This dissertation shows that qualitative and quantitative characterization of patterned structures in brain connectivity data obtained using diffusion MRI not only improves the exploration of the intricate space of brain connectivity but also provides clinically meaningful measures, quantifying normal and pathological variation in the brain. To this end, we introduce a set of computational and mathematical models, algorithms, and interactive tools to explore, understand, and characterize diffusion-derived structural brain connectivity. We contribute to all stages of modeling, visualization, and analysis of brain connectivity. In modeling, our contributions are twofold. First, we model the joint distribution of local neural fiber configurations with Markov random fields and infer the most likely configuration with maximum a posteriori estimation. We demonstrate this framework's use in resolving fiber crossings. Second, we introduce new planar map representations of three-dimensional neural tract datasets. These planar representations improve the exploration of brain connectivity by reducing visual and interaction complexity. In visualization, we contribute to structure-preserving color mappings. First, we introduce Boy's surface as a model for coloring 3D line fields and show results from its application in visualizing orientation in diffusion MRI brain datasets. This coloring method is smooth and one-to-one except on a set of measure zero. Second, we propose a general coloring method based on manifold embedding that conveys spatial relations among neural fiber tracts perceptually. We also introduce a new bivariate coloring model, the flat torus, that allows finer adjustments of coloring arbitrarily. We contribute to both local and global analysis of brain connectivity. In local analysis, we introduce a geometric slicing-based coherence measure for clusters of neural tracts. Clustering refinement based on this measure leads to a significant improvement in clustering quality that is not possible directly with standard methods. We also introduce tract-based probability density functions and demonstrate their effective use in nonparametric hypothesis testing and classification. In global analysis, we propose computing the ranks of persistent homology groups in the neural tract space. This captures the effects of diffuse axonal dropout and provides a global descriptor of structural brain connectivity.
Demiralp, Cagatay,
"Computational Brain Connectivity Using Diffusion MRI"
(2012).
Computer Science Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://doi.org/10.7301/Z0N014V6
