Review: Cortical Geometry Network and Topology Markers for Parkinson's Disease Diagnosis

Summary of reviews

Review 1 (Sarah Genon)

  • Reviewer's confidence: 1 (Novice)
  • Overall recommendation: 2 (Accept)

SUMMARY
The paper is well written and relatively accessible. The introduction gives an objective overview of the background with reference to relevant studies. The methods capitalize on a geometric framework that has been previously assessed in small samples of cerebral FDG-PET data from psychiatric and healthy pediatric populations. In the current study, this framework is applied to big samples of brain structural data from patients with neurodegenerative disease (Parkinson’s Disease, PD) and healthy subjects. The methods description provides a good overview of the methods. The results presentation is well structured and balanced. The results reveal that some persistent homology features show between-group differences supporting the perspective of using these features in a discrimination framework. Therefore, as suggested in the authors’ discussion, this study opens new perspectives in characterizing cortical changes in healthy and pathological aging. Future studies should examine whether the highlighted features capture brain morphological changes specific to PD when compared to other neurodegenerative pathology.

STRENGTHS
It is a well-conducted study and well-written paper, and the method appears promising in characterizing the impact of neurodegenerative disease on the cortical structure.

SHORTCOMINGS
Further assessment of the methods is needed to infer about the contribution of the proposed topology features in a discrimination framework.

CONSTRUCTIVE FEEDBACK
In the title “ for Parkinson's Disease Diagnosis”: this is an extrapolation of the potential contribution after further assessment of the method, at the current stage, the method does not address diagnosis issue.

Some conclusions should be tuned down, namely: “ the novel method has a strong ability to identify PD patients”: the methods identify metrics showing group differences, not subject discrimination performance

“Strong statistical evidence presented in our work…”,: what is the criterion for arguing for “strong” statistical evidence?

Illustration of the 70 cortical patches on the cortical surface could be provided.

Review 2 (Alessandra Griffa)

  • Reviewer's confidence: 2 (Knowledgeable)
  • Overall recommendation: 1 (Probably accept)

SUMMARY
In this work the authors investigate the geometrical arrangement of cortical regions in Parkinson's disease patients and healthy controls. To this end, the authors build a 'geometry network' for each subject included in the study. A geometry network is defined as a complete graph, with nodes corresponding to cortical ROIs, and edges representing the Euclidean distance between the connected ROIs. The authors characterize the geometry networks with classical network (degree, clustering, etc.) and algebraic topology (Betti numbers) measures, under different Euclidean distance thresholds (filtration).

The application of algebraic topology to brain network analysis is an original and emerging field of research, however the submitted manuscript could be substantially improved by providing missing methodological details and a clear interpretation of the results.

  • The Methods section is not straightforward. In my opinion, the 'Adaptive Cotical Parcellation', 'Skull Normalization', and 'Material' paragraphs should be combined and reformulated, using more specific terminology (for example: 'we TRANSFER parcellation for cortical surface.. ' is not really clear), and better explaining the sequence of performed operations. The authors investigate the geometrical re-arrangement of cortical structure in PD, and they should clearly motivate their choices in reducing complex cortical surfaces to 140-point clouds, which should preserve salient geometrical features of the cortex.
  • The inter-subject variability is taken into account in two ways: (i) using a spatial normalization based on skull registration, and (ii) normalizing the Euclidean distances between cortical ROIs to the range [0,1]. Is the distance normalization not sufficient to account for the inter-subject variability? Do the results hold without the spatial normalization based on skull registration? I'm concerned about how the affine transformations can impact the quantification of the cortical 'geometrical arrangement'.
  • The sections on network filtration and persistent homology are interesting as they introduce measures that are not classically used in brain network analysis. The authors could provide some context-related interpretation of the introduced measures and particularly of the Betti numbers. Moreover, it would be insightful to read some interpretation about the different behaviors of the Betti numbers as a function of the distance threshold. The curves describing the behavior of the classical network measures as a function of the threshold should also be reported.
  • The feature reduction via PCA and the association of the PCs to the single features (Tables 1,2) are not completely clear to me. Could the authors better elaborate on this? For the classical network features (local efficiency, clustering etc.), has the average across all the network nodes been considered? Could the authors please specify how the subgraph centrality was computed?
  • The authors state that 'VR filtration showed a variation over filtration threshold across the group', but it is not clear if Betti numbers for some thresholds were statistically different between the two groups.
  • Discussion: I don't get what is the relationship between the minimum number of vertices set for each patch, and the size of the distance matrices. From figure 1, I understand that only the distance matrices between the 140 ROI centroids were considered: is this not the case?
  • 'As a result, for each threshold value in the filtration we obtain a Betti number': rather a set of Betti numbers?
  • Various typos are present across the text. Please, proof-read the manuscript. Some examples: Introduction, line 1: 'ComputationAL techniques'; Introduction, line 9: 'for the Effect of disease'; Methods, line 9: 'with A workflow'; Persistent Homology, line 20: 'Figure 2'; Discussion, line 1: 'The current WORK presents'.

