Joint Colloquium for the Department of Mathematics and the Department of Statistics
Florida State University
Februrary 4, 1999

Mathematical and Computer Modelling of the Human Brain

Monica K. Hurdal, Department of Mathematics, Florida State University

The visual cortex is often studied in investigations of the human brain because it constitutes a relatively large part of the cerebral cortex and conclusions regarding the visual cortex can be extended to other regions of the brain. Much of the information from the visual system is recognized as first being processed by the primary visual cortex and is then passed to other regions of the brain involved in more complex processing. If the head is modeled as three concentric spherical shells and neural sources of brain activity are modeled as dipoles, then a mathematical model which incorporates biophysical properties can be used to estimate the location of sources which generate a set of electrical potentials measured on the surface of the scalp. This model is known as dipole source localisation. Monte Carlo simulations and mathematical analysis verify the benefits of proposed improvements to the localisation model.

The primary visual cortex has a retinotopic mapping in that one spot in the retinal visual field maps directly to a spot on the primary visual cortex. However, there is disagreement as to the amount of cortex that is allocated to the representation of central vision or other portions of the visual field. A mathematical formulation of this mapping will be presented. Then, a model which uses dipole source localisation and various brain research technologies, including magnetic resonance imaging and visual evoked potentials, will demonstrate how this mapping can be investigated non-invasively in humans. Finally, it will be shown how conformal flat maps of the brain can be created which offer several advantages over existing flat mapping approaches and will assist in comparing functional and anatomical information within and between subjects.


Updated February 1999.
Copyright 1999 by Monica K. Hurdal. All rights reserved.