As it is not yet possible to determine a threshold for a cortical stimulation site (with the exception of primary motor cortex and visual cortex) we do not know down to which relative field strength neurons respond to the TMS pulses.

Using the field model provided by Coll, Penton and Hobson in their comment, we compared the field distribution windowed from 0 to 2.2 (maximum of norm E-field) with a window from 0 to 1 norm E-field (figure 1).

Here, at least the upper part of the AI is directly reached by a field strength of about 0.5, about a quarter of the maximum norm E-field.

Of course, large parts of prefrontal and temporal cortex covering the insula are exposed to a higher field strength.

We can neither exclude a trans-synaptic activation of the AI from prefrontal cortex closer to the skull, nor a direct contribution of areas exposed under the coil to the observed effects.


The second main point refers to the question whether these effects are specific to interoceptive processes.

The authors argue that the study lacks a control condition not related to interoceptive processes targeting attention processes or working memory performance in general that might be affected by frontal stimulation.

We want to argue against the claim that attention processes or working memory performance in general might underlie the observed results after frontal stimulation.

Effects of inhibiting somatosensory cortices were comparable in many aspects to effects of inhibiting AI, both on performance level as well as on EEG level as assessed by the HEP.

These results contradict the idea that a change in interoceptive processes might be due to side effects of the TMS frontal stimulation site and therefore a general effect of affecting attention or working memory circuits.

We in contrast argue that the fact that major results were comparable between stimulation sites aiming to inhibit AI and somatosensory cortices is a strong empirical evidence that indeed nodes of the interoceptive network were affected by TMS and that these effects were specific for interoceptive processes and are not related to other main functions in attention or working memory.

We agree with the authors that a control task e.g. assessing performance and acoustic evoked potentials measured by EEG might have been a useful condition to prove whether TMS stimulation sites have an impact on other functions not related to interoceptive processes, but as TMS effects are time critical we decided to use a control site instead of a control condition as suggested by the authors.


We conclude that further empirical evidence is needed to further elucidate whether observed results can be replicated and are specific for interoceptive target areas, e.g. using new methodological approaches such as protocols with combined TMS stimulation and neuroimaging.


- Using the Heisenberg uncertainty principle, we may infer that for detecting an arbitrarily small scale, tools of sufficiently high energy (high momen- tum) are required.

Thus, essential quantum phenomena must be probed at high energies.

Interestingly, gravity also becomes important at high energies.

Therefore, we must resort to quantum gravity theories when trying to address fundamental areas of physics.

One of the major aims of physics has always been to reconcile gravity and quantum mechanics in the same framework and possibly arrive at a consistent and complete theory of quantum gravity.

In this regard, many theories such as string the- ory, canonical quantum gravity etc. have been formulated that have emerged as strong candidates for the same.


The commutator algebra between x i , p j from string theory and double special relativity can be reconciled into [11,13]: [x i , p j ] = i δ ij − α pδ ij + p i p j p + α 2 (p 2 δ ij + 3p i p j ) (2) where α = α0 M pl c = α0l pl .

Here α 0 is normally assumed to be of the order of unity.

Both ∆x min and ∆p min arise as an implication of the above algebra.

In one dimension, it leads to the following form of GUP [7]:


The above mentioned modified Heisenberg algebra can be derived if we represent the position and momentum oper- ators in the following way [7]: x i = x 0i , p i = p 0i (1 − αp 0 + 2α 2 p 2 0 ) (4) where x 0i and p 0j satisfy the usual canonical commuta- tion relations [x 0i , p 0j ] = i δ ij and are interpreted as low energy position and momenta respectively.

On the other hand x i and p i are the position and momentum at high energy respectively.

Since α 0 is of the order of unity, α dependent terms become important only at energy (mo- mentum) scales comparable to Planck energy (momen- tum) scale.

The GUP and its effects have been studied p-1 H. Verma et al. extensively over the past decade [14]- [35].

Apart from its important implications in cosmology [15-17] and black hole physics [18, 19], Klein-Gordan [30] and Dirac equa- tions [21, 31] have also been modified to include quantum gravity effects.

Various non-relativistic quantum systems such as particle in a box, SHO, Landau levels [7, 32], co- herent and squeezed states [26-29,33], PT symmetric non- Hermitian systems [23-25] have been investigated in the framework of GUP to note the effects of quantum gravity in those.

A particularly interesting case with a proba- ble observable effect has been developed in [7] by study- ing variations in current of scanning tunnel microscope (STM) when tunnelling phenomenon is subject to GUP corrections.


Recently, GUP modified angular momentum algebra has been constructed and the corrections in CG coefficients due to GUP are obtained [34].

However, their results are inconsistent (as mentioned by the authors themselves) as the CG coefficients obtained by applying J − to the highest J m value state and is different from that of obtained by applying J + to the lowest J m value state.

This motivate us to revisit the coupling angular momentum in the frame- work of GUP.

In this work, we construct GUP modified angular momentum algebra by using Schwinger's model of angular momentum (SMAM) [36].


In the first step we develop the operator formulation for the GUP modified SHO.

By modifying the creation/annihilation operators appropriately, we write the GUP modified SHO hamilto- nian as ω 2 [A † A + AA † ] with the commutation relation between A and A † as [A, A † ] = 1 + O(α).

Angular mo- mentum algebra is then constructed by considering two such independent oscillators.

This GUP modified alge- bra is then used to study two-particle angular momentum system.

We explicitly calculate the CG coefficients.

We found CG coefficients obtained by applying J − and J + are same unlike the case in Ref.

[ 34].

We further found that CG coefficients remain unaffected in upto quadratic GUP, even though the angular momentum algebra gets modi- fied.

This is very interesting result in the GUP framework.

However, it is not surprising as the GUP modified angular momentum algebra can be mapped to usual angular mo- mentum algebra by redefining the Planck constant.


We now present the plan of the paper.

In the next section, we develop the complete GUP modified formalism of SHO in the operator formulation and then use SMAM to derive GUP modified angular momentum algebra in Sec. 3.

We discuss angular momentum coupling in a composite two- particle system in the GUP framework in Sec.4.

In Sec. 5, CG coefficients are calculated explicitly for two particles system.

Finally, Sec. 6 is for the concluding remarks.


GUP modified Harmonic Oscillator. - In this section, we discuss the operator formulation of SHO in the framework of GUP using both high energy and low energy momentum variables.


The corrections to the harmonic oscillator model due to GUP have been ad- dressed mostly using perturbation theory [7] and also treated in phase space [35].

In the present work, we formulate the operator formalism for the GUP corrected SHO.

The GUP modified harmonic oscillator hamiltonian is given as: H = ω x 2 x ′2 + p 2 p ′2 (5) where x and p are the high energy position and momen- tum operators.

This GUP corrected Hamiltonian can be written in terms of low energy operators upto O(α 2 ) as :


Here, H 1 is the correction due to GUP, x ′ = 2 mω and p ′ = √ 2m ω and x 0 and p 0 are usual low energy position and momentum operators respectively.

Now we modify the usual creation (a † ) and annihilation (a) operators of 1-d harmonic oscillator in the following manner:


in which, the usual creation/annihilation operators a † = x0 x ′ − i p0 p ′ and a = x0 x ′ + i p0 p ′ are modified by replacing p = p 0 (1 − αp 0 + 2α 2 p 2 0 ) and x = x 0 and including corrections to the order α (β 1 (x 0 , p 0 )) and α 2 (β 2 (x 0 , p 0 )).

We demand the Hamiltonian in Eq.6 to be in the following form: H = ω 2 (AA † + A † A) (10) by constructing appropriate β 1 and β 2 as given by:


We now calculate the commutator [A, A † ], which comes out upto O(α 3 ) as: [A, A † ] = 1 − 2αp 0 + 6α 2 p 2 0 ≡ 1 − C. (13) where C is the correction due to GUP.

In absence of GUP corrections, i.e. when α = 0, this formulation reduces to p-2


Schwinger's Model of Angular Momentum with GUP the usual operator formulation of 1-d SHO.

We now wish to redefine the creation/annihilation operators in GUP corrected formalism.

For this purpose, we henceforth con- sider the GUP corrections as C rather than C. This has been considered under the assumption that, in experimen- tal conditions, GUP correction to any operator manifests as expectation value.

In the next section, we will use the GUP modified creation/annihilation operators to gener- ate the angular momentum algebra.

Therefore, C is the averaged value of GUP corrections and our assumption stands correct (Ref.

[ Eq.36] in [34]).

Hence, Eq. 13 is rewritten as:


We may now assume two new operatorsÃ andÃ † such that,


Here,Ã = A/ 1 − C andÃ † = A † / 1 − C .

If |1 , |2 , ..., |N are eigenvectors of Hamiltonian in Eq.10, then, in a general momentum regime, we can write,


where, C = 2α p 0 − 6α 2 p 2 0 such that commutation relation in Eq. 14 is satisfied.

In the above equations and in the later sections, we have expressed GUP effects solely in terms of expectation value of C based on aforementioned arguments.


Now, we would like to show that conclusion of the previous section can also be achieved while remaining in the high momentum regime (i.e. GUP modified momentum).

The GUP modified cre- ation/annihilation operators A and A † are defined in terms of high energy variables (x,p) as: A † = x x ′ − i p p ′ (20) A = x x ′ + i p p ′ (21) where x and p are in high momentum regime and x ′ = 2 mω and p ′ = √ 2m ω.

Then the GUP modified Hamil- tonian is written as H = ω 2 [AA † + A † A] and the commu- tator [A, A † ] in the regime is obtained as: [A, A † ] = 1 − 2αp + 4α 2 p 2 (22) which is exactly same as in Eq.13 when p is expressed in terms of low energy variables as p = p 0 (1 − αp 0 + 2α 2 p 2 0 ).


In general momentum regime, similar to the discussion for low energy momentum, we have,


Schwinger's Model of Angular Momentum. - In this section, we would like to calculate the GUP modified angular momentum algebra by considering two such GUP modified harmonic oscillators.

Two uncoupled SHOs (we call them type 1 and 2) are considered with number states denoted as n 1 and n 2 with their usual independent alge- bra.

Then the general eigenket is constructed in SMAM as:


and similar relations are obtained when a † 2 and a 2 act on these states.

Next, in SMAM the following angular mo- mentum operators are constructed [36]:


which satisfy the angular momentum algebra [L z , L ± ] = ± L ± , [L + , L − ] = 2 L z .

We now make a canonical trans- formation to n 1 and n 2 in the above.


