,2014 [34]	15, 73%	15, 67%	47.67 (9.53)	46.33 (11.36)	Unknown (15)	BDI 26.29 ± 11.17
+
+HRSD 17.93 ± 7.03
+
+	money game	FDR p < 0.05	
+Ubl B, 2015 [35]	23, 69%	23, 61%	41.17 (12.08)	42.74 (12.19)	Unmedicated (23)	BDI-II 5.08 ± 4.15	reward paradigm	p < 0.05	
+Takamura M, 2017 [36]	18, 67%	18, 67%	44(13.2)	38.3(8.46)	Antidepressants (18)	BDI-II 30.8 ± 11.29	monetary incentive delay task	FWE p < 0.05	
+Martin-Soelch C,2020 [37]	16, 75%	16, 75%	24.31 (4.08)	25.19 (4.79)	Unknown (16)	BDI-II 31.38 ± 10.94	monetary incentive delay task	p < 0.005	
+Rupprechter S,2021 [38]	18, 83%	16, 63%	18–33	17–41	Unknown (18)	HAMD 18.8 ± 6.9	a novel pavlovian conditioning task	p < 0.005	
+Mielacher C, 2024 [39]	53, 51%	41, 54%	41.58 (13.09)	40.61 (13.22)	Antidepressants (53)	BDI-II 33.34 ± 8.75	reward paradigm	p < 0.05	
+Taylor CT, 2024 [40]	45, 68.9%	23, 69.6%	30.2 (9.8)	29.7 (8.4)	Unknown (45)	PHQ-9 13.0 ± 4.4	social incentive delay task	p < 0.05	
+Emotion Tasks									
+Kerestes P,2012 [8]	19, 78%	20, 50%	33.6 (13.64)	35.8 (12.10)	Unmedicated (19)	HAMD 1.79 ± 1.27	emotional face gender-labeling task	FWE p < 0.05	
+Tak S, 2021 [15]	34, 100%	28, 100%	24.5(2.8)	24.4(2.6)	Unmedicated (34)	BDI 33.7 ± 7.1	negative emotional task	p < 0.005	
+Lemke H,2022 [17]	333,65%	333,60%	36.80 (12.57)	36.64 (12.49)	Unknown (333)	HDRS 19.61 ± 5.88	negative emotional face-processing paradigm	FWE p < 0.05	
+Zhang S,2022 [19]	42, 61.9%	32, 78.1%	22.19 (1.97)	21.50 (3.13)	Unknown (42)	HAMD-24 15.67 ± 3.56
+
+BDI 24.10 ± 7.43
+
+	fMRI stimuli and task	FWE p < 0.05	
+Alders GL,2019 [20]	48, 69%	30, 30%	34.7(12.2)	33.2(9.8)	Antidepressants (48)	MADRS 30 ± 6	emotional conflict task	p < 0.05	
+Beauregard M, 2006 [41]	12, 75%	12, 75%	43 (11)	45 (10)	Unknown (12)	HDRS 25 ± 6	sad affect face recognition task	p < 0.05	
+Aizenstein HJ ,2011 [42]	33, 64%	27, 70.3%	67.7 (5.2)	71.6 (7.5)	Antidepressants (33)	HAMD 19.7 ± 3.7	faces and shapes affective reactivity task	p < 0.005	
+Mannie ZN, 2011 [43]	28, 57%	28, 46%	18.79 (1.40)	19.68 (1.44)	Unknown (28)	BDI 4.21 ± 3.75	simple perceptual task	p < 0.05	
+Ritchey M, 2011 [44]	22, 59.1%	14, 64.3%	36.1 (10.1)	34.6 (6.9)	Unmedicated (22)	BDI 25.1 ± 8.8	emotion evaluation task	p < 0.05	
+Wang Y,2012 [45]	18, 61%	18, 61%	31.61(7.9)	31.67(6.8)	Unknown (18)	HAMD 19.9 ± 5.3	emotional pictures	p < 0.005	
+Aust S,2013 [46]	14, (64%)	14, (57%)	55.1(11.3)	54.9(11.8)	Unknown (14)	HDRS>8
+
+MADRS >11
+
+BDI 13
+
+	music and human emotional faces	FDR p < 0.05	
+Chechko N,2013 [47]	18, 72%	18, 72%	36.5 ( 10.8)	36.0 (10.3)	Unknown (18)	BDI 31.7 ± 8.2	emotional interference task	FWE p < 0.05	
+Feeser M,2013 [48]	19, 32%	19, 32%	43.9 (8.7)	38.2 (11.9)	Unmedicated (19)	HRSD 20.3 ± 4.3
+
+BDI 27.9 ± 9.6
+
+	anticipatory emotional processes	alpha p < 0.05	
+Furey ML, 2013 [49]	15, 27%	21, 43%	32.9(7.8)	30.5(8.5)	Unmedicated (15)	MADRS 30 ± 6.0	face-identity and face-emotion working memory tasks	alpha p < 0.05	
+Korgaonkar MS, 2013[50]	30, 60%	30, 60%	41.2 (15.8)	35.7 (14.1)	Unknown (30)	HRSD 19.2 ± 3.1	emotion task	p < 0.005	
+Victor TA, 2013 [51]	10, 60%	10,70%	33.2 (5.0)	28.4 (5.7)	Antidepressants (10)	HAMD 24.8 ± 5.8	back- ward masking task	FWE p < 0.05	
+Miskowiak KW, 2015 [52]	13, 62%	17, 65%	48.6 (14.7)	42.5 (10.2)	Unknown (13)	BDI 1.4 ± 2.1	faces dot-probe task	FWE p < 0.05	
+Koch K,2018 [18]	30, 53%	30, 47%	29.9(8.9)	26.8(4.3)	Unknown (30)	BDI 29.5 ± 8.3
+
+HRSD 20.9 ± 5.1
+
+	emotion task	FWE p < 0.05	
+Huang CM, 2019 [53]	40, 63%	55, 69%	68.10(5.3)	66.36(5.42)	Antidepressants (40)	HAMD 11.66 ± 6.41	color–word stroop task	FWE p < 0.05	
+Keller M,2021 [54]	39, 44%	37, 41%	35.2(13.6)	32.3(12.8)	Antidepressants (39)	HAMD 16.5 ± 7.5
+
+BDI 26.8 ± 11.5
+
+	NF task	FDR p < 0.05	
+Fang Z,2022 [55]	18, 78%	20, 75%	32.11(10.8)	29.5(8.6)	Unmedicated (18)	BDI 5.15 ± 5.52	emotional stroop task	FWE p < 0.05	
+Zhang Q,2022 [56]	36, 56%	36, 58%	34.32 (5.45)	32.38 (9.24)	Unmedicated (36)	HDRS 23.6 ± 3.64	emotional subregion	FDR p < 0.05	
+Klug M, 2024 [57]	37, 54%	37, 43%	38.43 (12.37)	32.95(10.67)	Unknown (37)	HDRS 23.08 ± 4.87	subliminal negative emotion processing	FWE p < 0.05	
+HCs: Healthy Controls; MADRS: Montgomery–Asberg Depression Rating Scale; HAMD: Hamilton Depression Rating Scale; HDRS: Hamilton Depression Rating Scale; HRSD: Hamilton Rating Scale for Depression; BDI: Beck Depression Inventory; IDS: Inventory of Depressive Symptomatology; DASS-21: Depression Anxiety Stress Scales-21; CES-D: Center for Epidemiologic Studies Depression Scale; PHQ-9: Patient Health Questionnaire-9
+
+Fig. 1 Flow chart of the study selection strategy
+
+In terms of paradigm distribution, n-back-related paradigms were the most frequently represented in the working memory domain, whereas monetary incentive delay paradigms were the most frequently represented in the reward-processing domain. By contrast, the emotion-processing domain was more heterogeneous, with no single paradigm clearly predominating across studies; the included studies covered a range of face-based, negative emotion-related, and other affective paradigms.
+
+Meta-analysis results
+
+Meta-analyses across all task types
+
+Compared with HCs, individuals with MDD exhibited hyperactivation in the left lenticular nucleus/putamen, right rolandic operculum, left anterior cingulate/paracingulate gyri, and right inferior frontal gyrus across all task types (Fig. 2). Egger’s test revealed no significant publication bias for the left lenticular nucleus/putamen (Bias = 0.21, Z = 0.51, p = 0.613), right rolandic operculum (Bias = 0.71, Z = 1.14, p = 0.252), left anterior cingulate/paracingulate gyri (Bias = 0.64, Z = 1.29, p = 0.198), or right inferior frontal gyrus (Bias = 0.71, Z = 1.14, p = 0.252), indicating low between-study heterogeneity (Table 2). However, no significant hypoactivation was observed across all the task types.
+
+Fig. 2 Abnormal brain regions identified through SDM meta-analysis across all task types in neuroimaging studies. Regions with significantly increased activation in patients with MDD relative to HCs are highlighted in red
+
+Table 2 Applying the SDM method to study brain functional changes across all task types in MDD
+
+Research methods	Anatomical label	Peak MNI coordinate	SDM-Z	p value	Voxels	Jackknife	Egger	
+X  	Y	Z	sensitivity analysis	Bias test	
+All task types	
+MDD > HCs	
+	Left lenticular nucleus / putamen, BA 48	-28	2	-2	4.379	0.01000009	7241	43 / 46	Bias:0.21
+
+Z:0.51
+
+p:0.613
+
+	
+	Right rolandic operculum, BA 48	52	-10	10	3.971	0.000999987	5962	44 / 46	Bias:0.71
+
+Z:1.14
+
+p:0.252
+
+	
+	Left anterior cingulate / paracingulate gyri, BA 24	-2	36	20	3.699	0.004999995	981	43 / 46	Bias:0.64
+
+Z:1.29
+
+p:0.198
+
+	
+	Right inferior frontal gyrus, BA 45	44	36	26	2.774	0.042999983	60	42 / 46	Bias:0.71
+
+Z:1.14
+
+p:0.252
+
+	
+HCs > MDD	 —	 —	 —	—	—	 —	 —	 —	 —	
+HCs: Healthy Controls; MDD: Major Depressive Disorder; MNI: Montreal Neurological Institute; BA: Brodmann Area
+
+Meta-analyses across working memory, reward processing and emotion processing
+
+Compared with HCs, individuals with MDD exhibited hyperactivation in the right amygdala and left striatum during emotion processing (Fig. 3). Egger’s test did not indicate significant publication bias for the right amygdala (Bias = 0.09, Z = 0.16, p = 0.870) or the left striatum (Bias = 0.08, Z = 0.15, p = 0.880), suggesting low heterogeneity among the included studies (Table 3). However, no significant hypoactivation was observed in this domain. Additionally, neither hyperactivation nor hypoactivation was identified in the working memory or reward-processing domains.
+
+Fig. 3 Abnormal brain regions identified through SDM meta-analysis across emotion processing domains in neuroimaging studies. Regions with significantly increased activation in patients with MDD relative to HCs are highlighted in red
+
+Table 3 Applying the SDM method to investigate brain functional alterations across emotion processing domains in MDD
+
+Research methods	Anatomical label	Peak MNI coordinate	SDM-Z	p value	Voxels	Jackknife	Egger	
+X 	Y	Z	sensitivity analysis	Bias test	
+Emotion processing domain		
+MDD > HCs		
+	Right amygdala, BA 34	32	-2	-18	4.032	0.003000021	866	20/23	Bias:0.09
+
+Z:0.16
+
+p:0.870
+
+	
+	Left striatum	-26	-4	-6	3.546	0.009000003	770	21/23	Bias:0.08
+
+Z:0.15
+
+p:0.880
+
+	
+HCs > MDD	 —	 —	— 	—	—	 —	 —	 —	 —	
+Working memory domain	— 	 —	 —	—	—	 —	 —	 —	 —	
+Reward processing domain	 —	— 	 —	—	—	 —	 —	 —	 —	
+HCs: Healthy Controls; MDD: Major Depressive Disorder; MNI: Montreal Neurological Institute; BA: Brodmann Area
+
+Exploratory analyses
+
+In exploratory analyses using a more lenient uncorrected threshold (p < 0.05, k ≥ 50 voxels), several subthreshold clusters were identified in both the working memory and reward-processing domains (Supplementary Tables S1–S2). However, none of these clusters survived the primary correction threshold applied in the main analyses.
+
+Jackknife sensitivity and meta-regression analysis results
+
+Jackknife sensitivity analysis demonstrated robust results, with findings for the left lenticular nucleus/putamen replicated in 43 of 46 iterations, the right rolandic operculum in 44 of 46 iterations, the left anterior cingulate/paracingulate gyri in 43 of 46 iterations, and the right inferior frontal gyrus in 42 of 46 iterations (Table 2). Findings for the right amygdala were replicated in 20 of 23 iterations and those for the left striatum were replicated in 21 of 23 iterations (Table 3). Meta-regression analysis revealed no significant impact of differences in age, sex, medication or severity of MDD between the groups.
+
+Discussion
+
+This AES-SDM meta-analysis synthesized task-based fMRI evidence in adults with MDD and identified convergent patterns of task-evoked hyperactivation. Specifically, the emotion-processing domain showed hyperactivation in the right amygdala and left striatum. By contrast, no clusters survived the primary corrected threshold in the working memory or reward-processing domains. When all task types were pooled, MDD was associated with increased activation in the left lenticular nucleus/putamen, right rolandic operculum, left anterior cingulate/paracingulate gyri, and right inferior frontal gyrus.
+
+Task-general functional abnormalities across all task types in MDD
+
+When all task types were considered together, compared with HCs, patients with MDD showed increased task-related activation in the left lenticular nucleus/putamen, right rolandic operculum, left anterior cingulate/paracingulate gyri, and right inferior frontal gyrus, whereas no consistent hypoactivation was observed. These findings suggest that cross-task neural abnormalities in MDD are not restricted to a single cognitive or affective dimension but may instead reflect a broader functional imbalance involving salience processing, cognitive control, response inhibition, and sensorimotor integration.
