Biophysical modelling of white matter structure

Brain white matter makes up the wires that connect different regions in the brain. It is affected in hundreds of brain diseases, and is the main target of many of these. It is important to be able to make detailed measurements of features of white matter if we are trying to understand the nature of a disease; if we want to watch the progression of a disease in a particular patient; or if we want to find out if a drug is being effective against the disease. At the moment, it is only possible to take these detailed measurements in a dead brain using a microscope. We can take measurements in living people using an MRI machine, but these are much coarser, only giving us a rough estimate that something about the white matter has changed. We propose to use different kinds of MRI data together with mathematical modelling techniques to make detailed measurements of specific features of white matter, such as the cell size, the density of the cells and the amount of electrical insulation. The ability to take these measurements in-vivo will give doctors and clinical researchers access to a great deal more information when they are suggesting treatment, or researching into the disease.

We aim to use diffusion MRI and T2-relaxometry data to infer cellular features (axon density, axon radius, and myelin content) along white matter pathways in the in-vivo brain. Although in-part measurable from ex-vivo diffusion MR data, such measurements have, to-date, required image acquisition protocols that are not possible in-vivo. We intend to address these problems using two strategies. First, we will combine two types of MR data that contain complementary information about these key parameters. This will help to resolve ambiguity about key biophysical parameters, such as myelination content and axon density, that exists when using diffusion data alone. Second, we will combine data across imaging voxels that lie within the same white matter pathways ? this will help to overcome the signal-to-noise limitations of in-vivo imaging data. In both cases we will use Bayesian strategies to combine data. We will build a biophysical model of white matter structure capable of predicting diffusion and relaxometry from a given set of parameters, and use both types of data symmetrically to invert the model. We will then place this model at the heart of a Bayesian global tractography approach that we have previously developed. We will extend this global approach to include a spatial model on the key biophysical parameters of interest to enforce only smooth, or no, change along a white matter pathway. This approach will have two important effects. First, it will essentially pool information across voxels in the same white matter pathway. This will reduce our SNR requirements for estimating key parameters. Second, it will automatically and seamlessly incorporate the biophysical information into the tractography routine that estimates the white matter pathways. This is potentially a significant step for tractography. Typically, tractography relies on orientation of diffusion within each voxel. In many cases there are ambiguities between neighbouring pathways that cause false positive and false negative connections from tractography. For example, it is not possible to distinguish two crossing fibres from two ?kissing? fibres with conventional tractography. Although biophysical parameters are expected to change slowly along a white matter pathway, they may vary to a greater extent between neighbouring pathways. The biophysical information will therefore inform the tractography routine in situations where the orientational information is ambiguous. Biophysical parameters inferred from our model will be validated against classical histological techniques in ex-vivo samples.