Then, the Eq.28, 29, 30 reduce to the usual form of angular momentum algebra as shown in Eq.32, 33, 34


where λ ± = [(l ∓ m)(l ± m + 1)] 1/2 and the eigenvalues of the quadratic operator L 2 become


The form L x , L y are then constructed using:


We now find the various commutation relations between


Thus, we have,


Similarly, on calculation using Eq.36,37,38,39, we get the following :


Commutation relation given by Eq.44 implies that the lad- der operator doesn't change the magnitude of total angu- lar momentum (l).

Also, due to occurrence of the correc- tion factor term, the spacing between consecutive eigen- values of L z changes.


Also, Eq. 47 implies that L ± |l, m is an eigenstate of L z .

Now, using,


we can calculate the norm of raised lowered states L ± |l, m as,


Therefore, as in the usual quantum mechanics [36] we have limit on the values of m, which we denote m max (maxi- mum m value or upper bound) and m min (minimum m value or lower bound).

Application of raising operator L + on state characterised by m max and lowering operator L − on state characterised by m min would both give zero i.e.


Clearly, we observe that if we consider → (1 − C ) in the usual QM, we get the GUP modified formalism, where C = 2α p − 4α 2 p 2 .


Effect on two-particle system.

- Till now all the algebra derived above involves single particle.

In this sec- tion, the effect of GUP on multi-particle algebra will be examined.

We will start with two-particle angular momen- tum algebra and the results can be extended for N-particle systems accordingly.


Consider the addition of angular momentum includ- ing GUP for a system of two particles with l i and m i (i = 1, 2) ,the azimuthal and magnetic quantum numbers of the particles.

The total angular momentum and the z−component for the composite system is


We have two alternative choices of the basis for represent- ing the combined system as


1. With simultaneous eigenkets of


We chose the later one and the combined state in Hilbert space is represented as,


Gordan coefficients.

The CG coefficients may be calcu- lated by applying J − .

To discuss the addition of angular momentum for this composite system further, we need the following equations.

Operating J z on the combined state we obtain Eq.53, 54.

The following point may be noted in analogy to ordinary quantum mechanics and as done in [34],


Now, let us consider the ladder operator for two - particle system.


From the commutation relations Eq.42,43 we find that,


where, C 1 , C 2 are the correction factors due GUP for |j 1 , j 2 ; m 1 , m 2 state for first and second particle respec- tively.

Also, for any state expressed as in Eq.52, we have found the operation of J z J ± on the RHS states.

As for the LHS of Eq.52, the solution is easy to calculate.

Eq.60 shows that the RHS is no longer an eigenstate of J z , un- like the α = 0 case.

The above discussions on two- particle system can be also generalised for a system of N-particles on similar lines as done above.


In this section we calculate the Clebsch-Gordan coeffi- cients explicitly for two particles.

We start with the high- est m value state in the highest multiplet and apply J − . which lowers the m value.

We now resort to the notation


The coefficient is j 1 ; j 2 | J m , J m = 1 by normaliza- tion.


2. For J = J m , M = J m − 1 :


By applying J − we calculate,


Normalization of |J m , J m − 1 in Eq.62 provides,


3. For J = J m , M = J m − 2 :


Applying J − again we obtain Eq. 64 Normalization of |J m , J m − 2 in Eq.64 provides Eq. 65 In the same manner we can find the coefficients for all other states in this (highest) multiplet.

The normalization conditions in the above states implies C 1 = C 2 = C .

This condition is further consistent with normalization of all other states.

This in turn implies that the CG coefficients are independent of C 1 , C 2 and C .

CG coefficients for states in other multiplets then are obtained by using standard method and naturally are found to be independent of C 1 , C 2 and C .


Now we proceed to find the coefficients using J + . Let us start with the initial lowest m value state in the highest multiplet.

We obtain the following results


1. For J = J m , M = −J m , where J m stands for J max = (j 1 + j 2 ):


The coefficient is −j 1 ; −j 2 | J m , J m = 1 by normal- ization.


2. For J = J m , M = −J m + 1 :


We get ,


On normalization of |J m , −J m + 1 in Eq.67 , we get the following condition:


J = J m , M = −J m + 2 which on calculation gives Eq.69 Again, on normalization, of |J m , −J m + 2 in Eq.69 , we get the condition given in Eq. 70.


The solution of normalization conditions in Eqs 68 and 70 implies that C 1 = C 2 = C .

This condition is fur- ther consistent with normalization of all other states.

This further implies that the C 1 , C 2 and C dependence is dropped out from the Eqs 67 and 69 and hence all the CG coefficients are independent of C 1 , C 2 and C .


The above results can be verified explicitly with specific examples.

We have verified it for J 1 = 1 2 = J 2 , J 1 = 1 = J 2 and J 1 = 1 2 , J 2 = 3 2 .

However, the results for two spin p-5 H. Verma et al.


1/2 particles only are presented below.


The normalization to the states |1, 0 and |1, −1 provide condition similar to Eq.63,65 and are now written as


Solving both the equations simultaneously, we get, C = C 1 = C 2 This condition is consistent with the normal- ization of the state |0, 0 .

Also, if the starting state is considered as the normalized state |J = 1, M = −1 = | − 1/2; −1/2 , we obtain from Eq.68, 70, the same condi- tions as Eq.63, 65 and hence conclude the same condition on C, C 1 , C 2 .

With this information, we find the CG co- efficients for the specific case where j 1 = j 2 = 1/2 and m 1 (or m 2 ) = ±1/2 from Eq.62, 64, 67, 69 and list them in the table 1 .


In case of standard QM, the CG-coefficients for a par- ticular state are always same irrespective of the method of calculation, i.e, using J + or J − .

The same thing is true for GUP modified quantum mechanics also.

This resolves the anomaly reported in [34] where CG coefficients obtained by applying J − to the highest J m value state are differ- ent than that of when calculated by applying J + to the lowest J m value state in the same multiplet.

We further showed that CG coefficients do not receive any correction due to quadratic order GUP and any angular momentum coupling remains unaffected even though the angular mo- mentum algebra gets modified.

Explicit examples were also considered to support our claim.

Further this result can be generalized for all composite systems in a straight- forward manner.


of which we have tried to address in the paper.


Using this formalism and SMAM, we have derived GUP mod- ified angular momentum algebra.


While the GUP SHO may be useful in its own right, the angular momentum al- gebra developed may be used to investigate GUP induced effects in Hydrogen atom, Quantum Rotor and other mod- els involving the angular momenta operators.


As such, a wide number of problems in atomic and molecular physics can be approached using the algebra developed.


Further, using this GUP modified angular momentum algebra, we have studied the effect of GUP in the coupling of angular momentum for an arbitrary two particle composite sys- tem.


We have also found the associated CG coefficients in the GUP modified systems.


Some anomalies in calculating CG coefficient reported in the literature are removed in our formulation.


Interestingly, we observe that CG coefficients receive no corrections up to quadratic GUP.


This has been verified explicitly for two particle systems.


The coupling of angular momentum remains unaffected to quantum grav- ity effects is indeed an important result and may have very important consequences in the study of Black holes and many other astro-physical problems where gravity plays an important role.


In this note, we show that the methodology and conclusions of “Schwinger’s Model of Angular Momentum with GUP” [2] are flawed and that the conclusions of “Generalized Uncertainty Principle and angular momentum” (P. Bosso and S. Das) [1] remain valid.


In [1], we studied the modification of the angular momentum algebra dictated by a modification of the commutation relations between position and momentum.

This led to interesting results concerning the angular momentum spectrum, energy spectrum of the hydrogen atom, interactions between magnetic fields and angular momenta, and a description of multi-particle systems, including corrections to Clebsch-Gordan coefficients.

Among the noteworthy results of that paper, we have that the commutation relations for angular momentum operators now involve also functions of the linear momentum operator.

However, following usual steps, we showed that the spectrum involves only expectation values of this function.

Notice that the appearance of expectation values at this level is not the result of any approximation or assumption.


On the other hand, when the radial Schrödinger equation for the hydrogen atom is studied, the assumption that the modification appears only via its expectation value is considered. This is clearly an approximation, useful in that the equation resembles that of standard quantum mechanics with corrections that have implications in the emission/absorption wavelengths.

It is important to notice that this approximation is considered only in the study of the hydrogen atom and of the interaction between magnetic fields and angular momenta.

The rest of [1] does not rely on this assumption.


That paper concludes with an analysis of the theory of angular momentum for systems of many particles.

Specifically, we computed some of the Clebsch-Gordan coefficients.

We showed that the Clebsch-Gordan coefficients are modified due to GUP.

However, we also showed that the modification is associated with an ambiguity: coefficients for the same system but computed starting from higher or lower angular momentum states are in general different.

This is something to expect, because the spectrum of the angular momentum operators, as well as the action of the ladder operators J+ and J-, is influenced by the linear momentum of the states to which they are applied.

This ambiguity is a direct consequence of the modified position-momentum uncertainty relation considered in [1] and needs further study.


Verma et al., in [2], have tried a possible resolution of the above ambiguity.

Below, we comment on the main aspects of their paper.


Ladder operators for a simple harmonic oscillator (SHO): The authors define a couple of operators, A and A†, in terms of the position and momentum operators.

As the authors themselves show, these operators are not ladder operators for a SHO since [A, A†] ≠ 1.

To avoid this problem, they divide each operator by the square root of the expectation value of [A, A†].

This strategy can only be considered as an approximation, not as a rigorous method to obtain ladder operators.

Furthermore, this approximation leads to trivial results, effectively accounting for a scaling of the Planck constant.

Finally, it is not necessary.

In fact, it is always possible to construct a new set of operators that act as ladder operators for the GUP-modified system under study, as shown in [3] (see [4] for an application).


Substituting the modification C by its expectation value: The authors motivate its use by saying that it was previously used in our work [1].

However, as we explained above, this is not entirely true.

This substitution was in fact used to obtain GUP-modifications for some specific examples, namely the hydrogen atom and the magnetic field-angular momentum interaction, and which can potentially be verified experimentally.

However, the rest of the results in [1] are not based on such substitution.

In particular, the commutation relations between angular momentum operators are computed implementing directly the modified commutation relation between position and momentum operators.

Furthermore, the appearance of the expectation value ⟨C⟩ in the angular momentum spectrum was derived from rigorous standard procedures.

Nonetheless, this does not motivate in general an indiscriminate substitution C → ⟨C⟩.


The Jordan map and Schwinger’s model for the angular momentum: The Jordan map connects a set of matrices to a set of harmonic oscillator operators [5].

In the specific case of the angular momentum, to each matrix representing an angular momentum operator, with elements J_ij, the Jordan map associates an operator J = Σ_ij J_ij a†_i a_j.

Therefore, in the standard theory of quantum mechanics, we find the following expressions [6].