STRENGTHS
The authors apply concept borrowed from the algebraic topology to the investigation of brain networks. This is an original and relatively new field of application.

SHORTCOMINGS

  • Poor interpretation of the results
  • Methodological details are missing
  • The structure of the text can be improved the facilitate the reading

CONSTRUCTIVE FEEDBACK
I think that the application of algebraic topology to brain network analysis is an original and emerging field of research, which deserve to be discussed at the BACON workshop. In this sense this work is relevant for the workshop. Nonetheless, I do not think that the submitted work is suitable for further publication in its present form, for the reasons listed to the authors.

Rebuttal

Dear organizers, We the co-authors thank the editorial and review team for their valuable time and feedback on our manuscript. We are pleased to learn the acceptance of our manuscript for presentation at the workshop. We are motivated by the constructive comments from the reviewers. We have addressed the concerns raised by the reviewers and provide a revised manuscript with the revisions.

We hope that the revisions and responses are able to resolve the queries posed by the reviewers. We are happy to provide more information as deemed necessary.

Regards Amanmeet Garg On behalf of co-authors

REVIEW 1

----------- Shortcomings -----------
Further assessment of the methods is needed to infer about the contribution of the proposed topology features in a discrimination framework.

RESPONSE: We thank the reviewer for their insightful comment. We have revised the manuscript to reflect the suggested changes.

----------- Constructive feedback -----------
In the title 'for Parkinson's Disease Diagnosis': this is an extrapolation of the potential contribution after further assessment of the method, at the current stage, the method does not address diagnosis issue.

RESPONSE: The title has been modified to remove the term 'diagnosis' to reflect the initial results and further need for experimentation for diagnostic utility.

Some conclusions should be tuned down, namely: 'the novel method has a strong ability to identify PD patients': the methods identify metrics showing group differences, not subject discrimination performance

RESPONSE: The text in the discussion section has been modified to reflect the suggested change to its ability to differentiate between groups.

'Strong statistical evidence presented in our work...',: what is the criterion for arguing for 'strong' statistical evidence?

RESPONSE: The word 'strong' referred to the small p-values (p<0.05) in a permutation statistics based group difference testing (section 2.4, revised manuscript). We have removed the word strong and revised the statement to read: 'In a permutation statistics test, a statistically significant ($p<0.05$) difference was observed in the homology features between PD and healthy control groups.'

Illustration of the 70 cortical patches on the cortical surface could be provided.

RESPONSE: We acknowledge that such an illustration would be informative for the reader, however, the space limitation prohibits us to include such a figure. In order to assist the reader, we have included a reference to previous work where a similar approach was utilized for dimensionality reduction of the cortical surface.

