Abstract
There is controversy and debate regarding the
mechanisms involved in cortical fold formation. Current cortical
morphogenesis theories describe folding using tension-based or
cellular-based arguments. Modeling and understanding cortical folding
pattern formation is important for quantifying cortical development.
Hypotheses concerning brain growth and development can lead to
quantitative biomarkers of normal and abnormal brain growth. Cortical
folding malformations have been related to a number of diseases, including
autism and schizophrenia. In this seminar I will present a biomathematical
model for cortical folding pattern formation in the brain. This model
takes into account global cortex characteristics and can be used to model
folds across species as well as specific diseases involving cortical
pattern malformations that can occur in human brain folding patterns, such
as polymicrogyria. We use a Turing reaction-diffusion system to model
cortical folding. Turing systems have been used to study pattern formation
in a variety of biological applications. They use an activator and
inhibitor and under certain conditions a pattern forms. We use our model
to study how global cortex characteristics, such as shape and size of the
lateral ventricle, affect cortical pattern formation. Due to the complex
shape and individual variability in folding patterns and the surface-based
functional processing of the brain, “flat” maps of the brain can lead
to improved analysis, visualization and comparison of anatomical and
functional data from different subjects. It is impossible to flatten a
surface with intrinsic curvature (such as the brain) without introducing
linear and areal distortion but it is possible to preserve angular
(conformal) information under flattening. I will also discuss a method
called “circle packing” which I am using to generate quasi-conformal
maps of the human brain. I will present examples of some of the brain maps
I have created and discuss how 150-year-old and modern mathematics may be
applied to enable neuroscientists to better understand the functioning of
the human brain.
Biography
Dr. Monica K. Hurdal is an Associate Professor of
Biomathematics in the Department of Mathematics at Florida State
University (FSU) in Tallahassee, Florida. She was awarded her Ph.D. in
1999 from Queensland University of Technology, Australia in Applied
Mathematics. She completed her Bachelor of Mathematics degree in Computer
Science and Statistics at the University of Waterloo, Canada in 1991 and
worked in industry as a programmer for a few years in Canada and Australia
before completing a Master of Science degree in Applied Mathematics and
Psychology at the University of Newcastle, Australia in 1994. After
completing her Ph.D., Dr. Hurdal was a postdoctoral research associate for
two years at FSU in Mathematics and in Computer Science, working on
conformal flat mapping the human brain and received funding from the Human
Brain Project. She continued her research at Johns Hopkins University in
the Center for Imaging Science as a Research Scientist, followed by her
position in 2001 at FSU. Her research interests include applying topology,
geometry and conformal methods to analyzing and modeling neuroscientific
data from the human brain. She is developing models to study cortical
folding pattern formation and she is investigating topology issues
associated with constructing cortical surfaces from MRI data, computing
conformal maps of the brain and applying topological and conformal
invariants to characterize disease in MRI studies. Her research has been
featured in Scientific American and in The Economist.