Notice that the expressions, used by Verma et al. in [2], are constructed from the representation of the angular momentum operators as Pauli matrices.

A property of the Jordan map is that it preserves commutation relations.

In other words, whatever the commutation relations for the angular momentum matrices are, the operators in terms of ladder operators will have the same relations, since they are inherited from the matrices.

Notice therefore that (i) the procedure used in [2] is flawed, because their A, A† operators are not ladder operators, as explained above, (ii) tautological, as starting from a representation of the standard (non GUP) angular momentum algebra, the authors use the Jordan map to find the commutation relations for the angular momentum operators, which necessarily are the standard one.


As a final comment, it is worth noticing that their results concerning the commutation relations of the angular momentum operators do not match the results in [1], obtained via direct computations.


Clebsch-Gordan coefficients for a system of two particles with GUP: Finally, we comment on the computation of the Clebsch-Gordan coefficients.

The authors compute the coefficients starting from a maximal angular momentum state and applying the operator J- = j1,- + j2,-.

They proceed by imposing normalization conditions.


It is important at this point to focus on a particular aspect.

Consider the tower of states derived by repeated applications of J- on the top state |L, L⟩. Each of these states has to be normalized independently from the others.

On the other hand, each of these states can be in general represented in multiple ways in terms of the constituent states.

More precisely, given a total angular momentum state |L, M⟩, this describes any composition of two systems, with angular momentum states |l1, m1⟩ and |l2, m2⟩, such that |l1 - l2| ≤ L ≤ l1 + l2 and M = m1 + m2.

In particular, for every value M, in general several configurations will be possible such to obtain different values of L. Every choice of these compositions is described by a different Clebsch-Gordan coefficient.


Having this picture in mind, it is clear that the normalization of Clebsch-Gordan coefficients has to be performed considering the independent normalization of states |L, M⟩ with different values M and the orthogonality among the states of equal M but different L. However, in [2] the authors seem to normalize states belonging to different values of M simultaneously, resulting in constraints such as ⟨C1⟩ = ⟨C2⟩ = ⟨C⟩, where C1 and C2 represent the modifications associated with the two constituent systems, while C is the modification associated with the entire system.

Such a relation is clearly unacceptable, since it implies conditions on the linear momenta of a composite system and its constituents.

Since the constituents’ momenta are independent physical quantities, no such conditions can exist.

Furthermore, the only condition on the composite momenta is that it is the vector sum of the constituent momenta.


The results of [1], therefore, still stand, and the objections raised in [2] are invalid.

Nevertheless, it is possible that a correct application of the Jordan map to the GUP-modified angular momentum operators may be a useful tool in gaining insight into the problem in question and its possible resolution.


Introduction.

– Through this document, we wish to respond to the comments [1] made on our manuscript entitled “Schwinger’s model of angular momentum with GUP”.

First of all, the authors have wrongly presumed that we have invalidated/questioned their results in [2].

In the abstract section, they claim that their work is valid, on which, we made no claims suggesting the contrary in the paper [3].

In fact we have used some of their results in our work.


The only issue which we found was that the Clebsch-Gordan (CG) coefficients for the same state, obtained in their work by applying J− and J+ operators were different.

This is clearly unacceptable.

This situation can be better described with the word “inconsistency” rather than with the word, “ambiguous”.

We feel that there was, in fact, no ambiguity in the mathematical calculations of CG coefficients using the operators J− and J+ in their works.

In our work we have removed this inconsistency.


Now, we shall try to address the specific points raised by the authors.


Comments.


Ladder operators for simple harmonic oscillator.

We tried to construct the ladder operators using the proposition that the Hamiltonian be expressed as H = ¯hω 2 (AA† + A†A).

We then found the commutation relation between the operators.


The authors have suggested that the method adopted is not rigorous and leads to a seemingly trivial result.

We would like to emphasize that the results are mathematically correct and may have led to rescaling of Planck’s constant but that is not wrong or violates any first principles in physics or more specifically, anything in operator formalism/algebra.


The later discovery of ladder operators for GUP-modified systems by the authors themselves [4] was absent during the formulation of the manuscript and we concur that it proposes a more rigorous method.

That does not deem any of the previous works unnecessary or wrong.


In fact any scientific progress does not necessarily negate or out-date the previous works.

Therefore, we strongly disagree with the comments made by the authors in this particular context.


Substituting the modification of C by its expectation value.

The authors seem to have not noticed the peculiarity in their own paper [2] or may have ignored an important aspect of the aforementioned substitution.

We certainly borrowed this result from their work which has been used in that paper extensively.

This has been done for many angular-momentum operators specifically ladder operators for angular momenta.

This is clear from eq. ( 104) which has been taken from eq. ( 30) [2].

If C is not replaced by ⟨C⟩ in the angular-momentum algebra, the algebra is not closed, which will lead to difficulties in describing angular-momentum coupling and calculating the CG coefficients.

We made the substitution motivated by their work only and, therefore, if the substitution of C by ⟨C⟩ is questionable in our work, it is questionable in their work, too.


In this reference, apart from the equations mentioned before, we would like to point out that eq. ( 30) falls under sect.

3 with heading “Modified angular momentum spectrum” in their paper and is specifically L±|plm⟩ = ¯h(1−C) L(L + 1) − M (M ± 1)|plm±1⟩ whereas eq. ( 104) falls under the sect.

6 with heading “Multi particles system” and reads L±|plm⟩ = ¯h(1 − ⟨C⟩) L(L + 1) − M (M ± 1)|plm ± 1⟩. The authors have wrongfully claimed that the above substitution of C with ⟨C⟩ was only made in the context of hydrogen atom.

On examination, one discovers that hydrogen atom is described in a totally different section, sect.

4, and in no way relates sect.

3 to sect.

In fact one can independently calculate “Multi particles systems” angular-momentum algebra from “Modified angular momentum spectrum” which we hope that the authors would inarguably agree with.


The introduction of hydrogen atom section in this discussion is totally unwarranted and serves no purpose at all.

This fact is clearly indicated just above eq. ( 104) in their paper where it is mentioned that eq. ( 104) is obtained from eq. ( 30).

Their final results on CG coefficients rely heavily on eq. ( 104) and hence, indirectly on the argued substitution.

That being said, we have also clearly mentioned our motivation in this context in the paper which is that we wish to use the harmonic-oscillator formalism to derive angular-momentum algebra which, in turn, is used to derive the coupling of angular momentum —essentially a physical phenomenon.


The Jordan map and Schwingers model for the angular momentum.

Nowhere have the authors questioned the mathematical formulation and calculation of the result using Schwinger’s model of angular momentum.

Rather they have pointed it out as trivial or “tautological”.

Again, we subscribed to the basic formalism suggested and used it to obtain angular-momentum algebra which, of course, is not incorrect.

Just because it leads to the same commutation result it should not be interpreted as “tautological”.

We do concur that the correction factor obtained for GUP correction in angular-momentum operators is different from [2].

This only invites more research and insight into the field.


Clebsch-Gordan coefficients for a system of two particles with GUP.

The coupled angular-momentum states in [2] are not normalized and hence, the CG coefficients associated in those states have no physical meaning.

This further leads to the inconsistency in the CG coefficients in their work (see, for example, eqs. ( 106), (107)).

We do concur that the different |L, M⟩ states should be normalized separately and should be orthogonal to states with different L value [5].


By the single solution suggested in our paper, one can carry out the normalizations and orthogonalization for all the angular-momentum states in a given system, simultaneously.

This formulation has been shown to work for 2-particles system of arbitrary individual spins.

We do not rule out the possibility of other solutions to this problem for systems with more than two particles.

Conforming to the proposed solution, one obtains a strong condition on C, C1 and C2.


Conclusions.

– In the light of the arguments being raised, we would reiterate the correctness in physics and mathematics in our paper.

In conclusion, we cannot agree with the comments made.

We do concur that our results affirm the angular-momentum algebra derived in their paper though using a different approach.

That being said, they have correctly pointed out that the correction factor due to GUP up to quadratic order is slightly different.

This is a point of worry and we feel that the understanding of angular momentum under GUP is not at all complete.


A 28-year-old man sought care for a diffuse vesicu- lar rash that had developed over the preceding 24-48 hours.

He had traveled on a flight from Lagos, Nige- ria, and arrived in the United States the day he sought care.

While in Nigeria, he visited relatives, stayed in hotel lodging without travel to rural regions, and had no interactions with animals or animal carcasses.

Dur- ing his flight from Lagos, he noticed a burning sensa- tion on his skin, followed by development of discrete vesicles on his forehead and nose, which spread to his arms, trunk, and inner thighs over several hours.

He denied having associated symptoms, including fever, chills, or headache.


At examination, we observed right cervical lymphadenopathy and numerous 2-4-mm pustules on an erythematous base.

Some of these pustules had central umbilication and were present dif- fusely with acrofacial propensity, favoring the face, neck, and hands.

A few 2-3-mm round erosions were noted on the oral mucosa, and an intact pus- tule was observed on the lower mucosal lip (Figure 1).

The patient was given intravenous acyclovir for empiric treatment of disseminated varicella zoster virus infection, admitted, and subjected to contact and airborne isolation precautions pending further evaluation.

Within 24 hours of admission, no new


A case of monkeypox was diagnosed in a returning trav- eler from Nigeria to Maryland, USA.

Prompt infection con- trol measures led to no secondary cases in 40 exposed healthcare workers.

Given the global health implications, public health systems should be aware of effective strat- egies to mitigate the potential spread of monkeypox.


We obtained a 4-mm punch biopsy specimen from an intact pustule on the abdomen of the pa- tient.

This specimen showed epidermal necrosis, reticular degeneration, and vesiculation by staining with hematoxylin and eosin.

We found dyskeratotic keratinocytes, neutrophil exocytosis, and intracyto- plasmic inclusion bodies consistent with Guarnieri bodies in the epidermis.

We also detected a diffuse, mixed, superficial dermal infiltrate of lymphocytes, histiocytes, neutrophils, and occasional eosinophils (Figure 2).


Based on the travel history of the patient and his- topathologic findings, we suspected monkeypox, likely acquired by human contact in the absence of any ani- mal exposures.

Additional specimens of the skin lesions were identified by the Maryland Department of Health as non-variola orthopox by real-time reverse transcrip- tion PCR (RT-PCR) and the CDC Laboratory Response Network protocol.

CDC used viral culture and RT-PCR to confirm the diagnosis of monkeypox, further iden- tifying the specimen as part of the West African clade, which has driven the outbreak in Nigeria since 2017.


Upon confirmation of the monkeypox diagno- sis, we identified all healthcare workers (HCWs) involved in the case and classified 40 as contacts by CDC guidelines (8).

