Model Selection and Estimation of Multi-compartment Models in Diffusion MRI with a Rician Noise Model

Multi-compartment models in diffusion MRI (dMRI) are used to describe complex white matter fiber architecture of the brain. In this paper, we propose a novel multi-compartment estimation method based on the ball-and-stick model, which is composed of an isotropic diffusion compartment ("ball") as well as one or more perfectly linear diffusion compartments ("sticks"). To model the noise distribution intrinsic to dMRI measurements, we introduce a Rician likelihood term and estimate the model parameters by means of an Expectation Maximization (EM) algorithm. This paper also addresses the problem of selecting the number of fiber compartments that best fit the data, by introducing a sparsity prior on the volume mixing fractions. This term provides automatic model selection and enables us to discriminate different fiber populations. When applied to simulated data, our method provides accurate estimates of the fiber orientations, diffusivities, and number of compartments, even at low SNR, and outperforms similar methods that rely on a Gaussian noise distribution assumption. We also apply our method to in vivo brain data and show that it can successfully capture complex fiber structures that match the known anatomy.