The authors would like to thank the reviewers for their helpful comments to improve the
manuscript. For detailed responses highlighted by blue font to the points raised by the reviewers,
please see below:
Referee: 1
Comments to the Author
The authors have addressed my comments on the first version of this paper extensively and
thoroughly. The revised paper is definitely improved. I have only a few comments left:
-The authors answered the first part of my question 2 (why networks become more random
during stroke recovery, see also question 6, referee no 3); however it seems they did not explicitly
address the second part of question 2 on increasing betweenness centrality in more random
networks.
We apologize for not providing an explicit answer to this question in our previous response.
Thank you for providing us with an opportunity to provide our interpretation of the relationship
between betweenness centrality and network randomness found in this study.
We agree with the reviewer that there may exist an inherent association between betweenness
centrality and network configuration. To investigate it, we simulated the evolutionary process in
which a regular network becomes a random network by rewiring each edge with probability P
from 0 to 1 with an increment of 0.01(Figure 1) as per Watts and Strogatz (1998). The initial
regular network had 20 nodes and 40 edges where, on average, each node is connected by four
edges. In addition to betweenness centrality used in the main text, we also specified closeness
centrality, clustering coefficient and degree to quantify local properties of nodes in a graph. The
value of closeness centrality is obtained via the following equation: Ci = (n-1)/sum(dij) (Sporns et
al., 2007), where n denotes the number of nodes in a graph and dij is the shortest path length from
node i to node j. The closeness centrality quantifies the connectivity of a node to all other nodes
of a network and is directly proportional to global efficiency as defined by Latora and Marchiori
(2001). The last two indices (i.e. clustering coefficient and degree) are the most general
measurements in graph analysis (for the detailed definitions on the measures involved, please
also see a recent review by Rubinov and Sporns (2009)). Figure 2 shows the average changes
over all nodes in all measurements of regional properties as a function of P. As the value of P
increases, we found that the network configuration gradually moves toward a random
1
configuration (Figure 1) and, on average, the betweenness centrality and clustering coefficient
values show reductions, whereas closeness centrality increased. Since the number of nodes and
edges are not changed in the graph, the average degree for each node is relatively stable over the
range of changes in the value of P. From visual examination of the formula for determining
closeness centrality, the distance functions involved in the calculation allow one to determine
which nodes are, on average, closest to all other nodes. Increasing the rewiring probability of the
edges leads to the appearance of an increasingly random organization pattern and further
reduces the shortest path length in the graph. Given the inversely proportional relationship
between closeness centrality and shortest path length, we think it is unsurprising to find increases
in closeness centrality when P is increased. Similarly, decreases in clustering coefficient are also
unsurprising because this measure assesses the degree to which nodes tend to cluster together
and a random graph is expected to show low clustering coefficient. In contrast, the relationship
between betweenness centrality and P is difficult to be determined. Although in this simulation,
the mean values of betweenness centrality showed reductions with P, we are at a loss to predict
how this measure will change as a function of P in every scenario, because both denominator and
nominator in the equation of betweenness centrality involve shortest path length. In spite of the
lack of a direct relationship between P and betweenness centrality, we feel it is worth noting that
the reduction in the mean betweenness centrality displayed in this figure did not reflect reduced
betweenness centrality in all regions, but show differential effects, with reductions and increases
in betweenness centrality dependent upon nodes. Therefore, although in our study of stroke cases
we observed both increased betweenness centrality in the ipsilesional primary motor area (and
contralesional cerebellum) and a gradual shift towards a more random organization, there is no
necessary association between the two findings. Moreover, in this study the ipsilesional
cerebellum showed decreased betweenness centrality during stroke recovery, which further
suggest that the relationship between increasing betweenness and more random networks may
not hold in every case.
Latora V, Marchiori M (2001) Efficient behavior of small-world networks. Phys Rev Lett
87:198701.
Rubinov M, Sporns O (2009) Complex network measures of brain connectivity: Uses and
interpretations. NeuroImage: in press.
Sporns O, Honey CJ, Kotter R (2007) Identification and classification of hubs in brain networks.
