The complete ellipsoidal shell-model in EEG imaging

This work provides the solution of the directElectroencephalography (EEG) problem for the complete ellipsoidalshell-model of the human head. The model involves four confocalellipsoids that represent the successive interfaces between thebrain tissue, the cerebrospinal fluid, the skull, and the skincharacterized by different conductivities. The electric excitationof the brain is due to an equivalent electric dipole, which islocated within the inner ellipsoid. The proposed model isconsidered to be physically complete, since the effect of thesubstance surrounding the brain is taken into account. The directEEG problem consists in finding the electric potential inside eachconductive space, as well as at the nonconductive exterior space.The solution of this multitransmission problem is givenanalytically in terms of elliptic integrals and ellipsoidalharmonics, in such way that makes clear the effect that each shellhas on the next one and outside of the head. It is remarkable thatthe dependence on the observation point is not affected by thepresence of the conductive shells. Reduction to simplerellipsoidal models and to the corresponding spherical models isincluded