The methods of group theory are applied to the problem of characterizing the diffusion measured in high angular resolution MR experiments. This leads to a natural representation of the local diffusion in terms of spherical harmonics. In this representation, it is shown that isotropic diffusion, anisotropic diffusion from a single finer, and anisotropic diffusion from multiple fiber directions fall into distinct and separable channels. This decomposition can be determined for any voxel without any prior information by a spherical harmonic transform, and for special cases the magnitude and orientation of the local diffusion may be determined. Moreover, non-diffusion-related asymmetries produced by experimental artifacts fall into channels distincts from the fiber channels, thereby allowing their separation and a subsequent reduction in noise from the reconstructed fivers. In the case of a single finer, the method reduces identically to the standard diffusion tensor method. The method is applied to normal volunteer brain data collected with a stimulated echo spiral high angular resolution diffusion weighted(HARDI) acquisition.
Lawrence R. Frank, “Characterization of Anisotropy in High Angular Resolution Diffusion-Weighted MRI“, Magn Reson Med 47:1083-1099, 2002