A concise continuous time random-walk diffusion model for characterization of non-exponential signal decay in magnetic resonance imaging

Abstract

Diffusion-weighted magnetic resonance imaging (dMRI) is a method of capturing the signal of water molecules diffusing in heterogeneous materials. Gaussian diffusion is interrupted when water mobility is hampered by obstructions in complex structures, and the dMRI signal decay does not match the single exponential decay in Brownian motion. In this study, a concise continuous time random-walk diffusion model is derived with less parameters than the continuous time random walk (CTRW) model and used to characterize the attenuation signal of brain tissue. The fitting results are compared with the CTRW model and the mono-exponential model reflecting the sub-diffusion and the long tail phenomenon of signal decay. Three sample experiments on rat brain and human brain are chosen to evaluate the validity in explaining the anomalous diffusion of water molecules in biological tissues, particularly in brain tissues in diverse directions, which also extends the applications of the concise continuous time random-walk diffusion model. Furthermore, we note that the concise continuous time random-walk diffusion model has practical advantages over the classical exponential model from the perspective of computational accuracy especially in the case of large b values, and has less parameters and is comparable to the CTRW model.