A discontinuous Galerkin Method for the EEG Forward Problem

In order to perform accurate electroencephalography (EEG) source reconstruction, i.e., to localize the sources underlying a measured EEG, the electric potential distribution at the electrodes generated by a dipolar current source in the brain has to be simulated, the so-called EEG forward problem. Therefore, it is necessary to apply numerical methods that are able to take the individual geometry and conductivity distribution of the subject’s head into account. The finite element method (FEM) has shown high numerical accuracy with the possibility to model complex geometries and conductive features, e.g., white matter conductivity anisotropy. In this article we introduce and analyze the application of a Discontinuous Galerkin (DG) method, a finite element method that includes features of the finite volume framework, to the EEG forward problem. The DG-FEM approach allows to fulfill the conservation property of electric charge also in the discrete case, making it attractive for a variety of applications. Furthermore, as we show, it can alleviate modeling inaccuracies that might occur in head geometries when using classical FE methods, e.g., so-called “skull leakage effects” for skull compartments with a thickness in the range of the mesh resolution. Therefore, we derive a DG formulation of the FEM subtraction approach for the EEG forward problem and present first numerical results which highlight the advantageous features and the potential of the proposed approach.