Deformation morphometry is arguably the most powerful approach ever developed to detect and analyze morphological changes in the living brain.
We and others have been developing nonlinear image deformation programs with extraordinary power to track subtle volumetric changes throughout the brain, in populations of hundreds of subjects scanned repeatedly with MRI. We use illustrative data and time-lapse movies to show detailed maps of growth processes in the living brains of children, as well as clinical applications to tracking brain degeneration in HIV/AIDS, Alzheimer’s disease and in methamphetamine users. We combine several new concepts in information theory and continuum mechanics to improve detection power in brain morphometry. We first describe a fluid registration approach to minimize the Jensen-Rényi divergence between pairs of images - to map brain changes over time in exquisite detail.
We use Bayesian prior distributions derived from information theory, such as the Chernoff distance on deformations, as well as Lie group statistics and Riemannian elasticity to identify abnormal brain changes with more statistical power, and less bias, than standard approaches. Using information theory again, we apply the symmetrized Kullback-Leibler (KL) divergence (or J-divergence) to align high angular resolution diffusion images (HARDI) with a fluid deformation. We describe examples where our collaborators use these tools to detect morphometric changes in longitudinal MRI and DTI data, processing thousands of images automatically. We will also present some open questions as a challenge for future development in the field. This is joint work with my students and postdocs Ming-Chang Chiang, Natasha Lepore, Caroline Brun, Agatha Lee and Alex Leow, and our colleagues Yalin Wang, Stanley Osher, Guillermo Sapiro, Xavier Pennec, and Arthur Toga. See http://www.loni.ucla.edu/~thompson/MATH/math.html for ongoing mathematical projects.