Capturing complexity of the diffusion-weighted MR signal decay

Abstract

Diffusion-weighted MRI (dMRI) is a key component of clinical radiology. When analyzing diffusion-weighted images, radiologists often seek to infer microscopic tissue structure through measurements of the diffusion coefficient, D₀ (mm²/s). This multi-scale problem is framed by the creation of diffusion models of signal decay based on physical laws, histological structure, and biophysical constraints. The purpose of this paper is to simplify the model building process by focusing on the observed decay in the effective diffusion coefficient as a function of diffusion weighting (b-value), D(b), that is often observed in complex biological tissues. We call this approach the varying diffusion curvature (VDC) model. Since this is a heuristic model, the exact functional form of this decay is not important, so here we examine a simple exponential function, D(b) = D₀exp(-bD₁), where D₀ and D₁ capture aspects of hindered and restricted diffusion, respectively. As an example of the potential of the VDC model, we applied it to dMRI data collected from normal and diseased human brain tissue using Stejskal-Tanner diffusion gradient pulses. In order to illustrate the connection between D₀ and D₁ and the sub-voxel structure we also analyzed dMRI data from families of Sephadex beads selected with increasing tortuosity. Finally, we applied the VDC model to dMRI simulations of nested muscle fiber phantoms whose permeability, atrophy, and fiber size distribution could be changed. These results demonstrate that the VDC model is sensitive to sub-voxel tissue structure and composition (porosity, tortuosity, and permeability), hence can capture tissue complexity in a manner that could be easily applied in clinical dMRI.

Keywords: Anomalous diffusion; Apparent diffusion coefficient; Brain cancer; High b-value; Magnetic resonance imaging.