A hybrid boundary element-finite element method to solve the EEG forward problem

This article presents a hybrid boundary element-finite element (BE-FE) method to solve the EEG forward problem and take advantages of both the boundary element method (BEM) and finite element method (FEM). Although realistic EEG forward problems with heterogeneous and anisotropic regions can be solved by FEM accurately, the FEM modeling of the brain with dipolar sources may lead to singularity. In contrast, the BEM can solve EEG forward problems with isotropic tissue regions and dipolar sources using a suitable integral formulation. This work utilizes both FEM and BEM strengths attained by dividing the regions into some homogeneous BE regions with sources and some heterogeneous and anisotropic FE regions. Furthermore, the BEM is applied for modeling the brain, including dipole sources and the FEM for other head layers. To validate the proposed method, inhomogeneous isotropic/anisotropic three- and four-layer spherical head models are studied. Moreover, a four-layer realistic head model is investigated. Results for six different dipole eccentricities and two different dipole orientations are computed using the BEM, FEM, and hybrid BE-FE method together with statistical analysis and the related error criteria are compared. The proposed method is a promising new approach for solving realistic EEG forward problems.