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. The objectives of this work are two-fold: to disentangle the various filtering methods proposed in the past for estimating asymmetric ODFs, and to study the occurrence of asymmetric patterns in dMRI brain acquisitions. Hence, we describe a new filtering equation for estimating asymmetric ODFs resulting from the unification of 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. Following its validation on toy datasets, we apply our method to multi-shell multi-tissue fiber ODF reconstructions for 21 subjects from the Human Connectome Project in test-retest acquisitions. Our results show that our method estimates branching, fanning, bending, ending and other complex asymmetric fiber configurations in less than 2 minutes. Also, our novel number of fiber directions (NuFiD) index reveals that the filtering reduces the number of peak directions in the resulting asymmetric representation. Finally, our MNI-aligned template of asymmetries, describing the degree of asymmetry of each voxel, suggests that at least 60% of brain voxels in a dMRI acquisition contain asymmetric fiber configurations.