+
+Specifically, the putamen, as a key component of the striatum, is closely involved in motivational drive, habitual response, and action selection [58]; the anterior cingulate/paracingulate cortex is implicated in conflict monitoring, emotion regulation, and cognitive control [59]; the inferior frontal gyrus plays important roles in inhibitory control and salience-oriented processing [60]; and the rolandic operculum may reflect abnormalities in sensorimotor integration and interoceptive-related processing [61]. The convergent hyperactivation across these regions may indicate that patients with MDD need to recruit greater amounts of neural resources to maintain task performance across different task demands, which is consistent with inefficient processing and/or compensatory engagement at the task-general level.
+
+Overall, these results suggest that task-general abnormalities in MDD may be more prominently characterized by widespread hyperactivation within salience-, control-, and sensorimotor-related networks under current meta-analytic conditions.
+
+Significance of hyperactivation in brain regions involved in emotion processing in patients with MDD
+
+Our meta-analysis revealed significant hyperactivation in the right amygdala and left striatum during emotion processing in patients with MDD, highlighting the pivotal role of these regions in the neuropathology of affective dysregulation. The amygdala is critically involved in the detection and appraisal of emotional stimuli [62], particularly those with negative valence, and its heightened activity has been consistently linked to increased emotional reactivity and biased processing of negative information in MDD [51, 54, 63]. This pattern may reflect heightened sensitivity to negative emotional cues, which is consistent with the clinical phenotype of persistent negative affect and increased reactivity to adverse stimuli observed in patients with MDD.
+
+Similarly, the striatum, which includes the putamen and caudate nucleus, plays an essential role in reward-related processing and the motivational aspects of emotion [64, 65]. Hyperactivation in this region may reflect altered salience attribution and/or atypical engagement of reward-related learning mechanisms, which have been linked to anhedonia and altered affective experience [66]. Together, the observed amygdala and striatal hyperactivation may indicate dysregulated recruitment of subcortical affective–motivational circuitry during emotion processing in MDD [67].
+
+Importantly, the present meta-analytic evidence is associative rather than causal. Nevertheless, the consistent involvement of the amygdala and striatum during emotion processing reinforces the view that dysregulated affective–motivational circuitry is a key neurobiological feature of MDD. From a translational perspective, these findings support the role of the amygdala–striatal circuit as a clinically relevant neural target that may help inform biomarker-based patient stratification and guide the development or optimization of circuit-focused treatments.
+
+Possible reasons for the lack of abnormal activation in working memory and reward processing in patients with MDD
+
+The absence of significant hyperactivation or hypoactivation in the working memory and reward-processing domains in this meta-analysis may be attributed to several methodological and neurobiological factors. First, the heterogeneity in task paradigms across studies may have reduced the statistical power to detect convergent neural alterations [68]. Working memory tasks often differ in terms of cognitive load (e.g., 1-back vs. 3-back), modality (verbal vs. visuospatial), and response demands, leading to variability in the activation of frontoparietal and dorsolateral prefrontal regions commonly associated with executive control [69, 70]. Similarly, reward-processing studies encompass multiple phases (anticipation, outcome, or feedback) and involve diverse reward types (monetary, social, or primary), potentially engaging distinct neural circuits [71, 72]. This task variability could obscure consistent activation patterns in meta-analytic models, particularly when sample sizes within subdomains are modest.
+
+Second, participant-related factors such as medication status, illness severity, comorbidities, and duration of illness may introduce interstudy variability. Qian’s study suggested that pharmacological interventions may alter neural responses during cognitive and reward tasks, particularly in frontostriatal circuits, potentially obscuring disorder-specific effects [73]. Moreover, reward deficits and executive dysfunction in MDD are often subtle and may be state dependent, emerging more clearly under conditions of acute symptom exacerbation or treatment resistance, which may not be fully captured in aggregated datasets.
+
+Third, the use of stringent statistical thresholds and conservative correction methods (TFCE-corrected p < 0.05, extent ≥ 50 voxels) may have limited the detection of small but meaningful effects, especially in regions with lower signal-to-noise ratios or high interindividual anatomical variability. Additionally, the AES-SDM method relies on peak coordinate data rather than raw statistical images, which may lead to the underestimation of distributed or subthreshold activation differences in small sample subgroups.
+
+Interpretive boundaries and potential reasons for the absence of significant differences in activation in working memory and reward processing
+
+In the present study, we did not detect statistically significant or consistently convergent whole-brain activation differences for working memory (11 studies) or reward processing (12 studies). Of note, this “null finding” should not be interpreted as evidence that working memory or reward-related processes are unaffected. A more plausible interpretation is that, given the currently available evidence base and the analytic framework and thresholding adopted in AES-SDM, we were unable to identify task-related activation abnormality patterns that were consistently reproducible across multiple studies and reached the statistical threshold.
+
+From a methodological perspective, substantial heterogeneity existed across the studies. With respect to working memory, studies differed in task load (e.g., varying n-back levels), baseline/control and contrast definitions, and statistical strategies. With respect to reward processing, studies varied in terms of task phase (anticipation vs. outcome/feedback), reward type, and task structure. In addition, preprocessing pipelines, statistical thresholding, and covariate adjustment strategies were not uniform across studies. Such methodological variability may disperse the spatial distribution of reported peak coordinates, thereby reducing cross-study convergence and statistical detectability [74]. Moreover, clinical heterogeneity (e.g., depression severity, illness stage, and medication status) may contribute to inconsistencies in effect direction or spatial localization, further limiting the stability of meta-analytic results [75].
+
+Although finer stratification by WM load/modality or reward phase/type may help reduce heterogeneity, the number of available studies within each subtype was too small and unevenly distributed to support reliable subgroup meta-analysis in the present dataset.
+
+Overall, we interpret these findings cautiously as reflecting a lack of robust, cross-study, spatially consistent evidence. Future studies with more standardized paradigms and reporting, together with finer clinical stratification, are needed to further clarify the neural mechanisms of working memory and reward processing in MDD.
+
+Limitations
+
+Several limitations of this meta-analysis should be acknowledged, which necessitate a cautious interpretation of the findings. First, the relatively small number of included studies may limit the robustness and generalizability of the results. Second, the use of peak coordinates extracted from published reports may not fully capture the spatial extent of alterations in brain activity, potentially introducing selection bias. Finally, because medication information was insufficiently reported in the primary studies—particularly given the presence of a substantial proportion of “unknown” cases—any medication-related conclusions should be interpreted with caution. Future studies should report medication details, including drug class, dosage, and treatment duration, more systematically.
+
+Conclusion
+
+This meta-analysis revealed consistent hyperactivation in the right amygdala and left striatum during emotion-processing tasks in patients with MDD, but no significant abnormalities in working memory or reward-processing domains were identified. These findings emphasize the central role of heightened emotional reactivity in MDD, supporting the role of the amygdala and striatal circuits as potential neurobiological markers for emotional dysregulation. The lack of significant abnormalities in working memory and reward-related tasks may reflect differences in sample size, task paradigms, and imaging parameters.
+
+Overall, our findings highlight the importance of targeting emotion-related neural circuits in future research and therapeutic interventions, while emphasizing the need for standardized task paradigms and larger, longitudinal samples to increase the translational relevance of neuroimaging biomarkers in clinical psychiatry.
+
+Electronic Supplementary Material
+
+Below is the link to the electronic supplementary material.
+
+Supplementary Material 1
+
+Author contributions
+
+H.D. and Y.L. led the literature review, data extraction, and drafted the initial manuscript. Y.Z.H. and Q.Z. conceived and supervised the study, coordinated the analysis process, and contributed significantly to manuscript revision as corresponding authors. X.C. and J.P. conducted the AES-SDM meta-analysis and prepared the figures. X.Z.C. and J.L. assisted with data quality control and interpretation of neuroimaging results. X.C. reviewed all statistical methods and provided critical revisions to improve intellectual content. All authors read and approved the final manuscript.
+
+Funding
+
+This work was supported by the Key Advantageous Discipline Construction Project of Guizhou Provincial Health Commission in 2025; 2025 Health Commission of Guizhou Province Project (gzwkj2025-488); 2025 Health Commission of Guizhou Province Project (gzwkj2025-045); 2024 Health Commission of Guizhou Province Project (gzwkj2024-475); Scientific and Technological Research Project of Traditional Chinese Medicine and Ethnic Medicine, and Guizhou Administration of Traditional Chinese Medicine (QZYY-2025-048).
+
+Data availability
+
+All data generated or analysed during this study are included in this published article and its supplementary information files. Further inquiries can be directed to the corresponding authors.
+
+Declarations
+
+Ethical approval and consent to participate
+
+This study was a meta-analysis based on previously published studies. All data were obtained from the published literature, and no individual participant data were collected or analyzed. Therefore, ethical approval and informed consent were not required.
+
+Consent for publication
+
+Not applicable.
+
+Competing interests
+
+The authors declare no competing interests.
+
+Abbreviations
+
+fMRI Functional magnetic resonance imaging
+
+AES-SDM Anisotropic effect-size signed differential mapping
+
+PRISMA Preferred Reporting Items for Systematic Reviews and Meta-Analyses
+
+PROSPERO International Prospective Register of Systematic Reviews
+
+WOS Web of Science
+
+CNKI China National Knowledge Infrastructure
+
+HCs Healthy controls
+
+MNI Montreal Neurological Institute
+
+ROI Region of Interest
+
+BA Brodmann area
+
+dlPFC Dorsolateral prefrontal cortex
+
+GRF Gaussian random field
+
+FDR False discovery rate
+
+FWE Family-wise error
+
+Publisher’s note
+
+Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
+
+Hui Ding and Ying Lu contributed equally to this work.
+
+
+References
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+Hall GB, Milne AM, Macqueen GM. An fMRI study of reward circuitry in patients with minimal or extensive history of major depression. Eur Arch Psychiatry Clin Neurosci. 2014;264(3):187–98. 10.1007/s00406-013-0437-9.23990079 10.1007/s00406-013-0437-9
+35. Ubl B Kuehner C Kirsch P Neural reward processing in individuals remitted from major depression Psychol Med 2015 45 16 3549 58 10.1017/S0033291715001452 26315103
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+Takamura M, Okamoto Y, Okada G, et al. Patients with major depressive disorder exhibit reduced reward size coding in the striatum. Prog Neuropsychopharmacol Biol Psychiatry. 2017;79(Pt B):317–23. 10.1016/j.pnpbp.2017.07.006.28705766 10.1016/j.pnpbp.2017.07.006
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+Martin-Soelch C, Guillod M, Gaillard C, Recabarren RE, et al. Increased Reward-Related Activation in the Ventral Striatum During Stress Exposure Associated With Positive Affect in the Daily Life of Young Adults With a Family History of Depression. Preliminary Findings. Front Psychiatry. 2021;11:563475. 10.3389/fpsyt.2020.563475.33584359 10.3389/fpsyt.2020.563475 PMC7873952
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+Borsini A, Wallis ASJ, Zunszain P, et al. Characterizing anhedonia: A systematic review of neuroimaging across the subtypes of reward processing deficits in depression. Cogn Affect Behav Neurosci. 2020;20(4):816–41. 10.3758/s13415-020-00804-6.32472419 10.3758/s13415-020-00804-6 PMC7395022
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+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Psychiatr Res Clin Pract
+Journal ID: Psychiatr Res Clin Pract
+NLM Journal ID: 101776485
+Journal ID: RCP2
+
+Psychiatric Research and Clinical Practice
+
+EISSN: 2575-5609
+Publisher: Wiley
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC12710517
+PMID: 41415524
+DOI: 10.1176/rcp2.70030
+Article ID: RCP270030
+Article version: 1
+Subjects: Correction, Correction
+
+Correction to “Quality of Life and Functioning Impairments Across Psychiatric Disorders in Adults Presenting for Outpatient Psychiatric Evaluation and Treatment”
+
+Electronic publication date: 2025 Oct 9
+Publication date: 2025 Winter
+Volume: 7
+Issue: 4
+First page: 286
+Last page: 286
+Copyright: © The Author(s). Psychiatric Research and Clinical Practice published by Wiley Periodicals, LLC on behalf of the American Psychiatric Association.
+License: This is an open access article under the terms of the http://creativecommons.org/licenses/by/4.0/ License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Erratum for: Quality of Life and Functioning Impairments Across Psychiatric Disorders in Adults Presenting for Outpatient Psychiatric Evaluation and Treatment 6 3 8 4 2024 68 77 Psychiatric Research and Clinical Practice 10.1176/appi.prcp.20230064 PMC11574459 39568501
+Figure count: 0
+Table count: 0
+Page count: 1
+
+source-schema-version-number: 2.0
+cover-date: Winter 2025
+details-of-publishers-convertor: Converter:WILEY_ML3GV2_TO_JATSPMC version:6.6.6 mode:remove_FC converted:17.12.2025
+
+Ÿ==============================Ÿ
+IsHak, W.W., Mirocha, J., Dang, J., Vanle, B., Metrikin, B., Tessema, K. and Danovitch, I. (2024), Quality of Life and Functioning Impairments Across Psychiatric Disorders in Adults Presenting for Outpatient Psychiatric Evaluation and Treatment. Psych Res Clin Pract, 6: 68–77. https://doi.org/10.1176/appi.prcp.20230064
+
+In the article cited above, Alexander J. Steiner, Psy.D. has been added as the seventh author by agreement of all other authors. Due to an inadvertent error, Dr. Steiner had been omitted from the initial manuscript submission.
+
+The corrected citation is shown below.
+
+IsHak, W.W., Mirocha, J., Dang, J., Vanle, B., Metrikin, B., Tessema, K., Steiner A.J. and Danovitch, I. (2024), Quality of Life and Functioning Impairments Across Psychiatric Disorders in Adults Presenting for Outpatient Psychiatric Evaluation and Treatment. Psych Res Clin Pract, 6: 68–77. https://doi.org/10.1176/appi.prcp.20230064
+
+We regret this error.
