Eigenanatomy improves detection power for longitudinal cortical change

Abstract

We contribute a novel and interpretable dimensionality reduction strategy, eigenanatomy, that is tuned for neuroimaging data. The method approximates the eigendecomposition of an image set with basis functions (the eigenanatomy vectors) that are sparse, unsigned and are anatomically clustered. We employ the eigenanatomy vectors as anatomical predictors to improve detection power in morphometry. Standard voxel-based morphometry (VBM) analyzes imaging data voxel-by-voxel--and follows this with cluster-based or voxel-wise multiple comparisons correction methods to determine significance. Eigenanatomy reverses the standard order of operations by first clustering the voxel data and then using standard linear regression in this reduced dimensionality space. As with traditional region-of-interest (ROI) analysis, this strategy can greatly improve detection power. Our results show that eigenanatomy provides a principled objective function that leads to localized, data-driven regions of interest. These regions improve our ability to quantify biologically plausible rates of cortical change in two distinct forms of neurodegeneration. We detail the algorithm and show experimental evidence of its efficacy.

Fig. 1. The eigenanatomy basis functions

The original eigenvector (far left) has both positive and negative components. These are separated into the positive and negative vector components (middle figures). The sparse eigenanatomy approximation to v⁻ is shown at far right. Because the entries of v^s− are either zero or negative, the sign of v^s− can be changed to positive. Thus, v^s− is an interpretable measurement of the data and provides a weighted average of the original signal. Ultimately, the weighted average of the imaging data provided by v^s− is used as a predictor in regression. The same is done with v^s+. In the lower portion of the figure, we see reconstruction results from the eigenanatomy method—see the results section for more explanation.

Fig. 2. Statistical comparison

Eigenanatomy detects the most effects and also with smallest p-values (FTLD: q < 0.0015, AD: q < 0.002) versus the next best soft-SVD (FTLD: q < 0.0035, AD: q < 0.009). Different colors represent different eigenvectors / predictors. Note that multiple disjoint, but related, voxel clusters (i.e. a network) may be involved in an eigenanatomy vector. VBM detects 20 voxels in FTLD (q < 0.015). In AD, univariate results are more robust, likely due to the widespread nature of AD atrophy, and 1382 significant voxels (q < 0.0270) were detected.