Tensor-based morphometry (TBM) is widely used in computational anatomy as a means to understand shape variation between structural brain images. A 3D nonlinear registration technique is typically used to align all brain images to a common neuroanatomical template, and the deformation fields are analyzed statistically to identify group differences in anatomy. However, the differences are usually computed solely from the determinants of the Jacobian matrices J that are associated with the deformation fields computed by the registration procedure. Thus, much of the information contained within those matrices gets thrown out in the process. Only the magnitude of the expansions or contractions is examined, while the anisotropy and directional components of the changes are ignored. Here we remedy this problem by computing multivariate shape change statistics using the strain matrices, defined as (JT J)1=2. As the strain matrices belong to the space of positive-definite matrices, we first transform them into a vector space using the 'Log-Euclidean metric' [1].We study the brain morphology of 26 HIV/AIDS patients and 14 matched healthy control subjects using our method. The goal of the work was to find out whether multivariate statistics on the strain tensor afforded additional power in detecting anatomical differences between patients and controls. The images are registered using a high-dimensional 3D fluid registration algorithm, which optimizes the Jensen-R'enyi divergence [2], an information-theoretic measure of image correspondence. A pixelwise Hotelling T2 test is used as a measure of variation between patients and controls. To assess the difference between our results and the ones found from the determinant of the Jacobian, these results are compared to the one-dimensional Student's t test on the determinant of the Jacobian matrices. Patterns of detected white matter atrophy were of greater spatial extent and the corresponding effect size was greater in the case of Hotelling's T2 test, indicating its better sensitivity. Group differences in brain structure between AIDS patients and healthy subjects are visible throughout the brain, with the greatest effect sizes in the corpus callosum and the basal ganglia. The cortical region is noisier, perhaps because the registration method is intensity-based and does not perform as well in that area. The anatomical profile of group differences is in line with studies using traditional volumetric methods, as the HIV virus is known to cause widespread neuronal loss and corresponding atrophy of the gray and white matter, especially in subcortical regions. Multivariate statistics on matrix-valued measures derived from deformation fields may therefore provide greater power to detect structural differences in the brain than more conventional methods that use the Jacobian determinant alone.