Solving the EEG Forward Problem by FDM and FEM

Abstract

In this paper, the finite element method (FEM) and the finite difference method (FDM) were compared for the resolution of the 3D isotropic EEG forward problem, from the point of view of computational complexity and accuracy. The effects of dipole eccentricity and grid model size on solution accuracy and efficiency are addressed in the simulations. The present simulation study indicates that the numerical accuracy of FEM is more sensitive to tangential dipoles, while FDM is more sensitive to radial dipoles, and the FEM provides similar computational efficiency as FDM for equivalent number of elements. But the reconstruction of grid model for FEM is more complex than for FDM, especially to reconstruct the realistic head model. (9)-(11) . Among these methods, BME can only get the voltage distribution on the boundaries of each tissue, rather than the inside part of the whole volume like FEM and FDM can. Although FDM and FEM have higher demands on computer resource and calculation time, more and more work is inclined to adopt them for the swiftly developing computer science. Considering that the FDM can get more realistic models for arbitrary geometrical volumes from the CT and MRI data, we aim to compare the applications of the FDM and FEM in EEG forward solution. In this study, we introduce the application of FDM and FEM in the EEG forward problem solution. And then we analyze the effects of the dipole source and mesh process on the solution of the forward problem in a three spherical head model by simulations.