Generalised Hierarchical Bayesian Microstructure Modelling for Diffusion MRI

Elizabeth Powell, Matteo Battocchio, Christopher S. Parker, Paddy J. Slator

Abstract: MicrostructureMicrostructure imaging combines tailored diffusion MRI acquisition protocols with a mathematical model to give insights into subvoxel tissue features. The model is typically fit voxel-by-voxel to the MRI image with least squares minimisation to give voxelwise maps of parameters relating to microstructuralMicrostructure features, such as diffusivities and tissue compartment fractions. However, this fitting approach is susceptible to voxelwise noise, which can lead to erroneous values in parameter maps. Data-driven Bayesian hierarchical modellingBayesian hierarchical model defines prior distributions on parameters and learns them from the data, and can hence reduce such noise effects. Bayesian hierarchical modellingBayesian hierarchical model has been demonstrated for microstructureMicrostructure imaging with diffusion MRIDiffusion MRI, but only for a few, relatively simple, models. In this paper, we generalise hierarchical Bayesian modelling to a wide range of multi-compartment microstructuralMicrostructure models, and fit the models with a Markov chain Monte Carlo (MCMC)Monte Carlo Markov chain algorithm. We implement our method by utilising Dmipy, a microstructureMicrostructure modelling software package for diffusion MRIDiffusion MRI data. Our code is available at github.com/PaddySlator/dmipy-bayesian.