Modeling the orientation distribution function by mixtures of angular central Gaussian distributions

In this paper we develop a tensor mixture model for diffusion weighted imaging data using an automatic model order selection criterion for the number of tensor components in a voxel. We show that the weighted orientation distribution function for this model can be expanded into a mixture of angular central Gaussian distributions. We investigate properties of this model in extensive simulations and in a high angular resolution scan of a human brain. The results suggest that the model improves imaging of cerebral fiber tracts. In addition, inference on canonical model parameters could potentially provide novel clinical markers of altered white matter. Software to compute the tensor mixture model from diffusion weighted MRI data is made available in the programming language R.