Quantization and analysis of hippocampal morphometric changes due to dementia of Alzheimer type using metric distances based on large deformation diffeomorphic metric mapping

Abstract

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.

Figure 1

Change in metric distance during diffeomorphic flow from template (I₀) to target ( $I_1={\varphi }_1{I}_0=I_0\circ {\varphi }_1^{-1}$). The numbers are the metric distance estimates at the three intermediate stages and the final stage of the LDDMM algorithm.

Figure 2

Generation of metric distances $d_k^{\{b,f\}}$ for subjects k = 1, … , 44 at baseline (b) and at follow-up (f).

Figure 3

Pairs plots of the continuous variables for the hippocampi at baseline and follow-up. HLV: volume of left hippocampus; HRV: volume of right hippocampus; HLM: metric distance for left hippocampus; HRM: metric distance for right hippocampus; BV: brain volume; ICV: intracranial volume. The numbers 1 and 3 stand for year 1 (i.e., baseline) and year 3 (i.e., follow-up), respectively.

Figure 4

Scatter plots of the metric distances for the left and right distances at baseline and follow-up. The metric distances are jittered for better visualization and the crosses represent the mean distance values.

Figure 5

Interaction plots for diagnosis levels over the timepoint levels for left and right metric distances demonstrating that the slopes are different between diagnostic groups (with slope differences in the right being larger).

Figure 6

Fitted probability for having mild dementia (CDR0.5) and observed proportion in metric distances with model (9) (top-left); model (10) (top-right); and model (11) (bottom),