Detecting dynamic and genetic effects on brain structure using high-dimensional cortical pattern matching

We briefly describe a set of algorithms to detect and visualize effects of disease and genetic factors on the brain. Extreme variations in cortical anatomy, even among normal subjects, complicate the detection and mapping of systematic effects on brain structure in human populations. We tackle this problem in two stages. First, we develop a cortical pattern matching approach, based on metrically covariant partial differential equations (PDEs), to associate corresponding regions of cortex in an MRI brain image database (N=102 scans). Second, these high-dimensional deformation maps are used to transfer within-subject cortical signals, including measures of gray matter distribution, shape asymmetries, and degenerative rates, to a common anatomic template for statistical analysis. We illustrate these techniques in two applications: (1) mapping dynamic patterns of gray matter loss in longitudinally scanned Alzheimer´s disease patients; and (2) mapping genetic influences on brain structure. We extend statistics used widely in behavioral genetics to cortical manifolds. Specifically, we introduce methods based on h-squared distributed random fields to map hereditary influences on brain structure in human populations.