Geometric models of brain white matter for microstructure imaging with diffusion MRI

The research presented in this thesis models the diffusion-weighted MRI signal within brain white matter tissue. We are interested in deriving descriptive microstructure indices such as white matter axon diameter and density from the observed diffusion MRI signal. The motivation is to obtain non-invasive reliable biomarkers for early diagnosis and prognosis of brain development and disease. We use both analytic and numerical models to investigate which properties of the tissue and aspects of the diffusion process affect the diffusion signal we measure. First we develop a numerical method to approximate the tissue structure as closely as possible. We construct three-dimensional meshes, from a stack of confocal microscopy images using the marching cubes algorithm. The experiment demonstrates the technique using a biological phantom (asparagus). We devise an MRI protocol to acquire data from the sample. We use the mesh models as substrates in Monte-Carlo simulations to generate synthetic MRI measurements. To test the feasibility of the method we compare simulated measurements from the three-dimensional mesh with scanner measurements from the same sample and simulated measurements from an extruded mesh and much simpler parametric models. The results show that the three-dimensional mesh model matches the data better than the extruded mesh and the parametric models revealing the sensitivity of the diffusion signal to the microstructure. The second study constructs a taxonomy of analytic multi-compartment models of white matter by combining intra- and extra-axonal compartments from simple models. We devise an imaging protocol that allows diffusion sensitisation parallel and perpendicular to tissue fibres. We use the protocol to acquire data from two fixed rat brains, which allows us to fit, study and evaluate the models. We conclude that models which incorporate non-zero axon radius describe the measurements most accurately. The key observation is a departure of signals in the parallel direction from the two-compartment models, suggesting restriction, most likely from glial cells or binding of water molecules to the membranes. The addition of the third compartment can capture this departure and explain the data. The final study investigates the estimates using in vivo brain diffusion measurements. We adjust the imaging protocol to allow an in vivo MRI acquisition of a rat brain and compare and assess the taxonomy of models. We then select the models that best explain the in vivo data and compare the estimates with those from the ex vivo measurements to identify any discrepancies. The results support the addition of the third compartment model as per the ex vivo findings, however the ranking of the models favours the zero radius intra-axonal compartments.