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Authors

Karoline Leiberg, Yujiang Wang, Christoforos Papasavvas

Abstract

The universal scaling law of cortical morphology describes cortical folding as a tight relationship between average grey matter thickness, pial surface area, and exposed surface area. It applies for mammalian species, humans, and across lobes, however it remains to be shown that local cortical folding obeys the same rules. Here, we develop a method to obtain morphological measures for small regions across the cortex and correct surface areas by curvature to account for differences in patch size, resulting in a map of local morphology. It enables a near-pointwise analysis of morphological variables and their regional changes due to processes such as healthy ageing. We confirm empirically that the theorised relation of morphological measures still holds at this level of local partition sizes as predicted, justifying the use of independent variables derived from the scaling law to identify regional differences in folding, subject-specific abnormalities, and local effects of ageing.

Link to paper

DOI: https://doi.org/10.1007/978-3-030-87234-2_65

SharedIt: https://rdcu.be/cyl9b

Link to the code repository

https://github.com/KarolineLeiberg/folding_pointwise

Link to the dataset(s)

http://fcon_1000.projects.nitrc.org/indi/pro/nki.html

Reviews

Review #1

Please describe the contribution of the paper

This work develops a method to obtain morphological measures for small regions across the cortex and correct surface areas by curvature to account for differences in patch size, resulting in a map of local morphology. It enables a near-pointwise analysis of morphological variables and their regional changes due to processes such as healthy ageing. The work confirms empirically that the universal scaling law still holds at the level of local partition.
Please list the main strengths of the paper; you should write about a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.

The main strength of the work is to verify empirically the universal scaling law still holds locally for cortical surface, this is an important rule in nature. The local applicability of the scaling law allows one to use it in terms of independent components derived from it to further analyze local morphology.
Please list the main weaknesses of the paper. Please provide details, for instance, if you think a method is not novel, explain why and provide a reference to prior work.

The method has to exclude around 20% of points on the pial surface, predominately located on the midline and in the insula. This can be further reduced. The radius is uniform, it can be chose to adapt to the local thickness. These points have been discussed by the authors.
Please rate the clarity and organization of this paper

Very Good
Please comment on the reproducibility of the paper. Note, that authors have filled out a reproducibility checklist upon submission. Please be aware that authors are not required to meet all criteria on the checklist - for instance, providing code and data is a plus, but not a requirement for acceptance

The authors have put the major computational tools on github, so the work is easy to reproduce.
Please provide detailed and constructive comments for the authors. Please also refer to our Reviewer’s guide on what makes a good review: https://miccai2021.org/en/REVIEWER-GUIDELINES.html

The concepts can be further clarified and defined more formally, rigorously. The concept of the exposed area needs to be defined in a more explicitly way. The gyrification index is used without definition. It is not clear why both smooth pial surface and the convex hull are defined.

The exposed surface can be computed using conventional visibility testing. We can sample the view points at infinity along different directions, the directions can densely sample the unit sphere. For each view direction, we can compute the visibility for each face, this can give us more accurate estimate of the exposed area. How to compare this method with the one proposed in the work ?

More theoretic interpretation of the universal scaling law will be helpful. Is there any theory to bridge this law with the folding pattern ?
Please state your overall opinion of the paper

strong accept (9)
Please justify your recommendation. What were the major factors that led you to your overall score for this paper?

This work validates the universal scaling law holds locally for human cortical surface, as a natural law this discovery is important. It can leads to novel methods for local morphological analysis.

The manuscript is well written, easy to follow, the experimental results are convincing. All the potential improvements have been thoroughly discussed as well.
What is the ranking of this paper in your review stack?

1
Number of papers in your stack

5
Reviewer confidence

Confident but not absolutely certain

Review #2

Please describe the contribution of the paper

Mota et al. (2015) found that morphometric measures cortical thickness, pial and exposed surface area show a consistent covariance across specifies, and developed a re-parametrization that promises a deeper understanding of the biophysical underpinnings of cortical folding. While this relationship was defined for the whole cortex, extend it to more useful local measures is difficult, because the definition of a relationship between local pial and exposed surface is conceptually difficult. This submission tries to address this issue by defining local patches, and reasonably demonstrates the usefulness at a finer scale.
Please list the main strengths of the paper; you should write about a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.

