Perturbation theory as a new analytical approach to the MEG forward problem for realistic volume conductor modeling of the head

Analytical solutions to the magnetic forward problem are known only for special volume conductors [1, 2, 3], which are insufficient to describe detailed head shapes. The forward calculation for a realistic volume conductor can so far only be solved by numerical algorithms, such as the boundary element method (BEM) [4, 5, 6, 7, 8, 9], which pose severe problems for superficial sources due to the discretization of the volume conductor surface. Here, we present an analytical approach using perturbation theory where we exploit the fact that for realistic head shapes the deviation of the inner skull from a spherical approximation is small compared to its radius.