Encoder-based Curvature-Aware Regularization for estimating asymmetric fiber orientation distribution functions in diffusion MRI

Abstract

Diffusion-weighted magnetic resonance imaging (dMRI) is used to study white matter microstructure and to delineate pathways by estimating fiber orientation distributions (FODs). Symmetric FODs represent the conventional model assuming antipodal symmetry in water diffusion. However, in complex regions with bending, branching or fanning fibers, this assumption is not guaranteed. To better capture such underlying fibers geometries, asymmetric FODs (A-FODs), derived from neighboring FODs, have been introduced. Here, we propose an Encoder-based Curvature-Aware Regularization (EnCAR) method for estimating A-FODs. Incorporating curvature features into the regularization weight applied to neighboring voxels improves reconstruction of A-FODs. A self-supervised Transformer network, combined with a Spherical Harmonics Semantic Encoder, learns region-specific regularization parameters from this local neighborhood to capture the diversity of fiber geometries across the brain. The EnCAR method was verified on the DiSCo challenge phantom, and applied to in vivo multi-shell Human data. The model estimated sharp, high-angular-resolution A-FODs that were well aligned with local fiber pathway. Compared with established FOD and A-FOD methods, it performed on par in regions dominated by symmetric FODs and outperformed them in complex asymmetric regions. Quantitative evaluation using the Asymmetry Index (ASI) and Model Discrepancy Index (MDI) confirmed improved consistency with the underlying diffusion signals. By ensuring smooth directional transitions, this work enhances the visibility of continuous fiber segments.