E(3) × SO(3)-Equivariant Networks for Spherical Deconvolution in Diffusion MRI.

Area of Science:

• Medical Imaging
• Neuroscience
• Machine Learning

Background:

• Diffusion MRI (dMRI) is crucial for mapping brain microstructure and connectivity.
• dMRI voxels often contain signals from multiple crossing white matter tracts, necessitating deconvolution techniques.
• Current methods may not fully leverage spatial relationships between dMRI measurements.

Purpose of the Study:

• To introduce Roto-Translation Equivariant Spherical Deconvolution (RT-ESD), a novel equivariant deep learning framework.
• To address the challenge of sparse deconvolution in 6D data from dMRI.
• To improve the recovery of crossing anatomical structures in the brain.

Main Methods:

• Developed equivariant deep learning layers respecting spatial and spherical rotation symmetries.
• Applied RT-ESD to sparse deconvolution of spherical signals within dMRI volumes.
• Integrated roto-translation equivariance into spherical deconvolution.

Main Results:

• RT-ESD demonstrated superior performance in fiber recovery tasks (DiSCo dataset).
• Improved deconvolution-derived partial volume estimation on in vivo human brain dMRI data.
• Achieved enhanced reconstruction of fiber tractograms (Tractometer dataset).

Conclusions:

• RT-ESD offers a significant advancement in dMRI analysis by incorporating equivariance.
• The framework effectively recovers complex crossing white matter structures.
• RT-ESD shows broad applicability in neuroimaging research and clinical diagnostics.