Convergence and Parameter Choice for Monte-Carlo Simulations of Diffusion MRI

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.