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 anyEnsemble Average Propagator (EAP) (b) to modify the KomaMRI simulatorto accommodate them as realistic spin movements to simulate diffusion MRI(dMRI) and (c) to compare these simulations with those based on the DiffusionTensor (DT) model. Theory and Methods: The rejection method is used for random sampling ofEAPs: starting from a probability law that is easily sampled, and whose densityfunction wraps the target EAP, samples are accepted when they lie inside thetargeted region. This is used to sample the EAP as described by Mean Appar-ent Propagator MRI (MAP-MRI) and in Spherical Convolution (SC) based onSpherical Harmonics (SH). With this methodology, MAP-MRI and SC repre-sentations are calculated over in-vitro pig hearts images, and a simulation of apulsed-gradient spin echo (PGSE) dMRI sequence inside the myocardial wall isundertaken with the KomaMRI simulator. Results: MAP-MRI shows better agreement with the actual acquisition thanconventional DT-based simulations, in terms of Mean Squared Errors and cor-relation with improvements up to 1.7 % for the former and 2.2 % for thelatter. Conclusion: dMRI sequences can be simulated accurately (yet, efficiently)if phantoms with a proper per-spin description of the diffusion process aremade available. Moreover, our findings suggest that the study of non-Gaussiandiffusion of the heart might be feasible, at least in vitro.