Boundary element method (BEM)

The boundary element method (BEM) is a numerical technique for solving the EEG/MEG forward problem in a realistically shaped, piecewise-homogeneous head model. It assumes each compartment (brain, skull, scalp) has constant isotropic conductivity, so the governing equation can be reformulated as an integral equation posed only over the compartment boundaries. The surfaces are tessellated into triangles, and the potential (or a secondary source density) is solved at the surface nodes.

BEM's advantage is efficiency: only two-dimensional surfaces are meshed rather than the whole three-dimensional volume, giving accurate solutions for smooth, nested surfaces at modest computational cost. Its limitation is the piecewise-constant, isotropic assumption — it cannot represent skull anisotropy, local conductivity inhomogeneities, or holes and lesions. For those, the finite element method is required.