Authors

Xinyu Nie, Yonggang Shi

Abstract

The fiber orientation distribution function (FOD) is an advanced model for high angular resolution diffusion MRI representing complex fiber geometry. However, the complicated mathematical structures of the FOD function pose challenges for FOD image processing tasks such as interpolation, which plays a critical role in the propagation of fiber tracts in tractography. In FOD-based tractography, linear interpolation is commonly used for numerical efficiency, but it is prone to generate false artificial information, leading to anatomically incorrect fiber tracts. To overcome this difficulty, we propose a flowbased and geometrically consistent interpolation framework that considers peak-wise rotations of FODs within the neighborhood of each location. Our method decomposes a FOD function into multiple components and uses a smooth vector field to model the flows of each peak in its neighborhood. To generate the interpolated result along the flow of each vector field, we develop a closed-form and efficient method to rotate FOD peaks in neighboring voxels and realize geometrically consistent interpolation of FOD components. By combining the interpolation results from each peak, we obtain the final interpolation of FODs. Experimental results on Human Connectome Project (HCP) data demonstrate that our method produces anatomically more meaningful FOD interpolations and significantly enhances tractography performance.

Link to paper

DOI: https://doi.org/10.1007/978-3-031-43993-3_5

SharedIt: https://rdcu.be/dnwM6

Link to the code repository

N/A

Link to the dataset(s)

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Reviews

Review #4

Please describe the contribution of the paper

Workflows for the analysis of diffusion-weighted data often use a fiber orientation distribution function based on spherical harmonics to represent voxel-wise diffusion properties. The interpolation in this data representation is difficult, because the biophysical plausibility must be maintained. This submission proposes an efficient solution for this interpolation problem: Peaks of the ODFs of voxels involved in the interpolation are detected, and a closed-form solution is used to rotate peaks between neighboring voxels. The use of this approach is demonstrated on a subset of a publicly available dataset (HCP).
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 submission is within the scope of this conference and of potential interest to its audience. The text is well-written and without major issues. The proposed method is a useful extension of current technology, and involves some “nasty” mathematical detail (Wigner D-matrices). Overall, a solid conference contribution.
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 evaluation would have been more convincing if authors demonstrated a quantitative advantage (e.g., reduction in computation time, higher precision) than just an arguable qualitative improvement (“smoother and better reflect the somatotopic organizational principle”).
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

Methods are reproducible.
Please provide detailed and constructive comments for the authors. Please also refer to our Reviewer’s guide on what makes a good review: https://conferences.miccai.org/2023/en/REVIEWER-GUIDELINES.html

None.
Rate the paper on a scale of 1-8, 8 being the strongest (8-5: accept; 4-1: reject). Spreading the score helps create a distribution for decision-making

6
Please justify your recommendation. What were the major factors that led you to your overall score for this paper?

A relatively minor but potentially useful advance is described here.
Reviewer confidence

Very confident
[Post rebuttal] After reading the author’s rebuttal, state your overall opinion of the paper if it has been changed

N/A
[Post rebuttal] Please justify your decision

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Review #3

Please describe the contribution of the paper

This work proposes a novel methodology to interpolate fiber orientation distribution (FOD) functions for applications in white matter tractography. The method first decomposes the FODs into multiple peaks which are then associated with peaks from FODs in the local neighborhood to untangle the over-lapping local vector field. A continuous model is then fit per unique vector field and used for interpolation.
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 deals with a relevant problem. The idea of untangling coherent vector fields and fitting them separately is interestin and the results seem promising.
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 main weakness is in the experimental section, which needs some more clarity and details and perhaps further evaluation. Please find more detailed comments below.
Please rate the clarity and organization of this paper

Satisfactory
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

Authors indicate code has been made available.
Please provide detailed and constructive comments for the authors. Please also refer to our Reviewer’s guide on what makes a good review: https://conferences.miccai.org/2023/en/REVIEWER-GUIDELINES.html

Major

This paper would be improved by providing mores supporting details for the experimental results. For instance, there are several tuning parameters used to control smoothness and sparsity of the peak estimates and vector field (optimization problems 2 + 3). How were the values of the selected parameters reported on page 7 determined? How sensitive are the results to these parameters?

One of the advantages of the linear interpolation is that it is very fast. How does the computational time of this method compare to the linear interpolation? In the high dimensional world of medical imaging, tradeoffs between computational time + accuracy of a method are important context to provide.

In the tractography example, is the comparison between the proposed method to up sample the data and the linear interpolation? If not, should it be?

The L2 error may not be the most relevant metric. It would be good to see angular errors, e.g. crossing error angle, proportion of false peaks, etc.

I found the descriptions in Section 2.3 to be unclear. The peaks are rotated to align with the polynomial interpolant and then used for interpolation? I would suggest perhaps that the descriptions related to the rotation of the spherical harmonics can be shortened and/or moved to the appendix, as this is well known. With the additional space, more details about the method can be provided and/or and expanded in Figure 4. This would help improve clarity around how the vector fields are interpolated, the crucial part of the proposed method.

Minor

Page 2 first paragraph: “However, Since …” Since should not be capitalized

Is equation 2 optimizing over U1, …, UK? If so, this should be written as such.

