Generalized tensor-based morphometry of HIV/AIDS using multivariate statistics on deformation tensors.

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 3-D nonlinear registration; the resulting deformation fields are analyzed statistically to identify group differences in anatomy. Rather than study the Jacobian determinant (volume expansion factor) of these deformations, as is common, we retain the full deformation tensors and apply a manifold version of Hotelling's $T(2) test to them, in a Log-Euclidean domain. In 2-D and 3-D magnetic resonance imaging (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 deformation 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-based morphometry.

Three-dimensional preoperative maps of hippocampal atrophy predict surgical outcomes in temporal lobe epilepsy.

The authors used surface-based anatomic mapping to detect features of hippocampal anatomy that correlated with surgical outcomes in patients undergoing surgery for mesial temporal lobe epilepsy with hippocampal sclerosis. Compared with a seizure-free group, hippocampal profiles for the non-seizure-free group had greater diffuse ipsilateral atrophy and more region-specific contralateral atrophy in the anterior, lateral hippocampus. These atrophic regions may indicate areas of increased epileptogenicity, contributing to poorer surgical outcomes.

Brain structural mapping using a novel hybrid implicit/explicit framework based on the level-set method.

This paper presents a novel approach to feature-based brain image warping, by using a hybrid implicit/explicit framework, which unifies many prior approaches in a common framework. In the first step, we develop links between image warping and the level-set method, and we formulate the fundamental mathematics required for this hybrid implicit/explicit approach. In the second step, we incorporate the large-deformation models into these formulations, leading to a complete and elegant treatment of anatomical structure matching. In this latest approach, exact matching of anatomy is achieved by comparing the target to the warped source structure under the forward mapping and the source to the warped target structure under the backward mapping. Because anatomy is represented nonparametrically, a path is constructed linking the source to the target structure without prior knowledge of their point correspondence. The final point correspondence is constructed based on the linking path with the minimal energy. Intensity-similarity measures can be naturally incorporated in the same framework as landmark constraints by combining them in the gradient descent body forces. We illustrate the approach with two applications: (1) tensor-based morphometry of the corpus callosum in autistic children; and (2) matching cortical surfaces to measure the profile of cortical anatomic variation. In summary, the new mathematical techniques introduced here contribute fundamentally to the mapping of brain structure and its variation and provide a framework that unites feature and intensity-based image registration techniques.