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 expl oit the full information in deformation tensor fields. In TBM, multi ple brain images are warped to a common neuroanatomical templat e via 3D nonlinear registration; the resulting deformation fields are analyzed statistically to identify group differences in anatomy. Rather than analyze the Jacobian determinant (volume expan sion factor) of these deformations, as is common, we retain the fu ll 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 analysiversus univariate tests of simpler tensor-derived indices: the Ja cobian determinant, the trace, geodesic anisotropy, and eigenval ues of the strain tensor, and the angle of rotation of its eigenvect ors. We detected consistent, but more extensive patterns of stru ctural abnormalities, with multivariate tests on the full tensor manifold. Their improved power was established by analyzing cumulati ve p-value plots using false discovery rate (FDR) methods, appr opriately controlling for false positives. This increased detection sensitivity may empower drug trials and large-scale studie s of disease that use tensor-morphometry.