Hierarchical Bayesian Modelling Improves Microstructural Parameter Mapping in Diffusion and Exchange MRI Data

Microstructure modelling quantifies subvoxel tissue features by combining an MRI acquisition with a mathematical model, which is typically fitted voxel-by-voxel with least-squares (LSQ) minimisation to give voxelwise maps of microstructural quantities such as diffusivity and compartmental fractions. Such approaches are susceptible to voxelwise noise, which can lead to erroneous values in parameter maps. Hierarchical Bayesian modelling (HBM) can address this limitation but has only been demonstrated for simple models. We previously derived an HBM approach for an arbitrary microstructure model with flexible parameter constraints, utilising a Markov chain Monte Carlo algorithm for parameter estimation; here, the method is demonstrated and evaluated using simulated and human data for two previously unexplored diffusion MRI techniques, namely, diffusion kurtosis imaging and blood-brain barrier filter exchange imaging. When compared with LSQ minimisation, HBM increased the accuracy, precision, contrast-to-noise ratio and parameter map quality in both simulated and human data. HBM was also able to resolve local parameter variations associated with white matter lesions in a small sample of cerebral small vessel disease subjects, which were obscured by high noise levels in the LSQ-derived parameter maps. Finally, a noise sensitivity assessment in simulations showed that HBM improved the contrast-to-noise ratio and parameter map quality even at low signal-to-noise ratios. This generalised HBM framework can improve parameter estimation for more complex diffusion MRI microstructural models that extend beyond linear combinations of exponentials.