Collaborators
De Witt Sumners and Phil Bowers, Department of Mathematics, Florida State
University;
Ken Stephenson, Deparment of Mathematics, University of Tennessee,
Knoxville;
Kelly Rehm, Kirt Schaper and David A. Rottenberg, VA Medical Center,
PET Imaging Center, University of Minnesota;
Kevin Kurtz, Department of Computer Science, Florida State University;
David C. Banks, School of Computational Science and Information Technology,
Florida State University.
Abstract
The cortical surface of the brain is very convoluted, with many folds and
fissures. It is known that most of the functional processing of the brain
occurs on the cortical surface but individual variability in folding
patterns makes it difficult to compare anatomical and functional data
across subjects. The cortical surface is topologically equivalent to a
sheet, so it is possible to "unfold" it and create a cortical flat map of
the brain. Flat maps of the cortical surface serve as a visualization tool
that can enhance the informational content of anatomical and functional
neuroimages by revealing spatial relationships that were not previously
apparent and by facilitating comparisons between individuals and groups of
subjects.
It is impossible to flatten a surface with intrinsic curvature (such as the brain) without introducing linear and areal distortion, but the Riemann Mapping Theorem proves that it is possible to preserve angular (conformal) information under flattening. I will describe a novel computational method which uses the mathematical theory of circle packings to create quasi-conformal flat maps of the cortical surface. Cortical maps obtained from this approach will be presented. These maps exhibit conformal behavior in that angular distortion is controlled and can be created in the Euclidean and hyperbolic planes and on a sphere. Möbius transformations can be used to interactively change the map focus and no extraneous cuts in the original cortical surface are required. A canonical coordinate system can be imposed on these maps. In addition, these maps are mathematically unique.