Diffusion MRI (dMRI) is a powerful imaging modality that allows us to non-invasively examine the organization and integrity of fibrous tissue, particularly the brain’s white matter. The result of a dMRI scan is a 3D image where each voxel contains a model that describes the local diffusion pattern of water molecules. The complicated nature and high dimensionality of these voxel-wise models make dMRI analysis especially challenging. The challenges increase when we look at dMRI scans from infants born prematurely. The smaller brain size for these infants, and the still-emerging brain structures these infants possess, increase the challenges involved in processing, analyzing, and interpreting dMRI scans. This thesis introduces four computational contributions in the area of dMRI analysis that attempt to address challenges exacerbated when imaging the preterm infant brain. Specifically, these four contributions are: (a) the first information content estimators for unaltered dMRI data, including a mutual information estimator for image registration; (b) a novel dMRI segmentation algorithm based on a cross-sectional piecewise constant image model; (c) the first global, closed-form probabilistic tractography algorithm, one where tracts compete for space in the brain; and (d) STEAM: the first patient-specific statistical abnormality mapping technique. In these four contributions, we model the dMRI data more accurately in order to improve the accuracy of dMRI analysis techniques, particularly in the presence of the small brain sizes and still-emerging brain structures seen in preterm infant dMRI. We further make the source code for these contributions publicly available to aid in the reproducibility of our research.
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