The topic of this manuscript is within the scope of this conference, and of potential interest to its audience. The text is well-written, without major errors (except where noted below), and readily understandable for a reader with a moderate background in medical image analysis. Overall, a solid submission to a conference is presented here.
Please list the main weaknesses of the paper. Please provide details, for instance, if you think a method is not novel, explain why and provide a reference to prior work.

The proposed extension to a smaller scale is straightforward, and bears little news.
Please rate the clarity and organization of this paper

Very Good
Please comment on the reproducibility of the paper. Note, that authors have filled out a reproducibility checklist upon submission. Please be aware that authors are not required to meet all criteria on the checklist - for instance, providing code and data is a plus, but not a requirement for acceptance

Most items on the checklist were answered as “not applicable” - which is arguable here.
Please provide detailed and constructive comments for the authors. Please also refer to our Reviewer’s guide on what makes a good review: https://miccai2021.org/en/REVIEWER-GUIDELINES.html
A few, rather minor details should be dealt with:
1. p.1, “if two brains of a similar age have the same total area, but one is thicker” Do you mean the brain or the cortex? Please, rephrase.
2. p.3: “We performed … inspections on a random sample of 50 subjects and applied manual corrections where needed.” Where corrections just applied to some of the 50 data sets or to all of the remaining samples?
3. p.3, bottom: “pial” - please, be specific whether you refer to a vertex, patch, or surface (here and elsewhere).
Please state your overall opinion of the paper

Probably accept (7)
Please justify your recommendation. What were the major factors that led you to your overall score for this paper?

Little news, but solid work.
What is the ranking of this paper in your review stack?

4
Number of papers in your stack

5
Reviewer confidence

Very confident

Review #3

Please describe the contribution of the paper

(1) The paper confirms empirically that the theorized covariance of morphological measures still obeys the universal scaling law. (2) The paper justifies the use of independent variables derived from the scaling law to identify regional differences in folding, subject-specific abnormalities, and local effects of ageing.
Please list the main strengths of the paper; you should write about a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.

Using Gaussian curvature to correct the surface areas makes it possible to compare local patches to each other and infer whether they align on the plane predicted by the scaling law.
Please list the main weaknesses of the paper. Please provide details, for instance, if you think a method is not novel, explain why and provide a reference to prior work.

The authors did not investigate the area with low curvature.
Please rate the clarity and organization of this paper

Good
Please comment on the reproducibility of the paper. Note, that authors have filled out a reproducibility checklist upon submission. Please be aware that authors are not required to meet all criteria on the checklist - for instance, providing code and data is a plus, but not a requirement for acceptance

The reproducibility of the paper is highly feasible as it provides the detailed code and data used in the paper.
Please provide detailed and constructive comments for the authors. Please also refer to our Reviewer’s guide on what makes a good review: https://miccai2021.org/en/REVIEWER-GUIDELINES.html

(1) The vertex on the smooth surface and pail surface cannot be one-one correspondent, and finding the nearest pial point only may lead to the reduction of the exposed area over the pial sulci. Using some methods like Laplacian-field mapping may improve it. (2) If the correspondence between the 2 surfaces is improved, the authors may investigate the other radii that defines the local patches, and may answer the question like which radius the universal scaling law may fail. (3) In the section 3.3, the authors told that the S can have additional value while I still don’t understand the explanation of it and what’s the value it can bring us.
Please state your overall opinion of the paper

accept (8)
Please justify your recommendation. What were the major factors that led you to your overall score for this paper?

(1) The paper confirms empirically that the theorized covariance of morphological measures still obeys the universal scaling law. (2) The paper justifies the use of independent variables derived from the scaling law to identify regional differences in folding, subject-specific abnormalities, and local effects of ageing.
What is the ranking of this paper in your review stack?

1
Number of papers in your stack

2
Reviewer confidence

Confident but not absolutely certain

Review #4

Please describe the contribution of the paper

The paper claims that folding within small partitions (termed local cortical folding) of the human cortex follows the universal scaling law.
Please list the main strengths of the paper; you should write about a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.

