Analytic expansion of the EEG lead field for realistic volume conductors

EEG forward calculation in realistic volume conductors using the boundary element method suffers from the fact that the solutions become inaccurate for superficial sources. Here we propose to correct an analytical approximation of the respective lead fields with series of spherical harmonics with respect to multiple expansion points. The necessary correction depends very much on the chosen analytical approximation. We constructed the latter such that the correction can be modelled adequately within the chosen basis. Simulations for a 3-shell prolate spheroid demonstrate the accurate modelling of the lead fields. Explicit comparison with analytically known solutions was done for the 3-shell spherical volume conductor showing that relative errors are mostly far below 1% even for the most superficial sources placed directly on the innermost surface.