Apparent Intravoxel Fibre Population Dispersion (FPD) Using Spherical Harmonics

The vast majority of High Angular Resolution Diffusion Imaging (HARDI) modeling methods recover networks of neuronal fibres, using a heuristic extraction of their local orientation. In this paper, we present a method for computing the apparent intravoxel Fibre Population Dispersion (FPD), which conveys the manner in which distinct fibre populations are partitioned within the same voxel. We provide a statistical analysis, without any prior assumptions on the number or size of these fibre populations, using an analytical formulation of the diffusion signal autocorrelation function in the spherical harmonics basis. We also propose to extract features of the FPD obtained in the group of rotations, using several metrics based on unit quaternions. We show results on simulated data and on physical phantoms, that demonstrate the effectiveness of the FPD to reveal regions with crossing tracts, in contrast to the standard anisotropy measures.