+
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+
+JOURNAL INFORMATION
+==============================
+NLM Title Abbreviation: Polymers (Basel)
+Journal ID: Polymers (Basel)
+NLM Journal ID: 101545357
+Journal ID: polymers
+
+Polymers
+
+EISSN: 2073-4360
+Publisher: Multidisciplinary Digital Publishing Institute (MDPI)
+
+ARTICLE INFORMATION
+==============================
+PMCID: PMC13119897
+PMID: 42076293
+DOI: 10.3390/polym18080910
+Article ID: polymers-18-00910
+Article version: 1
+Subjects: Article
+
+A First-Order Shear Deformation Theory-Based Analytical Approach for Acoustic-Vibration Research of Rib-Stiffened PVC Foam Sandwich Structures with Reinforcing and Weakening Phases
+
+Ma Zhaozhe 1
+Dai Ruijie 2
+https://orcid.org/0000-0002-8753-3509 Zhou Zhiwei 1 *
+Li Ying 3
+1 School of Naval Architecture, Ocean and Energy Power Engineering, Wuhan University of Technology, Wuhan 430070, China; 13395594994@163.com
+2 Wuhan Second Ship Design and Research Institute, Wuhan 430205, China; hust_dairj@163.com
+3 Beijing Key Laboratory of Lightweight Multi-Functional Composite Materials and Structures, Institute of Advanced Structure Technology, Beijing Institute of Technology, Beijing 100080, China
+* Correspondence: zhouzw92@whut.edu.cn
+Electronic publication date: 2026 Apr 8
+Publication date: 2026 Apr
+Volume: 18
+Issue: 8
+Electronic Location ID: 910
+Received 2026 Jan 31; Revised 2026 Mar 30; Accepted 2026 Apr 2
+Copyright: © 2026 by the authors.
+Copyright year: 2026
+License: Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.
+License URL: https://creativecommons.org/licenses/by/4.0/
+
+Keywords: rib-stiffened PVC foam sandwich structures, reinforcing and weakening phases, underwater environment, analytical approach, acoustic vibration analyses
+
+Funding: Open Fund of Key Laboratory of High Performance Ship Technology [Wuhan University of Technology], Ministry of Education https://ror.org/05tqgjy81 gxnc24113004 This work was supported by the Open Fund of Key Laboratory of High Performance Ship Technology [Wuhan University of Technology], Ministry of Education [No. gxnc24113004].
+
+Ÿ==============================Ÿ
+This paper presents a theoretical approach based on the FSDT to study the acoustic vibration performance of rib-stiffened PVC foam sandwich structures with reinforcing and weakening phases when submerged in water. The complex core layer with reinforcing and weakening phases is homogenized to an equivalent orthotropic layer. Building upon this framework, the governing equations of motion for rib-stiffened PVC foam sandwich structures under the boundary conditions of a simply supported type are derived, incorporating the coupling interaction between the reinforcing ribs and the sandwich plates. Considering the influence of the underwater environment, with the Helmholtz equation governing the continuity of the acoustic pressure field and the Euler equation regulating the fluid–structure interaction interface continuity, the Navier method is subsequently employed to solve for the natural frequencies and acoustic vibration responses. For the purpose of verifying the proposed approach, the predicted results are contrasted with both the literature-derived data and numerical simulation results. Finally, parametric research is further conducted to explore the effect of the parameters of the rib and core layers on the underwater acoustic vibration characteristics. The conclusions drawn from this study can provide meaningful guidance for engineering design and optimization of such rib-stiffened sandwich structures, incorporating both reinforcing and weakening phases in underwater engineering applications.
+
+1. Introduction
+
+The sandwich structures integrated with both generalized reinforcing and weakening phases have found widespread applications in aerospace, automotive, marine, and other related engineering fields owing to their excellent performance characteristics, including their remarkable strength-to-weight characteristics, excellent anti-corrosion performance, and acoustic function design flexibility [1,2]. The reinforcing phases include metal particles and glass/carbon fiber-enhanced lattice columns, trusses, and honeycomb partitions [3,4,5]. The weakened phases generally contain porous sound-absorbing or sound-insulating foam, a soft vibration damping layer, an acoustic functional cavity, and so on [6,7]. In marine engineering, the rib-stiffened PVC foam sandwich structures with reinforcing and weakening phases could be applied on superstructures, such as the sail and rudder plate of an underwater vehicle. With an appropriate acoustic function design, the sandwich structure could gain excellent performances of vibration attenuation and noise isolation or absorption [8,9], as well as its lightweight and high rigidity characteristics. Once excited by the external load in the underwater environment, it is imperative to investigate the acoustic vibration characteristics of the rib-stiffened sandwich in acoustic-structural coupling analysis.
+
+The research on composite structures has a long history, among which the most representative theories are the CLT (classical lamination theory) and FSDT (first-order shear deformation theory) [10]. The CLT assumes that plane sections remain plane and normal to the mid-surface after deformation, which is well-suited for thin composite plates where shear deformation effects are negligible [11,12,13]. The FSDT, by contrast, incorporates the role of rotary inertia and shear deformation, rendering it more appropriate for moderately thick composite plates [14,15,16]. These classical theories have not only elucidated fundamental mechanical responses of composite plates but have also been widely adopted as essential tools in the preliminary design and performance analysis of composite plate structures across various engineering domains. Based on the CLT and the FSDT, scholars have developed and derived various higher-order shear deformation theories (HSDTs). Tu et al. [17] adopted the third-order shear deformation theory (TSDT) as the theoretical basis and derived the calculation formula for the driving force of macroscopic fiber composite materials. To conduct static mechanical analysis of functionally graded saturated porous plates resting on the Paschen–Narkovsky elastic foundation, Tru et al. [18] proposed a novel quasi-3D-HSDT and employed it for the analysis. Lakhemissi et al. [19] used the integral-type-HSDT, in consideration of the transverse shear effect, to investigate the mechanical behavior of bidirectional functionally graded materials plates under elastic bending conditions. As an expansion of the CLT and the FSDT, HSDTs are widely applied in the field of composite laminated plate design. Compared with traditional theories, it could make more accurate predictions of structural stress and deformation.
+
+Over the past few decades, researchers have conducted extensive research on the mechanical and acoustic properties of rib-stiffened homogeneous plates. Hou et al. [20] conducted experiments and numerical methods to study the low-speed impact (LVI) and post-impact compression (CAI) behaviors of rib-strengthened CFRP panels. In the stability analysis of U-shaped rib-stiffened plates, Wang et al. [21] explored how aspect ratios affect stability performance via tests and numerical simulations, and put forward reasonable width-to-height ratio recommendations for engineering practice. Yekta et al. [22] derived an analytical method by solving the generalized Bragg wave incidence, which was used to consider the acoustic properties of multiple rib-stiffened plates connected in series. Chen et al. [23] investigated the influence of varying welding energy inputs on the vibro-acoustic characteristics of stiffened plate structures, performing a series of experiments on the vibration modes, underwater vibration responses, and acoustic radiation behaviors of such structures under different welding energy input conditions. In conclusion, the current extensive research on rib-stiffened plates mainly focuses on homogeneous structures. By combining experimental methods, numerical simulations, and analytical methods, the influences of the structural parameters, loading conditions, and processing techniques on the mechanical properties and acoustic characteristics of the structure have been systematically investigated, providing data and theoretical support for the design optimization of the base reinforcement plate structure.
+
+To meet the comprehensive requirements of underwater equipment, such as lightweighting, high strength, shock absorption, and pressure resistance, researchers have gradually broken through the limitations of homogeneous structures and achieved improvements in structural performance by introducing reinforcing phases in the core. Roun et al. [24] proposed a new type of nanocomposite material, which was used to integrate GPLs into the plate structure of a traditional functional graded matrix, and the performance of such plates was evaluated through free vibration and buckling analyses. Wang et al. [25] combined topological optimization to design three bimodal lattice/CFRP sandwich structures. Through testing the bending behavior and damage process, they revealed the complex failure modes and energy absorption enhancement mechanisms of this type of structure. Leveraging the interfacial stress transfer mechanism between the fiber-reinforced composite layer, damping layer, and reinforcing ribs, Wang et al. [26] proposed an innovative dynamic analytical model to investigate the dynamic performance of rib-reinforced composite damping plates integrated with randomly aligned carbon nanotubes. Madenci et al. [27,28] investigated the bending behavior of FG-CNTRC sandwich beams with a pultruded GFRP core, revealing the influence of the pultruded composite core on the bending mechanical response of the sandwich beam; meanwhile, systematic experimental and analytical studies on the buckling performance of FG-CNTRC sandwich beams have also been carried out, and the critical buckling load and failure mode of such structures have been clarified with a verifiable analytical prediction model. Most of the current research on enhanced phase-related studies focus on the modification of a single reinforcing phase and mostly target the optimization of the mechanical properties of the structures in an air environment. The research on the acoustic vibration coupling characteristics of rib-stiffened composite structures containing reinforcing phases in underwater environments is relatively insufficient, and there is even less involvement in the coordinated regulation with other functional phases.
+
+Unlike the reinforcing phases, which aim to improve the structural mechanical load-bearing capacity and vibration resistance stiffness as its main goal, the introduction of the functional weakening phases are guided by the core objective of actively dissipating vibration energy and optimizing the acoustic radiation characteristics [29]. Kong et al. [30] investigated a butterfly-like double-layer Helmholtz resonator structure lined with porous materials. By virtue of a distinctive resonant mechanism, this structure enabled efficient acoustic wave absorption at specific frequencies, thus achieving effective ambient noise attenuation. Wang et al. [31] designed a sound-absorbing periodically arrayed structure (SPAS) by leveraging the synergistic effects of cavity resonance and impedance transition. This structure exhibited a sound absorption coefficient of 0.9 within the frequency range of 2400–10,000 Hz at a water pressure of 1.5 MPa, and further realized broadband sound absorption at a water depth of 300 m. Liu et al. [32] proposed a new type of Helmholtz resonant metamaterial composed of perforated rigid panels and perforated porous materials. This structure dissipated acoustic energy via the porous material lining the back cavity, enabling nearly perfect sound absorption across a broad range of neck diameters. In the field of bio-inspired sandwich structures, Song et al. [33,34] studied the acoustic properties of honeycomb sandwich panels filled with paper fibers/cement panels, and conducted an in-depth analysis of the effects of the filling material, panel configuration, and core material type on the FHW sound insulation performance. In addition, the vibration characteristics of the foam-filled Beetle elytron plate (BEP) were also investigated by changing the structural parameters.
+
+Most current studies have mainly focused on rib-stiffened homogeneous plates and sandwich plates that contain only a single reinforcing phase or a single weakening phase; however, there is still a lack of research on the underwater acoustic vibration response characteristics of composite plates that have both rib stiffeners and simultaneously contain reinforcing and weakening phases. Such composite plates have broad application potential in the field of ship engineering. However, due to their complex form and the diverse components of the core layer materials, vibration analyses of these composite plates is difficult to conduct, except in cumbersome specific structural refinement modeling based on numerical simulations.
+
+To deal with the problem, this paper has constructed a theoretical method applicable to analyzing the acoustic vibration characteristics of rib-stiffened PVC foam sandwich structures with reinforcing and weakening phases in underwater environments. The composite core containing reinforcing and weakening phases is equivalently represented as a single orthotropic layer to simplify characterization. For the rib-stiffened sandwich under simply supported boundary constraints, the motion equations are derived by considering the coupling effect between the ribs and the sandwich plates. Regarding the coupling relationship between the underwater environment and the structure, the distribution of sound pressure fields is described by the Helmholtz equation, while the continuity condition on the fluid–solid interaction interface is controlled by the Euler equation. The control equations are solved using the Navier method to obtain the natural frequencies and acoustic vibration response. Parametric studies are further conducted to explore the influence of the parameters of the rib and core layers on the underwater acoustic vibration characteristics.
+
+The main innovations of this paper are reflected in the following three aspects. First, by focusing on rib-stiffened PVC foam sandwich structures with both reinforcing and weakening phases, a novel theoretical method has been established to realize the rapid and accurate calculation of acoustic vibration response. Unlike the existing analytical methods, the proposed method achieves a balance between calculation efficiency and precision, effectively filling the gap in efficient analytical methods for such complex sandwich structures with dual-phase core defects. Furthermore, the proposed equivalent single-layer theoretical method possesses excellent universality. It can be flexibly extended to the acoustic vibration analysis of other composite structures with complex core layers, providing a unified theoretical framework for similar complex structure analyses. Finally, this paper conducts systematic variable analyses of material and geometric parameters for the rib-stiffened PVC foam sandwich structures with reinforcing and weakening phases. This not only reveals the intrinsic influence laws of key parameters on the acoustic vibration characteristics of such structures but also provides targeted theoretical references and reliable data support for future related studies and engineering design optimization, which has important engineering application value.
+
+2. Analytical Method
+
+2.1. Structural Characterization of the Rib-Stiffened Sandwich
+
+The geometry and corresponding dimensions of orthogonal rib-stiffened PVC foam sandwich structures with reinforcing and weakening phases are illustrated in Figure 1. In this composite structure, the reinforcement cylinders serve as the reinforcing phase, while the cylindrical cavities act as the functional weakening phases. The planar dimensions of the structure are specified as a length of Lx and a width of Ly; meanwhile, the thicknesses corresponding to the lower face sheet, the core layer, and the upper face sheet are denoted by h1, h2, and h3. The total thickness is H=h1+h2+h3. The diameters of the reinforcements are expressed as dr, and the diameters of cavities are indicated as dc, with a uniform spacing of l between individual reinforcements or cavities. There are n1 and n2 rib stiffeners parallel to the x- and y-axes, respectively. The i-th rib is parallel to the y-axis and the j-th rib is parallel to the x-axis, as shown in the Figure 1 with i=1,2,…,n2 and j=1,2,…,n1. For rectangular section cases, the height and width of the i-th rib are hbi and bi, and those of the j-th rib are hbj and bj.