No HCW met the criteria for high-risk exposure, and no doses of preventive small- pox vaccine were administered.

Hospital-based pub- lic health officials contacted each HCW daily for 21 days (the duration of incubation period for monkey- pox) and instructed them to measure their tempera- ture twice a day and monitor any symptoms.

At the conclusion of the surveillance period, we did not de- tect disease transmission.


Previously considered a rare zoonotic infection, hu- man monkeypox has reemerged as a clinically seri- ous disease after decades of quiescence.

Monkeypox has an overall case-fatality rate of up to 11% (1), and increasing human populations have no immunity to poxvirus; therefore, future progress in understanding monkeypox is critical.

The World Health Organization Research and Development Blueprint in 2018 classi- fied monkeypox as an emergent disease requiring ac- celerated research, development, and public health action (8).

The epidemic potential of monkeypox was demonstrated during the outbreak in the United States in 2003, and had the predominant virus strain been the more virulent and aggressive Congo Basin strain instead of a virus in the West African clade, a higher mortality rate would have been possible (9).


Although the public health experience addressing monkeypox in the United States has been limited, this case illustrates the effectiveness of the basic principles of infection control: rapid identification and isolation of the index patient; use of personal protective equip- ment by HCWs; and thorough contact tracing, includ- ing monitoring for secondary cases throughout the totality of the incubation period.

Using these interven- tions alone, our hospital system and community were able to avoid additional disease transmission.

Hospital systems should ensure that their healthcare teams, par- ticularly frontline workers, are aware of infection con- trol policies, especially pertaining to patients with pos- sible infectious diseases.

In particular, any patient who has a fever and disseminated vesicular or pustular rash should immediately be placed on airborne and contact precautions because these are the typical symptoms as- sociated with orthopoxvirus infection (10).


In addition to smallpox vaccine, vaccinia im- mune globulin is available and can be used as pro- phylaxis for severely immunocompromised pa- tients (when smallpox vaccine should be avoided), although the benefit is unclear (10).

The Food and Drug Administration-approved antiviral drugs to treat smallpox are tecovirimat and brincidofovir, which can also be used to treat monkeypox, but there are no monkeypox-specific antiviral drugs for treatment or postexposure prophylaxis.

Because there are multiple orthopoxvirus vaccine guidance documents, formulation of consolidated recommen- dations is ongoing (14).


In summary, we report a case of monkeypox in a traveler returning to the United States from Nigeria and review infection control measures to prevent sec- ondary cases.

Multiple appearances beyond disease- endemic countries indicate that monkeypox has be- come a relevant travel-related disease, and physicians should remain vigilant in combatting transmission of this virus.


To the Editor: Costello et al. described a patient in Maryland, USA, with a diffuse vesicular rash initially diagnosed as disseminated varicella zoster virus (VZV) infection.

Only after a biopsy revealed unexpected findings was monkeypox suspected [1].

Monkeypox is commonly confused with VZV in countries where both infections are endemic.

High fever, lymphadenopathy, and a deep-seated, well-circumscribed, umbilicated rash in the same stage of development (i.e., macule, papule, vesicle, or scab) in distinct anatomic locations are characteristic of monkeypox [2].

Although the patient in Maryland experienced lymphadenopathy and rash with umbilicated lesions suggestive of monkeypox, he was afebrile, denied other prodromal signs and symptoms (e.g., headache and chills) that typically precede monkeypox rash, and improved while receiving intravenous acyclovir, features more consistent with VZV.


However, the unusual clinical signs and symptoms experienced by this patient were similar to those observed in other patients in the evolving 2022 multinational monkeypox response.

Because differential diagnosis can be challenging, public health authorities should be consulted promptly when monkeypox is possible.

US Laboratory Response Network laboratories (https://emergency.cdc.gov/lrn) can enable rapid testing of specimens (e.g., lesions swab), and pathogen-specific antiviral medications can be acquired through consultation with the Centers for Disease Control and Prevention.

Public health investigation for a single case of monkeypox can be intensive and complicated; case-patient contacts outside of the hospital must be identified, monitored, and potentially given 1 of the 2 orthopoxvirus vaccines offered for postexposure prophylaxis in the United States [3-5].


Factors that should raise suspicion for monkeypox in a patient with related signs and symptoms include history of travel outside of the United States to a country with confirmed cases or where monkeypox virus is endemic, contact with a person with a similar-appearing rash or who has received a diagnosis of confirmed or probable monkeypox, contact with Africa-endemic wild animal or pet species (living or dead), or use of a product derived from those animals (e.g., game meat, creams, lotions, powders).

Monkeypox should also be considered in patients with close or intimate contact with persons in social networks experiencing high monkeypox activity, including men who have sex with men who meet partners through a website, digital application, or social event.

Prompt consultation with public health authorities is essential for providing clinical guidance, expediting testing and treatment, and preventing secondary cases [3].


We appreciate Minhaj et al. for their correspondence regarding our experience treating an imported case of monkeypox from an international traveler [1].

Their letter reaffirms the instructive points of our case: monkeypox poses a diagnostic challenge because its clinical presentation shares features with a variety of additional infectious diseases, including varicella zoster virus (the infection we initially suspected), and prompt coordination with public health officials is critical for diagnosing, treating, and mitigating secondary spread.


Since our report of monkeypox in November 2021, there have been outbreaks of monkeypox throughout multiple countries [2], including one case identified in the United States [3].

Monkeypox had never previously been diagnosed in several of these countries and, remarkably, in only 1 of these cases [4] was there a history of travel to a monkeypox-endemic country, in direct contrast to nearly all prior cases that have been reported outside of Africa [5-7], which were epidemiologically linked to a monkeypox-endemic region.


In our case report [8], we had concluded that monkeypox had become clinically relevant within the confines of a travel-related illness.

However, the additional cases diagnosed since November 2021 strongly suggest that community transmission is now occurring, and a history of travel to a monkeypox-endemic country is no longer prerequisite to contracting this disease.

Community prevalence rates remain unknown, so healthcare providers should consider monkeypox in any patient who manifests with fever and lymphadenopathy accompanied by a disseminated vesicular, pustular, or umbilicated rash.

Under those conditions, the provider should immediately initiate infection control and contact public health authorities.

Monkeypox is an emerging zoonotic disease with incompletely appreciated clinical features, and healthcare providers should be made aware of its increasingly widespread incidence.


The objective of the present study was to evaluate the use of a single lumen 16 G central venous catheter for the drainage of uncomplicated pleural effusions in intensive care unit patients.


A prospective observational study was performed in two intensive care units of university- affiliated hospitals.

The study involved 10 intensive care unit patients with non-loculated large effusions.

A 16 G central venous catheter was inserted at the bedside without ultrasound guidance using the Seldinger technique.

The catheter was left in situ until radiological resolution of the effusion.


Fifteen sets of data were obtained from 10 patients.

Three patients had catheters inserted for bilateral pleural effusions.

One of these patients, who suffered from chronic pancreati- tis, subsequently had a unilateral left pleural effusion drained twice during further re-admissions to hospital.

Twelve sets of data were obtained when the patients were mechanically ven- tilated.


Four patients had pancreatitis, with the remaining six patients having a variety of underlying medical conditions including perforated intra-abdominal viscus, liver transplantation and recent cardiac surgery.

Three of these patients had pneumo- nia complicating their primary medical condition.

Table 1 summarises the biochemical profile of the pleural fluid and the cumulative volume of effusion drained at 1, 6 and 24 hours post catheter insertion.

The mean volumes drained at 1, 6 and 24 hours were 454 ± 241 ml, 756 ± 403 ml and 1010 ± 469 ml, respectively.

As we did not simultaneously determine serum lactate dehydrogenase levels and serum total protein levels, we classified exudates as having pleural fluid lactate dehydrogenase levels ≥ 200 IU [6] or pleural fluid total protein levels ≥ 30 g/l [7].

Twelve samples were classi- fied as exudates and two samples as transudates.

The results for one sample were not available.


No patients had a pneumothorax on the first radiograph per- formed within 8-12 hours after catheter insertion and on review of subsequent radiographs.

There were no instances of hemothorax or re-expansion pulmonary edema.

None of the catheters slipped out and there were no accidental discon- nections of the drainage system.


All ventilated patients were successfully weaned.

Mechanical ventilation was avoided in the three instances where the large effusions had caused respiratory distress in these non- intubated patients.

The longest duration that a single catheter remained in situ was 14 days, and it drained a total of 5050 ml over this period.

This same patient had a contralateral catheter inserted, which drained 6030 ml over 11 days.

In total, five patients had the catheter in situ for between 7 and 9 days.

The daily drainage ranged from 70 to 1700 ml/day.

There were no instances of catheter blockage despite fibrinous material being seen in the collection bag of two patients.


The use of an indwelling 16 G central venous catheter is efficacious in draining uncomplicated large pleural effusions.

It is well tolerated by patients and is associated with minimal complications.

It has the potential to avoid repeated thoracentesis or the use of large-bore chest tubes.


This study was conducted in the ICUs of a Singaporean hos- pital and an Australian hospital.

Informed consent was obtained from the patient or a relative.

Ten patients were studied prospectively.

Patients were included if they had large pleural effusions clinically and on a chest radiograph, which were judged to be contributing significantly to their res- piratory impairment.

Patients were excluded if there was a suspicion that the effusions were loculated, if they had signifi- cant pre-existing coagulation abnormalities or if they had structural chest abnormalities.

Ultrasound confirmation of the non-loculated nature of the effusion was obtained in three patients.


The procedure was performed with the patient lying in a semi- recumbent manner at an angle of 45° because most of the patients were ventilated and sedated.

The ipsilateral arm was raised over the head and held in place by the nurse assistant.

The site of insertion was determined by physical examination or had been marked by the ultrasound technician in the three cases where the ultrasound investigation had been per- formed.

The skin was prepared with 0.05% chlorhexidine (Baxter, Old Tongabbie, Australia) and 10% povidine-iodine solution and was then draped in a sterile manner.

Local anes- thetic (3-5 ml of 1% lidocaine) was infiltrated from the subcu- taneous plane down to the parietal pleura with a 21 G needle.

Pleural fluid was aspirated via this needle to confirm its free flowing consistency.


The insertion kit used was the ARROW ® 16 G central venous catheterisation set (product no ES-04301; Arrow, Reading, Pennsylvania, USA).

The 18 G trocar needle attached to the supplied syringe was inserted into the speci- fied intercostal space in the mid-axillary line until it breached the parietal pleura and confirmed that free flowing pleural fluid could be obtained.

The Seldinger technique was applied with the flexible guide wire inserted 2 cm beyond the distance of the trocar needle.

The tract was subsequently dilated prior to the insertion of the catheter.

