Elucidating intravoxel geometry in diffusion-MRI: Asymmetric orientation distribution functions (AODFs) revealed by a cone model

A diffusion-MRI processing method is presented for representing the inherent asymmetry of the underlying intravoxel geometry, which emerges in regions with bending, crossing, or sprouting fibers. The orientation distribution functions (ODFs) obtained through conventional approaches such as q-ball imaging and spherical deconvolution result in symmetric ODF profiles at each voxel even when the underlying geometry is asymmetric. To extract such inherent asymmetry, an inter-voxel filtering approach through a cone model is employed. The cone model facilitates a sharpening of the ODFs in some directions while suppressing peaks in other directions, thus yielding an asymmetric ODF (AODF) field. Compared to symmetric ODFs, AODFs reveal more information regarding the cytoarchitectural organization within the voxel. The level of asymmetry is quantified via a new scalar index that could complement standard measures of diffusion anisotropy. Experiments on synthetic geometries of circular, crossing, and kissing fibers show that the estimated AODFs successfully recover the asymmetry of the underlying geometry. The feasibility of the technique is demonstrated on in vivo data obtained from the Human Connectome Project.