+
+2.2. Homogenization of the Core Layer
+
+Homogenization treatment is indispensable for the PVC foam core layer with reinforcing and weakening phases when conducting vibration characteristic analysis of the rib-stiffened sandwich. This treatment is then applied to derive its equivalent elastic constants. For the classical average-field approximation theory of two-phase composite materials, this study adopts the Mori–Tanaka method [35] to complete the above homogenization analysis. This method has a simple mathematical expression and explicit analytical solution:(1) Lh−1=I+CiLm+(Li−Lm)(CiI+CmS)−1(Lm−Li)/Lm
+
+For generally orthotropic materials, the stiffness tensor L takes the following form:(2) L=1/Exx−μxy/Eyy−μxz/Ezz000−μyx/Exx1/Eyy−μyz/Ezz000−μzx/Exx−μzy/Eyy1/Ezz0000001/Gyz0000001/Gxz000000 1/Gxy−1
+
+where Exx, Eyy, and Ezz denote the Young’s modulus along the three principal directions; Gxy, Gyz, and Gxz represent the shear modulus; μxy, μxz, and μyz denote the primary Poisson’s ratios; μyx, μzx, and μzy correspond to the secondary Poisson’s ratios; C refers to the volume fraction of the inclusion phase, where the subscripts ‘i’, ‘m’, and ‘h’ indicate the inclusion phase, matrix phase, and homogenized material, respectively; I is the identity tensor; and S is the Eshelby tensor, which is determined by the geometric shape of the inclusion and the Poisson’s ratio μm of the matrix phase. For cylindrical inclusions, this tensor satisfies the following expression:(3) S=000000μm21−μm5−4μm81−μm4μm−181−μm000μm21−μm4μm−181−μm5−4μm81−μm0000003−4μm41−μm0000001/20000001/2
+
+However, the classical Mori–Tanaka method is only applicable to composite material systems containing a single inclusion phase and lacks the capability to directly determine the equivalent elastic constants of rib-stiffened PVC foam sandwich structures with reinforcing and weakening phases. To address this limitation, this paper adopts the two-level progressive homogenization strategy proposed in Ref. [36]. Firstly, with isotropic PVC foam core material as the matrix phase, the voids are equivalently regarded as weakly elastic isotropic inclusions with Poisson’s ratio consistent with that of the core material. The volume fraction of cavities is defined as the ratio of the total volume of cavities to the total volume of the core matrix and cavities. Through the Mori–Tanaka method, they are homogenized into an anisotropic material A. Then, using material A as the new matrix phase and the reinforcements as the inclusion phase, the volume fraction of reinforcements is defined as the ratio of the total volume of reinforcements to the total volume of material A and reinforcements. Following the Eshelby tensor assumption in the first-level homogenization, the Mori–Tanaka method is again applied to obtain an anisotropic material B, achieving the equivalent homogenization of the three-phase reinforced foam core with cavities and reinforcements. Through this process, the orthogonal rib-stiffened PVC foam sandwich structures with reinforcing and weakening phases is simplified to a standard orthogonal rib-stiffened sandwich structure.
+
+2.3. Motion Equations of Rib-Stiffened Sandwich
+
+2.3.1. Constitutive Relations and Displacement Fields for Sandwich Structures
+
+The orthogonal rib-stiffened sandwich structure is made of a three-layer sandwich plate and ribs, as shown in Figure 2. To define the geometry of the sandwich plate, a global Cartesian coordinate system (x, y, z) is introduced, where the x-y-zero plane is positioned at the mid-plane of the structure. For each layer k (k = 1, 2, 3), the z-coordinates corresponding to its top and bottom interfaces are given by zk and zk−1. The ribs are exhibited in local Cartesian coordinate systems. Taking the j-th rib parallel to x-axis as an example, there are the coordinates (x, y, zb) and y = yj, and the x-y-zero plane is located on the neutral plane of rib.
+
+The Sandwich Plate
+
+The mechanical behavior of the interlayer plate is described using FSDT, and the following simplified assumptions are introduced: (1) after deformation, the line segments that were perpendicular to the middle plane prior to deformation remain straight, though they are no longer perpendicular to the middle plane; and (2) prior to deformation, the line segments are perpendicular to the middle plane, they do not undergo axial elongation after deformation, and their points maintain consistent lateral displacements. Based on these assumptions, the displacement field (U, V, W) of the interlayer plate can be expressed as:(4) Ux,y,z,t=u0(x,y,t)+z⋅θxx,y,tVx,y,z,t=v0(x,y,t)+z⋅θyx,y,tWx,y,z,t=w0x,y,t
+
+Based on the small deformation principle, the normal and shear strains are:(5) εxxεyyγxy=εxxm+z⋅εxxfεyym+z⋅εyyfγxym+z⋅γxyf ,  γyzγxz=θy+w0,yθx+w0,x
+
+with(6) εxxm=u0,x,  εxxf=θx,xεyym=v0,y,  εyyf=θy,yγxym=u0,y+v0,x,  γxyf=θx,y+θy,x
+
+where the subscript ‘,’ signifies partial differentiation with respect to the associated coordinate, as illustrated by the example: u0,x=∂u0/∂x.
+
+The k-th layer’s normal and shear stress distributions are defined as:(7) σxxσyyτxy(k)=Q11(k)Q12(k)0Q12(k)Q22(k)000Q66(k)εxxεyyγxy(k),  τxzτyz(k)=Q55(k)00Q44(k)γxzγyz(k)
+
+in which the stiffness parameters are(8) Q11k=Exxk1−μxykμyxk,Q22k=Eyyk1−μxykμyxk, Q12k=μ12kE11k1−μxykμyxkQ44k=Gyzk,Q55k=Gxzk,Q66k=Gzyk
+
+where Exxk, Eyyk, μxyk, μyxk, Gyzk, Gxzk, and Gzyk are the elastic constants.
+
+Subsequently, the internal force, shear forces, and bending moment resultants are then derived by integrating stress distributions across the thickness of the k-th layer, as given by:(9) NxxNyyNxyMxxMyyMxy=A11A120B11B120A12A220B12B22000A6600B66B11B120D11D120B12B220D12D22000B6600D66εxxmεyymγxymεxxfεyyfγxyf
+
+where Aij, Bij, and Dij (i,j=1,2,6) represent the coupling bending stiffness, expressed as:(10) Aij=∑k=13Qijk(zk−zk−1), Bij=12∑k=13Qijk(zk2−zk−12), Dij=13∑k=13Qijk(zk3−zk−13)
+
+For the composite sandwich plate, its top and bottom surfaces unsatisfied the shear stress-free boundary conditions. A shear-corrected expression [37] of the transverse shear force resultants is expressed as:(11) QxzQyz=C5500C44θx+w0,xθy+w0,y
+
+in which(12) 1C44=∑k=139Zk4Q44k/H2,  1C55=∑k=139Zk4Q55k/H2
+
+(13) Zk=zk−zk−1−83zk3−zk−13/H2+165zk5−zk−15/H4
+
+The Orthogonal Ribs
+
+The orthogonal ribs are also described by the FSDT of beams. According to the basic assumptions of FSDT, transverse normal stress is neglected, and the displacement components vary linearly through the thickness direction while maintaining continuity. Translational displacements and transverse rotations are assumed to be continuous at the conjunction lines of the first layer and the ribs. Perfect bonding without relative slip or separation is adopted between the ribs and the face sheets, ensuring displacement compatibility and force transmission at the interfaces. For the j-th rib oriented in a direction parallel to x-axis and the i-th rib oriented in a direction parallel to y-axis (x = xi), the displacement fields (Ub, Vb, Wb) are defined as:(14) Ub(yj)=ub(yj)+zb⋅θx(yj),  Wb(yj)=w0
+
+(15) Vb(xi)=vb(xi)+zb⋅θy(xi),  Wb(xi)=w0
+
+where ub and vb are the displacements on the neutral axes of ribs at the x and y directions, and can be written as:(16) ub(yj)=u0(yj)−ej⋅θx(yj)
+
+(17) vb(xi)=v0(xi)−ei⋅θy(xi)
+
+where ej = h2/2 + h1 + hbj/2 and ei = h2/2 + h1 + hbi/2
+
+The corresponding strains are given as:(18) εbxx(yj)=u0,x(yj)−ej⋅θx,x(yj)+zb⋅θx,x(yj),  γbxz(yj)=θx(yj)+w0,x
+
+(19) εbyy(xi)=v0,y(xi)−ei⋅θy,y(xi)+zb⋅θy,y(xi),  γbyz(xi)=θy(xi)+w0,y
+
+Then, the normal stress and shear stress are given as:(20) σbxx(yj)=Q11bjεbxx(yj),  τbxz(yj)=ksQ55bjγbxz(yj)
+
+(21) σbyy(xi)=Q22biεbyy(xi),  τbyz(xi)=ksQ44biγbyz(xi)
+
+where the shear correction factor ks = 5/6. For symmetrical laminates with relatively low anisotropy, using 5/6 as the shear correction factor is a common practice in both engineering and academic research. It can ensure calculation accuracy while also considering solution efficiency, and it is consistent with the analysis conditions and structural characteristics of this paper.
+
+Therefore, the stiffness parameters for the isotropic rib are expressed as:(22) Q11bj=Eb1−μb2,  Q55bj=Eb2(1−μb),  Q22bi=Eb1−μb2,  Q44bi=Eb2(1−μb)
+
+Subsequently, the internal forces, bending moments, and shear forces of the rib-stiffened sandwich are determined as:(23) Nbxx(yj)=A11bjεbxxm(yj),  Mbxx(yj)=D11bjεbxxf(yj),  Qbxz(yj)=C55bjγbxz(yj)
+
+(24) Nbyy(xi)=A22biεbyym(xi),  Mbyy(xi)=D22biεbyyf(xi),  Qbyz(xi)=C44biγbyz(xi)
+
+with(25) A11bj=Q11bjhbj,    D11bj=Q11bjhbj3 /12,    C55bj=ksQ55bjhbjεbxxm(yj)=u0,x(yj)−ej⋅θx,x(yj),    εbxxf(yj)=θx,x(yj)
+
+(26) A22bi=Q22bihbi,    D22bi=Q22bihbi3 /12,    C44bi=ksQ44bihbiεbyym(xi)=v0,y(xi)−ei⋅θy,y(xi),    εbyyf(xi)=θy,y(xi)
+
+2.3.2. Derivation of Motion Equations
+
+In the dynamic analysis of the rib-stiffened sandwich, the equations of motion are derived based on Hamilton’s principle, and the strain energy as well as the kinetic energy of the structure are presented as:(27) ∫t1t2δUpdt=∫t1t2∫Ω∑k=13∫zk−1zkσxxδεxx+σyyδεyy+τxyδγxy+τyzδγyz+τxzδγxzdzdxdydt=∫t1t2∫ΩNxxδεxxm+Nyyδεyym+Nxyδγxym+Mxxδεxxf+Myyδεyyf+Mxyδγxyf+Qxzδγxz+Qyzδγyzdxdydt
+
+(28) ∫t1t2δTpdt=∫t1t2∫Ω∑k=13∫zk−1zkρkU˙δU˙+V˙δV˙+W˙δW˙dzdxdydt=−∫t1t2∫Ω(ρ¯0u¨0+ρ¯1θ¨x)δu0+(ρ¯1u¨0+ρ¯2θ¨x)δθx+(ρ¯0v¨0+ρ¯1θ¨y)δv0+(ρ¯1v¨0+ρ¯2θ¨y)δθy+ρ¯0w¨0δw0dxdydt
+
+where ρ¯0,ρ¯1,ρ¯2=∑k=13∫zk−1zkρk⋅1,z,z2dz and the overdot ‘U˙’ denotes the differentiation with respect to time ‘t’; and ρk is the mass density of the k-th layer.
+
+The strain and kinetic energies of the n1 ribs parallel to x-axis are expressed as:(29) ∫t1t2δUbxdt=∫t1t2∑j=1n1bj∫−hbj/2hbj/2∫0Lxσbxx(yj)δεbxx(yj)+τbxz(yj)δγbxz(yj)dxdzdt=∫t1t2∑j=1n1bj∫ΩNbxxδεbxxm+Mbxxδεbxxf+Qbxzδγbxzδ¯(y−yj)dxdydt
+
+(30) ∫t1t2δTbxdt=∫t1t2∑j=1n1bj∫−hbj/2hbj/2∫0LxρbjU˙b(yj)δU˙b(yj)+W˙bδW˙bdxdzdt=−∫t1t2∑j=1n1bj∫Ω(ρ¯x0bju¨0+ρ¯x1bjθ¨x)δu0+(ρ¯x1bju¨0+ρ¯x2bjθ¨x)δθx+ρ¯x0bjw¨0δw0δ¯(y−yj)dxdydt
+
+where ρ¯x0bj,ρ¯x1bj,ρ¯x2bj=∫−hbj/2hbj/2ρbj⋅1,(zb−ej),(zb−ej)2dzb; δ¯ is the Dirac function; and ρbj is the mass density of the j-th rib parallel to x-axis.
+
+For the n2 ribs parallel to y-axis, these are expressed as:(31) ∫t1t2δUbydt=∫t1t2∑i=1n2bi∫−hbi/2hbi/2∫0Lyσbyy(xi)δεbyy(xi)+τbyz(xi)δγbyz(xi)dydzdt=∫t1t2∑i=1n2bi∫ΩNbyyδεbyym+Mbyyδεbyyf+Qbyzδγbyzδ¯(x−xi)dxdydt
+
+(32) ∫t1t2δTbydt=∫t1t2∑i=1n2bi∫−hbi/2hbi/2∫0LyρbiV˙b(xi)δV˙b(xi)+W˙bδW˙bdydzdt=−∫t1t2∑i=1n2bi∫Ω(ρ¯y0biv¨0+ρ¯y1biθ¨y)δv0+(ρ¯y1biv¨0+ρ¯y2biθ¨y)δθy+ρ¯y0biw¨0δw0δ¯(x−xi)dxdydt
+
+where ρ¯y0bi,ρ¯y1bi,ρ¯y2bi=∫−hbi/2hbi/2ρbi⋅1,(zb−ei),(zb−ei)2dzb; and ρbi is the mass density of the i-th rib parallel to y-axis.
