Abstract and Applied Analysis
Volume 2006 (2006), Article ID 57429, 18 pages

The complete ellipsoidal shell-model in EEG imaging

S. N. Giapalaki1 and F. Kariotou2

1Department of Chemical Engineering, University of Patras, Patras 26504, Greece
2Hellenic Open University, 16, Sahtouri Street & Ag. Andreou Street, Patras 262 22, Greece

Received 5 December 2004; Accepted 16 December 2004

Copyright © 2006 S. N. Giapalaki and F. Kariotou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This work provides the solution of the direct Electroencephalography (EEG) problem for the complete ellipsoidal shell-model of the human head. The model involves four confocal ellipsoids that represent the successive interfaces between the brain tissue, the cerebrospinal fluid, the skull, and the skin characterized by different conductivities. The electric excitation of the brain is due to an equivalent electric dipole, which is located within the inner ellipsoid. The proposed model is considered to be physically complete, since the effect of the substance surrounding the brain is taken into account. The direct EEG problem consists in finding the electric potential inside each conductive space, as well as at the nonconductive exterior space. The solution of this multitransmission problem is given analytically in terms of elliptic integrals and ellipsoidal harmonics, in such way that makes clear the effect that each shell has on the next one and outside of the head. It is remarkable that the dependence on the observation point is not affected by the presence of the conductive shells. Reduction to simpler ellipsoidal models and to the corresponding spherical models is included.