Tensor-Based Surface Morphometry

We present a unified statistical approach to deformation-based morphometry applied to the cortical surface. The cerebral cortex has the topology of a 2D highly convoluted sheet. As the brain develops over time, the cortical surface area, thickness, curvature and total gray matter volume change. It is highly likely that such age-related surface deformations are not uniform. By measuring how such surface metrics change over time, the regions of the most rapid structural changes can be localized. By formulating the surface deformation in tensor geometry, surface flattening, which distorts the inherent geometry of the cortex, can be avoided. To increase the signal to noise ratio, diffusion smoothing, which generalizes Gaussian kernel smoothing to an arbitrary curved cortical surface, has been developed and applied to surface data. Afterwards, statistical inference on the cortical surface will be performed via random fields theory. As an illustration, we demonstrate how this new surfacebased morphometry can be applied in localizing the cortical regions of the gray matter tissue growth and loss in the brain images longitudinally collected in the group of children and adolescents.