Care was taken that the dilator should not be inserted more than the expected distance from the chest wall to parietal pleura, in order to decrease the risk of lung injury.

The length of the catheter in the pleural space ranged from 5 to 15 cm, the final depth being dependent on the ease of aspiration of the pleural fluid.

The catheter was then connected to a urine drainage bag with a non-return valve (Polymedicure, Haryana, India) via a three-way stopcock (B Braun, San Goncalo, Brazil) and a modification from the end of an intra- venous drip set (B Braun, Penang, Malaysia).


A piece of transparent dressing (Tegaderm™; 3M, St Paul, Minnesota, USA) was applied over the junction of the urine bag tubing and the rubber bung of the intravenous drip set to prevent a disconnection.

The central venous catheter was stitched down to the skin and a similar transparent dressing applied over the insertion site.


A record of complications (pneumothorax, hemothorax, re- expansion pulmonary edema and equipment failure) was made.

A chest radiograph was performed routinely post catheter insertion for pneumothorax detection.

Subsequent radiographs made as part of the ICU management of the patient were also reviewed.

The catheter site was inspected daily for evidence of redness, swelling or discharge and the duration of the catheter's presence in situ was noted.

The daily and total volumes of pleural fluid drained were recorded.

Recurrence of the effusion after catheter removal and the need for a repeat thoracentesis was noted.


The means and standard deviations of the volumes of pleural fluid drained at 1, 6 and 24 hours post catheter insertion are presented.


Single puncture thoracentesis has been found to be a safe technique in mechanically ventilated patients [8] although there are still reservations about its use [9,10].

The procedure may need to be repeated frequently, however, and may thus cause some discomfort to the patient and an increased risk of complications associated with repeated puncture.

The bedside placement of large-bore chest tubes, 24-32 Fr gauge in diameter, is an alternative technique but its limita- tions are that the indwelling chest tubes are often associated with much patient discomfort and a relatively higher risk of mechanical complications.

This can be overcome using fine pig-tail catheters of 8.0-14.0 Fr [11].

This corresponds approximately to a diameter of 2.66 and 4.66 mm [12], respectively, and is usually placed under ultrasound guidance by radiologists.


The present technique describes the use of a similar flexible tube, but smaller in diameter (1.7 mm), which can be kept in situ to facilitate continuous drainage and thus avoid patient discomfort and potential complications from repeated thora- centesis.

Our patients reported minimal, if any, discomfort from the indwelling catheter and were able to cooperate with our physiotherapists and respiratory therapists to facilitate alveolar recruitment.


Ultrasound-guided techniques have been advocated for use in ICU patients [9,10].

Thoracentesis under ultrasound guid- ance is not complication free, however [13].

We ourselves seek the help of our radiological colleagues to insert pig-tail catheters in patients with difficult chest wall anatomy, with significant coagulation abnormalities or with possible locu- lated effusions.

In these instances, however, insertion is fre- quently delayed as arrangements have to be made with the radiologists and patients may need to be transported to the radiology department for the procedure.

Our complication rate is no worse than those rates reported by Lichtenstein


The first reported use of a central venous catheter to aspirate a pleural effusion might be attributed to Cooper who used it in a single patient to aspirate an effusion, after which it was removed [14].

We have been unable to trace any other pub- lished material on this technique except for the follow-up cor- respondence [15].

We therefore believe that the present paper is the first to document in detail the indwelling nature of this technique in a larger group of patients.

Grodzin and Balk have described a similar technique of leaving a 7 Fr indwelling pleural catheter (Turkel thoracentesis systems) for intermit- tent pleural drainage [5].

We are unable to determine the widespread availability or use of this system.


Our small study has also shown the feasibility and safety of using a urine drainage bag system instead of a water seal system in mechanically ventilated patients.

The bag is always placed below the level of the patient's chest.

We do not routinely flush the drainage system.

The catheter is removed if pleural drainage is less than 100 ml for two consecutive days and there is resolution of the effusion on the chest radiograph.


There are several potential advantages of this technique over repeated thoracentesis, use of pig-tail catheters and use of conventional large-bore chest drains.

This single lumen catheter is well tolerated with minimal patient discomfort and, in our small series, is not associated with catheter blockage, problems with the drainage system and with infection.

The technique thus avoids the need for repeated punctures, which are painful.


In our two hospitals, the advantage over the pig-tail catheters can be viewed from the point of logistics and cost.

Once the decision is taken to insert the single lumen catheter, this can be accomplished rapidly by the intensivist with the assistance of the bedside nurse.

For pig-tail catheter insertion, either the radiology team comes to the intensive care unit or the patient needs to be transported to the radiological suite.

We are also able to avoid the procedural charges of the radiol- ogy team.

The cost in our institution of the catheter and dis- posable preparation set is less than US$15.00.


In comparison with conventional large-bore chest drains, the catheter is asso- ciated with less discomfort during insertion and when it is in situ.

This facilitates nursing and physiotherapy care.

We are able to avoid the use of conventional chest drainage bottles which are expensive.

Demands on nursing care are minimal as the catheter entry site is small and not associated with pleural fluid leaks around it and because we have not needed to regu- larly flush the catheter while it is in situ.


In summary, the present article provides preliminary data on the use of a 16 G indwelling central venous catheter to drain large non-loculated pleural effusions in the ICU.

Although our case series is small, it appears that this technique is useful and safe in selected individuals.


• A number of techniques have been described to drain pleural effusions


• Each technique has its advantages and disadvantages


• In selected individuals, non-ultrasound guided placement of small bore catheters such as central lines provide effective and safe drainage of pleural effusions with minimal discomfort


I read with interest the paper by Singh and coworkers on the subject of pleural drainage [1].

In the respiratory field, this is a hot topic and guidelines were recently published [2].

Singh and coworkers used a 16-French gauge catheter, which is broadly in agreement with the British Thoracic Society guidelines (and this is what we sometimes use in our hospital).

However, the British Thoracic Society guidelines [2] do advocate a slightly smaller gauge.

The move is certainly away from large bore drains, and I would strongly support this.


Our unit has also achieved good success using 12-French gauge drains inserted using a Seldinger technique (Thal-Quick Chest Tubes, Cook Critical Care, Bloomington, IN, USA) in patients on a respiratory ward.

They seem to be patient-friendly with little initial morbidity.

However, it has been noted that blockage by fibrinous or clotted material does occur.

I am surprised that the authors did not encounter this problem, even with the larger drain.


I note the comments on the use of ultrasound guidance to access the pleural space.

A recent article [3] reported increased efficacy using ultrasound guidance in the hands of an interventional radiologist, performing the procedure in ‘real time’.

This seems a useful method but it is a luxury that is often not available.

The use of ultrasound to locate the most suitable position for access, using an ‘X marks the spot’ methodology, has in our experience often been unreliable.

I suspect that this is because the pleural access is not performed in ‘real time’.

I would be interested to know the authors’ thoughts on this and whether any of their catheters were inserted using ultrasound guidance.


I would urge caution on behalf of Singh and coworkers in interpreting some of the data.

This is a highly selected, small group of patients.

In this setting, the absence of infection or blockage is probably of limited value.

Our experience has revealed that there are definite, although low, rates of blockage and infection.

A larger, prospective, ‘real world’ study is needed.


We would like to thank Dr Kelly [1] for his interest in our recent article [2] on the use of central venous catheters for pleural drainage.

His comments add to those recently highlighted by MacDuff and Grant [3].

Potential medicolegal pitfalls with the use of the central venous catheters that we have described.

We believe, however, that cost issues should be taken into account when designing this study.

We would like to comment on the use of ultrasound (USS)-guided drainage of the pleural cavity.


The technique we have described is a cheaper and less traumatic alternative to the use of bigger bore chest tubes.

It is, however, not meant as an alternative for situations where USS guidance is needed, such as in difficult patient anatomy or in the drainage of loculated effusions.

As Kelly has pointed out correctly, it is a luxury and in our context also expensive, and it involves logistical arrangements that delay the performance of the procedure.

We have also encountered situations of failure despite the ‘X marks the spot’ methodology.

To avoid this, in situations where we seek the aid of the radiologist, we either perform the insertion with the radiologist present or get them to insert their fine bore catheters at the first attempt.

This avoids the double cost and logistical arrangements needed should we fail.


In our experience there have been occasions where chest radiograph diagnosis of significant pleural effusions was not confirmed by USS, and we invite caution in performing this procedure without USS information.

As we have highlighted in our paper and in our recent reply [4], our reported group is small and selective.

We recognize that we cannot accurately predict the rate of infection as well as catheter blockage with our sample size, although thus far we have not encountered these problems.

We agree that a ‘real world’ study is needed to answer a number of issues.

MacDuff and Grant have highlighted.


Diabetes mellitus is a bihormonal disorder, in which both insulin deficiency and absolute or relative glucagon excess contribute to the metabolic disturbances (1, 2).

Insulin re- sistance and beta-cell dysfunction are core defects in type 2 diabetes mellitus (T2D) (3).

Increased glucagon secre- tion and hyperglucagonemia also contribute to hypergly- cemia in T2D patients (2, 4, 5).

In the fasting state, plasma glucagon levels in T2D are elevated (1, 6) and fail to sup- press normally after a meal or glucose challenge (7-10).

Enhanced glucagon response to arginine also has been dem- onstrated (11).

In nonhuman primate models, worsening glycemia is associated not only with decreased beta-cell volume but also relative increase in alpha-cell volume and hyperglucagonemia (12-14).


In individuals with prediabetes, an increased glucagon response to arginine challenge has been shown to predict the development of T2D (15).

In nondiabetic (16-18) and T2D (16-20) subjects, impaired suppression of glucagon secre- tion after glucose ingestion is associated with postprandial hyperglycemia, and hyperglucagonemia has been shown to correlate with insulin resistance (16, 18, 21-23).

However, in these studies, subjects with impaired glucose tolerance (IGT) and T2D had a higher body mass index (BMI), and obesity is an insulin-resistant state (24, 25).

Dysregulation of glucagon secretion has been shown in obese individuals with and without T2D as compared with lean individuals (26, 27).

However, it is not clear whether the altered glu- cagon secretion in these subjects was secondary to obesity, abnormal glucose tolerance, or the underlying defects in insulin sensitivity and insulin secretion.

To further examine the regulation of glucagon secretion by insulin and glucose in obese subjects, we assessed insulin-mediated suppres- sion of plasma glucagon levels and its relationship with insulin resistance and beta-cell function in obese Hispanic Americans with variable levels of glucose tolerance.


The participants included 275 obese subjects of Hispanic American descent who participated in the Veterans Administration Genetic Epidemiology Study (VAGES) study (28).

