Comparison of Standard and Riemannian Fluid Registration for Tensor-Based Morphometry in HIV/AIDS

Tensor-based morphometry (TBM) is an analysis approach that can be applied to structural brain MRI scans to detect group differences or changes in brain structure. TBM uses nonlinear image registration to align a set of images to a common template or atlas. Detection sensitivity is crucial for clinical applications such as drug trials, but few studies have examined how the choice of deformation model (regularizer or Bayesian prior) affects sensitivity. Here we tested a new registration algorithm based on a fluid extension of Riemannian Elasticity [17], which penalizes deviations from zero strain in a log-Euclidean tensor framework, but has the desirable property of enforcing one-to-one mappings. We compared it to a standard large-deformation continuummechanical registration approach based on hyperelasticity. To compare the sensitivity of the two models, we studied corpus callosum morphology in 26 HIV/AIDS patients and 12 matched healthy controls. We analyzed the spatial gradients of the deformation fields in a multivariate Log-Euclidean framework [1] [12] to map the profile of systematic group differences. In cumulative p-value plots, the Riemannian prior detected disease-related atrophy with greater signal-to-noise than the standard hyperelastic approach. Riemannian priors regularize the full multivariate deformation tensor, yielding statistics on deformations that are unbiased in the associated Log-Euclidean metrics. Compared with standard continuum-mechanical registration, these Riemannian fluid models may more sensitively detect disease effects on the brain.