Equivariant spatio-hemispherical networks for diffusion MRI deconvolution

Summary

The paper presents a convolutional neural network for spherical deconvolution of DWI data to estimate fiber orientation distribution. The main contributions over previous approaches include the introduction of Spatio-Hemispherical Equivariant Convolution, Dense Matrix Multiplication, and the use of Pre-computed Chebyshev Polynomials. These innovations improve overall efficiency. Evaluation was conducted on simulated data, assessing efficiency in terms of memory and runtime, and accuracy, demonstrating reduced false positive rates and angular error.

Strengths

1. Enhanced efficiency for DWI spherical deconvolution using deep neural networks. 2. Improved accuracy compared to current methods, demonstrated with simulated data designed for such experiments. 3. Provided code for reproducibility.

Weaknesses

1. Limited Novelty: The primary innovations over previous approaches focus on the network's efficiency (Section 3.2). Consequently, the main factors contributing to the reported improvement in accuracy remain unclear. 2. Clarity of Presentation: The paper is highly detailed, making it difficult to follow and understand the main contributions that actually lead to improvements in performance (Section 3.2) and accuracy. 3. Limited Demonstration of Impact: The practical impact beyond accuracy on simulated Tractometer data is not clearly demonstrated. It remains uncertain whether the proposed approach offers any significant clinical or scientific applications. 4. Mixed Results: Figure 6D is particularly disappointing, as the results produced by the proposed method noticeably differ from the reference.

Questions

1. Please clearly describe the main novel contributions of the paper and how they contributed to the results. 2. Please thoroughly discuss Figure 6D, where the results of the proposed approach appear to deviate substantially from the reference.

Rating

3

Confidence

4

Soundness

2

Presentation

2

Contribution

2

Limitations

The authors discuss the limitations of the paper. However, the lack of demonstration of clinical applications and the generalization to multiple clinical/scientific DWI acquisition settings should be discussed more thoroughly.

Summary

The authors extend previous [work done](https://proceedings.mlr.press/v227/elaldi24a.html) in the diffusion MRI (dMRI) fibre orientation distribution function (fODF) domain with an efficient $\mathbf{E}(\mathbf{3}) \times \mathbf{SO}(\mathbf{3})$ equivariant network. The proposed model directly leverages the antipodal symmetry of dMRI data to reduce computation time by 65%, as compared to previous work. The authors demonstrate the efficacy of this approach in a number of experiments; including an analysis of fODF estimation in simulated data and real world data, as well as in a downstream tractography task. They find that their method often performs best, whilst maintaining relatively high compute and memory efficiency.

Strengths

The writing and format of this work is excellent. The attention to detail, as provided within the main text and the appendix, rivals that of full length journal articles within this domain.

Weaknesses

This work represents a continuation of a previous method developed within [Elaldi et al](https://proceedings.mlr.press/v227/elaldi24a.html). Whilst the authors here present a significant increase in computational efficiency, this study is an iterative improvement on previous approaches, rather than a leap forward. I caveat that by acknowledging the importance of iterative improvements within scientific research. Overall, the writing is of an excellent standard. However, I have a small number of suggestions/mistakes enumerated below. - Line 98 you state that "trainable models have the advantage of decreasing the reliability of the method...". Here, _reliability_ evokes “reliable, as in you can count on it” rather than “rely on, as in this is a prerequisite”. I would maybe switch to “need for” or similar. - Line 151 I think you're missing a word at the end of the sentence "sparse matrix multiplication significant computational..." - Line 162 "Fig. 3 overviews", I would use "presents an overview" rather than using overview as a verb. - Line 269 I think "unsupervisedly" sounds a little clunky, would swap for "in an unsupervised manner" or similar. - Line 270 you state "...to extract fODFs and then use the estimated fODF to investigate the effect of improved local fODF estimation on...". I think this could be reworked to use the words fODF and estimat(ed/ion) a little less, perhaps by swapping "the estimated fODF" for "them", or swap "investigate the effect of improved local fODF estimation" for "investigate their effect".

Questions

Given that your experiments either involve simulated data or healthy patient data, when tasked with reconstructing fODFs for subjects with significant brain pathologies, would you reasonably expect to see a drop in performance? Or do you suspect that the regularisation enforced via the equivariant properties and loss functions would be enough such that the difference in performance would be minimal?More generally, how would you expect this method to perform when tasked with prediction on out-of-distribution data, as compared to the iterative per-subject CSD method?

Rating

7

Confidence

4

Soundness

4

Presentation

4

Contribution

3

Limitations

The authors have adequately addressed the limitations of their work

Summary

This work introduces a novel framework for fODF estimation through equivariant spatio-hemispherical networks that achieve dMRI deconvolution. Experiments on simulated dMRI datasets with known ground truth, as well as on real in vivo dMRI data are conducted, showing promising results while improving over previous methods.

