Modeling the Spatio-Temporal Electrical Activity of Neuron Sources

Abstract

An evolutionary dipole model is constructed describing the spatio-temporal behavior of the electric potential on the surface of the head (EEG data). An approach is proposed to the solution of the direct three-dimensional EEG problem (finding the induced field). This approach finds the solution as a semi-analytical representation of an approximate solution in spherical functions with indeterminate coefficients. The coefficients are then determined by least squares. The method works with arbitrary (nonspherical) boundary surfaces, unbounded regions, finite conductivity outside the head, and complex spatial dependence of electrical conductivity. A nonhomogeneous conductivity model is considered with conductivity varying sharply across layers. An accurate numerical solution can be obtained if the conductivity of the layers differs by a factor of 80, which ensures sufficient accuracy in estimating dipole localization. Optimal dipole placement is reconstructed by a genetic algorithm, which also determines the best combination and the best number of dipoles. The method works also when several brain zones are active simultaneously. During the iterative fitting of the dipole parameters to minimize the error functional, the evolution of the genetic algorithm is directly linked with the temporal variation of the EEG signal.