Hierarchical modelling of crossing fibres in the white matter.

While diffusion MRI is typically used to estimate microstructural properties of tissue in volumetric elements (voxels), more specificity can be obtained by separately modelling the properties of individual fibre populations within a voxel. In the context of cross-subjects modelling, these fixel-based analyses are usually performed in two stages. Crossing fibre modelling is first performed in each subject to produce fixels, and these are subsequently modelled across subjects following registration and fibre population reassignment. Here, we introduce a new hierarchical framework for fitting crossing fibre models to diffusion MRI data in a population of subjects. This hierarchical setup guarantees that the crossing fibres are consistent by construction and, therefore, comparable across subjects. We propose an expectation-maximisation algorithm to fit the model, which can scale to large number of subjects. This approach produces a template for crossing fibre populations in the white matter which can be used to estimate fibre-specific parameters that are consistent across subjects, hence providing data that are by construction suitable for fixel-based statistical analyses.