Metric distances between hippocampal shapes indicate different rates of change over time in nondemented and demented subjects

Abstract

In this article, we use longitudinal morphometry (shape and size) measures of hippocampus in subjects with mild dementia of Alzheimer type (DAT) and nondemented controls in logistic discrimination. The morphometric measures we use are volume and metric distance measures at baseline and follow-up (two years apart from baseline). Morphometric differences with respect to a template hippocampus were measured by the metric distance obtained from the large deformation diffeomorphic metric mapping (LDDMM) algorithm. LDDMM assigns metric distances on the space of anatomical images, thereby allowing for the direct comparison and quantization of morphometric changes. We also apply principal component analysis (PCA) on volume and metric distance measures to obtain principal components that capture some salient aspect of morphometry. We construct classifiers based on logistic regression to distinguish diseased and healthy hippocampi (hence potentially diagnose the mild form of DAT). We consider logistic classifiers based on volume and metric distance change over time (from baseline to follow-up), on the raw volumes and metric distances, and on principal components from various types of PCA analysis. We provide a detailed comparison of the performance of these classifiers and guidelines for their practical use. Moreover, combining the information conveyed by volume and metric distance measures by PCA can provide a better biomarker for detection of dementia compared to volume, metric distance, or both.

Figure 1

Generation of metric distances $d_k^{\{b,f\}}$ based on binary images for subjects k = 1,2,…,44 at baseline (b) and at follow-up (f).

Figure 2

Pair plots of the volume and metric distance measures 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. The numbers 1 and 3 stand for year 1 (i.e., baseline) and year 3 (i.e., follow-up), respectively.