PLoS ONE 2:e1049.
Watts DJ, Strogatz SH. Collective dynamics of 'small-world' networks. Nature 1998; 393: 440-2.
2
Figure 1. Random rewiring procedure from a regular ring lattice to a random network without
altering the number of vertices or edges in the graph.
Figure 2. Changes in measures of regional properties as a function of rewiring probability P.
-my main problem remains the way the correlation matrices are converted to graphs (question 7,
see also question 5 by referee 3): The authors new give better arguments why the chosen 'cost' is
likely to results (mainly) in significant connections. However, fixing the cost (or the degree),
while resulting in networks with the same N and k, really can produce networks with different
thresholds in terms of significance. The validity of the main results would have been strengthened
if at least the most important findings could be reproduced with fixed threshold as well. Please
3
note that determining this threshold in terms of significance has to take into account the effect of
multiple comparisons (an arbitrary threshold is not enough).
We agree with the reviewer’s comments that fixing the cost will lead to different thresholds used
to construct a network. As the reviewer suggested, we also used different correlation values (from
0.2 to 0.55) to directly threshold functional connectivity in order to build functional networks for
each subject in each session. To adjust for multiple comparisons, a false discovery rate (FDR)
procedure (Genovese et al., 2002) was performed (corrected statistical threshold α = 0.05).
Figure S3 illustrates the effect of changes in significance levels on Gamma. The P values
surviving the multiple comparison correction were marked by black arrows. We found that
Gamma was significantly reduced between the correlation range of 0.3 - 0.5. As the reviewer
mentioned, such a result did strengthen our previous finding of reduced Gamma in the main text.
The new result has been added in the revised supplementary materials (see page 2).
Figure S3. Changes in P values corresponding to statistical tests on Gamma during stroke
recovery.
Genovese CR, Lazar NA, Nichols T (2002) Thresholding of statistical maps in functional
neuroimaging using the false discovery rate. NeuroImage 15:870-878.
-with respect to the minor comment, relating to page 11 of the original manuscript: I agree that
setting the distance between disconnected vertices to infinity solves the problem for the
pathlength, at least if a harmonic mean is used. However, what will happen to the clustering
coefficient based upon Barrat's formula?
4
In this study, the strength of functional connectivity between two regions was considered as the
weight of an edge connecting the two regions. In general, the distance of an edge was defined as
the inverse of the edge weight, considering the notion that a path length is inversely proportional
to a weight, i.e. lij =1/wij if wij ≠ 0, and lij =+∞ if wij = 0 (Achard and Bullmore, 2007; Rubinov et
al., 2009; Stam et al., 2009). The formula of the harmonic mean used to compute weighted
shortest path length in the main text eventually reflect the inversely proportional relation: the
denominator in the equation is related to the weights in a graph. Specifically,
Lw  N ( N  1)
N
N
1 l
i 1 j i
ij
(where, lij  min (sum (d ij )) and d ij  1 / wij mentioned in the
i j
main text) could be equivalently converted to Lw  N ( N  1)
N
N
 max( w
i 1 j i
ij
) if the weights of
disconnection between nodes are directly set to zero, i.e. lij =+∞ if wij = 0 where node i is
unconnected to node j. In contrast, given that weighted clustering coefficient is generally
proportional to weights of edges, the computation of clustering coefficient based on Barrat's
formula was preserved. The same processing has been widely used in graph theoretical
approaches and investigations of complex brain networks (Rubinov et al., 2009; Stam et al.,
2009). In addition, a recent review on network measures also illustrated the manipulation
(Rubinov and Sporns, 2009).
Achard S, Bullmore ET (2007) Efficiency and Cost of Economical Brain Functional Networks.
PLoS Comput Biol 3:e17.
Rubinov M, Sporns O (2009) Complex network measures of brain connectivity: Uses and
interpretations. NeuroImage: in press.
Stam CJ, de Haan W, Daffertshofer A, Jones BF, Manshanden I, van Cappellen van Walsum AM,
Montez T, Verbunt JP, de Munck JC, van Dijk BW, Berendse HW, Scheltens P (2009)
Graph theoretical analysis of magnetoencephalographic functional connectivity in
Alzheimer's disease. Brain 132:213-224.
