Filtering Methods for Asymmetric ODFs: Where and How Asymmetry Occurs in the White Matter

Numerous filtering methods have been proposed for estimating asymmetric orientation distribution functions (ODFs) for diffusion magnetic resonance imaging (dMRI). It can be hard to make sense of all these different methods, which share similar features and result in similar outputs. Furthermore, these methods are not readily available as part of a software package, further complexifying their usage and adoption as part of a standard processing pipeline. In this work, we propose a novel general filtering equation for estimating asymmetric ODFs by merging together features from these previously proposed filtering methods. Our method is distributed as an open-source GPU-accelerated python software to facilitate its integration into any existing dMRI processing pipeline. Then, we describe a novel measure of the number of fiber directions, an extension of the number of fiber orientations for the case of asymmetric ODFs. We also present a novel template quantifying the degree of asymmetry of the brain from multi-shell multi-tissue white matter fiber ODFs. When applied to full brain fiber ODFs, our method reveals asymmetric configurations, such as bending, branching and fanning ODFs, in more than 40% of the white matter and 70% of the gray matter. ### Competing Interest Statement The authors have declared no competing interest.