Brain Morphometry by Distance Measurement in a Non-Euclidean, Curvilinear Space

Inspired by the discussion in most recent neurological research about the role of callosal fiber connections with respect to brain asymmetry [1, 2] we developed a technique that can measure distances between brain hemispheres in a non-Euclidean, curvilinear space. The new technique is a generic morphometric tool for measuring minimal distances within and across 3-D structures, but the project described herein is focused on assessing brain asymmetry in schizophrenia research. We use segmented brain white matter as a mask and measure distances from the cortical gray/white matter boundary to the cross-section of the corpus callosum through white matter tissue. The midsagittal cut through the corpus callosum serves as a symmetry center between the two hemispheres. The method uses a 3-D extension of a graph search algorithm, called F*. We search for minimum cost paths between a seed point or a seed region, respectively, and all the other points in space, constrained by the mask acting as a cost matrix. The algorithm is not limited to binary masks but allows us to use the original inhomogeneity-corrected MR volume with appropriate transfer function as a cost matrix. The resulting distances are mapped to the cortical surface and differences on the two hemispheres can be visually compared. Distances were also projected back to the corpus callosum along their minimum cost trajectories to represent asymmetry by comparing left and right measurements. Whereas a comparison between homologous points and regions on each hemisphere and thus a complete brain asymmetry map is still in development, we can present preliminary results obtained by processing 11 3-D magnetic resonance data sets representing a normal control group.