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Even if a number of methods have been proposed for resolving crossing fibres from diffusion-weighted (DW) MRI, other complex fibre geometries have drawn minimal attention. In this study, we focus on fibre orientation dispersion induced by within-voxel fanning. We use a multi-compartment, model-based approach to estimate fibre dispersion. A Bingham distribution is employed to represent a continuum of fibre orientations, centred around a main orientation. We evaluate the accuracy of the model for different simulated fanning geometries, under different acquisition protocols and we illustrate the high SNR and angular resolution needs. We apply the proposed model on high-quality, postmortem macaque data and present whole-brain maps of fibre dispersion.