Two confocal ellipsoids are employed for modeling the human head in the direct Electroencephalography (EEG) problem. The internal ellipsoid represents the surface of the brain tissue, while the space between the two ellipsoids models the membranes, fluid, bone and scalp, which have different conductivity from that of the brain. 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 more realistic than the single ellipsoidal one, since the effect of the substance surrounding the brain is now taken into account. The direct EEG problem consists in finding the electric potential inside the conductive core and the ellipsoidal shell, as well as at the non ? conductive exterior space. The solution of this transmission problem is given analytically in terms of elliptic integrals and ellipsoidal harmonics. Reduction to the single ellipsoidal and the spherical ? shell model recovers corresponding known results. Comparing the analytic expressions obtained for the exterior potential for the cases of the single and of the double ellipsoidal model, we observe that in the second one a more complicated factor appears in every multipole term. This factor is expressed in terms of the conductivity of the shell as well as the difference of the two conductivities and depends on the geometrical parameters of the two ellipsoidal boundaries. In the case of equal conductivities, or when the two ellipsoids coincide this factor reduces to the conductivity of the single model.

Στοιχεία Άρθρου

Περιοδικό	Δελτίο της Ελληνικής Μαθηματικής Εταιρίας
Αρ. Τεύχους	Τεύχος 50
Περίοδος	2005
Συγγραφέας	F. Kariotou, G. Kamvyssas
Αρ. Αρθρου	11
Σελίδες	119-133
Γλώσσα	-
Λέξεις Κλειδιά	-

Confocal Ellipsoidal Boundaries in EEG Modeling