Surface-based approaches for spatial normalization of the cerebral cortex: Geometry-driven cortical mappings for structural and functional analysis

The increasing interest in carrying out studies with large numbers of subjects to understand the structure and function of the human cerebral cortex brings a major challenge to develop automated spatial normalization methods that allow analysis of data from multiple subjects in a standard coordinate system. The focus of this dissertation is the development of a methodology for geometry-driven cortical surface normalization that will automatically identify homologous cortical structures and map them to the same coordinates on a standard manifold, and the subsequent use of this spatial normalization technique in neuroscience applications. This work addressed two key challenges in the spatial normalization of the cerebral cortex: automatic identification of homologous cortical structures and development of geometry-driven mapping techniques to provide a standard coordinate system on the cerebral cortex. In addition, the spatial normalization technique is applied to a number of human brain magnetic resonance images and we carry out several structural and functional analysis studies to show the utility of this technique in neuroscience studies.; In this research, we make four major contributions. First, we have conducted two different studies to assess the accuracy and precision on the reconstruction of cortical surfaces. The spatial normalization technique aligns homologous cortical landmarks on a standard manifold only if the original cortical surfaces are accurate in representing the cortical geometry. Second, we have developed a conformal mapping technique with minimum metric distortion, providing a well-defined spherical coordinate system on the cortex. Third, we have developed unfolding methods based on the conformal mapping which automatically yield maps on the spherical surface on which the major sulcal regions of any brain are mapped to approximately the same location. Finally, we have enhanced the surface mapping to a geometry mapping technique that leads to the possibility of providing a standard cortical map. A detailed analysis of the cortex has been performed using shape measures to get an implicit representation of the key anatomical features. This was followed by an optical flow warping technique aiming to match shape measures of individuals. Using this feature matching procedure after cortical unfolding yields a spatial normalization method for the cortical surface.