Author details

minimum error. Another characteristic example of rigorous mathematical analysis is the quantitative description of the non-uniqueness for the EEG inverse problem, presented in Ref. [36]. Therein, splitting the current into components, the authors prove that none of those components contributes to both the electric and scalar magnetic potential; in other words, recordings of EEG and MEG do not contain overlapping information about the current. However, afore-

Analogous conclusions are valid for the ellipsoidal geometry as well. For example, the authors consider in Ref. [37] the frequent case when clinical data of unknown origin are implemented in computational simulations. We mentioned earlier that there exist a plethora of combinations of the product a1, a2, a<sup>3</sup> furnishing the same value for the volume of the brain. If we look at the instance where EEG measurements originate from a brain with fixed values a1, a2, a<sup>3</sup> but are interpreted in the sequel by different values, what would be the error? Well, it turns out that the error can reach as high as 20%, depending on the position and strength of the primary current.

The error analysis presented in Ref. [37] can be considered as rather straightforward, since both ellipsoids under consideration were confocal, that is, members of the same ellipsoidal system enjoying the same foci. In plain words, no member of a confocal family touches another. Consequently, there exists a single curve, which cuts both ellipsoids normally, and the corresponding intersecting points consist of the most proximate pair between the two ellipsoids in each direction. These two points are employed in the analysis calculating the aforementioned error. But what would happen if the two ellipsoids would not be considered

In order to provide an answer to the latter, a sophisticated correspondence is needed connecting two points on the surface of two ellipsoids which are now non-confocal. This means that there probably exists a point shared by both ellipsoids. In Ref. [38], the authors investigated the effect implied by a deviation of the eccentricities of the ellipsoidal model on the electric potentials

Turning our attention from the geometrical deformation of the conductor model, to the physical assumption of homogeneity, we acknowledge the significance of the non-homogeneity imposed by the layers of different conductivity that cover the host tissue of the EEG source. The conductive elements that constitute the scalp, the scull and the meninges, which interfere between the EEG measurements and the cerebrum, are affected by the electromagnetic field produced by activation of the source. Hence, they induce a volume current that perturbs the total electric potential registered on the EEG receptors on the scalp. The effect of this physical perturbation of the potential has been studied by incorporating a layered conductivity profile in all the models discussed in the present review, by characterizing each layer by a distinct but

Indicatively, we infer that switching to a layered ellipsoidal model of the head-brain system, the functional form of the electric potential, is basically unaltered. One of the authors has showed [39] that the conductivity profile of the layered structure enters the potential formula by normalizing each term by a constant which incorporates the conductivity jumps across the interfaces and the geometrical characteristics of the layers. Analogous results show a similar

registered as the EEG data. In this case, the error reaches high values up to almost 100%.

mentioned property holds no longer true if the spherical conductor is disregarded.

to be confocal? This interesting case is also more realistic.

constant conductivity value.

50 Electroencephalography

Michael Doschoris<sup>1</sup> \* and Foteini Kariotou<sup>2</sup>

\*Address all correspondence to: mdoscho@chemeng.upatras.gr

1 Department of Chemical Engineering, University of Patras, University Campus, Patras, Hellas

2 School of Science & Technology, Hellenic Open University, Patras, Hellas