The paper presents a study relies on the scaling law to use 3 independent variables (K, I, S; proposed in [7]) that characterize the cortical folding/thickness properties.
Please list the main weaknesses of the paper. Please provide details, for instance, if you think a method is not novel, explain why and provide a reference to prior work.

The very first line of the abstract is unclear. Covariance is defined between two random variables, but the said line mentions three. The terminology used here is very loose and must be avoided.

Previous works has shown that morphology in lobes adheres to the scaling law. So, the authors have extended this to the scale of about a half/third of a lobe. This isn’t surprising.

Just as K,I,S are independent components, other 3-variate measures have been proposed, e.g., in: https://pubmed.ncbi.nlm.nih.gov/20630489/ https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5794037/
Please rate the clarity and organization of this paper

Very Good
Please comment on the reproducibility of the paper. Note, that authors have filled out a reproducibility checklist upon submission. Please be aware that authors are not required to meet all criteria on the checklist - for instance, providing code and data is a plus, but not a requirement for acceptance

The description as it is leaves a lot of engineering in the unknown. If they share code, then reproducibility can be verified.
Please provide detailed and constructive comments for the authors. Please also refer to our Reviewer’s guide on what makes a good review: https://miccai2021.org/en/REVIEWER-GUIDELINES.html

Please see my comments above.

The studies are very interesting and may span new directions.

When the authors say “analysing cortical thinning without accounting for surface area changes could miss signs of atrophy”, in what context do they mean this ? Typical studies involve only relative changes between cohorts (or over time) that wouldn’t suffer from this limitation.
Please state your overall opinion of the paper

Probably accept (7)
Please justify your recommendation. What were the major factors that led you to your overall score for this paper?

Methodological novelty is minimal.

The paper shows some interesting empirical analyses.
What is the ranking of this paper in your review stack?

2
Number of papers in your stack

2
Reviewer confidence

Very confident

Primary Meta-Review

Please provide your assessment of this work, taking into account all reviews. Summarize the key strengths and weaknesses of the paper and justify your recommendation. In case you deviate from the reviewers’ recommendations, explain in detail the reasons why. In case of an invitation for rebuttal, clarify which points are important to address in the rebuttal.

This paper present a new method enabling studying cortical morphological measures to confirm that cortical folding within small partitions of the human cortex follows universal scaling law. All reviewers are positive on this solid work despite that the methodolgical novelty/innovation and new knowledge is very limited in the paper. Main strengths: clear motivation and presentation, sound method and reasonable results. Main weaknesses: little technical novelty (most pieces of works are published) and very limited new knowledge.
What is the ranking of this paper in your stack? Use a number between 1 (best paper in your stack) and n (worst paper in your stack of n papers).

1

Author Feedback

We thank all reviewers for their helpful comments. We have incorporated all suggestions and clarifications. Below we respond to two suggestions in more detail.

Our paper was previously lacking a clear definition of the exposed/smooth pial surface, which we have now added. In response to reviewer 1, who suggested an alternative sampling of the exposed pial surface as a collection of vertices visible from each view direction, we would like to clarify that the term “exposed” does not imply we are using a surface made up of all visible points. It is rather to be thought of as a surface which tightly wraps around the pial surface, computed by closing the sulci of the pial surface with a sphere of 15mm in diameter (see10.1109/TMI.2007.903576). This surface does not have as concave parts as the suggested visible pial surface would have. We have now clarified the term to be “smooth surface” throughout the paper, in agreement with Freesurfer’s terminology.

Reviewer 4 suggested to use an alternative method for matching the points on the smooth pial surface to the pial surface, such as Laplacian field mapping, since our method of finding the nearest point on the pial surface for each point on the smooth pial surface does not ensure a one-to-one correspondence. We do not require this one-to-one correspondence, since we are only using the mapping in one direction (to map a labelling from the pial surface to the smooth pial surface). Our method could be thought of as draping the smooth pial surface over the pial surface and using all points of the smooth pial surface that have a patch-point on the pial surface as the closest neighbour. This will only be the case on the gyri, and therefore we do not need to map the smooth pial surface onto points inside the sulci of the pial surface.

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Local Morphological Measures Confirm that Folding within Small Partitions of the Human Cortex Follows Universal Scaling Law