-the authors indicate that analysis of the whole network (in contrast to the motor network) did not
show significant differences in graph indices; could this mean that the non motor network showed
opposite changes?
5
This is an excellent question; the question of whether abnormalities in a functional subsystem can
spread to the whole brain is an excellent research topic that, as far as we know, has yet to be
addressed. We speculated that the reviewer’s comments may arise from considerations about
bucking effect, since the observations of significant changes in functional subnetwork topological
organization and nonsignificant changes in that of the whole network easily allow one to imagine
that changes in non-motor network may show opposite direction to that of motor network and
then lead to an appearance of the bucking effect. As is well-known, however, stroke recovery
involves more complex processes, such as axonal degeneration, axonal sprouting and
neurogenesis. Although the subcortical infarctions in patients of this study in general were
mainly involved in motor pathways, we cannot guarantee that the brain lesions only affected the
motor pathway in all patients. If other functional subnetworks were impaired by stroke lesions,
how topological patterns in these subnetworks might change over time may also depend on the
extent to which the involved regions had been affected in individual patient. Therefore, although
analysis of the whole network did not show significant differences in graph indices compared to
the motor network, it was more difficult to generally claim that the non motor networks showed
opposite changes to that of the motor network. We think the lack of significant changes in the
whole brain network may at least partially explained by the involved brain regions being not
large enough to bring a significant results in the terms of the whole brain analysis. In addition,
our recent study has demonstrated that the topological organization of specific functional brain
networks cannot be captured by examining the network properties of the whole brain (He et al.,
2009), which may, at least in part, account for our findings. Although in this study we mainly
focused on changes in the topological organization in a set of motor-related regions during
stroke recovery, it would be interested in investigating whether and how abnormalities in a
functional subsystem could spread to the whole brain. Future studies using a simulated injury
model are needed to explore this important issue.
He Y, Wang J, Wang L, Chen ZJ, Yan C, Yang H, Tang H, Zhu C, Gong Q, Zang Y, Evans AC
(2009) Uncovering intrinsic modular organization of spontaneous brain activity in
humans. PLoS ONE 4:e5226.
Referee: 2
Comments to the Author
6
From the changes made it may be concluded that other reviewers had comments on the methods.
For myself it remains unclear what this application of graph theory has as advantages in
comparison to other connectivity measures (such as Granger causality, Learning Bayesian
networks etc.). I am not ´saying that others are better but we don’t really understand and can
interprete those datas, so why start with new techniques. This makes interpretation somehow
difficult and although the wordening has become more cautious now, the manuscript may offer
some alternative explanations.
We apologize for not providing a clear account of the features that distinguish graph theory
approaches from other connectivity measures. In the revised manuscript, we have added relevant
descriptions of this topic to the Introduction section (see pages 3-5) and relevant discussions as
one of several potential limitations (see page 24) of the revised manuscript.
The Introduction section:
In recent years, graph theory has been introduced as a novel method of studying functional
networks in the central nervous system (for a recent review, see Bullmore and Sporns, 2009). This
approach, based on an elegant representation of nodes (vertices) and links (edges) between pairs
of nodes, describes important properties of complex systems by quantifying topologies of network
representations (Boccaletti et al., 2006). Nodes in large-scale brain networks usually represent
anatomically-defined brain regions, while links represent functional or effective connectivity
(Friston, 1994). Functional connectivity corresponds to magnitudes of temporal correlations in
activity (Friston et al., 1993) and may occur between pairs of anatomically unconnected regions.
