On the Geometric Sensitivity of the EEG Inversion Algorithm

Electroencephalography (EEG) is a noninvasive method of brain imaging. In particular, the inverse EEG problem consists of identifying the electrical activity inside the brain from measurements of the electric potential on the scalp. Since the mathematics of EEG are modeled by a linear boundary value problem with sources which are distributed electric dipoles, it follows that the main effort is focused in the problem of identifying the location and the moment of a single dipole from recorded EEG data. In medical practice the developed algorithms for this problem are based on the assumption that the brain is a sphere. However, the realistic model of the shape of the brain is that of an ellipsoid. Consequently, that generates an error on the medical practice due to the interpretation of the data, which are obtained on an ellipsoidal figure and are processed as they were obtained on a sphere. The present work provides an analysis of this problem and proves that for moderate values of the principal eccentricities of the ellipsoid the error remains insignificant, while as the values of the eccentricities increase the error becomes large. The comparison is between a realistic ellipsoid and a sphere of equal volume. In fact, discrepancies higher than 20% are found when the maximum eccentricity of the ellipsoid becomes larger than 0.9. Fortunately, the principal eccentricities of the human brain are within the region of insignificant errors and therefore the credibility of the medical practice is saved.