Obesity was defined as a BMI ≥30 kg/m 2 .

All subjects received a 75-gram 2-hour oral glucose tolerance test (OGTT).

Based on American Diabetes Association cri- teria, individuals were classified as having normal glucose tolerance (NGT) (n = 69, BMI = 32.7 ± 0.6, M/F = 23/46); prediabetes, with fasting plasma glucose (FPG) of 100 to 125 mg/dL and a 2-hour plasma glucose of ≥140 to 199 mg/dL (n = 115, BMI = 33.8 ± 0.5, M/F = 37/78); or T2D (n = 91, BMI = 33.9 ± 0.5, M/F = 38/53).


All subjects had normal liver, cardiopulmonary, and kidney function as determined by medical history, physical examination, screening blood tests, electrocardiogram, and urinalysis.

NGT and prediabetes subjects were not taking any medi- cation known to affect glucose tolerance.

T2D subjects were either on diet or metformin, which was held on the day of study.

No subject participated in any regular phys- ical activity program.

Body weight was stable (±2 kg) for at least 3 months before study in all participants.


The study protocol was approved by the Institutional Review Board of University of Texas Health Science Center at San Antonio, and informed written consent was obtained from each subject before participation.


All OGTT studies were performed at the Bartter Clinical Research Unit (BCRU) in the Audie L. Murphy Memorial VA Hospital at 7:30 to 8:00 am after a 10- to 12-hour overnight fast.

Before the start of the OGTT, a small poly- ethylene catheter was placed into an antecubital vein for blood withdrawal.

At time 0, subjects ingested a 75-g glu- cose solution.

Blood samples were collected at −30, −15, 0, 30, 60, 90, and 120 minutes for measurement of plasma glucose, insulin, C-peptide, and glucagon concentrations.

On the day of the OGTT, waist and hip circumference was measured with a Gulick tape measure.


After a 10- to 12-hour overnight fast, a subset of parti- cipants (26 NGT, 37 prediabetes, 27 T2D) received a 120-minute euglycemic insulin clamp (40 mU/m 2 •min) (29).

Before the start of the euglycemic insulin clamp, a catheter was placed into an antecubital vein for the infu- sion of all test substances.

A second catheter was placed retrogradely into a vein on the dorsum of the hand which was placed in a heated box (60 °C) for arterialized blood withdrawal.

During insulin administration, plasma glu- cose was measured every 5 minutes and a variable glucose infusion was adjusted to maintain each subjects' plasma Downloaded from https://academic.oup.com/jcem/article/106/5/1398/6125730 by Stanford University user on 07 October 2025 1400 The Journal of Clinical Endocrinology & Metabolism, 2021, Vol. 106, No. glucose at his/her fasting level.

In T2D subjects, the plasma glucose concentration was allowed to decline to 100 mg/ dL, at which level it was maintained.

The coefficient of vari- ation of plasma glucose was less than 5%.


Plasma glucose was measured by glucose oxidase reaction (Glucose Analyzer from Beckman, Fullerton, CA).

Plasma insulin and C-peptide concentrations were measured by radioimmunoassay (Linco Research, St. Louis, MO).

Plasma glucagon concentration was measured by radio- immunoassay (Millipore Sigma, Burlington, MA).

The intra-assay coefficient of variation for glucagon was 4.9%.


Insulin-mediated suppression of glucagon secretion was determined by plasma glucagon/insulin ratio.

Glucagon suppression at 60 minutes during the OGTT was calcu- lated as follows: [1-(glucagon 60 min /glucagon 0 min )] × 100%.

The Matsuda index (30) was used to assess whole-body insulin sensitivity, using the plasma glucose and C-peptide (CP) concentrations measured during the 2-hour OGTT.

The mean rate of insulin-stimulated glucose metabolism (M value) during the euglycemic hyperinsulinemic clamp was calculated to provide an independent measure of in- sulin sensitivity.

Beta-cell function was calculated using the formula ΔCP/ΔG ÷ IR, where ΔCP/ΔG is the ratio of the incremental area under the curve (AUC) for plasma C-peptide to the incremental AUC for plasma glucose (ΔAUC-CP/ΔAUC-G) during the 2-hour OGTT, and IR is insulin resistance measured by the inverse of the Matsuda index (31, 32).

Subjects were stratified into 4 groups based on their insulin sensitivity (Matsuda index and M value), and beta-cell function (insulin secretion/insulin resist- ance or disposition index).

Subjects in Quartile 1 (lowest Matsuda insulin sensitivity index or M value) were the most insulin-resistant and subjects in Quartile 4 were the most insulin-sensitive.


Statistical comparisons were performed using Graph Pad Prism 9 (Graph Pad Software, San Diego, CA, USA) and NCSS (Version 12, Chicago IL).

Study participants were categorized into equal quartiles of Matsuda index of insulin sensitivity and insulin secretion (ΔCpep 0-120 / ΔGlu 0-120 ).

Plasma glucagon levels and suppression of glucagon during OGTT were related to glucose tolerance status and to quartiles of insulin sensitivity and insulin secretion using Spearman's correlation.

Comparison between the quartiles of insulin sensitivity and beta-cell function was performed using 2-way ANOVA with Bonferroni post hoc testing when appropriate.

Group comparisons (baseline vs OGTT and baseline vs euglycemic insulin clamp) were performed by Student t test.

Data represent the mean ± standard error of the mean.

The relationship between plasma glucagon/ insulin ratio versus insulin sensitivity and versus insulin se- cretion were determined by Spearman's correlation.


The clinical and metabolic characteristics of study participants are shown in Table 1.

Of the 115 subjects with prediabetes, 30 had impaired fasting glucose (IFG), 42 had impaired glu- cose tolerance (IGT) and 43 had combined IFG/IGT.

Subjects with NGT were slightly younger than prediabetic and T2D subjects.

There was no difference in BMI, waist and hip cir- cumference, or male/female ratio between the 3 groups.

The FPG and 2-hour OGTT glucose concentration increased from NGT to prediabetes to T2D (Fig. 1A).


There was no difference in fasting plasma glucagon con- centration between NGT, prediabetes, and T2D subjects.

However, the fasting plasma glucagon in T2D subjects tended to be higher compared with both NGT and prediabetes (Fig. 1B).


The mean plasma glucagon concen- tration during the OGTT at 60 minutes and 120 minutes were similar in NGT and prediabetes groups and slightly, although significantly (P < 0.05), increased in T2D (Fig. 1B).

The fasting plasma insulin and C-peptide concentra- tions rose progressively from NGT to prediabetes to T2D (Fig. 1C and 1D).


The mean plasma insulin and C-peptide concentrations during the OGTT at 60 minutes and 120 minutes were significantly increased in prediabetes versus NGT (P < 0.001) and reduced in T2D versus both NGT and prediabetes groups (P < 0.001) (Fig. 1C and 1D).

The fasting plasma glucagon/insulin ratio declined progres- sively from NGT to prediabetes to T2D (P < 0.001) (Fig. 2A).


When subtypes of prediabetes, (ie, IFG, IGT, and IFG/ IGT) are compared, there was a progressive decline in the fasting glucagon/insulin ratio from IFG to IGT to combined IFG/IGT (Fig. 2B).

At 60 minutes (Fig. 2C) and 120 min- utes (Fig. 2D) during OGTT, the plasma glucagon/insulin ratio was similar in prediabetes and NGT groups but mark- edly increased in T2D versus both NGT and prediabetes (P < 0.001).


When subtypes of prediabetes, (IFG, IGT, and IFG/IGT) were compared, there was a progressive decline in the glucagon/insulin ratio fasting glucagon/insulin ratio at 120 minutes from IFG to IGT to combined IFG/IGT (Fig. 2E).

Suppression of plasma glucagon at 60 minutes during OGTT compared with fasting glucagon was similar in NGT (10.4%) and prediabetes (9.1%) groups, but sig- nificantly impaired in T2D individuals (3.3%) (P < 0.05).


During the OGTT, the number of subjects in whom the 2-hour plasma glucagon concentration was lower than the fasting plasma glucagon was 53/69 (77%) in NGT, 88/115 (77%) in prediabetes, and 64/91 (71%) in T2D (P = NS).

There were no significant differences in age, BMI, FPG, 2-hour glucose, Matsuda insulin sensitivity index, and in- sulin secretion/insulin sensitivity (disposition) index between subjects with suppressed (2-hour plasma glucagon below fasting plasma glucagon) versus nonsuppressed (2-hour plasma glucagon above fasting plasma glucagon) in the entire group, as well as between NGT, prediabetic, and T2D groups.


Insulin sensitivity, measured with both the Matsuda index of insulin sensitivity and the rate of insulin-mediated glucose metabolism (M values) during the euglycemic hyperinsulinemic clamp, decreased progressively from NGT to prediabetes to T2D (Fig. 3A and 3B).

Subjects were stratified into 4 groups based on their insulin sensitivity; subjects in Quartile 1 were the most insulin-resistant, while those in Quartile 4 were the most insulin-sensitive (Table 2).

As expected, the greatest number of NGT subjects were in Quartile 4 (most insulin-sensitive) of Matsuda insulin sensitivity index or the M value, and the largest number of individuals with T2D were in Quartile 1 (most insulin- resistant).


The mean plasma glucagon concentration in the fasting state and during the OGTT (0-120 minutes) in relation to quartile of insulin sensitivity is displayed in Fig. 4.

Both fasting and 2-hour plasma glucagon concentra- tions increased progressively with decreasing insulin sensi- tivity, measured both with the Matsuda index or M value during the euglycemic insulin clamp (Fig. 4A and 4B).

The plasma glucagon/insulin ratio progressively declined with worsening insulin resistance (Figs. 5A-5D).


Beta-cell function, measured with insulin secretion/in- sulin resistance (disposition) index, gradually decreased from NGT to prediabetes to T2D (Fig. 3C).

The rela- tionship between plasma glucagon concentration and insulin secretion/insulin resistance (disposition) index is displayed in Fig. 4.

As expected, the highest quar- tile of disposition index (Quartile 4, Table 2) contained the highest percentage of individuals with NGT, while the lowest quartile of disposition index contained the highest percentage of individuals with T2D (Quartile 1, Table 2).

Both fasting and 2-hour plasma glucagon levels increased progressively with worsening beta-cell function (Fig. 4C and 4D) and the glucagon/insulin ratio decreased progressively with declining beta-cell function (Fig. 5E and 5F).


Fig. 6A) and beta-cell function (disposition index, r = 0.35; P < 0.001) (Fig. 6B).

