A rotation-invariant spherical harmonic decomposition method for mapping intravoxel multiple fiber structures

Abstract

A new rotation-invariant spherical harmonic decomposition (SHD) method is proposed in this paper for analyzing high angular resolution diffusion (HARD) imaging. Regular SHD methods have been used to characterize the features of the apparent diffusion coefficient (ADC) profile measured by the HARD technique. However, these regular SHD methods are rotation-variant, i.e., the magnitude and/or the phase of the harmonic components changes with the rotation of the ADC profile. We propose a new rotation-invariant SHD (RI-SHD) method based on the rotation-invariant property of a diffusion tensor model. The basic idea of the proposed method is to reorient the measured ADC profile into a local coordinate system determined by the three eigenvectors of the diffusion tensor in each imaging voxel, and then apply a SHD to the ADC profile. Both simulations and in vivo experiments were carried out to validate the method. Comparisons were made between the component maps from a regular SHD method, diffusion circular spectrum mapping (DCSM) method and the proposed RI-SHD method. The results indicate that the regular SHD maps vary significantly with the rotation of the diffusion-encoding scheme, whereas the maps of the DCSM and the proposed method remain unchanged. In particular, the (0,0)-th, (2,2)-th and (4,4)-th component maps from the RI-SHD method exhibited good consistency with the 0th, 2nd and 4th order maps of the DCSM method, respectively. Compared with the regular SHD methods used in HARD imaging, the proposed RI-SHD method is superior in characterizing the diffusion patterns of multiple fiber structures between different brain regions or across subjects.