A hemispherical map for the human brain cortex

Understanding the function of the human brain cortex is a primary goal in human brain mapping. Visualization and mapping of function on the cortical surface, however, is difficult because of its sulcal and gyral convolutions. Methods to unfold and flatten the cortical surface for visualization and measurement have been described in the literature. This makes visualization and measurement possible, but comparison across multiple subjects is still difficult because of the lack of a standard mapping technique. We describe a new approach that maps each hemisphere of the cortex to a portion of a sphere in a standard way, making comparison of anatomy and function across different subjects possible. Starting with a three-dimensional magnetic resonance image of the brain, the cortex is segmented and represented as a triangle mesh. Defining a cut around the corpus collosum identifies the left and right hemispheres. Together, the two hemispheres are mapped to the complex plane using a conformal mapping technique. A Mobius transformation, which is conformal, is used to transform the points on the complex plane so that a projective transformation maps each brain hemisphere onto a spherical segment comprising a sphere with a cap removed. We determined the best size of the spherical cap by minimizing the relative area distortion between hemispherical maps and original cortical surfaces. The relative area distortion between the hemispherical maps and the original cortical surfaces for fifteen human brains is analyzed.