I would suggest increasing the font of figure 6 and the sizes of figures in figure 7.
Rate the paper on a scale of 1-8, 8 being the strongest (8-5: accept; 4-1: reject). Spreading the score helps create a distribution for decision-making

4
Please justify your recommendation. What were the major factors that led you to your overall score for this paper?

This work has potential, but further experimental evaluation of several aspects of the method that are laid out above need to be addressed first. Additionally, the clarity of the exposition could use some improvements.
Reviewer confidence

Confident but not absolutely certain
[Post rebuttal] After reading the author’s rebuttal, state your overall opinion of the paper if it has been changed

N/A
[Post rebuttal] Please justify your decision

N/A

Review #1

Please describe the contribution of the paper

This paper presents a spatial interpolation/super-resolution (SR) method specifically designed for Diffusion Fiber Orientation Distribution (FOD). The proposed method achieves the SR decomposing each FOD according to its peaks. The decomposed peak components guided by flow of vector fields ensure the geometrical consistency of the interpolated FOD representation. The FODs are then corrected by a specific rotation scheme according to the neighbouring voxels.
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.

This paper presents an interesting algorithm to achieve Diffusion FOD SR while maintain the geometrically consistency of the FOD components. This method is specifically designed for FOD according to the spherical harmonic representation.

The method focus more on the analysis of neighbouring voxels of the decomposed FOD peak component and try to maintain a geometrical consistency of the interpolated FOD using optimisation functions. All the decomposed FODs are then corrected by rotation calculation to compose the final FOD spatial SR results.
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.

Although the paper presents a complete algorithm which is specifically designed for FOD, there contains some problems.

Finding the peak lobes is the core step for FOD decomposition which serves as pre-processing of the proposed method. However, the authors decide to use a threshold when finding the peaks which lower the usability of the method. Also, authors did not define the threshold THD they used (only mention e.g., 0.1). I think the authors may simply use the MRtrix for the peak calculation, however, the proper reference is not included if it is the case. Other than this THD, there are a few hyper parameters need to be defined in the algorithm, e.g., weights for optimisation problem, search tube size (r and h), which further limits the usability of the method. There is also no ablation study to show the effectiveness of the chosen value of these parameters.

The FOD decomposition and modelling the flow of vector fields of single-peak FOD component focus on the analysis of neighbouring voxels, however, this approach may limit the algorithm to be aware of the global information.

Another problem of this work is the lack of variety in the evaluation. The authors only report the full area at half maximum which is a metric that describing curves. I am wondering why not using direct FOD spherical harmonic coefficient difference metrics? In addition, only the visualisation results of the tractography is provided. There are two problems with tractography. First, it is hard to tell if the tractography produced by the super-resolved is improving unless the authors also show the results of the linear interpolation and indicating the significant differences. Second, the SIFT method used here is not deterministic where 10K may not sufficient to mitigate the randomness brought by the method.

According to the visualisation result in Figure 5, the proposed method seems to underestimate the peaks in some regions while overestimate in others. The proposed method seems inconsistent on predicting the original FOD peaks.
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 provide a clear description of the propose method but checking for some details details may require publishing the code.
Please provide detailed and constructive comments for the authors. Please also refer to our Reviewer’s guide on what makes a good review: https://conferences.miccai.org/2023/en/REVIEWER-GUIDELINES.html

The authors may used serveral functions from MRtrix, where their proper references should be included. The authors also use the SIFT1 for tractography where SIFT2 has already been used as a default for FOD-based tractography. Here are the corresponding references:

Raffelt, D.A., Tournier, J.D., Smith, R.E., Vaughan, D.N., Jackson, G., Ridgway, G.R., Connelly, A.: Investigating white matter fibre density and morphology using fixel-based analysis. Neuroimage 144, 58–73 (2017);

Smith, R.E., Tournier, J.D., Calamante, F., Connelly, A.: SIFT: Spherical- deconvolution informed filtering of tractograms. Neuroimage 67, 298–312 (2013);

Smith, R.E., Tournier, J.D., Calamante, F., Connelly, A.: SIFT2: Enabling dense quantitative assessment of brain white matter connectivity using streamlines trac- tography. Neuroimage 119, 338–351 (2015).

The authors may need to justify the choice of their hyper parameters and their corresponding influence to the results to prove the effectiveness of the method design.

In terms of evaluation, as discussed above, no deterministic 10K streamlines can be not sufficient to mitigate the randomness brought by the method, tractography with more than1M streamlines is suggested. The tractography is hard to be analysed but its derivatives e.g., structural connectivity matrix, is a good media to analysis the performance of the SR method. It summaries the information from the massive tractography and provide an overall picture of the brain region connectivity.

According to the visualisation result in Figure 5, the proposed method seems to underestimate the peaks in some regions while overestimate in others, could authors explain why this happened?
Rate the paper on a scale of 1-8, 8 being the strongest (8-5: accept; 4-1: reject). Spreading the score helps create a distribution for decision-making

5
Please justify your recommendation. What were the major factors that led you to your overall score for this paper?

The authors present an interesting super-resolution method specifically designed for FOD. Although each step in the method pipeline takes the characteristics of the FOD into account, but there are a few designs which are questionable and limits the usability of the method. The evaluation does not provide sufficient information to prove the effectiveness of the proposed method.
Reviewer confidence

Confident but not absolutely certain
[Post rebuttal] After reading the author’s rebuttal, state your overall opinion of the paper if it has been changed

N/A
[Post rebuttal] Please justify your decision

N/A

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 work proposes a super-resolution method of dMRI FOD to improve tractography. All reviewers agree that the paper is an interesting topic to be presented at MICCAI this year and provide constructive feedback in particular about experimental results and evaluation. The authors please make proper updates accordingly.

Author Feedback

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Flow-based Geometric Interpolation of Fiber Orientation Distribution Functions