A discontinuous Galerkin Method for the EEG Forward Problem using the Subtraction Approach

TL;DR

This paper introduces a discontinuous Galerkin finite element method for solving the EEG forward problem, improving accuracy and charge conservation, and reducing modeling errors like skull leakage effects.

Contribution

It develops a novel DG-FEM formulation for the EEG forward problem based on the subtraction approach, enhancing modeling robustness and numerical properties.

Findings

DG-FEM preserves charge conservation in discretization.

The method reduces skull leakage effects in head models.

Numerical results demonstrate improved accuracy over classical FEM.

Abstract

In order to perform 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, which is the so-called EEG forward problem. To solve it accurately, 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. In this context, 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 fulfills the conservation property of electric charge also in the discrete case, making it attractive for a variety of applications. Furthermore, as we show, this approach can alleviate modeling inaccuracies that might occur in head geometries when using classical FE methods, e.g., so-called "skull leakage effects", which may occur in areas where the thickness of the skull is 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 numerical results that highlight the advantageous features and the potential benefits of the proposed approach.