REVIEW 2

----------- Summary -----------

The Methods section is not straightforward. In my opinion, the 'Adaptive Cortical Parcellation', 'Skull Normalization', and 'Material' paragraphs should be combined and reformulated, using more specific terminology (for example: 'we TRANSFER parcellation for cortical surface.. ' is not really clear), and better explaining the sequence of performed operations.

RESPONSE: The methods section has been modified based on this feedback to first introduce the methodology in its abstract sense, then explain the steps followed in our Geometry networks framework and followed by the materials for the specific experimental case under evaluation. We thank the reviewer for this feedback and hope that our revisions have now improved the readability of the manuscript.

The authors investigate the geometrical rearrangement of cortical structure in PD, and they should clearly motivate their choices in reducing complex cortical surfaces to 140-point clouds, which should preserve salient geometrical features of the cortex.

RESPONSE: The choice of reducing the cortical surface to 140 ROI point cloud was initially motivated by the desire to remove the effect of curse-of-dimensionality and the computation and memory limitations of the persistent homology computation methods. In our published previous work, we also found that clustering the vertices into regional patches offered a good trade-off between localization on one hand and the problem of multiple-comparison correction on the other. The text in the adaptive parcellation paragraph has now been modified to reflect the changes as outlined above.

The inter-subject variability is taken into account in two ways: (i) using a spatial normalization based on skull registration, and (ii) normalizing the Euclidean distances between cortical ROIs to the range [0,1]. Is the distance normalization not sufficient to account for the inter-subject variability? Do the results hold without the spatial normalization based on skull registration? I'm concerned about how the affine transformations can impact the quantification of the cortical 'geometrical arrangement'.

RESPONSE: Our approach to geometric normalization is based on the assumption that the brain development into the adult healthy brain closely follows the space restriction enforced by the bony cranial vault and is therefore contoured along the shape of the cranial vault. Our feeling is that the first step of normalization by an affine transformation between the ‘cranial vault shapes’ is important as it offers a potentially anatomically-meaningful way to normalize the geometry based on the estimated contour of each brain in its adult disease-free state. This affine-based normalization can be interpreted as an extension of intra-cranial vault volume (ICV)-based scaling that is commonly used to normalize volumes of brain structures before comparison across the database. The affine transformations estimate potentially different scaling in the x,y and z directions based on registering the cranial-vault shapes which could be important when the goal is to study the relative geometrical arrangement of brain regions, and not just the volumes of brain regions.

The second normalization of Euclidean distances to range [0,1] accounts for the remaining variability in the cerebral cortex size by normalizing the largest inter-regional geometrical distance to the value of 1 and computing all other distances relative to this largest common value. Such normalization is important in the computation of filtrations for each individual brain to make the classical network and homology features comparable across the groups.

We agree that these two steps in the normalization of the geometry network are a first attempt at a reasonable anatomically-motivated approach towards addressing this issue, and further work is needed to validate and potentially improve upon this issue in studying variation of brain geometry across individuals.

The sections on network filtration and persistent homology are interesting as they introduce measures that are not classically used in brain network analysis. The authors could provide some context-related interpretation of the introduced measures and particularly of the Betti numbers. Moreover, it would be insightful to read some interpretation about the different behaviors of the Betti numbers as a function of the distance threshold. The curves describing the behavior of the classical network measures as a function of the threshold should also be reported.

RESPONSE: The contextual explanation of the Betti number feature has been added to the text along with the details of the persistent homology method (section 2.2). Likewise, the interpretation of the Betti number feature for our data has been added in the results section. The figure with the curves for the classical network features is expected to be of limited visual utility as they do not show statistical difference between the groups. Therefore, in the interest of limited space available, and in order to maintain focus on the homology features and readability of the document, this figure has not been included in the manuscript.

The feature reduction via PCA and the association of the PCs to the single features (Tables 1,2) are not completely clear to me. Could the authors better elaborate on this? For the classical network features (local efficiency, clustering etc.), has the average across all the network nodes been considered? Could the authors please specify how the subgraph centrality was computed?

