Sampling of non-Gaussian Ensemble Average Propagators for the simulation of diffusion magnetic resonance images.

Abstract

Purpose: (a) To design a methodology for drawing random samples of any Ensemble Average Propagator (EAP) (b) to modify the KomaMRI simulator to accommodate them as realistic spin movements to simulate diffusion MRI (dMRI) and (c) to compare these simulations with those based on the Diffusion Tensor (DT) model.

Theory and methods: The rejection method is used for random sampling of EAPs: starting from a probability law that is easily sampled, and whose density function wraps the target EAP, samples are accepted when they lie inside the targeted region. This is used to sample the EAP as described by Mean Apparent Propagator MRI (MAP-MRI) and in Spherical Convolution (SC) based on Spherical Harmonics (SH). With this methodology, MAP-MRI and SC representations are calculated over in-vitro pig hearts images, and a simulation of a pulsed-gradient spin echo (PGSE) dMRI sequence inside the myocardial wall is undertaken with the KomaMRI simulator.

Results: MAP-MRI shows better agreement with the actual acquisition than conventional DT-based simulations, in terms of Mean Squared Errors and correlation with improvements up to 1.7 % for the former and 2.2 % for the latter.

Conclusion: dMRI sequences can be simulated accurately (yet, efficiently) if phantoms with a proper per-spin description of the diffusion process are made available. Moreover, our findings suggest that the study of non-Gaussian diffusion of the heart might be feasible, at least in vitro.