Realistic voxel sizes and reduced signal variation in Monte-Carlo simulation for diffusion MR data synthesis

To synthesize diffusion MR measurements from Monte-Carlo simulation using tissue models with sizes comparable to those of scan voxels. Larger regions enable restricting structures to be modeled in greater detail and improve accuracy and precision in synthesized diffusion-weighted measurements. We employ a localized intersection checking algorithm during substrate construction and dynamical simulation. Although common during dynamics simulation, a dynamically constructed intersection map is also applied here during substrate construction, facilitating construction of much larger substrates than would be possible with a naive "brute-force" approach. We investigate the approach's performance using a packed cylinder model of white matter, investigating optimal execution time for simulations, convergence of synthesized signals and variance in diffusion-weighted measurements over a wide range of acquisition parameters. The scheme is demonstrated with cylinder-based substrates but is also readily applicable to other geometric primitives, such as spheres or triangles. The algorithm enables models with far larger substrates to be run with no additional computational cost. The improved sampling reduces bias and variance in synthetic measurements. The new method improves accuracy, precision, and reproducibility of synthetic measurements in Monte-Carlo simulation-based data synthesis. The larger substrates it makes possible are better able to capture the complexity of the tissue we are modeling, leading to reduced bias and variance in synthesised data, compared to existing implementation of MC simulations.