Parallel transport in diffeomorphisms distinguishes the time-dependent pattern of hippocampal surface deformation due to healthy aging and the dementia of the Alzheimer's type

Hippocampal surface structure was assessed at twice 2 years apart in 26 nondemented subjects (CDR 0), in 18 subjects with early dementia of Alzheimer type (DAT, CDR 0.5), and in 9 subjects who converted from the nondemented (CDR 0) to the demented (CDR 0.5) state using magnetic resonance (MR) imaging. We used parallel transport in diffeomorphisms under the large deformation diffeomorphic metric mapping framework to translate within-subject deformation of the hippocampal surface as represented in the MR images between the two time points in a global template coordinate system. We then performed hypothesis testing on the longitudinal variation of hippocampal shape in the global template. Both subjects with early DAT and converters showed greater rates of hippocampal deformation across time than nondemented controls within every subfield of the hippocampus. In a random field analysis, inward surface deformation across time occurred in a non-uniform manner across the hippocampal surface in subjects with early DAT relative to the nondemented controls. Also, compared to the controls, the lateral aspect of the left hippocampal tail showed inward surface deformation in the converters. Using surface deformation patterns as features in a linear discriminant analysis, we were able to respectively distinguish converters and patients with early DAT from healthy nondemented controls at classification rates of 0.77 and 0.87, which were obtained in the same training set using the leave-one-out cross validation approach.