The metric distance obtained from the large deformation diffeomorphic metric mapping (LDDMM) algorithm is used to quantize changes in morphometry of brain structures due to neuropsychiatric diseases. For illustrative purposes we consider changes in hippocampal morphometry (shape and size) due to very mild dementia of the Alzheimer type (DAT). LDDMM, which was previously used to calculate dense one-to-one correspondence vector fields between hippocampal shapes, measures the morphometric differences with respect to a template hippocampus by assigning metric distances on the space of anatomical images thereby allowing for direct comparison of morphometric differences. We characterize what information the metric distances provide in terms of size and shape given the hippocampal, brain and intracranial volumes. We demonstrate that metric distance is a measure of morphometry (i.e., shape and size) but mostly a measure of shape, while volume is mostly a measure of size. Moreover, we show how metric distances can be used in cross-sectional, longitudinal analysis, as well as left-right asymmetry comparisons, and provide how the metric distances can serve as a discriminative tool using logistic regression. Thus, we show that metric distances with respect to a template computed via LDDMM can be a powerful tool in detecting differences in shape.
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