Probabilistic Inference on Q-ball Imaging Data

Diffusion-weighted magnetic resonance imaging (MRI) and especially diffusion tensor imaging (DTI) have proven to be useful for the characterization of the microstructure of brain white matter structures in vivo. However, DTI suffers from a number of limitations in characterizing more complex situations. The most notable problem occurs when multiple fibre bundles are present within a voxel. In this paper, we have expanded the existing Q-ball imaging method to a Bayesian framework in order to fully characterize the uncertainty around the fibre directions, given the quality of the data. We have done this by using a recently proposed spherical harmonics decomposition of the diffusion-weighted signal and the resulting Q-ball orientation distribution function. Moreover, we have incorporated a model selection procedure which determines the appropriate smoothness of the orientation distribution function from the data. We show by simulation that our framework can indeed characterize the posterior probability of the fibre directions in cases with multiple fibre populations per voxel and have provided examples of the algorithm's performance on real data where this situation is known to occur.