Equivariant spatio-hemispherical networks for diffusion MRI deconvolution

TL;DR

Developing convolutional network layers that are equivariant to the E(3) \times SO(3) group and account for the physical symmetries of dMRI including rotations, translations, and reflections of space alongside voxel-wise rotations lead to better and more practical resolution of crossing neuronal fibers and fiber tractography.

Abstract

Each voxel in a diffusion MRI (dMRI) image contains a spherical signal corresponding to the direction and strength of water diffusion in the brain. This paper advances the analysis of such spatio-spherical data by developing convolutional network layers that are equivariant to the $\mathbf{E(3) \times SO(3)}$ group and account for the physical symmetries of dMRI including rotations, translations, and reflections of space alongside voxel-wise rotations. Further, neuronal fibers are typically antipodally symmetric, a fact we leverage to construct highly efficient spatio-hemispherical graph convolutions to accelerate the analysis of high-dimensional dMRI data. In the context of sparse spherical fiber deconvolution to recover white matter microstructure, our proposed equivariant network layers yield substantial performance and efficiency gains, leading to better and more practical resolution of crossing neuronal fibers and fiber tractography. These gains are experimentally consistent across both simulation and in vivo human datasets.

Figures (13)

• Figure 1: A diffusion MRI (columns 1--3) and a T1w MRI (column 5) derived from a subject in the HCP Young Adult dataset van2013wu. The inset (column 4) visualizes a region's spatio-spherical diffusion signal ($b-1000mm/s^2$), highlighting crossing-fiber patterns and the grey/white matter interface.
• Figure 2: A deconvolution visualization comparing recovered fiber orientation distribution functions (fODFs) produced by the widely-used iterative CSDtournier2007robust model (top row) and our proposed SHD-TV model (bottom row) with high-resolution / clinically-infeasible (left) and low-resolution / clinically-feasible (right) spherical sampling. At high-resolutions (left), SHD-TV demonstrates enhanced localization of fiber orientations, heightened sensitivity to small-angle crossing fibers, and improved spatial consistency in the recovered fibers. At clinical low-resolutions (right), CSD struggles with the loss of input information, whereas our approach exhibits greater robustness to resolution losses and single-shell imaging protocols, yielding higher fidelity and spatially coherent fODFs. Appendix Fig. \ref{['fig:marketing_appendix']} visualizes comparisons with additional baselines.
• Figure 3: Contribution overview. A. We reduce the spherical graph ($\mathcal{G},\mathbf{L}$) to an hemispherical graph ($\mathcal{H},\mathbf{L}^+$). B. The SHD deconvolution framework operates on a grid of spherical signals and reduces computation complexity while improving neuronal fiber deconvolution.
• Figure 4: Efficiency analysis. Runtime (A & C) and GPU memory usage (B & D) expressed as the percentage of the baseline elaldi20233, for both: (line plots) a convolutional layer applied to increasing angular resolution samplings and (bar plots) a U-Net applied to high-angular resolution. The proposed convolution is more efficient than existing equivariant spatio-spherical convolutions.
• Figure 5: Overview of the diffusion MRI experiments in Section \ref{['sec:dmri_exp']}. [A] We perform super-resolved fODF estimation experiments on two datasets, DiSCo and HCP, respectively. Here, we study the impact of using either high-angular or low-angular resolution as input. [B] We perform quantitative fODF and tractography estimation experiments on Tractometer. We extract fODFs and tractograms from the dMRI with both input and output having low-angular resolution.

Theorems & Definitions (1)

• Theorem 1