Summary of reviews
- Anonymous reviewer: -1 (3) View Review 1
- Anonymous reviewer: 2 (3) View Review 2
Review 1 (Anonymous)
- Reviewer's confidence: 3 (Expert)
- Overall recommendation: -1 (Probably Reject)
SUMMARY
The paper proposed using Poisson point process to model connectivity derived from diffusion MRI data. Heat kernel was used to estimate the intensity parameter of the model. The approach was applied to real data of 731 subjects from the Human Connectome Project. Differences between tractography algorithms in terms of “node degree” were demonstrated.
STRENGTHS
- The Introduction clearly lays out the challenges with parcellation.
- The idea of using point process to model connectivity is interesting.
- Large sample size of 731 subjects was used.
SHORTCOMINGS
- The writing is a bit unclear and choppy (seems to be sections of a larger paper copied and pasted together).
- The definition of lambda(x,y) is extremely unclear. What’s the physical meaning of the heat kernel, and how do tractography/endpoints come into play in the kernel estimation? The lambda(x,y) is the key to the paper, yet described in such abstract terms that no intuition can be drawn.
- It is unclear how different the proposed approach is compared to performing connectome estimation at voxel level (which also does not require parcellation). Results in Fig. 2 can be generated with voxel level connectome estimation. It is important to compare to this base case and quantitatively demonstrate improvements. The paper currently has no quantitative validation.
- Connectome estimation at parcel level has the advantage of being robust to endpoint uncertainty introduced during tractography. How robust is the proposed approach to this limitation of tractography?
CONSTRUCTIVE FEEDBACK
- Grammar check needed for the abstract.
- The paper mentioned care is necessary when choosing Ei, but what should be done exactly?
- Claimed to be continuous, but only in theory. The surface comprises discrete vertices.
- Is there a principled way in choosing the sigma range?
Review 2 (Anonymous)
- Reviewer's confidence: 3 (Expert)
- Overall recommendation: 2 (Accept)
SUMMARY
The connections between different parts of the brain may be estimated with neuroimaging
via the definitions for regions of interest (ROIs), i.e. for a given pair of ROIs, the imaging can provide an estimate of the 'strength of connection' between them. While most such work concentrates, often for good reasons, on a fixed number of ROI,
leading to a discrete representation of connectivity, this work presents some insight into
how a continuous representation of connectivity may be formulated. The approach represents
this as a continuous real-valued function ($lambda(x,y)$), defined over the product space
of all point pairs on the cortex. In practice, this theoretical formulation is actually
represented with a kernel density estimate of the same; i.e. tractography is used to sample
the space of all possible fiber connections, and this finite sample is used to model the function required with an appropriate kernel ($K_sigma$).
STRENGTHS
There is sufficient merit in the methodological aspects to stimulate good discussion at the workshop and I feel it is these aspects upon which the emphasis should be made.
SHORTCOMINGS
While the work is theoretically and methodologically interesting, the absence of a strong validation detracts somewhat. Really, the exploration of the 'degree distributions' that the approach provides (or at least the nearest approximation to such distributions) should, I feel, have been accorded much more weight in the paper. The comparision of two different methods to do the tractography appears tangential and not really a suitable target for what the proposed approach is seeking to achieve.
CONSTRUCTIVE FEEDBACK
In principle, the most appropriate benchmark comparison would be one which compares measured obtained from the continuous-kernel representation with those obtained from a conventional discrete parcellation-based approach, keeping the tractography method fixed.
Further points:
It complicates the exposition to describe the kernel as using associated Legendre polynomials of order zero and going on to justify why the non-zero order ones are not used. It would be simpler to just say that you are using the 'ordinary' Legendre polynomials without mentioning the associated ones.
It is very hard to make sense of the scale of marginal connectivity in the log-log plot why is the range or $M$ so much greater in the log-log plot, what does it usefully show?
As described above, I feel section 3.2 is potentially the most interesting part and should be expanded. At least, some expansion and references for why the authors ''note the similarity of the degree sequence equivalents to other real world networks'' - why not brain networks specifically?
It is indeed difficult to visualise the function over its full domain (Sect. 3.3) but surely it should be possible to pick points, ROIs and marginalise the function to produce a map of connectivity for the selected region, these should be informative and make for ready comparison with know connectivity patterns from the literature.
The first sentence of the abstract has unclear grammar and needs to be rephrased to clarify - viz. ''... leverages Poisson point processes describe ....''
Please ensure consistency of 'track' vs. 'tract' throughout.
Rebuttal
First, we would like to thank both the reviewers for their time, effort, and service.
Hopefully we have corrected the grammar and writing issues to your satisfaction.
Reviewer 1
In response to reviewer 1, shortcoming 2, we hopefully have clarified this somewhat in the camera ready version. The physical meaning of the recovery method (in this case, KDE) is less meaningful in our opinion than the physical meaning of the object which it is trying to estimate. In this case, lambda is the asymptotic relative rate at which tracks are observed assuming that each is independent of the other (working assumptions that are still somewhat wrong; we hope to move past this for now). The (spherical) heat kernel is simply the natural choice for (half of) our domain. We hope that our new version has clarified its use. To respond to your second inquiry, at each test point on the connectivity space (the space of all possible pairs of cortical points) estimate the KDE separately. The details of this method are made more clear in ref [11], the companion paper.
In response to reviewer 1's feedback points 2 and 4, these are also found in ref [11].
In response to reviewer 1's feedback point 3, we have expanded the text to include a short section on this; even though in the end the representation is discrete, it represents the point estimates of a continuous object, and not the areal connectivity of a discrete connectome. Furthermore they are necessarily smooth, due to the KDE and according to our assumptions about the underlying connectivity lambda. (This indeed also needs empirical validation, but at this scale we take it as a safe assumption).
Reviewer 2
In response to reviewer 2's further point 1, yes, we are using only the 'ordinary' legendre polynomials. However, since the spherical harmonics are usually given in terms of the associated legendre polynomials, we chose the latter nomenclature.
We found your comments on section 3.2 and 3.3 particularly helpful, and have added (and subtracted) text accordingly. Unfortunately on the model side we cannot progress further without a deep dive into random network theory, so this publication will not include further results. However, we agree that this warrants further attention.
Some but not all of the requested benchmarks may be found in ref [11]. (Comparisons to conventional tractographies). Unfortunately we were not able to produce satisfying degree comparisons, since marginal connectivity is not entirely comparable. While it is analogous, direct comparisons beyond shape are difficult at this time.
Again, we thank both reviewers for their time and service.