Hierarchical Modelling of Crossing Fibres in the White Matter

While diffusion MRI is typically used to estimate microstructural properties of tissue in volu-metric 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 so-called fixel-based analyses require identifying equivalent fibre populations. This is usually done post-hoc, after estimating fibre orientations for individual subjects independently and subsequently matching the fixels between subjects. This approach can fail due to individual differences in fibre orientation distributions. Here, we introduce a 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 approach to fit the model, which can scale to large numbers of subjects. This approach produces a crossing-fibre white matter fibre template, which can be used to estimate fibre-specific parameters that are consistent across subjects and, hence, can be used in fixel-based statistical analyses. ### Competing Interest Statement The authors have declared no competing interest.