Depending on the measure, functional connectivity may reflect linear or nonlinear interactions
(Zhou et al., 2009), which can be estimated using many methods such as linear correlation (Fox
et al., 2005; Horwitz et al., 1998; Salvador et al., 2005), coherence (Sun et al., 2004),
synchronization likelihood (Stam and van Dijk, 2002), (constrained) principal (Friston et al.,
1993; Woodward et al., 2006) or independent component analysis (McKeown and Sejnowski,
1998) and partial least squares (McIntosh et al., 1996). Effective connectivity represents direct or
indirect influences that one brain region exerts over another one (Friston, 1994), quantified by
various mathematical models, such as structural equation modeling (McIntosh and GonzalezLima, 1994), Granger causality (Roebroeck et al., 2005), multivariate autoregressive modeling
(Harrison et al., 2003), dynamic causal modeling (Friston et al., 2003) and Bayesian networks
(Zheng and Rajapakse, 2006). The above mentioned methods can really introduce measures
describing the relationships between nodes. Based on these measures, graph theoretical methods
7
can build abundant models of complex networks to further characterize connection patterns
within the brain from a perspective of topological organization. It has been generally believed
that functional segregation and integration are two major organizational principles of the human
brain. An optimal brain requires a balance between local specialization and global integration of
brain functional activity (Tononi et al., 1998). This is properly supported by graph indices [e.g.
clustering coefficients (an index of functional segregation) and path length (an index of
functional integration)] used in analysis of functional brain networks (Bassett and Bullmore,
2006; Stam and Reijneveld, 2007). The resultant coordinated patterns with high clustering
coefficients and short path length, known as a small-world network model (Watts and Strogatz,
1998), reflect the need of the brain networks to satisfy the competitive demands of local and
global processing (Kaiser and Hilgetag, 2006). In addition, graph theoretical methods also allow
one to evaluate regional centrality in a graph using measures of centrality in contrast to the
connectivity methods mentioned above.
The Discussion section:
In this study, Pearson correlation was employed to estimate the relationships between brain
regions. However, in recent years, computational methods of neuroimaging have made enormous
advances and provided various approaches mentioned above to perform the estimation. In future
studies, it would be worthwhile to investigate the effect of different methods on topological
characteristics of the brain networks in order to better understand the relations between network
structure and the processes taking place on these networks.
Bassett DS, Bullmore E. Small-world brain networks. Neuroscientist 2006; 12: 512-23.
Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang DU. Complex networks: Structure and
dynamics. Physics Reports 2006; 424: 175-308.
Bullmore E, Sporns O. Complex brain networks: graph theoretical analysis of structural and
functional systems. Nat Rev Neurosci 2009; 10: 186-98.
Fox MD, Snyder AZ, Vincent JL, Corbetta M, Van Essen DC, Raichle ME. The human brain is
intrinsically organized into dynamic, anticorrelated functional networks. Proc Natl Acad
Sci U S A 2005; 102: 9673-8.
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Mapping 1994; 2: 56-78.
Friston KJ, Frith CD, Liddle PF, Frackowiak RS. Functional connectivity: the principalcomponent analysis of large (PET) data sets. J Cereb Blood Flow Metab 1993; 13: 5-14.
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Friston KJ, Harrison L, Penny W. Dynamic causal modelling. Neuroimage 2003; 19: 1273-302.
Harrison L, Penny WD, Friston K. Multivariate autoregressive modeling of fMRI time series.
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reading and dyslexia. Proc Natl Acad Sci U S A 1998; 95: 8939-44.
Kaiser M, Hilgetag CC. Nonoptimal component placement, but short processing paths, due to
long-distance projections in neural systems. PLoS Comput Biol 2006; 2: e95.
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images using partial least squares. Neuroimage 1996; 3: 143-57.
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analysis in functional brain imaging. Human Brain Mapping 1994; 2: 2-22.
McKeown MJ, Sejnowski TJ. Independent component analysis of fMRI data: examining the
assumptions. Hum Brain Mapp 1998; 6: 368-72.
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Stam CJ, Reijneveld JC. Graph theoretical analysis of complex networks in the brain. Nonlinear
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Stam CJ, van Dijk BW. Synchronization likelihood: an unbiased measure of generalized
synchronization in multivariate data sets. Physica D: Nonlinear Phenomena 2002; 163:
236-251.
Sun FT, Miller LM, D'Esposito M. Measuring interregional functional connectivity using
coherence and partial coherence analyses of fMRI data. Neuroimage 2004; 21: 647-58.