Strengths

1. The paper improves upon previous methods in both processing time, and quantitative results. 2. The evaluation is sound and the experiments nicely show results on synthetic datasets with known ground truth.

Weaknesses

The main weakness of this manuscript is in the way the contributions section is written (at the end of the Introduction section, lines 57--71). The authors would potentially increase readability of their paper by making this paragraph as clear and as sound as possible. It would also help readers quickly identify if they wish to continue reading this paper and if it is of interest to their own research. My suggestions are: 1) Introduce this paragraph by restating what the main aims of this paper are (similar to what you wrote on lines 20--23). 2) Clearly introduce the technical contributions as they are backed by the experiments / results section with a short description of what was achieved. 3) Some of the contributions (specifically, the in vivo qualitative results) are not present in the main manuscript, but are part of the appendix. The exception is Figure 2 which does not have enough description in the main text (lines 254--256), and appears in the middle of a paragraph discussing the synthetic data results. I believe that the experiments section should be clearly reflected in the main aims and contributions of the paper, and the appendix should be used for optional / additional results which do not take away from the main contributions. I understand that there is a limit of 9 content pages to the paper, and I am happy to discuss this further.

Questions

Please find below some questions and general suggestions: 1. Figure 1 introduces the readers to an example of how dMRI data looks, and it is an important prelude towards understanding the problem statement of your paper. For this reason, I suggest the authors include further explanations in this figure, in either visual form or in the captions, such as: 1. How does gradient 25 differ from gradient 288 (maybe try to explain / show that these are different gradient directions and/or strengths instead of the 1/25/288 indices which have no specific meaning in this context)? 2. I think it is also important to show a zoomed-in version of the T1w image, to not confuse the reader that the spatio-spherical signal is also present in the structural data. 2. Please be consistent with referencing your figures in the manuscript: you sometimes write Figure x, and sometimes write Fig. x 3. I suggest you introduce the name of your proposed spatial-hemispherical deconvolution (SHD) framework in the contributions section (lines 57--71) as on the next page Figure 2 shows examples of your model. 4. In Figure 6B, could you discuss whether the low-resolution input to high-resolution output experiments could produce unrealistic reconstructions in the presence of noise / in a real dMRI data setting, as high-angular resolution is needed for higher contrast in the angular domain? I am wondering if for crossing fibers, for example, as shown in Figure 6D, none of the methods can accurately reconstruct the ground truth then maybe we cannot trust these reconstructions for low-angular resolution data? 5. Can you also please label the x-axes in Figures 6A and 6B to make it clear that the values are in degrees? 6. In Figure 6C can you explain the “narrowness” of your result as compared to the ground truth or CSD? 7. Can you provide a short description (in section 4.2.1) of how the peak angular error and false positive rates are calculated? I understand that these are described in A.3, but to improve readability I suggest that they are introduced a bit sooner with the details left for the appendix, or at least to make it more clear that the details are in A.4. Moreover, it would be interesting to understand the slight increase in FPR in both Figures 6A and 6B when comparing SHD(-TV) with RT-ESD.

Rating

6

Confidence

3

Soundness

3

Presentation

3

Contribution

3

Limitations

The authors have attempted to address some potential limitations, but would be nice to see a lengthier discussion on how their proposed method would perform on other in vivo clinical datasets, under different noise levels, patient motion, etc.

Summary

This paper introduces a novel method for analyzing diffusion MRI data, leveraging convolutional network layers equivariant to the E(3)×SO(3) group, which respects the physical symmetries of dMRI data. The proposed spatio-hemispherical graph convolutions reduce computational complexity while maintaining high deconvolution accuracy.

Strengths

This paper presents a novel method for dMRI deconvolution by introducing equivariant convolutional network layers that account for the physical symmetries in dMRI data. The use of spatio-hemispherical graph convolutions, leveraging the antipodal symmetry of neuronal fibres, reduces computational complexity while maintaining accuracy. The proposed method addresses important challenges in dMRI analysis, focusing on the need for accurate deconvolution at clinically feasible resolutions. The theorical foundation and empirical validation is sufficient, and the methodology is well-presented with clear explanations. The results are consistently validated, showcasing the method's efficiency and accuracy improvements. Additionally, The clarity of the paper is good with well-organized structure.

Weaknesses

1. The reliance on specific assumptions may limit the scope of the model. It would be better to improve the flexibility of the model so that it could be applied to diverse scenarios. 2. Diverse clinical conditions can be considered in future studies, involving varying levels of image quality and pathological changes. Conditions such as specific noise or artifacts are not fully explored.

Questions

1. Can the authors clarify the limitations of the antipodal symmetry assumption? Are there specific scenarios where this assumption might not hold, and how might this impact the model's performance? 2. Can the authors discuss the generalizability of their method across different clinical conditions and patient populations? How adaptable is the model to varying clinical data qualities?

Rating

6

Confidence

4

Soundness

3

Presentation

3

Contribution

3

Limitations

Yes.