Handling Anisotropic Conductivities in the EEG Forward Problem with a Symmetric Formulation

The electroencephalography (EEG) forward problem, the computation of the electric potential generated by a known electric current source configuration in the brain, is a key step of EEG source analysis. In this problem, it is often desired to model the anisotropic conductivity profiles of the skull and of the white matter. These profiles, however, cannot be handled by standard surface integral formulations and the use of volume finite elements is required. Leveraging on the representation theorem using an anisotropic fundamental solution, this paper proposes a modified symmetric formulation for solving the EEG forward problem by a surface integral equation which can take into account anisotropic conductivity profiles. A set of numerical results is presented to corroborate theoretical treatments and to show the impact of the proposed approach on both canonical and real case scenarios.