The surface of the human brain is a highly folded structure with considerable differences in the folding patterns and anatomical variability between individuals. This variation makes it difficult to compare anatomical and functional information within and between subjects. An approach which attempts to overcome this problem is to visualize anatomical and functional data in a new way which facilitates comparison across subjects. Creating a flat map of the brain is one such approach.
The convoluted surface of cortical grey matter is topologically equivalent to a two-dimensional sheet. There is no way to flatten a piecewise flat simply connected curved surface without linear and areal distortion. However, the Riemann mapping theorem indicates that theoretically, conformal information can be preserved under flattening. Beginning with raw magnetic resonance imaging (MRI) data, I will demonstrate the difficulties and some solutions to creating a piecewise flat simply connected surface representing the human cerebellum. I will then describe and present results from a novel approach which attempts to flatten the cerebellar surface so that the conformal structure of the original surface is preserved in the flattened surface.