Evaluating the Performance of the Hybrid Boundary Element- Finite Element (BE-FE) Method to Solve Electroencephalography (EEG) Forward Problem Based on the Mesh Quality: A Simulation Study

Purpose: The Boundary Element (BE) and Finite Element (FE) methods are widely used numerical techniques to solve the Electroencephalography (EEG) forward problem. However, the FE Method (FEM) has difficulty in simulating current dipoles due to singularity, and the BE method (BEM) cannot simulate inhomogeneous and anisotropic conductivity profiles. Recently, a hybrid BE-FE method has been proposed to benefit from the advantages of both BEM and FEM in solving the EEG forward problem. Generally, the type of mesh may significantly influence the results of numerical EEG forward solvers and should be carefully studied. Materials and Methods: In this paper, the performance of the hybrid BE-FE method is compared with an approach of FEM (partial integration) using three types of meshes. The ground truth is the analytical EEG forward solutions obtained from inhomogeneous and isotropic/anisotropic four-layer spherical head models with dipoles of radial and tangential directions at four eccentricities. Results: The minimum mean of Relative Difference Measure (RDM) obtained from Partial Integration (PI)-FEM is 0.0596 at 70% source eccentricity while by using the hybrid BE-FE method it is improved to 0.0251 at the same eccentricity. On the other hand, the maximum mean of Magnitude Ratio (MAG) obtained from PI-FEM is 0.6216 at 50% source eccentricity while it is improved to 0.9734 at the same eccentricity. Conclusion: The results show that the hybrid BE-FE method outperforms PI-FEM in solving the EEG forward problem using three types of meshes regarding RDM and MAG error criteria.