Tononi G, Edelman GM, Sporns O. Complexity and coherency: integrating information in the
brain. Trends in Cognitive Sciences 1998; 2: 474-484.
Watts DJ, Strogatz SH. Collective dynamics of 'small-world' networks. Nature 1998; 393: 440-2.
Woodward TS, Cairo TA, Ruff CC, Takane Y, Hunter MA, Ngan ET. Functional connectivity
reveals load dependent neural systems underlying encoding and maintenance in verbal
working memory. Neuroscience 2006; 139: 317-25.
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1601-13.
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Zhou D, Thompson WK, Siegle G. MATLAB toolbox for functional connectivity. Neuroimage
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The authors refer to some changes in the “ipsilesional” hemisphere in stroke patients, which
indeed may represent changes in location of maxima (e.g.; “lateral extension” of motor
representation) and still don’t use fMRI based ROIs. Despite all this I judge this as very valid and
interesting data
In our previous response, we have provided several reasons for not using explicit tasks to
indentify ROIs. In the new revised manuscript, we have added this point and other potential
issues as limitations of this study (see page 25).
Referee: 3
Comments to the Author
The paper has substantially improved after revision. The authors have rephrased and toned down
some of their statements regarding functional ‘importance’ of the resting state data (e.g., on p.14)
and rephrased the conclusions (p.23).
The interpretation that ‘progressive network randomization’ is a substrate of recovery after stroke
and that this might be due to outgrowth of suboptimal axonal connections is interesting. However,
I am not convinced about the time scale. Axonal outgrowth takes time, especially if axons need to
reach new targets. There are still many questions open regarding whether or not those
connections are functionally meaningful. According to figure 2, gamma values decrease, at least
in some patients, within the first 10-14 days after stroke. Is there any evidence that axonal
sprouting can result in novel connections that affect the large-scale network so fast? In this period
of time, I would assume that an axon will not sprout more than a couple of 100 µm (at best). To
some extent, the timing issue also relates to the fact that in the acute stage there are no differences
between stroke patients and controls. If one argues that axonal sprouting might influence Gamma
within 10-14 days, then it is surprising that the tremendous changes in the acute phase after the
ischemia do not affect the network. Acute changes are not restricted to local neuronal assemblies
as we know from diaschisis findings or from neurophysiological phenomena in the penumbra.
Finally, if I understand the data of Honey and Sporns (2008) and of Alstott et al. (2009) correctly,
10
focal lesions resulted in non-local, disturbed interactions among regions by deleting central nodes
and edges. This would be a reason to expect Gamma changes in the acute phase, wouldn’t it?
Thank you for raising an important issue. We agree with the reviewer’s opinion that axonal
sprouting cannot propagate quickly enough (within 7-14 days) to affect the network
characteristics. In the revised manuscript, we have re-organized this part and toned down some
of statements while interpreting the results (see page 19).
On a cellular level, one of major regenerative events occurring in periinfarct cortex involves
axons sprouting new connections and establishing novel projection patterns (Carmichael, 2006;
Carmichael, 2008). Meanwhile, stroke induces a unique permissive environment for axonal
sprouting, when neurons activate growth-promoting genes in successive waves and many growthinhibitory molecules are not yet activated (Carmichael, 2006; Carmichael, 2008). Many animal
studies suggested that axonal sprouting after stroke progresses through specific biological time
points: trigger (1-3 days after stroke) (Carmichael and Chesselet, 2002), initiation and
maintenance (7-14 days after stroke) (Leon et al., 2000; Stroemer et al., 1995) and maturation
(28 days after stroke) phases (Carmichael et al., 2001). Moreover, the time points might be
prolonged after stroke in the human brain. In addition, computational neuroscience has indicated
that synaptic formation can be described as a process with random outgrowth patterns (Kaiser et
al., 2009). This evidence suggests that new axonal outgrowth may partly account for the
randomized network organization found in patients during stroke recovery. However, caution
must be taken when interpreting the results on this level. Since a few of the patients did show
reduced Gamma within the first 10-14 days after stroke (Figure 2), the interpretation mentioned
above can only, at best, partially account for the results because novel connections could not lead
to the changes in the large-scale networks found during this early time period based on the
estimated time points mentioned above. Hence, axonal outgrowth may be one reason for network
randomization but it cannot be the only one. After stroke, other changes in structural and
functional plasticity (Schaechter et al., 2006) may also contribute to the continued randomization
of the network configuration.
