Numerical model of electrical potential within a human head

This paper is made available with the permission of the Australian Mathematical Society Inc. Copyright © Australian Mathematical SocietyAreas of activity within the human brain can result from a variety of external stimuli. This paper discusses a technique for determining the location of sources of this activity as a result of some stimulus. Source location inside a human head is determined numerically by way of coupled forward and inverse models. The forward model determines the electrical potential on the scalp as a result of a source inside the brain, and the inverse model uses measured values of electrical potential on the scalp to determine the location of the source. Previous models have used structural magnetic resonance imaging (sMRI) for determining the boundaries of the larger structures of the head, these being the white and grey matter of the brain, cerebrospinal fluid, skull and scalp. They have also assumed a homogeneous conductivity for each of these units. It has been shown, however, that the electrical conductivities of these substructures can vary considerably. A three-dimensional, finite-difference model of the human head is developed and compared against a known analytical solution. sMRI data is then used to define the grid size of the finite-difference model and the conductivities within these grid points. The forward model presented here uses conductivities obtained by assuming a functional relationship between the intensity values of the sMRI and conductivity.P.E. Rasser, M.D. Teubner and C.R. Clar