The MR Physics of Advanced Diffusion Imaging

Over the last decade, the number of models used to analyse and interpret diffusion MRI data has increased dramatically. Exponentials and biexponentials have been joined by stretched exponentials, HARDI methods, compartment-based microstructure models and effective medium theories. At the same time, the field has experienced a cultural shift away from MR physics and towards computer science, emphasising Bayesian statistics and Machine Learning. This has meant that understanding imaging methodology whilst still keeping in mind the underlying physical assumptions can be challenging. This chapter reviews the Diffusion MR modelling literature from the point of view of the underlying physics. We show how the Bloch-Torrey equation can be derived, and then how different physical assumptions and formulations lead to different models. The intention is to show the different assumptions made in different models, to aid understanding and model selection.