Compositional measures of diffusion anisotropy and asymmetry

Diffusion MRI (dMRI) can be used to examine white matter structures in the living human brain. A common approach to dMRI analysis involves calculating a scalar value that reflects how different the observed diffusion is from an isotropic diffusion profile in each voxel. Current methods require either an oversimplified model (Fractional anisotropy, FA), use an abstract measure of "sharpness" (Generalized Fractional Anisotropy, GFA) or perform inconsistently across scans (Quantitative anisotropy, QA). Here we propose two novel statistically-motivated anisotropy measures based on fiber transition probabilities to neighboring voxels, calculated from orientation distribution functions (ODFs) using recently developed analytic tractography. Compositional Distance from Isotropy (CoDI) is the Aitchison distance between a voxel's analytic transition probabilities to its 26 neighbors and the corresponding transition probabilities that would arise from an isotropic ODF. Compositional Asymmetry (CoAsy) incorporates ODF similarities between neighboring voxels to highlight asymmetric patterns in transition probabilities to better reflect complexities of white matter structures. CoAsy is higher where fascicles split/fan/curve within white matter. We demonstrate on a fiber phantom that CoAsy reflects these properties. Using a cohort of 25 individuals, each scanned 8 times, we show that CoDI and CoAsy values reflect underlying fiber populations and that these measurements are reproducible across repeated scans.