Local Parameter Estimation

In this section we present 3 models of the local diffusion process. The first is the familiar diffusion tensor model ([10]), which models the local diffusion as a 3 dimensional Gaussian. Then we choose two different models which attempt to model underlying fiber structure in a voxel and, from this, predict the diffusion weighted signal. The first of these is a simple partial volume model allowing for a single fibre direction mixed with an isotropically diffusing compartment in a voxel. The second is a parametrized model of the transfer function between a distribution of fibre orientations in a voxel and the measured diffusion weighted signal. We infer on the first two of these models, using MCMC to estimate the posterior distributions on parameters of interest. We present detailed results from a single white matter voxel showing recovered distributions from both models. We go on to present a validation study, comparing distributions throughout a slice with those recovered from empirical measurements of uncertainty ([14]).