Models of diffusion signal decay in magnetic resonance imaging: Capturing complexity

Abstract

Diffusion-weighted MRI is a key diagnostic component of clinical medicine. Radiologists use models of the effects of diffusion weighting to connect the decay of the signal intensity in tissues with macroscopic (diffusion tensor imaging) and microscopic (q-space imaging) structures. This multi-scale problem has stimulated the creation of many diffusion models spanning phenomenon in cells, in tissues, and in organs. Such models can be heuristic or based on simulations, stochastic processes, histological structure or physical and physiological constraints. The goal of this paper is to provide an overview of these approaches by considering several different classes of mathematical models (linear, nonlinear, integer, and fractional orders) that can, and have in some cases, been used to fit diffusion attenuation in complex biological tissues, such as brain white and gray matter. The focus here is not on solving the Bloch-Torrey equation or on fitting curves to data, but on the choices (Gaussian, anomalous, isotropic, anisotropic) one often has to make when beginning the analysis of diffusion data. It is hoped that this presentation, while oversimplified, will be of use to students and to new investigators who seek an introduction to diffusion attenuation model selection and characterization. Examples are given that illustrate the relationship between the functional form of the diffusion decay rate and, in the case of a Stejskal-Tanner gradient pulse sequence, the expected signal decay. Model limitations are noted and connections to more advanced treatments of diffusion modeling methods are provided.

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