Neuronal currents and EEG-MEG fields

In a recent paper by the author, Fokas and Hadjiloizi proved that a neuronal current within a spherical homogeneous conductor can be split into two orthogonal components in such a way that one component provides the electroencephalography (EEG)-related fields and the other component provides the fields related to magnetoencephalography (MEG). Hence, in spherical geometry, the EEG and MEG measurements contain no overlapping information about the current. In the present work, we utilize a new integral representation for the magnetic potential, introduced recently by Fokas, Kariotou and the author, to prove that this elegant property is not true once the highly symmetric spherical environment is abandoned. It seems that any ambiguity concerning overlapping information coming from EEG and MEG measurements has its origin in the fact that in most clinical applications the spherical model is used although the actual data never come from a perfect sphere.