Conventional and Reciprocal Approaches to the Forward Problem of Electroencephalography

The conventional approach to forward problem solutions in electroencephalography entails computing the surface potentials starting from source current dipoles. The reciprocal approach, on the other hand, first solves for the electric field at the source dipole location when the surface electrodes are reciprocally energized with a unit current. A scalar product of this electric field with the source dipole then yields the surface potential. Using a common weighted-residual formulation, this paper initially develops the boundary-element field equations for both approaches, next describes the discretization and matrix deflation techniques to be used with them, and, using a three-concentric-spheres head model, finally evaluates their performance for two widely different skull conductivities. It was found that while a conventional vertex method, in which the desired potentials are calculated at the vertices as opposed to the centroids of the discretization triangles, in general yields the most accurate forward solutions for skull conductivities close to recently measured values, the reciprocal approaches offer the least variation in error for different skull conductivities.