| Summary: | <p>The normal microstructure of the heart is fundamental to its healthy mechanical and electrical function. In diseases such as hypertrophic cardiomyopathy or myocardial infarction there is remodelling of the microstructure which can lead to heart dysfunction and even death. Diffusion MRI measures the magnitude and direction of the diffusion of water molecules within tissue, and can therefore be used to infer structural information about biological tissue. There remains some uncertainty about the relationship between cardiac microstructure and the diffusion MRI signal that it produces. Monte Carlo models can be used to increase the understanding of this relationship as well as to design optimal MRI sequences and propose image biomarkers related to specific microstructural changes. This Thesis presents a computational framework for the simulation of diffusion MRI in cardiac tissue, including an anatomically realistic model of cellular geometry, a Monte Carlo method to simulate the diffusion of water molecules and the calculation of diffusion MRI signals. The model is shown to simulate diffusion MRI results which correspond well with experimental data from five ex vivo rat hearts over a range of gradient strengths and diffusion times. Neither introducing membrane permeability nor increasing the diffusivity in the extracellular space compared with that within the cells showed a marked effect. The introduction of type IB disarray into the model, as commonly found in hypertrophic cardiomyopathy, caused the diffusion to become less anisotropic while the amount of diffusion remained constant. This model will allow the investigation of the relationship between different types and degrees of remodelling and the diffusion MRI signal, which will further the use of diffusion MRI as a clinical tool in the detection and quantification of cardiac remodelling in disease.</p>
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