During OGTT, the glucagon/insulin ratio at 60 minutes (Fig. 6C) and 120 min- utes (Fig. 6D) was inversely correlated with beta-cell func- tion (disposition index, r = −0.47; P < 0.001 and r = −0.32; P < 0.001, respectively).

Glucagon suppression during the OGTT (r = −0.53; P < 0.001) was inversely correlated with the glycated hemoglobin (HbA1c) in nondiabetic subjects, but not in prediabetic or T2D subjects.


To identify factors contributing to the impaired suppres- sion of glucagon and fasting hyperglycemia, we performed a multiple regression analysis using glucagon/insulin ratio as a dependent variable and Matsuda insulin sensitivity index, fasting glucose, and insulin secretion (ΔI I0-120 /ΔG 0-120 ) as independent variables.

Together, Matsuda insulin sensi- tivity index, fasting glucose, and the insulinogenic index explained 61% (r 2 = 0.605; P < 0.001) of the variation in fasting glucagon/insulin ratio.

Similarly, when the FPG con- centration was the dependent variable, and fasting glucagon to insulin ratio, glucagon suppression at 120 minutes, and glucagon to insulin ratio at 60 minutes were independent variables, together they explained 51% of variation in fasting glucose level (r 2 = 0.506; P < 0.005).


The present results demonstrate that, in a large cohort of obese Hispanic American subjects with a wide range of glu- cose tolerance, both the fasting and OGTT plasma glucagon concentrations and the glucagon/insulin ratio progressively worsened with increasing insulin resistance and declining beta-cell function.

Impaired suppression of glucagon by in- sulin during the euglycemic hyperinsulinemic clamp also progressively declined with worsening glucose tolerance.


In the present study we focused on obese subjects be- cause: (i) obese subjects are at high risk of developing dia- betes; (ii) a recent study (33) suggested that obese subjects have a lower fasting plasma glucagon concentration that results from elevated fasting insulin levels secondary to insulin resistance; and (iii) although several studies (15- 17) have reported increased plasma glucagon levels in prediabetes versus NGT subjects, there were significant dif- ferences in BMI between the 2 groups (16, 18, 27).

Despite similar BMIs between the NGT, prediabetes, and T2D groups, the results clearly show that fasting and 2-hour plasma glucagon levels increase with worsening glucose tolerance as well as with worsening insulin resistance and declining beta-cell function.

The plasma glucagon concentration during the OGTT failed to suppress (ie, return to the fasting level during the OGTT) in 21% to 28% of the participants.

Importantly, there were no significant differences in the prevalence of nonsuppressed plasma glucagon levels between NGT, prediabetic, and T2D individuals.

However, when stratified by quartiles of insulin sensitivity, there was a marked dif- ference in mean plasma glucagon concentration during the OGTT between subjects in the lowest and highest quar- tiles of insulin sensitivity (Fig. 4A and 4B).

This suggests that the impaired glucagon suppression is more strongly related with insulin resistance than with plasma glucose levels.

Our results are consistent with those reported by Faerch et al in Danish subjects (16).


Both glucose and insulin are important regulators of the plasma glucagon concentration.

Insulin inhibits glucagon secretion both by paracrine mechanisms and elevated plasma levels (34, 35), while glucose inhibits glucagon by increasing cyclic adenosine monophosphate (cAMP) levels in the alpha-cell (36).

The current study design does not allow us to determine whether there is resistance to the suppressive effect of glucose or insulin or both.

In the current study, plasma glucagon levels are clearly more affected by insulin sensitivity and beta- cell function than by the plasma glucose level per se.

The changes in plasma glucagon levels were more pro- nounced when measured by change in quartiles of in- sulin sensitivity than changes in plasma glucose.

Elevated fasting glucagon levels have been associated with insulin resistance, measured by the euglycemic hyperinsulinemic clamp, in nondiabetic subjects, suggesting insulin resist- ance at the level of pancreatic alpha-cells (37).

In the present study, we show that a similar relationship also exists in individuals with prediabetes and T2D.

Among the subtypes of prediabetes, our data suggests that there is a progressive worsening in suppression of glucagon when moving from isolated IFG to combined IFG/IGT, which could be explained by worsening insulin sensi- tivity and insulin secretion in isolated IFG versus com- bined IFG/IGT.


Impaired plasma glucagon suppression in response to meals and hypersecretion in response to arginine have pre- viously been shown (11, 38).

The present study demon- strates that elevated plasma glucagon levels are present in the fasting state as well as at the 60-minute and 120-minute time points during an oral glucose load.

Our results differ from those of Faerch et al, who showed that impaired glu- cagon suppression in T2D patients during an OGTT was most marked at 30 minutes, while a normal decrease was observed at 120 minutes (16).

Our results demonstrate that both early and late glucagon suppression are impaired in T2D subjects during the OGTT and contribute to hyper- glycemia.

This difference could be related to the different ethnic populations that were studied (Mexican Americans versus Caucasians) or the greater severity of insulin resist- ance in our subjects.

Of note, glucagon response to a mixed meal is different from the glucagon response to OGTT.

While glucose load leads to suppression of glucagon, fol- lowing a mixed meal there is an initial increase in glucagon followed by suppression (39, 40).

It is possible that the glu- cagon response to mixed meal in relation to insulin sensi- tivity could differ from that seen with OGTT.


How insulin sensitivity modulates plasma glucagon levels is not clear.

It is possible that insulin resistance is present at the level of the pancreatic alpha-cells, which contain insulin receptors and the insulin signal transduction system (34, 41).

Deletion of pancre- atic alpha-cell insulin receptors in mice (αIRKO mice) causes impaired glucose tolerance, hyperglycemia, and hyperglucagonemia, demonstrating the important role of the insulin receptor in the regulation of glucagon se- cretion (34).

Our results are consistent with the concept that insulin resistance at the level of pancreatic alpha- cell, as well as impaired insulin secretion, contribute to impaired glucagon suppression in T2D.

Consistent with this scenario, insulin has been shown to modulate glucagon secretion by reducing the sensitivity of Katp channels in pancreatic alpha-cells, resulting in decreased phosphatidylinositol 3-kinase (PI3K) and Akt activity (42).

An increase in plasma free fatty acid concentrations has been shown to decrease glucagon secretion in hu- mans (42).

In contrast, a recent study showed that ex- posure of human cultured islets to increased fatty acid levels enhanced glucagon secretion (43).

Plasma free fatty acid levels were not measured in the present study.


In rats, chronic (7 days) exposure to elevated plasma glu- cose levels was shown to augment glucagon secretion, and this was attributed to glucotoxicity (44).

Consistent with these results in rodents, we have shown that mild physiologic hyperglycemia (+50 mg/dL) in healthy NGT individuals for 72 hours markedly impairs suppression of glucagon during euglycemic hyperinsulinemic clamp (45).

As expected, a novel human monoclonal antibody and competitive antagonist of the glucagon receptor im- proved glycemic control, reduced hepatic glucose pro- duction, and improved skeletal muscle insulin sensitivity in rodent models of obesity and insulin resistance (46).

A glucotoxic effect on pancreatic alpha-cell secretion of glucagon also has been demonstrated in vitro (33), and correction of the hyperglycemia with phlorizin restored the ability of glucose to suppress glucagon secretion (47).


In summary, the present results demonstrate that sup- pression of glucagon secretion is impaired with increasing severity of glucose intolerance and is closely associated with insulin resistance and to a lesser extent with beta-cell dysfunction in obese Hispanic Americans.


We read the article titled “Impaired Suppression of Glucagon in Obese Subjects Parallels Decline in Insulin Sensitivity and Beta-cell Function” by Chen and colleagues [1] with great interest.

The study has evaluated the relationship of glucagon suppression with insulin resistance and beta-cell function assessed by oral glucose tolerance test (OGTT) and euglycemic hyperinsulinemic clamp studies in obese normal glucose tolerance (NGT), prediabetes, and type 2 diabetes (T2DM) Hispanic population.

It demonstrated a progressive increase in both fasting and 2-hour plasma glucagon levels during OGTT, which had a positive correlation with the severity of insulin resistance (IR).

Moreover, the study also showed the decrease in fasting glucagon/insulin ratio to be associated with increasing insulin resistance and declining beta-cell function.

This interesting finding supports that impaired alpha-cell function is more closely related to the development of IR and beta-cell function rather than solely depending on the glycemic levels alone.


This prompted us to reanalyze the data of our recently published study [2] involving Asian-Indians with impaired glucose tolerance (IGT), impaired fasting glucose (IFG) and NGT.

At baseline, the mean age of the population (n = 60) was 36.8 ± 7.6 years and mean body mass index was 25.7 ± 2.8 kg/m2.

Among the included participants, 80% were females (n = 48) and 20% (n = 12) were males.

There was no difference in either fasting glucagon (measured by ELISA; R & D Systems, catalog #DGCG0, AB_2893019) or total area under the curve (AUC) glucagon across body mass index or age quartile.

Sex had also no effect on the plasma glucagon level.


Notably, we also found that fasting glucagon/insulin ratio decreased progressively with increasing insulin resistance, as measured by Matsuda Index derived from a 2-hour mixed meal tolerance test (MMTT).

The difference in the fasting glucagon/insulin ratio across 4 quartiles of IR was also statistically significant (P < 0.001).


Moreover, across the quartiles of increasing IR, fasting insulin secretion increased significantly as expected, but fasting glucagon levels were almost similar, suggesting that even in the face of increased insulin, fasting glucagon was not suppressed.

This finding is comparable to that of the study being discussed.

We also found a positive correlation between the fasting glucagon/insulin ratio with the Matsuda Index (Spearman’s rho: 0.704; P < 0.0001).

However, the relationship between the beta-cell function as measured by insulin secretion and sensitivity index-2 from the 2-hour MMTT [3] and fasting glucagon/insulin was weak (Spearman’s rho: 0.31; P = 0.014).

On the other hand, we found a trend of decreasing fasting glucagon/insulin ratio with declining insulin secretion and sensitivity index-2 values.

However, this relationship did not reach statistical significance, possibly reflecting small sample size of our study.


On the contrary, meal-stimulated glucagon did not have any relationship with either IR or beta-cell function in our study.

There was also no correlation found between total AUC glucagon with Homeostatic Model Assessment-IR and beta.

This may reflect the difference in methodology because we used MMTT instead of OGTT and clamp study.

Furthermore, our study did not have a T2DM group.

Paradoxically, we found a lesser glucagon secretion during MMTT in the prediabetes individuals compared with the NGT population at 60 and 120 minutes.

Hence, there was a negative correlation found between total AUC glucagon and total AUC glucose.


The finding from our study consolidates the idea of impaired glucagon suppression (at least fasting) as a correlate of IR across ethnicities, including Asian-Indians.

