Dr. Monica K. Hurdal
Florida State University, Department of Mathematics, Tallahassee, FL
Creating Quasi-Conformal Maps of the Human Brain using the Riemann Mapping
Theorem
Investigations of the human brain have revealed that most of the functional processing of the brain occurs on the surface of the brain in the thin layer called the grey matter. It is also known that the grey matter of the human brain is topologically equivalent to a sheet. A consequence of this is that there is great interest in unfolding or flattening this surface to create maps of the brain. Then functional brain activity from functional MRI scans and PET scans can be represented on these maps.
I am using a novel computer realization of the Riemann Mapping Theorem that uses circle packings to create quasi-conformal flat maps of the cortical surface obtained from MRI scans. This approach offers a number of advantages including maps can be created in the Euclidean and hyperbolic planes and on a sphere and the maps are mathematically unique. I will present some of the brain maps I have produced using this approach and discuss some of the mathematical, topological and computational challenges involved in creating brain maps.