Computational modelling of diffusion magnetic resonance imaging based on cardiac histology

Abstract

The exact relationship between changes in myocardial microstructure as a result of heart disease and the signal measured using diffusion tensor cardiovascular magnetic resonance (DT-CMR) is currently not well understood. Computational modelling of diffusion in combination with realistic numerical phantoms offers the unique opportunity to study effects of pathologies or the efficacy of improvements to acquisition protocols in a controlled in-silico environment. In this work, Monte Carlo random walk (MCRW) methods are used to simulate diffusion in a histology-based 3D model of the myocardium. Sensitivity of typical DT-CMR sequences to changes in tissue properties is assessed.

First, myocardial tissue is analysed to identify important geometric features and diffusion parameters. A two-compartment model is considered where intra-cellular compartments with a reduced bulk diffusion coefficient are separated from extra-cellular space by permeable membranes. Secondary structures like groups of cardiomyocyte (sheetlets) must also be included, and different methods are developed to automatically generate realistic histology-based substrates. Next, in-silico simulation of DT-CMR is reviewed and a tool to generate idealised versions of common pulse sequences is discussed. An efficient GPU-based numerical scheme for obtaining a continuum solution to the Bloch--Torrey equations is presented and applied to domains directly extracted from histology images. In order to verify the numerical methods used throughout this work, an analytical solution to the diffusion equation in 1D is described. It relies on spectral analysis of the diffusion operator and requires that all roots of a complex transcendental equation are found. To facilitate a fast and reliable solution, a novel root finding algorithm based on Chebyshev polynomial interpolation is proposed. To simulate realistic 3D geometries MCRW methods are employed. A parallel simulator for both grid-based and surface mesh--based geometries is presented. The presence of permeable membranes requires special treatment. For this, a commonly used transit model is analysed. Finally, the methods above are applied to study the effect of various model and sequence parameters on DT-CMR results. Simulations with impermeable membranes reveal sequence-specific sensitivity to extra-cellular volume fraction and diffusion coefficients. By including membrane permeability, DT-CMR results further approach values expected in vivo.