This paper describes a general and flexible Monte- Carlo simulation framework for diffusing spins that generates realistic synthetic data for diffusion magnetic resonance imaging. Similar systems in the literature consider only simple substrates and their authors do not consider convergence and parameter optimization. We show how to run Monte-Carlo simulations within complex irregular substrates. We compare the results of the Monte-Carlo simulation to an analytical model of restricted diffusion to assess precision and accuracy of the generated results. We obtain an optimal combination of spins and updates for a given run time by trading off number of updates in favor of number of spins such that precision and accuracy of sythesized data are both optimized. Further experiments demonstrate the system using a tissue environment that current analytic models cannot capture. This tissue model incorporates swelling, abutting, and deformation. Swelling-induced restriction in the extracellular space due to the effects of abutting cylinders leads to large departures from the predictions of the analytical model, which does not capture these effects. This swelling-induced restriction may be an important mechanism in explaining the changes in apparent diffusion constant observed in the aftermath of acute ischemic stroke.

This work shows that multi-fibre reconstruction techniques, such as Persistent Angular Structure (PAS) MRI or QBall Imaging, provide much more information than just discrete fibre orientations, which is all that previous tractography algorithms exploit from them. We show that the shapes of the peaks of the functions output by multiple-fibre reconstruction algorithms reflect the underlying distribution of fibres. Furthermore, we show how to exploit this extra information to improve Probabilistic Index of Connectivity (PICo) tractography. The method uses the Bingham distribution to model the uncertainty in fibre-orientation estimates obtained from peaks in the PAS or QBall Orientation Distribution Function (ODF). The Bingham model captures anisotropy in the uncertainty, allowing the method to track through fanning and bending structures, which previous methods do not recover reliably. We devise a new calibration procedure to construct a mapping from peak shape to Bingham parameters. We test the accuracy of the calibration using a bootstrap experiment. Finally, we show that exploiting the peak shape in this way can provide improved PICo tractography results.