Diffusion MRI tractography algorithm development is increasingly moving towards global techniques to incorporate "downstream" information and conditional probabilities between neighbouring tracts. Such approaches also enable white matter to be represented more tangibly than the abstract lines generated by the most common approaches to fibre tracking. However, previously proposed algorithms still use fibre-like models of white matter corresponding to thin strands of white matter tracts rather than the tracts themselves, and therefore require many components for accurate representations, which leads to poorly constrained inverse problems. We propose a novel tract-based model of white matter, the 'Fourier tract', which is able to represent rich tract shapes with a relatively low number of parameters, and explicitly decouples the spatial extent of the modelled tract from its 'Apparent Connection Strength (ACS)'. The Fourier tract model is placed within a novel Bayesian framework, which relates the tract parameters directly to the observed signal, enabling a wide range of acquisition schemes to be used. The posterior distribution of the Bayesian framework is characterised via Markov-chain Monte-Carlo sampling to infer probable values of the ACS and spatial extent of the imaged white matter tracts, providing measures that can be directly applied to many research and clinical studies. The robustness of the proposed tractography algorithm is demonstrated on simulated basic tract configurations, such as curving, twisting, crossing and kissing tracts, and sections of more complex numerical phantoms. As an illustration of the approach in vivo, fibre tracking is performed on a central section of the brain in three subjects from 60 direction HARDI datasets.
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