Diffusion MRI for well-posed and optimal white matter microstructure characterisation : beyond single diffusion encoding

The human brain hosts a colossal number of water molecules which are constantly moving due to Brownian motion. Their movement, random by nature, is restricted by the brain tissue walls. Magnetic Resonance Imaging (MRI) provides macroscopic measurements of the diffusion process in a non-invasive manner, i.e. diffusion MRI. Hidden in these measurements lies information about the underlying architecture. The ability to unravel tissue microstructure from the coarse-grained diffusion measurements is extremely valuable since this information is 2-3 orders of magnitude below typical MRI resolution. This makes diffusion MRI sensitive to pathological and developmental processes occurring at the mesoscopic scale, in the order of microns. Accessing this level of detail can lead to clinical biomarkers specific to early stages of neurodegenerative diseases or brain development. Computational models of biophysical tissue properties have been widely used in diffusion MRI research to elucidate the link between microstructural properties and MR signal formation. The potential increase in sensitivity and specificity in detecting brain microstructural changes is their major driving force. However, these models establish complex relationships between biophysical properties and the MR signal, making the inverse problem of recovering model parameters from noisy measurements ill-conditioned with conventional diffusion MRI acquisitions. This thesis explores ways to make diffusion MRI biophysical modelling more robust while maintaining time and hardware requirements that are feasible in clinical conditions. Firstly, we explore theoretically the benefits of incorporating functionally independent measurements, such as double diffusion encoding. Secondly, we propose an optimal experiment design framework that gives us, after exploring the whole multidimensional diffusion MRI measurement space, the acquisition that maximises accuracy and precision in the parameter estimation. Finally, we extract relevant information from histology images that can be used to feed or benchmark diffusion MRI models.