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of the Human Brain With Reference to Cortical Magnification and Dipole Source Localisation in the Visual Cortex |

Mathematical and computer models are important tools that are available to investigate natural phenomena. They can be used to model many systems. In this thesis, mathematical models are developed, implemented and applied to research involving the human brain and in particular, the human visual cortex. The visual cortex constitutes a relatively large part of the cerebral cortex. It is often used in investigations of the human brain because conclusions regarding the visual cortex can be extended to other regions of the brain. Virtually all information from the visual system is recognised as first being processed by the primary visual cortex and is then passed to other regions of the brain involved in more complex processing.

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 is presented
and mapping functions which transform the surface representing the retina
to the surface representing the visual cortex are developed.**

If the head is modelled as three concentric spherical shells and
neural sources of brain activity are modelled 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. The forward
problem, which is the prediction of a potential distribution due to a given
electrical source is implemented, and the inverse problem, which is to
determine a dipole source that is the best generator of a given potential
distribution is solved in the least squares sense. **Monte Carlo simulations
and mathematical analysis show that the optimal reference electrode to use
in dipole analysis is a weighted version of the common average reference.**
Monte Carlo simulations are also used to investigate
the accuracy of confidence regions surrounding the estimated dipole parameters.

Subsequently, **a methodology for modelling a region of cortex from magnetic
resonance images is developed.** This methodology is applied to the
calcarine fissure and surrounding grey matter to produce a three dimensional
surface reconstruction of the visual cortex. This model is used to
provide anatomical constraints in the dipole source localisation model.
These models are then applied to visual evoked potential data obtained from
an experiment which uses a chromatic grating stimulus. **Results reveal
that these mathematical and computer models, combined with imaging and
experimental approaches, elicit new information and improved results in
investigations of the human brain.**

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Copyright 1998 by Monica K. Hurdal. All rights reserved.