Moreover, this finding paves the way for further studies to assess the relationship of impaired glucagon suppression with both IR and beta-cell function using the gold standard clamp studies in different ethnicities across the world, including Asian-Indians in whom the prevalence of prediabetes and diabetes is rising alarmingly.

Nonetheless, it would be interesting to observe the effect of improved IR through weight loss (including dietary modifications and exercises) on the impaired glucagon suppression in insulin-resistant obese individuals.


Roy et al [1] analyzed plasma glucagon levels in relation to insulin sensitivity in Asian Indians with normal glucose tolerance (NGT), impaired fasting glucose (IFG), and impaired glucose tolerance (IGT) and found that their observations are mostly consistent with the results seen in Mexican Americans, particularly in the fasting state [2].

Since underlying metabolic abnormalities in pathogenesis of type 2 diabetes mellitus (T2DM) in different populations should be similar, one should not expect to see major differences in results across different ethnicities.

The authors demonstrate a progressive decline in fasting glucagon/insulin ratio from NGT to IGT and with worsening insulin sensitivity, based on quartiles of insulin sensitivity.

They did not observe any difference in glucagon/insulin ratio between IFG and IGT individuals.


Of note, although we showed a trend in declining glucagon/insulin ratio between IFG and IGT groups, the difference was not statistically significant.

The other possibility could be that the number of participants in each category appears too small in their study.

Insulin sensitivity was measured by the Matsuda insulin sensitivity index (MI) during a mixed meal test.

Though their observations may be similar, it is not equivalent to MI obtained from an oral glucose tolerance test (OGTT) [3].


The other differences between their observations and our results could be explained by the following.

Our study enrolled exclusively obese individuals with a body mass index (BMI) greater than 27, and there was no difference in BMI between the groups (NGT vs IFG/IGT vs T2DM).

It is not clear if there was a difference in BMI in their study population.

Although plasma glucagon did not differ in relation to BMI, plasma insulin levels are usually higher in obese individuals, which will therefore affect the glucagon/insulin ratio.

Roy et al [1] also note that meal-stimulated glucagon responses did not correlate with either insulin sensitivity or insulin secretion.

It is well known that glucagon response following OGTT and a mixed meal are different [4].

Following an oral glucose load in NGT and IGT patients, there is a progressive decline in glucagon levels whereas following a mixed meal there is usually a transient rise in plasma glucagon followed by a decline, thus the glucagon area under the curve following OGTT and mixed meal cannot be compared.


Overall, there is congruence between plasma glucagon levels and insulin sensitivity in Asian Indians and Mexican Americans, and we agree that future studies with euglycemic insulin clamps at least in a subset of patients will better characterize this relationship.

Evaluation of this relationship after interventions such as weight loss will provide further insights into the role of glucagon in pathogenesis of T2DM.


In keeping with editorial convention, Sbriglia and Žižek spend a number of pages summarizing the chapters of their various authors.⁹ Before doing so, they lay out their own general position from pages 2 through 16, beginning gently and progressing gradually toward the technical heart of their argument.

The editors note that from the 1980s until recently, "materialism" in the humanities and social sciences referred to a cultural rather than physical materialism, as embodied especially in the works of Louis Althusser and Michel Foucault: "cultural materialism holds that subjects are by-products of their respective cultural milieus - epiphenomena of socio-symbolic networks and matrices, ideological state apparatuses, and disciplinary techniques and epistemes" (3).

They capably observe that at least two different strands of opposition to cultural materialism have emerged, as embodied in two prominent anthologies now roughly a decade old.

Diana Coole and Samantha Frost introduce their New Materialisms collection by rejecting "substantialist Cartesian or mechanist Newtonian accounts of matter […] [as] simply passive or inert. "¹⁰ A year later, in The Speculative Turn, Bryant, Nick Srnicek, and I emphasized the need for a realist turn against cultural materialism's obsession with "texts, discourse, social practices, and human finitude. "¹¹ Nonetheless, Sbriglia and Žižek assert, "whatever their differences from cultural materialism, the materialisms and realisms that Bennett and Bryant advocate alongside Coole, Frost, and Harman […] not only share in but also advance the cultural materialist project of placing the subject under In one sense, this assertion of genuine novelty against the hidden traditionalism of one's opponents is simply the sort of thing that philosophers do.

Everyone places a more or less educated bet on where the crux of contemporary philosophy is located; this having been done, all those who fail to follow our own preferred bet are proclaimed to be victims of the same traditional presupposition that we ourselves have overcome.

In precisely this way, Heidegger depicts the entire previous history of philosophy as a long forgetting of Being countered only by Heidegger himself, and Kant's Copernican Revolution treats his illustrious chain of predecessors as equally "dogmatic" through their assumption that the thing-in-itself is accessible to rational proof.

There is always a dose of exaggeration in such tactics, but also - in successful cases - the glimmer of a new insight that leaves philosophy different from what it was before.

The "wager" of the Ljubljana School - to use a term so dear to their fellow traveler Badiou - is that the path forward for philosophy leads not through a rejection of the subject, but instead through a "doubling down" (9) on Hegel's claim that substance is subject.

Additionally, there is a further wager that we must also replace the lucid modern "Cartesian subject" with a "barred" Lacanian subject traumatized by its disgusting encounter with the real: a model said to be already at work in both Hegel and his one-time friend F. W. J. Schelling.

Ljubljana's commitment to this twofold vision is famously durable, intense, and prolific.


Must we now follow the lead of the Ljubljana School and push forward with subject-oriented philosophy grounded in psychoanalysis, or should we instead view this current as a once-refreshing challenge to continental orthodoxy that is now showing its age in the face of one or more newly emerging trends? These are the stakes of the half-declared war of Subject Lessons.

As a helpful analogy, let's imagine that the pre-Socratic thinker Thales of Miletus, famous for his doctrine that water is the first principle of everything, had lived to see Kant's Copernican Revolution replace the Wolffian rendering of Leibnizian philosophy that preceded it in Germany.

We might well picture Thales speaking as follows, in the manner of Sbriglia and Žižek: "Whatever Kant's differences from Leibniz, the transcendental philosophy he advocates not only shares in but also advances Leibniz's project of placing water under erasure." Since water is no longer taken seriously as one of the building blocks of philosophy, we would probably just laugh at Thales and move on.


Yet the claim would be far from laughable for any odd soul who might still think that water is the root of all existence.

There is a crucial difference from the present case, of course, since water is philosophically irrelevant to both Kant and Leibniz, while the subject is anything but irrelevant to the "New Materialists": for all of them, the supremacy of the human subject is the chief obstacle to any philosophy that foregrounds the object.

Yet the point remains: to claim that cultural materialism and the "New Materialisms" are united in "erasing the subject" is only relevant to those who assume in advance that the subject is the necessary core of a genuine contemporary philosophy.

It makes no difference whether we accept the "Cartesian subject," replace it in cultural materialist fashion with "ideological interpellation and discursive formation," (3) or embrace an edgier, Ljubljanized subject characterized by a "tarrying with the negative," plunged into "the night of the world," betrayed by the "cunning of reason," standing at the mercy of the unconscious, or haunted by a death drive (3).

The problem is that in all three of these cases, we have human thought on one side and everything else on the other, no matter how turbulent our model of the subject may be.


What neither Foucault, nor Althusser, nor Kant, nor Hegel, nor Schelling, nor Husserl, nor Heidegger, nor Žižek himself is able to think is the interaction of two non-human entities when not under some sort of human surveillance: this is simply ruled out of court as a form of pre-Kantian dogmatism.

It will be said, according to the old post-Kantian trope, that even to think this interaction is already to put it under surveillance, so that the very idea is nonsensical.

This attitude is precisely what OOO rejects as "onto- taxonomy," referring to the assumption that there are two and only two basic kinds of things in the cosmos: (1) humans, and (2) everything else.¹² This is what makes it so pointless when Sbriglia and Žižek complain that "from the Hegelo-Lacanian perspective, what new materialists and realists understand as  12 See Harman, "The Only Exit from Modern Philosophy."


Sbriglia and Žižek's Subject Lessons  317 'subject' simply fails to meet the criteria of the subject" (14-15).

For by the same token we could say that from Thales' perspective, what Leibniz and Kant understand as "water" is merely a minor chemical substance, and therefore simply fails to meet the criteria of water as the arche of everything.

Perhaps more to the point, from a OOO perspective what Hegelo-Lacanians call objet petit a simply fails to meet the criteria of the object, since it reduces the object to a correlate of the subject's desire.

This sort of dispute needs to be conducted at a more basic level than merely accusing one's opponents of an inability to account for one's own pet entities.

The need for such entities to exist must first be established, and this certainly holds for the "subject" of modern philosophy, whose theoretical downside is at least as obvious as its benefits.

Otherwise, we might just as well invite Reichians to dismiss Lacan on the basis that he cannot account for the existence of "orgone."


Sounding the alarm about the disappearance of the subject is just one of several ways that Subject Lessons preaches to the converted.

Another can be found in Sbriglia and Žižek's mockery of the quest for a "re-enchantment" of the world by way of a "posthumanist reversion to a pre-modern ontology" (9).

The word "pre-modern" seems to have been deliberately chosen to evoke not just a specific period of philosophy, but a purported allegiance by "New Materialists" to an irrational, unenlightened, unscientific, and mythical past.

I do not exaggerate.

Just one page later, the editors compare flat ontology - the fairly basic notion that all entities must be treated by philosophy on an equal footing - to "a Tolkienesque world of magical forces in which the subject is merely one among countless vital objects," (10) before repeating the slap in a footnote: "little wonder, then, that the pluriverse envisioned by neovitalists resembles the Middle-Earth of Tolkien's Lord of the Rings, the defining work of fantasy literature" (27n57).


Since no argument in particular is made for the purported resemblance between the "New Materialists" and the workings of Middle Earth, this would appear to be an instance of reverse projection: rather than the "New Materialists" being obsessed with enchantment, Ljubljana seems obsessed with the disenchantment of the world, as if this were the very key to enlightenment.

Žižek's first critique of OOO, published in 2016, already sounded this note: "the main target of OOO is thus not transcendental philosophy with its subject/ object dualism, but modern science with its vision of 'gray' reality reduced to mathematical formalization: OOO tries to supplement modern science with a premodern ontology which describes the 'inner life' of things"¹³ (177).

Not at all.

The OOO critique of modern science is not for its "grayness," but for its literalism in reducing objects to bundles of qualities: a pivotal argument mentioned nowhere in Subject Lessons.

In any case, the "Tolkien" jabs will no doubt earn much laughter from Žižek's loyal readership, but they fail to advance the discussion a single step.

They are little more than morale-boosting jests among friends in a beer hall.