+
+When the rib-stiffened sandwich plate is subjected to a normal excitation load qz(x,y) within the fluid domain, the external work is expressed as:(33) ∫t1t2δWdt=∫t1t2∫Ωqz(x,y)+p¯(x,y)δw0dxdydt
+
+where p¯(x,y) represents the pressure jump induced by the transverse structural vibration.
+
+The equation of Hamilton’s principle for the presented rib-stiffened sandwich is as follows:(34) ∫t1t2δ(Tp+Tbx+Tby)−δ(Up+Ubx+Uby)+δWdt=0
+
+Then the motion equations are derived as:(35) δu0:Nx,x+Nxy,y+∑j=1n1bjNbxx,xδ¯(y−yj)−ρ¯0u¨0+ρ¯1θ¨x−∑j=1n1bjρ¯x0bju¨0+ρ¯x1bjθ¨xδ¯(y−yj)  =0
+
+(36) δv0:Ny,y+Nxy,x+∑i=1n2biNbyy,yδ¯(x−xi)−ρ¯0v¨0+ρ¯1θ¨y−∑i=1n2biρ¯y0biv¨0+ρ¯y1biθ¨y δ¯(x−xi)=0
+
+(37) δθx:Mx,x+Mxy,y+∑j=1n1bj(Mbxx,x−ejNbxx,x−Qbxz)δ¯(y−yj)−Qxz−(ρ¯1u¨0+ρ¯2θ¨x)−∑j=1n1bjρ¯x1bju¨0+ρ¯x2bjθ¨xδ¯(y−yj)  =0
+
+(38) δθy:My,y+Mxy,x++∑i=1n2biMbyy,y−eiNbyy,y−Qbyzδ¯(x−xi)−Qyz−(ρ¯1v¨0+ρ¯2θ¨y)−∑i=1n2biρ¯y1biv¨0+ρ¯y2biθ¨yδ¯(x−xi)=0
+
+(39) δw0:Qxz,x+Qyz,y−ρ¯0w¨0+qz+p¯+∑j=1n1bj(Qbxz,x−ρ¯x0bjw¨0)δ¯(y−yj)+∑i=1n2bi(Qbyz,y−ρ¯y0biw¨0)δ¯(x−xi)=0
+
+2.3.3. Fluid–Solid Coupling and Acoustic Pressure Distribution
+
+Equation (39) describes the lateral vibration response of the rib-stiffened sandwich under the action of fluid–solid coupling. The acoustic pressure distribution at the spatial field point satisfies the Helmholtz equation, and its expression is as follows:(40) ∂2p∂x2+∂2p∂y2+∂2p∂z2+ω2c02p=0
+
+where c0 is the acoustic velocity in fluid; ω is the circular frequency; and the acoustic wave number is k0=ω/c0.
+
+Ref. [38] has presented an expression for the acoustic pressure associated with a thin plate as follows:(41) p(M0)=∫Spp¯(x,y)∂G(M,M0)∂zMdSp
+
+where Sp is defined as the plate surface; M(x,y,z) is an arbitrary point on Sp; zM denotes the normal direction to the surface at M; and the Green’s function G(M,M0) is expanded in the wavenumber domain, as given by:(42) G(M,M0)=∫−∞+∞∫−∞+∞j1ejkx(x−x0)ejky(y−y0)ejkzz−z08π2kzdkx dky
+
+with(43) kz=k02−kx2−ky2,  k02≥kx2+ky2j1kx2+ky2−k02,  k02<kx2+ky2
+
+where j1 is the imaginary unit; and kx and ky are the Fourier’s variables.
+
+The Green’s function G(M,M0) in the wavenumber domain is strictly valid for all r > 0. In the near-field (r≤O(λ)), its full form must be retained to capture evanescent waves for accurate fluid–solid coupling, while in the far-field (k0r≫1), the evanescent component decays, allowing for simplified radiation noise calculations under the Sommerfeld condition.
+
+The continuity condition of normal acceleration at the fluid–structure interface is derived from the Euler equation of fluid dynamics, which governs the motion of inviscid fluids. For small-amplitude acoustic perturbations, the convective acceleration term υ⋅∇υ is negligible, and the linearized Euler equation in the normal direction to the interface is as follows:(44) ρ0∂υn∂t=−∂p∂n
+
+where ρ0 is the fluid density; υn is the normal component of the fluid velocity; t is time; p is the acoustic pressure; and n is the unit normal vector to the interface. At the fluid–solid interface, the kinematic continuity condition requires that the normal velocity of the fluid equals the normal velocity of the solid structure:(45) υn=∂w∂t
+
+where w is the normal displacement of the solid. Substituting this into the linearized Euler equation yields:(46) ρ0∂2w∂t2=−∂p∂n
+
+where, in the frequency domain, the time derivative ∂/∂t is replaced by jω; while ω is the angular frequency. The normal acceleration of the solid is then ∂2w/∂t2=−ω2w, leading to the frequency-domain form of the continuity condition:(47) ρ0ω2w=∂p∂n
+
+By invoking this condition, the continuity of normal acceleration at the fluid–structure interface is expressed as:(48) ρ0ω2w0(x0,y0)=∂p(M0)∂z0z0=0=∫Spp¯(x,y)∂2G(M,M0)∂z0∂zMdSp
+
+Treating the current rib-stiffened sandwich structure as a thin plate and substituting Equation (39) into Equation (48), the transverse vibration equation is reformulated as:(49) δw0: −∫ΩQxz,x+Qyz,y−ρ¯0w¨0+qz+∑j=1n1bj(Qbxz,x−ρ¯x0bjw¨0)δ¯(y−yj)+∑i=1n2bi(Qbyz,y−ρ¯y0biw¨0)δ¯(x−xi)∂2G∂zM∂z0zM,z0=0dxdy=ρ0ω2w0
+
+Thus, Equations (35)–(38) and (49) constitute the new motion equations. Subsequently, by leveraging the derived internal force and moment resultants, the equations are expressed in five unknown variables (u0, v0, θx, θy, w0), as listed in Appendix A. In addition, the equations can also degenerate into the vacuum case when ρ0=0.
+
+2.4. Analytical Solution
+
+For the rib-stiffened sandwich under the four-sided simply supported boundary conditions, the displacement field is expanded in the form of a double trigonometric series to meet the displacement and rotation constraint requirements of the simply supported boundaries:(50) (u0,θx)(v0,θy)w0=ej1ωt∑m,n(u0mn,θxmn)ψxφy(v0mn,θymn)φxψyw0mnφxφy
+
+where ∑m,n denotes ∑m=1∞∑n=1∞; m and n denote the half-wave numbers; and φx=sinαx, φy=sinβy, ψx=cosαx, ψy=cosβy. u0mn, v0mn, w0mn, θxmn, and θymn are the modal amplitudes of the displacement and rotation components, with the wavenumbers given by α=mπ/Lx and β=nπ/Ly.
+
+The external force is written as:(51) qz=ej1ωt∑m,n(qzmnφxφy)
+
+where qzmn=∫0Lx∫0Ly(4qzφxφy/LxLy)dxdy.
+
+2.4.1. Free Vibration
+
+For the free vibration case, the external excitation is specified as qz = 0. By employing the Navier solution procedure, the five governing equations of motion are projected onto the orthogonal modal shapes, which include cos(pπx/Lx)sin(qπy/Ly), sin(pπx/Lx)cos(qπy/Ly), and sin(pπx0/Lx)sin(qπy0/Ly), where p,q=1,2…+∞. To extract the vibration mode (m, n), we set p=m and q=n, leading to the free vibration equations for this mode:(52) R¯11R¯12R¯13R¯14R¯15R¯21R¯22R¯23R¯24R¯25R¯31R¯32R¯33R¯34R¯35R¯41R¯42R¯43R¯44R¯45R¯51R¯52R¯53R¯54R¯55u0mnv0mnθxmnθymnw0mn=00000
+
+where the coefficient matrices R¯ij (i,j=1,2,…,5) are provided in detail in Appendix B. By setting the determinant of the system coefficient matrix to 0, the natural frequency corresponding to the vibration mode (m, n) can be solved explicitly.
+
+2.4.2. Forced Vibration
+
+For the forced vibration analysis, the external excitation is non-zero. To obtain the vibration response using the Navier solution approach, a modal truncation is introduced where m,p=1,2,3…M and n,q=1,2,3…N. This truncation procedure leads to the transformed forced vibration equations:(53) S¯11S¯12S¯13S¯14S¯15S¯21S¯22S¯23S¯24S¯25S¯31S¯32S¯33S¯34S¯35S¯41S¯42S¯43S¯44S¯45S¯51S¯52S¯53S¯54S¯555MN×5MNU¯1MN×1U¯2MN×1U¯3MN×1U¯4MN×1U¯5MN×1=0MN×10MN×10MN×10MN×1F¯MN×1
+
+with(54) U¯1MN×1=u011,u012,…,u01N,u021,u022,…,u02N,…,u0MNTU¯2MN×1=v011,v012,…,v01N,v021,v022,…,v02N,…,v0MNTU¯3MN×1=θx11,θx12,…,θx1N,θx21,θx22,…,θx2N,…,θxMNTU¯4MN×1=θy11,θy12,…,θy1N,θy21,θy22,…,θy2N,…,θyMNTU¯5MN×1=w011,w012,…,w01N,w021,w022,…,w02N,…,w0MNT
+
+(55) F¯MN×1=O¯11,O¯12,…O¯1N,O¯21,O¯22,…O¯2N,…O¯pq,…O¯MNT
+
+where S¯ij=T¯ij(pN−N+q,mN−N+n)MN×MN and O¯pq, and are listed in Appendix C.
+
+Once the displacement responses are derived, the normal mean square velocity (MQV) level is defined as:(56) MQV=10lg12LxLy∫0Lx∫0Lyvz2dxdy/refm
+
+Here, vz=2jπfw0 denotes the vibration velocity in the z-direction, where the excitation frequency is defined as f=ω/2π and the reference level for MQV is refm=1×10−18 m2s−2. The sound pressure distribution is obtained from Equation (41), with a reference sound pressure level of 1 × 10−6 Pa.
+
+3. Validation of Method Effectiveness
+
+Free and forced vibration investigations of the orthogonal rib-stiffened PVC foam sandwich structures with reinforcing and weakening phases in vacuum and water are conducted in this section, where the acoustic velocity and mass density of water are ρ0=1000 kg/m3 and c0=1500 m/s.
+
+3.1. Simulation Verification Description
+
+The orthogonal rib-stiffened PVC foam sandwich structures with reinforcing and weakening phases are further considered. For the geometric parameters of the structure, the plate length and width are specified as Lx=1.26 m and Ly=0.9 m. The thicknesses of the lower face sheet, core layer, and upper face sheet are defined as h1=0.005 m, h2=0.04 m, and h3=0.005 m. Additionally, the spacing between the adjacent reinforcements, the reinforcement diameter, and the cavity diameter are given as l=0.06 m, dr=0.01 m, and dc=0.02 m. The height and width of the rectangular rib is 0.03 m and 0.01 m. The face sheets comprise glass fiber-reinforced plastics (GFRP), with its Young’s modulus as E11 = E22 = 23.5 GPa and E33 = 4.5 GPa; shear modulus as G12 = G13 = G23 = 3.23 GPa; a Poisson’s ratio of μ12=μ13=μ23=0.14; and a mass density of 1800 kg/m3. The rib stiffeners comprise polyurethane (PU), with the Young’s modulus as Eb = 14 GPa; a Poisson’s ratio of μb=0.28; and a mass density of 760 kg/m3. The core material is PVC-H320, with its Young’s modulus as Ecm = 0.45 GPa; a Poisson’s ratio of μcm=0.30; and a mass density of 320 kg/m3. The reinforcement has the Young’s modulus as Ere = 55 GPa; a Poisson’s ratio of μre=0.30; and mass density of 1300 kg/m3. The weak modulus of the cavity is assumed as 1Pa. The theoretically predicted vibration results under vacuum and when submerged in water are validated by comparisons with the numerical simulation outcomes, including FE analyses conducted in ANSYS 16.0 and coupled FE/BE analyses performed in Virtual.Lab 13.3. Three cases of orthogonal ribs are taken into account as: (1) n1 = 1 and n2 = 2 (y1 = 0.45 m, x1 = 0.42 m, x2 = 0.84 m); (2) n1 = 2 and n2 = 2 (y1 = 0.30 m, y2 = 0.60 m, x1 = 0.42 m, x2 = 0.84 m); and (3) n1 = 2 and n2 = 3 (y1 = 0.30 m, y2 = 0.60 m, x1 = 0.30 m, x2 = 0.63 m, x3 = 0.96 m).
+
+To demonstrate the numerical analysis procedure, a rib-stiffened sandwich structure with n1 = 2 and n2 = 2 is selected as a case study, and its FE implementation in ANSYS is detailed as follows: a convergent FE model is established through iterative mesh refinement, consisting of 238,152 elements with a minimum mesh size of 2.5 mm (as illustrated in Figure 3), where the face sheets, core layer (including both the core material and internal reinforcements), and ribs are assigned SHELL181, SOLID185 and BEAM188 elements respectively, and the rib-stiffened structure is subjected to simply supported boundary conditions.(57) v=0, w=0   at  x=0, Lxu=0, w=0   at  y=0, Ly
+
+FE analyses are first performed to investigate the free vibration of the rib-stiffened sandwich structure in a vacuum environment. Using the obtained dry-mode vibration characteristics, coupled FE/BE analyses are subsequently carried out in Virtual.Lab to predict the vibration response of the structure submerged in water. To establish the acoustic coupling, the structural FE mesh is enclosed within an acoustic envelope mesh, and the FE/BE model is constructed via mesh mapping, as depicted in Figure 4. This acoustic envelope mesh comprises 7420 shell elements and is validated to ensure the convergence of FE/BE analyses, with the direct BE method adopted for acoustic field calculations.
+
+3.2. Convergence Verification
+
+Before performing the simulation calculation and after the two steps of the Mori–Tanaka homogenization method, the equivalent elastic constants for each stage are shown in the following Table 1.
