A numerical study of the effects of inhomogeneous media in diffusion weighted imaging

Abstract

Diffusion Weighted Imaging (DWI) -a common Magnetic Resonance Imaging (MRI) technique - is used to infer material properties of tissues from the average diffusion of water molecules over brief time intervals. In particular, the Apparent Diffusion Coefficient (ADC), a measure of the magnitude of diffusion within tissues, can be derived from the MR signal under the assumption of homogeneous medium. Unfortunately, the complex structure of a typical volume element of physiological tissue contains many types of cells separated from extracellular space by semi-permeable barriers and is thus far from homogeneous. In this thesis, we define an idealized tissue model as a system of cells separated by non-uniformly spaced semi-permeable membranes and extracellular space. Finite-difference solutions of the associated PDE model can be used to compute a Displacement Probability Density Function (DPDF). Having numerically computed the DPDF it is possible to simulate the intensity of the MRI signal and, from it, compute the ADC as in a real Diffusion Weighted-MRI experiment. The ADC is measured by averaging the second moments of the DPDF. Finally, we investigate the changes in the ADC in an inhomogeneous model by including higher order moments of the DPDF and we discuss the possible advantages of these alternative definitions.