RESPONSE: The classical network features (1 value per node, 140 nodes x 100 thresholds = 14000 dimensions) and Betti number features (100 dimension) live in a high dimensional space relative to the sample size in our dataset (339 PD, 150 CN). In order to minimize the effects of the curse of dimensionality (small sample size, high dimensionality), we mapped the features into a reduced dimensionality space created by the principal components of the PCA decomposition of these features. Data for a feature (Local efficiency or Betti-3 etc.) from all subjects in the two groups were mapped into its reduced space of $m$ dimensions. We retained $m$ PCs sufficient to account for 95% of the variability in the original features across the dataset. Consequently, each feature obtained a different number of PCs (Table 1). The data mapped into this new dimension space (principal component loadings) was further tested for statistical difference between the groups in the Fisher’s exact test.

Further details for the PCA dimensionality reduction in our analysis (as above) have been added (section 2.4, paragraph 1).

For the current work we did not consider the average value of the features over all the nodes in the brain graphs. In this work we focussed on geometry network change with disease and the comparison of the homology and classical network features, hence, we restricted the evaluation to the comparison of raw features. The derived features for classical as well as homology features form a work for future direction of investigation and related textual changes have been added to the discussion as potential future work.

The subgraph centrality was computed as a weighted sum of closed walks of different lengths in the network starting and ending at the node. For the exact mathematical underpinnings of the algorithm please refer to the seminal work of Rubinov and Sporns (Rubinov, M., & Sporns, O. (2010). Complex network measures of brain connectivity: uses and interpretations. Neuroimage, 52(3), 1059-1069.)

The reader in the text has been guided to the relevant reference for the details of computation of classical network features. The mathematical explanation of these features has been limited in the text to retain the focus on the new method and good readability of the manuscript.

The authors state that 'VR filtration showed a variation over filtration threshold across the group', but it is not clear if Betti numbers for some thresholds were statistically different between the two groups.

RESPONSE: The central premise of utilizing a filtration in comparison to the choice of a fixed threshold value is to obtain the characteristics of the brain network as the threshold changes. Therefore, the set of Betti numbers over the whole filtration is the feature of interest versus the Betti number as a particular threshold.

Discussion: I don't get what is the relationship between the minimum number of vertices set for each patch, and the size of the distance matrices. From figure 1, I understand that only the distance matrices between the 140 ROI centroids were considered: is this not the case?

RESPONSE: Yes, for our work in the present manuscript we utilized a minimum vertices per patch (mvcpp = 2000) constraint in adaptive cortical parcellation (section 2.3) leading to a total of 140 patches on the cortical surface. A detailed explanation regarding the computation from cortical surface to patches and its influence on the network matrix size has been included in the adaptive cortical parcellation paragraph.

'As a result, for each threshold value in the filtration we obtain a Betti number': rather a set of Betti numbers?

RESPONSE: The computation of persistent homology feature (Betti number) is based on the premise that we study the appearance and disappearance of topological features as we increase the threshold of the underlying metric (Euclidean distance in our case). For each threshold the Betti number (Betti-k) counts the number of k+1 dimensional features present in the point cloud space. As a result, at each threshold value the Betti numbers (Betti-0, Betti-1, Betti-2 and Betti-3) obtain a single value. Collectively, over the set of thresholds in the filtration the Betti numbers provide with a set of values. The number of elements in the set as equal to the number of thresholds applied to create the network filtration. Section 2.2 has been further refined to explain the concept of filtration and homology feature computation in further detail.

Various typos are present across the text. Please, proof-read the manuscript. Some examples: Introduction, line 1: 'ComputationAL techniques'; Introduction, line 9: 'for the Effect of disease'; Methods, line 9: 'with A workflow'; Persistent Homology, line 20: 'Figure 2'; Discussion, line 1: 'The current WORK presents'.

RESPONSE: The authors thank the reviewer for highlighting the typos. All efforts have been made to remove all possible errors in the revised manuscript.