+
+In order to analyze the relationship between the truncation orders (M, N) and the natural frequencies, convergence analysis was performed by gradually increasing the values of M and N. The calculation results show that the natural frequency gradually converges with the increase in truncation orders, and when M and N reach a certain threshold, the natural frequency value tends to be stable and no longer changes significantly, as clearly demonstrated by the convergence curves in the Figure 5.
+
+On this basis, the natural frequencies of the underwater (m, n) modes of the composite structure are listed in the following Table 2 (m = 1, 2, 3, 4, 5, 6, and n = 1, 2, 3, 4, 5), which complements the graphical results and provides specific data supporting the convergence analysis. From the table, it can be seen that the natural frequencies of modes (6, n) and (m, 5) are both greater than 500 Hz, which is consistent with the high-frequency distribution law reflected in the Figure 5. Therefore, by choosing M = 5 and N = 4 as the truncation values, we can ensure that all the modes that contribute to the response within the analysis frequency range are included without wasting computing resources due to the inclusion of too many non-essential higher-order modes—this is the optimal choice that balances accuracy and efficiency.
+
+To ensure the reliability of the numerical results and to eliminate the influence of mesh discretization error, a mesh convergence study was performed in ANSYS. As shown in Table 3, two finite element mesh schemes were established: an original mesh with 238,152 elements and a refined mesh with 365,640 elements. The results showed that the relative differences in the natural frequencies of all considered modes between the refined and original meshes were less than 0.6%. This level of discrepancy satisfied the accuracy requirements for both engineering and academic analyses, confirming that the original mesh scheme has achieved mesh convergence and is sufficiently refined to yield reliable results for the subsequent vibro-acoustic response investigations.
+
+In addition, the influence of acoustic grid density on the calculation results was verified, and the calculation results of each mode under the two grid schemes (7420 and 11,280) were compared, as shown in Table 4. The results show that under the calculated modes, the calculation differences in the two grids are all less than 0.5%, which proves that when the number of acoustic grids reaches 7420, the numerical solution is close to the grid-independent solution. Further increasing the grid density has a limited effect on improving the accuracy; therefore, in this study, 7420 is selected as the benchmark density for the acoustic grid, which can ensure calculation accuracy and improve calculation efficiency.
+
+3.3. Validity for Free Vibration
+
+Table 5 displays the comparison of achieved analytical and numerical natural frequencies, both in vacuum and in water. The first five modes of presented sandwich structures with three cases of orthogonal ribs are listed, and the errors of the analytical results are calculated. It can be seen that there is good consistency between the first five analytical and numerical natural frequencies, while all the errors were no more than 3.87%. Hence, the correctness of the proposed analytical method is confirmed for the free vibration analysis of the rib-stiffened sandwich structure. In addition, when the number of ribs increases and the cases of ribs tend to be concentrated, all of the first five natural frequencies show rising trends, except for the mode (1, 2) of rib case (n1 = 2, n2 = 2) and the mode (3, 1) of rib case (n1 = 2, n2 = 3)—in general, the ribs enhance the global bending stiffness of whole sandwich structure.
+
+Under the three different rib arrangement conditions, the natural frequencies in the water environment are significantly lower than those in the vacuum environment. The frequency ratio fv/fw is greater than 2.9 in all cases. This clearly indicates that the additional mass effect of the water significantly reduces the natural frequencies of the structure. At the same time, the frequency ratio decreases as the modal order increases; for example, in the (n1 = 1, n2 = 2) condition, from the mode (1, 1) of 4.25 to the mode (2, 2) of 2.99, it shows that the influence of the additional mass on higher-order modes is relatively small. Moreover, the influence of different rib arrangements on the frequency ratio is small, indicating that the additional mass effect is mainly dominated by the coupling effect between the fluid and the structure, rather than the stiffness change in the ribs themselves.
+
+3.4. Validity for Forced Vibration
+
+Calculating the underwater forced vibration response of orthogonal rib-stiffened PVC foam sandwich structures with reinforcing and weakening phases based on the second reinforcement rib case (n1 = 2, n2 = 2). A concentrated force in the z-direction is applied to the surface of the reinforced plate. The point of application of the excitation force is at (0.3, 0.3, 0), and the magnitude of the force is 1 N. The frequency range of the analysis is 1–500 Hz, with a step size of 1 Hz. In the underwater acoustic analysis, the fluid domain is assumed to be infinite, homogeneous, compressible, inviscid, and quiescent water, which satisfies the Helmholtz equation in the frequency domain. For the sound pressure evaluation, the coordinate of the field point in the sound pressure is (0.63, 0.45, 5), which is located in the far field to characterize the underwater acoustic radiation characteristics of the structure. The results of the ESL theoretical modeling approach based on core equivalent homogenization are compared with the results of the FE/BE numerical simulation approach, as shown in Figure 6. As can be seen, the analytical solution of the ESL theoretical modeling approach agrees well with the numerical solution. In the region of low frequencies, the MQV curves essentially overlap, but the peaks of the curves are shifted in the region of high frequencies. For the field point sound pressure, there are good agreements between the present analytical results and the ones from FE/BE simulation. Thus, the present FSDT-based analytical approach has good accuracy for the underwater acoustic vibration research of rib-stiffened PVC foam sandwich structures with reinforcing and weakening phases.
+
+Figure 7 compares the influence of different shear correction factors on the calculated vibro-acoustic results. Parametric studies confirm that the shear correction factor (ks) exhibits a frequency-dependent impact on vibro-acoustic responses. At low frequencies, the influence of ks on both the MQV and field point sound pressure is negligible with the curves for different values nearly coinciding. Nevertheless, in the high-frequency domain (>200 Hz), a larger ks value significantly amplifies the vibration response, inducing distinct deviations in the radiated sound pressure. These results emphasize that while the low-frequency analysis can tolerate a certain flexibility in selecting α, a rational and physically justified choice of ks is critical for high-frequency simulations to guarantee reliable predictions of structural vibration and noise.
+
+4. Acoustic Vibration Performance
+
+The underwater acoustic vibration radiation performance of orthogonal rib-stiffened PVC foam sandwich structures with reinforcing and weakening phases is analyzed by varying the material and geometrical parameters based on the rib case (n1 = 2, n2 = 2).
+
+4.1. Influence of Core Layer Parameters
+
+4.1.1. Effect of Core Layer Materials
+
+To explore the influence of core layer materials on the acoustic vibration performances of the orthogonal rib-stiffened PVC foam sandwich structures with reinforcing and weakening phases, three cases of PVC foam are respectively adopted as core layer materials, as listed in Table 6. The underwater natural frequencies of the sandwich are given in Table 7. It can be observed that across PVC-H100, PVC-H250, and PVC-H320, the Young’s modulus and mass density of the core layer both present a gradually increasing tendency. All the natural frequencies increase significantly, indicating that the stiffness of PVC foam core exhibits greater effects on the inherent vibrations. The underlying mechanism is that the added mass of water dominates the mode mass of the underwater, and thus the increase in the mass density of the core material has little influence.
+
+Figure 8 presents the MQV and field point sound pressure of the sandwich with different core layer material. Across PVC-H100, PVC-H250, and PVC-H320, both the MQV and field point sound pressure curves shift to the right with the increases in the natural frequencies. The MQV curve generally displays the diminishing trend and the total level at the whole range decreases, owing to the enhanced stiffness of the sandwich by the harder core material. The sound pressure curve also declines, especially at the higher frequency. The total level of sound pressure at the whole range 1–500 Hz decreases from 126.26 dB with PVC-H100 to 121.74 dB with PVC-H250, and to 122.52 dB with PVC-H320.
+
+4.1.2. Effect of the Cavity Diameter
+
+For the orthogonal rib-stiffened PVC foam sandwich structures with reinforcing and weakening phases, three typical cavity column diameters, namely 20 mm, 30 mm, and 40 mm, are designed to investigate their effects on the underwater dynamic characteristics. As presented in Table 8, the cavity diameter is negatively correlated with the underwater natural frequencies of the sandwich structure. Increasing the cavity diameter simultaneously reduces both the overall stiffness and mass of the PVC foam core layer. Nevertheless, the variation in natural frequencies is mainly dominated by the reduction in structural stiffness, which outweighs the effect of the mass reduction and thus, leads to a decrease in natural frequencies. Furthermore, the discrepancies in natural frequencies among the three different cavity diameter configurations become increasingly significant with the increase in frequency, exhibiting more pronounced differences in the high-frequency region.
+
+Figure 9 shows the MQV and field point sound pressure curves of the structure under different cavity diameter schemes. From the above discussion, it can be concluded that variations in the cavity diameter give rise to corresponding changes in the structural natural frequencies, which is then manifested as a curve shift in the acoustic vibration curve graph, especially in the high-frequency range where this shift phenomenon is more obvious. The total level of the MQV rose from 125.18 dB with a cavity diameter of 20 mm to 126.01 dB with a cavity diameter of 30 mm, and to 126.91 dB with a cavity diameter of 40 mm, whereas the total level of field point sound pressure decreased.
+
+4.1.3. Effect of Reinforcing Column Diameter
+
+The diameters of the reinforcing columns are modified successively as 5 mm, 10 mm, and 15 mm. Table 9 lists the influence of the different diameters of reinforcing columns on the underwater natural frequencies of the structure. Analysis shows that under the same mode, the larger the diameter of the reinforcing column, the greater the underwater natural frequencies of the structure. Because increasing the diameter of the reinforcing column will enhance the overall stiffness and mass of the structure within this frequency range, the effect of structural stiffness on natural frequencies predominates over other influencing factors; however, from an overall perspective, fluctuations in the natural frequencies of the rib-stiffened structures under the three different diameter reinforcement column schemes are not particularly significant.
+
+As can be seen in Figure 10, the MQV curves and the field point sound pressure curves under three different enhanced column diameter schemes almost coincide in the low-frequency region. Only in the high-frequency region can the curve shift be observed, though the amplitude of the shift is not very large. By observing the overall level data of the curve, it can be found that the difference in the total levels among the three schemes does not exceed 0.6 dB, indicating that changing the diameter of the reinforcing column does not have a particularly significant impact on the MQV and the field point sound pressure of the structure
+
+4.1.4. Effect of Structural Damping
+
+The influence of structural damping on the vibro-acoustic characteristics of composite structures is systematically investigated in consideration of two representative damping coefficients, 0.02 and 0.2. As illustrated in Figure 11, structural damping exerts a significant modulation effect on both sthe tructural vibration and underwater acoustic radiation. For the low-damping condition, sharp and prominent resonant peaks are observed in both the MQV and field point sound pressure curves, with the total vibration level reaching 125.18 dB and the total sound pressure level reaching 122.52 dB. In contrast, increasing the structural damping to 0.2 effectively suppresses the resonant amplitudes across the entire frequency range, resulting in a 4.30 dB reduction in the total MQV level and a 4.99 dB reduction in the total field point sound pressure level. This quantitative comparison fully demonstrates that structural damping is a critical parameter for vibration and noise reduction design of underwater composite structures, where appropriately increasing the damping coefficient can achieve remarkable noise reduction performance.
+
+4.2. Influence of Rib Parameters
+
+4.2.1. Effect of Rib Material
+
+The ribs were fabricated from CFRP, PU, and steel, with material parameters listed in Table 10. Table 11 shows that rib material properties significantly affect the underwater natural frequencies of the structure. The natural frequencies of the CFRP and steel rib schemes are very close, while those of the PU rib scheme are distinctly lower. This is attributed to the similar Young’s modulus of CFRP (230 GPa) and steel (210 GPa), leading to negligible stiffness differences. Despite the much higher density of steel, its mass contribution to the overall structure is limited. In contrast, the far lower Young’s modulus of PU causes a significant reduction in structural stiffness K and the natural frequency parameter K/M, resulting in substantially lower natural frequencies.
+
+By observing Figure 12, it can be seen that for the structure with CFRP and steel ribs, whether it is the MQV curve or the field point sound pressure curve, the peak positions of the curves almost overlap, and their shapes are also highly similar. This is a direct manifestation of the close natural frequencies of the two, indicating that their vibration and acoustic resonance characteristics are basically the same. The peak value of the structural response curve of the rib material PU is concentrated in the lower-frequency region, which is significantly staggered from the peak distribution of CFRP and steel. This is the result of the relatively low natural frequency of the PU, which reflects that the frequency band characteristics of its response are significantly different from the previous two. The total level values of the three are close (CFRP total level = 122.67 dB; PU total level = 125.18 dB; steel total level = 123.19 dB), indicating that the overall response intensity difference is small, though the frequency distribution characteristics of the response are significantly different.
+
+4.2.2. Effect of Rib Widths
+
+The underwater natural frequencies of the orthogonal rib-stiffened PVC foam sandwich structures with reinforcing and weakening phases are calculated by varying the rib width as 10 mm, 20 mm, and 30 mm, respectively, with the results presented in Table 12. The data demonstrate a significant positive correlation between the rib width and the underwater natural frequencies of the structure: as the rib width increases, the natural frequencies of the structure increase monotonically across all analyzed modes. Increasing the rib width simultaneously enhances both the overall structural stiffness and its mass; however, within the analyzed frequency range of 1–500 Hz, the influence of stiffness on the natural frequencies is significantly more pronounced than that of mass, resulting in a net increase in the natural frequencies with the increase in rib width.
+
+As the natural frequencies of the structure are in direct proportion to the rib width, the MQV curves and field point sound pressure curves of the three different rib width schemes in Figure 13 mainly show that the characteristic peaks have shifted. The overall level of MQV shows a decreasing trend (10 mm total level = 122.67 dB; 20 mm total level = 121.96 dB; 30 mm total level = 121.88 dB), but the overall level of field point sound pressure shows an increasing trend (10 mm total level = 123.62 dB; 20 mm total level = 124.19 dB; 30 mm total level = 124.80 dB). It indicates that although the increase in rib width suppresses vibration, the overall sound pressure intensity at the field point rises instead, and the conversion efficiency of vibration energy to sound radiation changes with the variation in rib width.
