A Riemannian model of regional degeneration of the hippocampus in Alzheimer´s disease

We develop a Riemannian model of shape of solids in 3D space to map and compare localized hippocampal atrophy in normal aging, conversion to Alzheimer´s disease (AD), and progression of the disorder over a 1-year period. The study is based on magnetic resonance scans of 428 subjects acquired 12 months apart by the Alzheimer´s Disease Neuroimaging Initiative. Shape geodesics are used to model the spatiotemporal evolution of the anatomy of the hippocampus of each subject and to uncover regional differences in shape that are characteristic of the three dynamical processes. We identify regions where changes in shape due to neurodegeneration in conversion to AD differs significantly from normal aging suggesting potential morphological markers of incipient AD.