Diffusion tensor images (DTIs) provide information about deep white matter anatomy that structural magnetic resonance images typically fail to resolve. Non-linear registration of DTIs provides a way to capture the deformations of these structures that would otherwise go unobserved. Here we use an existing method that fully incorporates a useful vector space parameterization of diffeomorphisms, thereby allowing simple and well defined calculation of deformation statistics. An initial analysis of the statistics produced by registration of a group of 37 HIV/AIDS patients illustrates principal modes of deformation that are anatomically meaningful and that corroborate with previous findings. The registration method is developed by incorporating these modes into a statistical regularization criterion. Even though initial results suggest this new criterion over-constrains the registration method, we discuss plausible ways to address this.