+
+4.2.3. Effect of Rib Height
+
+The height of the ribs was varied as 20 mm, 30 mm, and 40 mm in sequence. The data analysis in Table 13 indicates that the influencing trend of rib height on the underwater natural frequency of the structure was the same as that of width, and both are in direct proportion. Both the global stiffness and total mass of the structure increase simultaneously with an elevation in rib height; however, since the influence of stiffness is dominant within this frequency range, it has manifested as the higher the rib height, the greater the natural frequency under the same mode.
+
+Figure 14 shows the MQV curves and field point sound pressure curves of the structures across three different rib height schemes, as well as their total levels. Within the frequency interval of 1–500 Hz, the data indicate that both the MQV curve and the field point sound pressure curve have experienced a shift in their peak values due to the increase in rib height. As the rib height increases, the total level of MQV shows a downward trend, but the total level of sound pressure gradually rises. Because the rib height increases, the stiffness of the structure becomes greater. Under the same external excitation, the vibration displacement and velocity amplitude of the structure will relatively decrease. The increase in the rib height of the field point sound pressure curve causes the resonance peak to shift to the right, slightly increasing the acoustic radiation efficiency of structural vibration and leading to a gradual rise in the total sound pressure level.
+
+4.3. Anova-like Contribution Analysis
+
+To quantify the influence weights of each design parameter on the dynamic performance of the structure, based on the principle of single-factor analysis of variance (ANOVA), the sum of squared deviations of each parameter is calculated and its proportion to the total sum of squared deviations is defined as the contribution degree, thereby identifying the key parameters.
+
+For each design parameter j with three levels (j=A,B,…,F), the sum of squared deviations Sj is obtained by squaring the differences between each level’s response value and its mean:(58) Sj=∑i=13(xji−x¯j)2
+
+where x¯j represents the mean response value of parameter j for the three levels; and the total deviation squared sum ST is the sum of the squared deviations of all parameters. The final contribution degree ηj is calculated as follows:(59) ηj=SjST×100%
+
+Based on the total level data obtained from the previous test in Section 4, the squared sum of deviations and the contribution degree of various parameters of the MQV and the sound pressure at the field points were calculated. The results are shown in the Table 14.
+
+From the Table 14, it can be seen that the core material is the most crucial factor affecting the level of structural vibration with a contribution rate of 47.28%, followed by the material of ribs (22.50%) and then the height of ribs (12.42%). The combined contribution rate of these three parameters exceeds 80%, making them the key design variables for controlling the magnitude of structural vibrations. In addition, the core material also plays a decisive role in the sound radiation performance, with a contribution rate of up to 83.15%. This indicates that the acoustic impedance characteristics of the core material are the dominant factor determining the amount of noise radiated outward by the structure. The secondary influencing factors are the height of ribs (9.01%) and the material of ribs (8.51%), while the contributions of the cavity diameter and the reinforcing diameter column are both less than 2%, having a negligible impact on the overall sound pressure level.
+
+5. Conclusions
+
+This paper proposed and deduced a novel semi-analytical method for calculating the underwater vibration response of orthogonal rib-stiffened PVC foam sandwich structures with both reinforcing and weakening phases based on the ESL theory. This method was employed to efficiently predict the underwater natural frequencies, MQV, and field point sound pressure of the target structure. The numerical results were systematically compared with both the published literature data and FE/BE numerical solutions, and excellent agreement was achieved, which rigorously validated the accuracy, reliability, and engineering applicability of the presented method. Furthermore, to reveal the unique underwater acoustic vibration response laws and regulation mechanisms of orthogonal rib-stiffened PVC foam sandwich structures with reinforcing and weakening phases, parametric studies were carried out by adjusting the rib material and dimensions, as well as the core layer parameters. The main conclusions that were drawn are as follows. When the core layer adopts materials such as PVC-250 and PVC-320, the overall levels of structural MQV and field point sound pressure can be remarkably reduced simultaneously. Increasing the cavity diameter leads to an increase in the total MQV level but a decrease in the total field point sound pressure level. In contrast, increasing the diameter of the reinforcing columns reduces the total MQV level, but it results in an elevated total field point sound pressure level. The rib material properties exert a pronounced regulatory effect on the acoustic vibration response characteristics of the structure, and its selection should comprehensively consider key indicators such as stiffness and density. The increase in the rib height and width shows a consistent influence trend, as both can lead to a decrease in the total MQV level and a corresponding increase in the total field point sound pressure level. The fluid–solid coupling model of the orthogonal rib-stiffened PVC foam sandwich structures with both reinforcing and weakening phases established in this paper only takes into account the additional mass effect of water, and it does not calculate acoustic damping and radiation loss. Future work can introduce radiation impedance, structural damping, and fluid damping, with further studies on the underwater vibration response of the structure and the acoustic radiation characteristics.
+
+Author Contributions
+
+Conceptualization, R.D. and Y.L.; Methodology, Z.M. and Y.L.; Validation, Z.M.; Formal analysis, R.D.; Investigation, Z.Z.; Resources, R.D.; Data curation, Z.M.; Writing—original draft, Z.M.; Writing—review & editing, Z.Z.; Visualization, R.D.; Supervision, Z.Z.; Project administration, Y.L.; Funding acquisition, Z.Z. All authors have read and agreed to the published version of the manuscript.
+
+Institutional Review Board Statement
+
+Not applicable.
+
+Data Availability Statement
+
+The raw/processed data required to reproduce these findings cannot be shared at this time due to legal or ethical reasons.
+
+Conflicts of Interest
+
+The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
+
+Appendix A
+
+Motion equations of the submerged rib-stiffened sandwich are as follows:(A1) δu0:A11u0,x,x+A66u0,y,y+A12+A66v0,x,y+B11θx,x,x+B66θx,y,y +B12+B66θy,x,y+∑j=1n1bjA11bju0,x,x −ejθx,x,xδ¯(y−yj) −ρ¯0u¨0+ρ¯1θ¨x−∑j=1n1bjρ¯x0bju¨0+ρ¯x1bjθ¨xδ¯(y−yj) =0
+
+(A2) δv0:A12+A66u0,x,y+A66v0,x,x+A22v0,y,y+B12+B66θx,x,y+B66θy,x,x+B22θy,y,y+∑i=1n2biA22biv0,y,y−eiθy,y,yδ¯(x−xi) −ρ¯0v¨0+ρ¯1θ¨y−∑i=1n2biρ¯y0biv¨0+ρ¯y1biθ¨yδ¯(x−xi)=0
+
+(A3) δθx:B11u0,x,x+B66u0,y,y+B12+B66v0,x,y  +D11θx,x,x+D66θx,y,y−C55θx−∑j=1n1bjC55bjθxδ¯(y−yj)     +D12+D66θy,x,y  −C55w0,x+∑j=1n1bjD11bjθx,x,x−ejA11bju0,x,x−ejθx,x,x−C55bjw0,xδ¯(y−yj) −ρ¯1u¨0+ρ¯2θ¨x−∑j=1n1bjρ¯x1bju¨0+ρ¯x2bjθ¨xδ¯(y−yj) =0
+
+(A4) δθy:B12+B66u0,x,y+B66v0,x,x+B22v0,y,y +D66θy,x,x+D22θy,y,y−C44θy−∑i=1n2biC44biθyδ¯(x−xi)+D12+D66θx,x,y−C44w0,y+∑i=1n2biD22biθy,y,y−eiA22biv0,y,y−eiθy,y,y−C44biw0,yδ¯(x−xi)−ρ¯1v¨0+ρ¯2θ¨y−∑i=1n2biρ¯y1biv¨0+ρ¯y2biθ¨yδ¯(x−xi)=0
+
+(A5) δw0:−∫ΩC55θx,x+C55w0,x,x−ρ¯0w¨0+C44θy,y+C44w0,y,y+qz+∑j=1n1bjC55bjθx,x+C55bjw0,x,x−ρ¯x0bjw¨0δ¯(y−yj) +∑i=1n2biC44biθy,y+C44biw0,y,y−ρ¯y0biw¨0δ¯(x−xi) ⋅∂2G∂zM∂z0zM,z0=0dxdy=ρ0ω2w0
+
+Appendix B
+
+The coefficients in Equation (48) are as follows:(A6) R¯11=−A11α2+A66β2−ρ¯0ω2−∑j=1n1bjA11bjα2−ρ¯x0bjω2⋅κ(j)   R¯12=−αβA12+A66R¯13=−B11α2+B66β2−ρ¯1ω2+∑j=1n1bjejA11bjα2+ρ¯x1bjω2⋅κ(j)   R¯14=−αβB12+B66   R¯15=0
+
+(A7) R¯21=−αβA12+A66   R¯22=−A66α2+A22β2−ρ¯0ω2−∑i=1n2biA22biβ2−ρ¯y0biω2⋅ι(i)R¯23=−αβB12+B66   R¯24=−B66α2+B22β2−ρ¯1ω2+∑i=1n2bieiA22biβ2+ρ¯y1biω2⋅ι(i)   R¯25=0
+
+(A8) R¯31=−B11α2+B66β2−ρ¯1ω2+∑j=1n1bjejA11bjα2+ρ¯x1bjω2⋅κ(j)   R¯32=−αβB12+B66R¯33=−D11α2+D66β2+C55−ρ¯2ω2 −∑j=1n1bjD11bjα2+ej2A11bjα2+C55bj−ρ¯x2bjω2⋅κ(j)R¯34=−αβD12+D66   R¯35=−αC55−α∑j=1n1bjC55bj⋅κ(j)
+
+(A9) R¯41=−αβB12+B66   R¯42=−B66α2+B22β2−ρ¯1ω2 +∑i=1n2bieiA22biβ2+ρ¯x1biω2⋅ι(i)R¯43=−αβD12+D66   R¯45=−βC44−β∑i=1n2biC44bi⋅ι(i)R¯44=−D66α2+D22β2+C44−ρ¯2ω2−∑i=1n2biD22biβ2+ei2A22biβ2+C44bi−ρ¯y2biω2⋅ι(i)
+
+(A10) R¯51=0   R¯52=0R¯53=−αC55⋅γmn mn−α∑j=1n1bjC55bj⋅γmn  mnbj   R¯54=−βC44⋅γmn mn−β∑i=1n2biC44bi⋅γmn  mnbiR¯55=−C55α2+C44β2−ρ¯0ω2  ⋅γmn mn+ρ0ω2⋅g(m,m,Lx)g(n,n,Ly)           −∑j=1n1bjC55bjα2−ρ¯x0bjω2⋅γmn  mnbj−∑i=1n2biC44biβ2−ρ¯y0biω2⋅γmn  mnbi
+
+where(A11) κ(j)=2Lysin2[yjnπ/Ly],   ι(i)=2Lxsin2[ximπ/Lx]
+
+(A12) f(m1,m2,l0)=∫0l0cosm1πξl0cosm2πξl0dξ=0  ,  m1≠m2l0/2 ,m1=m2g(m1,m2,l0)=∫0l0sinm1πξl0sinm2πξl0dξ=0  ,  m1≠m2l0/2 ,m1=m2
+
+(A13) γpq mn=∫Sp∫SpsinmπxLxsinnπyLysinpπxLxsinqπyLy∂2G(M,M0)∂zM∂z0zM,z0=0dxdydx0dy0=2j1Lx2Ly2π2∫0∞∫0∞pqmnk02−kx2−ky2(1−(−1)pcoskxLx)(1−(−1)qcoskyLy)(Lx2kx2−p2π2)(Ly2ky2−q2π2)(Lx2kx2−m2π2)(Ly2ky2−n2π2)dkxdky
+
+As the parity of p and m (or q and n) is different, there is γpq mnbj =0 (or γpq  mnbi =0). On the contrary, when the parity is same, these are as follows:(A14) γpq  mnbj =∫Sp∫SpsinmπxLxsinnπyLyδ¯(y−yj)sinpπx0Lxsinqπy0Ly⋅∂2G(M,M0)∂zM∂zM0zM,z0=0dxdydx0dy0 =j1Lx2π2∫−∞+∞∫0+∞pqmLyk02−kx2−ky2[1−(−1)pcoskxLx][(−1)qe−jkyLy−1](Lx2kx2−m2π2)(Lx2kx2−p2π2)(Ly2ky2−q2π2)sinnπyjbejkyyjdkxdky
+
+(A15) γpq   mnbi=∫Sp∫SpsinmπxLxsinnπyLyδ¯(x−xi)sinkπx0Lxsinlπy0Ly⋅∂2G(M,M0)∂zM∂zM0zM,z0=0dxdydx0dy0  =j1Ly2π2∫−∞+∞∫0+∞pqnLxk02−kx2−ky2[1−(−1)qcoskyLy][(−1)pe−jkxLx−1](Ly2ky2−q2π2)(Ly2ky2−n2π2)(Lx2kx2−p2π2)  sinmπxiLxejkxxidkydkx
+
+Appendix C
+
+The expressions of T¯ij and O¯pq in Equations (49)–(51) are as follows:κ¯(j)=f(p,m,Lx)sin2[yjnπ/Ly],   ι¯(i)=sin2[ximπ/Lx]f(q,n,Ly)
+
+(A16) T¯11=−A11α2+A66β2−ρ¯0ω2⋅ξ1−∑j=1n1bjA11bjα2−ρ¯x0bjω2⋅κ¯(j)T¯13=−B11α2+B66β2−ρ¯1ω2⋅ξ1+∑j=1n1bjejA11bjα2+ρ¯x1bjω2⋅κ¯(j)   T¯1k=R¯1k⋅ξ1  (k=2,4,5)
+
+(A17) T¯22=−A66α2+A22β2−ρ¯0ω2⋅ξ2−∑i=1n2biA22biβ2−ρ¯y0biω2⋅ι¯(i)T¯24=−B66α2+B22β2−ρ¯1ω2⋅ξ2+∑i=1n2bieiA22biβ2+ρ¯y1biω2⋅ι¯(i)   T¯2k=R¯2k⋅ξ2  (k=1,3,5)
+
+(A18) T¯31=−B11α2+B66β2−ρ¯1ω2⋅ξ1+∑j=1n1bjejA11bjα2+ρ¯x1bjω2⋅κ¯(j)   T¯32=−αβB12+B66⋅ξ1T¯33=−D11α2+D66β2+C55−ρ¯2ω2 ⋅ξ1−∑j=1n1bjD11bjα2+ej2A11bjα2+C55bj−ρ¯x2bjω2⋅κ¯(j)T¯34=−αβD12+D66⋅ξ1   T¯35=−αC55⋅ξ1−α∑j=1n1bjC55bj⋅κ¯(j)
+
+(A19) T¯41=−αβB12+B66⋅ξ2   T¯42=−B66α2+B22β2−ρ¯1ω2⋅ξ2+∑i=1n2bieiA22biβ2+ρ¯x1biω2⋅ι¯(i)T¯43=−αβD12+D66⋅ξ2   T¯45=−βC44⋅ξ2−β∑i=1n2biC44bi⋅ι¯(i)T¯44=−D66α2+D22β2+C44−ρ¯2ω2⋅ξ2−∑i=1n2biD22biβ2+ei2A22biβ2+C44bi−ρ¯y2biω2⋅ι¯(i)
+
+(A20) T¯51=0   T¯52=0T¯53=−αC55⋅γpq mn −α∑j=1n1bjC55bj⋅γpq mnbj   T¯54=−βC44⋅γpq mn −β∑i=1n2biC44bi⋅γpq mnbiT¯55=−C55α2+C44β2−ρ¯0ω2 ⋅γpq mn+ρ0ω2⋅ξ3           −∑j=1n1bjC55bjα2−ρ¯x0bjω2⋅γpq mnbj−∑i=1n2biC44biβ2−ρ¯y0biω2⋅γpq mnbi
+
+where(A21) κ¯(j)=f(p,m,Lx)sin2[yjnπ/Ly],   ι¯(i)=sin2[ximπ/Lx]f(q,n,Ly)
+
+(A22) ξ1=f(p,m,Lx)g(q,n,Ly)ξ2=g(p,m,Lx)f(q,n,Ly)ξ3=g(p,m,Lx)g(q,n,Ly)
+
+Figure 1 Geometry and dimension of orthogonal rib-stiffened PVC foam sandwich structures with reinforcing and weakening phases.
