Estimation of Anisotropic Water Diffusion Indexes on Axon Bundle Crossings

The estimation of principal diffusion directions in brain white matter has been extensively studied by processing Diffusion Weighted Magnetic Resonance Images. Those studies present competitive results for both, a single diffusion orientation, as well as for multiple diffusion orientations at voxels where the axon fibers cross or split. However, in the best of our knowledge, all the available methods are unable to estimate the an isotropic indexes in the multiple diffusion direction case. Those an isotropic indexes are used to determine properties of the axon packs in the brain, thus are related to the diagnosis of brain diseases. In this paper we propose a new method based on the selection of Diffusion Basis Functions which is capable to detect the an isotropic indexes. Our approach is composed of two steps: the first stage estimates the diffusion orientation based on a raw an isotropic model, the second stage estimates the an isotropic indexes by setting a high resolution Diffusion Basis built from statistical analysis of parallel and radial diffusion coefficients on the brain white matter. Our experiments are presented on synthetic diffusion weighted data.