In addition, we agree with the reviewer’s comments regarding the data from Honey and Sporns
(2008) and Alstott et al. (2009) regarding focal lesions resulting in non-local, disturbed
interactions among regions through the deletion of central nodes and edges. In these studies, the
central nodes were mainly comprised of association cortex, whereas the central edges were
11
believed to correspond to the corpus callosum connecting bilateral homogenous regions of cortex.
In this regard, these studies differed from ours, although they all focused on the effect of brain
lesions on brain networks. Some of the relevant differences are: 1) in our study, patients with
subcortical motor pathway stroke were recruited. Such a lesion damages only a few connections
(such as the corticospinal tract) within the executive motor network, rather than cutting off all
connections, while the two previous studies mentioned above simulated the process of removing
edges by cutting off all connections in corpus callosum. Thus, it remains unclear how the network
organization would be changed if only part of anatomical connections was removed; 2) it has
been suggested that the subcortical infarction may further impair the structural anatomy of the
ROIs (such as primary motor cortex) through the process of axonal degeneration. Although the
two previous studies demonstrated that instantly removing primary cortices would show very
little effect on network organization, the effect of these subsequently degenerative changes on
network configuration were not investigated in those studies. We feel that the longitudinal design
of our study complemented these studies by investigating the dynamic changes in network
structure over the stroke recovery continuum, as many of the apparent contradictions can be
explained by the differences in study design. In the revised manuscript, we have re-organized this
part and explained the differences in the results across these studies (see pages 20-21).
Alstott J, Breakspear M, Hagmann P, Cammoun L, Sporns O. Modeling the impact of lesions in
the human brain. PLoS Comput Biol 2009; 5: e1000408.
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Ann Neurol 2006; 59: 735-42.
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poststroke epoch. Stroke 2008; 39: 1380-8.
Carmichael ST, Chesselet M-F. Synchronous Neuronal Activity Is a Signal for Axonal Sprouting
after Cortical Lesions in the Adult. J Neurosci 2002; 22: 6062-6070.
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after focal cortical stroke. Neurobiol Dis 2001; 8: 910-22.
Honey CJ, Sporns O. Dynamical consequences of lesions in cortical networks. Hum Brain Mapp
2008; 29: 802-9.
Leon S, Yin Y, Nguyen J, Irwin N, Benowitz LI. Lens injury stimulates axon regeneration in the
mature rat optic nerve. J Neurosci 2000; 20: 4615-26.
12
Schaechter JD, Moore CI, Connell BD, Rosen BR, Dijkhuizen RM. Structural and functional
plasticity in the somatosensory cortex of chronic stroke patients. Brain 2006; 129: 272233.
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The authors have responded to the problem of using only few ROIs. Nevertheless, the risk of
false negative results remains, e.g., by shifting of hot spots, and needs to be explicitly addressed
in the discussion as a limitation of the study. The approach of using 12 mm spheres in addition to
the main analysis with 10 mm spheres is helpful, as is the additional analysis to rule out
influences of non-cortical structures (see response to reviewer 1).
In the revised manuscript, we have added a discussion of the problem as a limitation of this study
as per the reviewer’s comments and provided relevant discussion involving using other methods
to reduce the influence. For instance, we created ROIs with 12 mm diameter spheres and
repeatedly computed network parameters (Gamma and Lambda). Significant reductions in
Gamma but non-significant changes in Lambda were observed again, which did repeat previous
results in motor-related network constructed based on ROIs with 10 mm diameter. See the revised
manuscript for detailed descriptions (see pages 25).
The new supplementary material is helpful.
Thank you for this comment.
The validation with the Hanakawa coordinates is reassuring.
Thank you for this comment.
The clinical data in Table S1 of the revised supplementary materials are helpful.
Thank you for this comment.
13