+
+Figure 2 Deformations and coordinate system of the rib-stiffened sandwich: (a) x-z section; (b) y-z section.
+
+Figure 3 The FE model of orthogonal rib-stiffened PVC foam sandwich structures with reinforcing and weakening phases: (a) the whole structure; (b) the partial section.
+
+Figure 4 The mesh mapping and FE/BE mesh in Virtual.Lab.
+
+Figure 5 Convergence of natural frequencies versus truncation orders M and N.
+
+Figure 6 Comparison of the ESL theoretical modeling approach with the results of the FE/BE numerical approach: (a) MQV; (b) field point sound pressure.
+
+Figure 7 Influence of shear correction factors: (a) MQV; (b) field point sound pressure.
+
+Figure 8 Underwater forced vibration response of sandwich plates with different core layer materials: (a) MQV; (b) field point sound pressure.
+
+Figure 9 Underwater forced vibration response of sandwich plates with different cavity diameters: (a) MQV; (b) field point sound pressure.
+
+Figure 10 Underwater forced vibration response of sandwich plates with different reinforcing column diameters: (a) MQV; (b) field point sound pressure.
+
+Figure 11 Underwater forced vibration response of sandwich plates with different structural damping: (a) MQV; (b) field point sound pressure.
+
+Figure 12 Underwater forced vibration response of sandwich plates with different rib materials: (a) MQV; (b) field point sound pressure.
+
+Figure 13 Underwater forced vibration response of sandwich plates with different widths of ribs: (a) MQV; (b) field point sound pressure.
+
+Figure 14 Underwater forced vibration response of sandwich plates with different rib heights: (a) MQV; (b) field point sound pressure.
+
+polymers-18-00910-t001_Table 1 Table 1 Equivalent elastic constants after two step Mori–Tanaka homogenization.
+
+	First Equivalence	Second Equivalence	
+E11 (GPa)	0.461	0.475	
+E22 (GPa)	0.461	0.475	
+E33 (GPa)	0.527	1.72	
+G12 (GPa)	0.137	0.141	
+G13 (GPa)	0.145	0.152	
+G23 (GPa)	0.145	0.152	
+Mass density (kg/m3)	305.92	313.46	
+Structural damping	0.02	0.02	
+
+polymers-18-00910-t002_Table 2 Table 2 First few natural frequencies of (m, n) modes for the composite structure in water.
+
+(m, n)	Natural Frequencies (Hz)	
+	n	n = 1	n = 2	n = 3	n = 4	n = 5	
+In water	m = 1	35.75	126.10	267.05	440.20	635.52	
+m = 2	82.78	167.59	302.16	471.83	662.00	
+m = 3	161.76	235.59	352.26	511.43	690.18	
+m = 4	266.13	335.44	443.22	608.37	790.69	
+m = 5	388.11	450.91	541.62	703.72	875.16	
+m = 6	523.92	578.55	650.05	806.59	958.02	
+
+polymers-18-00910-t003_Table 3 Table 3 ANSYS meshes convergence verification for different (m, n) modes.
+
+Mode Half-Wave Numbers	Number of ANSYS Meshes	
+m	n	238,152	365,640	Difference (%)	
+1	1	35.75	35.90	0.42	
+1	2	126.10	126.78	0.54	
+1	3	267.05	268.12	0.40	
+2	1	82.78	82.70	0.10	
+2	2	167.59	167.80	0.13	
+2	3	302.16	302.74	0.20	
+3	1	161.76	161.60	0.10	
+3	2	235.59	235.48	0.05	
+3	3	352.26	352.45	0.05	
+
+polymers-18-00910-t004_Table 4 Table 4 Acoustic mesh convergence verification for different (m, n) modes.
+
+Mode Half-Wave Numbers	Number of Acoustic Meshes	
+m	n	7420	11,280	Difference (%)	
+1	1	35.75	35.74	0.03	
+1	2	126.10	125.90	0.16	
+1	3	267.05	266.10	0.36	
+2	1	82.78	82.74	0.05	
+2	2	167.59	167.28	0.18	
+2	3	302.16	301.02	0.38	
+3	1	161.76	161.48	0.17	
+3	2	235.59	234.94	0.28	
+3	3	352.26	350.70	0.44	
+
+polymers-18-00910-t005_Table 5 Table 5 First five natural frequencies: theoretical predictions versus numerical results for simply supported structures in vacuum and water.
+
+Cases of Ribs	(m, n)	Natural Frequencies (Hz)	
+In Vacuum (fv)	In Water (fw)	fv/fw	
+Analytical	ANSYS	Errors	Analytical	Virtual.Lab	Errors	
+n1 = 1 n2 = 2	(1, 1)	151.47	154.56	2.04%	35.66	35.52	0.39%	4.25	
+(2, 1)	281.68	287.82	2.13%	80.72	81.56	1.04%	3.49	
+(1, 2)	417.38	409.94	1.81%	129.20	125.81	2.62%	3.23	
+(3, 1)	478.30	484.23	1.22%	157.34	158.80	0.93%	3.04	
+(2, 2)	485.22	496.93	2.36%	162.23	165.36	1.93%	2.99	
+n1 = 2 n2 = 2	(1, 1)	151.89	154.73	2.03%	35.87	35.75	0.33%	4.23	
+(2, 1)	288.40	290.70	0.80%	82.92	82.78	0.14%	3.48	
+(1, 2)	414.71	405.89	2.13%	129.89	126.10	2.93%	3.19	
+(3, 1)	496.93	490.79	1.24%	164.08	161.76	1.41%	3.03	
+(2, 2)	498.47	497.83	0.13%	168.91	167.59	0.78%	2.95	
+n1 = 2 n2 = 3	(1, 1)	153.92	155.60	1.09%	35.92	36.02	0.25%	4.29	
+(2, 1)	289.21	290.72	0.52%	83.01	82.94	0.08%	3.48	
+(1, 2)	426.33	409.83	3.87%	131.52	127.77	2.85%	3.24	
+(3, 1)	497.18	486.09	2.23%	164.47	162.06	1.47%	3.02	
+(2, 2)	508.55	501.07	1.47%	170.65	169.05	0.94%	2.98	
+
+polymers-18-00910-t006_Table 6 Table 6 Material parameters of the core layer.
+
+Core Layer Material	PVC-H100	PVC-H250	PVC-H320	
+Young’s modulus (MPa)	135	300	450	
+Poisson’s ratio	0.3	0.3	0.3	
+Mass density (kg/m3)	100	250	320	
+Structural damping	0.02	0.02	0.02	
+
+polymers-18-00910-t007_Table 7 Table 7 Underwater natural frequencies of rib-stiffened PVC foam sandwich structures with reinforcing and weakening phases using different core layer materials (Hz).
+
+Mode Half-Wave Numbers	Core Layer Materials	
+m	n	PVC-H100	PVC-H250	PVC-H320	
+1	1	31.10	34.37	35.75	
+1	2	97.08	116.60	126.10	
+1	3	190.55	239.67	267.05	
+2	1	67.20	77.91	82.78	
+2	2	126.31	153.71	167.59	
+2	3	213.64	270.25	302.16	
+3	1	122.63	148.55	161.76	
+3	2	171.44	213.21	235.59	
+3	3	243.18	312.54	352.26	
+
+polymers-18-00910-t008_Table 8 Table 8 Underwater natural frequencies of rib-stiffened PVC foam sandwich structures with reinforcing and weakening phases using different cavity diameters (Hz).
+
+Mode Half-Wave Numbers	Cavity Diameters (Volume Fraction)	
+m	n	20 mm (6.21%)	30 mm (13.96%)	40 mm (24.82%)	
+1	1	35.75	34.83	33.86	
+1	2	126.10	121.86	114.62	
+1	3	267.05	255.45	235.14	
+2	1	82.78	79.67	76.08	
+2	2	167.59	161.68	151.43	
+2	3	302.16	288.99	265.67	
+3	1	161.76	154.12	144.17	
+3	2	235.59	225.67	209.16	
+3	3	352.26	335.98	306.89	
+
+polymers-18-00910-t009_Table 9 Table 9 Underwater natural frequencies of rib-stiffened PVC foam sandwich structures with reinforcing and weakening phases using different reinforcing column diameter (Hz).
+
+Mode Half-Wave Numbers	Reinforcing Diameters (Volume Fraction)	
+m	n	5 mm (0.44%)	10 mm (1.75%)	15 mm (3.93%)	
+1	1	35.29	35.75	35.79	
+1	2	124.66	126.10	128.39	
+1	3	262.67	267.05	274.13	
+2	1	81.45	82.78	83.08	
+2	2	164.38	167.59	170.71	
+2	3	295.83	302.16	310.35	
+3	1	158.99	161.76	163.54	
+3	2	230.23	235.59	240.50	
+3	3	343.50	352.26	362.55	
+
+polymers-18-00910-t010_Table 10 Table 10 Material parameters of the ribs.
+
+Materials of Ribs	CFRP	PU	Steel	
+Young’s modulus (GPa)	230	14	210	
+Shear modulus(GPa)	/	/	80	
+Poisson’s ratio	0.25	0.28	0.3	
+Mass density (kg/m3)	1800	760	7850	
+
+polymers-18-00910-t011_Table 11 Table 11 Underwater natural frequencies of rib-stiffened PVC foam sandwich structures with reinforced and weakened phases using different rib materials (Hz).
+
+Mode Half-Wave Numbers	Materials of Ribs	
+m	n	CFRP	PU	Steel	
+1	1	46.11	35.75	45.20	
+1	2	148.67	126.10	145.72	
+1	3	283.19	267.05	295.53	
+2	1	104.52	82.78	102.27	
+2	2	195.82	167.59	191.88	
+2	3	326.86	302.16	324.71	
+3	1	194.63	161.76	191.70	
+3	2	261.10	235.59	257.73	
+3	3	356.06	352.26	355.33	
+
+polymers-18-00910-t012_Table 12 Table 12 Underwater natural frequencies of rib-stiffened PVC foam sandwich structures with reinforced and weakened phases using different rib widths (Hz).
+
+Mode Half-Wave Numbers	Widths of Ribs	
+m	n	10 mm	20 mm	30 mm	
+1	1	46.11	50.17	52.86	
+1	2	148.67	157.51	164.27	
+1	3	298.06	309.57	317.04	
+2	1	104.52	112.77	118.69	
+2	2	195.82	206.83	215.25	
+2	3	326.86	337.25	339.31	
+3	1	194.63	208.65	219.42	
+3	2	261.10	273.20	282.64	
+3	3	356.06	359.92	362.23	
+
+polymers-18-00910-t013_Table 13 Table 13 Underwater natural frequencies of rib-stiffened PVC foam sandwich structures with reinforced and weakened phases using different rib heights (Hz).
+
+Mode Half-Wave Numbers	Heights of Ribs	
+m	n	20 mm	30 mm	40 mm	
+1	1	41.38	46.11	51.54	
+1	2	137.06	148.67	162.91	
+1	3	281.74	298.06	311.85	
+2	1	94.17	104.52	116.56	
+2	2	181.48	195.82	212.45	
+2	3	314.52	326.86	334.61	
+3	1	177.67	194.63	213.25	
+3	2	247.66	261.10	275.54	
+3	3	354.88	356.06	356.94	
+
+polymers-18-00910-t014_Table 14 Table 14 The sum of squared deviations of each parameter and the analysis results of contribution degree.
+
+		MQV	Pressure	
+Number	Design parameter	Sj	ηj (%)	Sj	ηj (%)	
+A	Core material	7.373	47.28	11.662	83.15	
+B	Cavity diameter	1.498	9.61	0.142	1.01	
+C	Reinforcing diameter	0.098	0.63	0.183	1.31	
+D	Material of ribs	3.509	22.50	1.193	8.51	
+E	Width of ribs	0.378	2.42	0.696	4.96	
+F	Height of ribs	1.937	12.42	1.263	9.01	
+	ST	15.595	100.00	14.039	100.00	
+
+Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.
+
+
+References
+
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