The signal for diffusion weighted magnetic resonance imaging has previously been represented analytically and simulated numerically for a variety of model problems with idealized geometries. Numerical simulations hold the promise of computing the diffusion weighted MR signal for more complex realistic tissue architectures and physiological models. This paper investigates a white matter model consisting of a matrix of coated cylinders with distinct diffusion coefficients and spin concentrations for each of the cylinder core, the coating, and the surrounding bath and compares results with an the analytical solution developed by Sen and Basser for the long diffusion time limit.
Numerical simulations of diffusion weighted imaging experiments are performed for the three-medium model using a Monte Carlo diffusion simulation. Experiments are carried out for model parameters representing normal white matter. Pulse sequence parameters range from a low b value, long time limit, short pulse approximation to realistic clinical values.
For simulations in the short pulse width, long diffusion time limit, numerical simulations agree with the Sen–Basser analytical result. When tested with realistic pulse sequence parameters, numerical simulations show lower anisotropy than the analytical model predicts.