Surface Shape Morphometry for Hippocampal Modeling in Alzheimer's Disease

Shape morphometry of subcortical surfaces plays an important role in analyzing normal developmental changes as well as in quantifying disease-related effects in the human brain. We present a geometric approach for joint registration, deformation, and statistical analysis of shapes of subcortical surfaces. Here, subcortical surfaces are mathematically represented by vector-fields, termed square-root normal vector fields (SRNFs), on the spherical domain. The SRNF representation allows modeling of the action of the re-parameterization group to by isometries under the standard Hilbert norm, and thus enables an elastic shape analysis. This elastic analysis results in optimal deformations between shapes and helps to quantify shape differences using geodesic lengths. Importantly, the joint registration of observed shapes in a shape class removes nuisance variability due to mis-registration in the shape data and results in parsimonious statistical shape models with improved inferences for characterizing population-based subcortical structural variability. We demonstrate the ideas for shape matching and statistical analysis of hippocampal shapes for (N=120) subjects from the Alzheimer's disease Neuroimaging Initiative (ADNI) dataset. Specifically, we present results for assessing group differences both by using global descriptors such as principal components and local descriptors such as deformations induced by the tangent vectors from the mean shapes to the individuals.