Propagation Model of Bio- Electric Potential through the Shells of the Brain

The discrepancy between potential distributions recorded on the scalp and on the cerebral cortex~ as a result of the electric field propagation through the surrounding shells, requires development of techniques which enable us to compute one distribution as a function of the other. The method presented is based on a physical model consistent with neurophysiological patterns~ and in which the sources (encephalitic charges and currents) are multipolar distributions. The general field equations, applied to a convenient closed domain, lead to a family of Helmholtz equations which govern the transmission of the potential pseudo-periodic components. Local boundary conditions having been imposed by the multipolar assumption, the solutions are deduced from an elementary source system. It is then shown that the distribution of the surface potential (on the scalp) is obtained by convolution of the cortical potential distribution and a transfer function which is a solution of the Helmholtz equation associated with an elementary source system. An approximation of the cortical distribution can be computed by discrete deconvclution. Finally, various simulation experiments on digital computer allowed us to test the model, by comparison with empirical data.