Generalized Tensor-Based Morphometry of HIV/AIDS Using Multivariate Statistics on Strain Matrices

This paper investigates the performance of a new multivariate method for Tensor-Based Morphometry (TBM). Statistics on Riemannian manifolds are developed that exploit the full information in deformation tensor fields. In TBM, multiple brain images are warped to a common neuroanatomical template via 3D nonlinear registration; the resulting deformation fields are analyzed statistically to identify group differences in anatomy. Rather than analyze the Jacobian determinant (volume expansion factor) of these deformations, as is common, we retain the full strain tensor and apply a manifold version of Hotelling’s T 2 test to the strain matrices, in a log-Euclidean domain. In 2D and 3D MRI data from 26 HIV/AIDS patients and 14 matched healthy subjects, we compared multivariate tensor analysis versus univariate tests of simpler tensor-derived indices: the Jacobian determinant, the trace, geodesic anisotropy, and eigenvalues of the strain tensor, and the angle of rotation of its eigenvectors. We detected consistent, but more extensive patterns of structural abnormalities, with multivariate tests on the full tensor manifold. Their improved power was established by analyzing cumulative p-value plots using false discovery rate (FDR) methods, appropriately controlling for false positives. This increased detection sensitivity may empower drug trials and large-scale studies of disease that use tensor-morphometry.