Circular spectrum mapping for intravoxel fiber structures based on high angular resolution apparent diffusion coefficients

A method is presented for mapping intravoxel fiber structures using spectral decomposition onto a circular distribution of measured apparent diffusion coefficients (ADCs). The zeroth-, second-, and fourth-order harmonic components of the ADC distribution on the circle spanned by the major and median eigenvectors of the diffusion tensor can be used to provide quantitative indices for isotropic, linear, and fiber-crossing diffusion, respectively. A diffusion-weighted MRI technique with 90 encoding orientations was implemented to estimate the circular ADC distribution and calculate the circular spectrum. A digital phantom was used to simulate various diffusion patterns. Comparisons were made between the circular spectrum and regular DTI-based index maps. The results indicated that the zeroth- and second-order circular spectrum maps exhibited a strong consistency with the DTI-based mean diffusivity and linear indices, respectively, and the fourth-order circular spectrum map was able to identify the fiber crossings. MRI experiments were performed on seven healthy human brains using a 3T scanner. The in vivo fourth-order maps showed significantly higher densities in several brain regions, including the corpus callosum, cingulum bundle, superior longitudinal fasciculus, corticospinal tract, and middle cerebellar peduncle, which indicated the existence of fiber crossings in these regions.