Bioelectromagnetic forward problem: isolated source approach revis(it)ed

Electro- and magnetoencephalography (EEG and MEG) are non-invasive modalities for studying the electrical activity of the brain by measuring voltages on the scalp and magnetic fields outside the head. In the forward problem of EEG and MEG, the relationship between the neural sources and resulting signals is characterized using electromagnetic field theory. This forward problem is commonly solved with the boundary-element method (BEM). The EEG forward problem is numerically challenging due to the low relative conductivity of the skull. In this work, we revise the isolated source approach (ISA) that enables the accurate, computationally efficient BEM solution of this problem. The ISA is formulated for generic basis and weight functions that enable the use of Galerkin weighting. The implementation of the ISA-formulated linear Galerkin BEM (LGISA) is first verified in spherical geometry. Then, the LGISA is compared with conventional Galerkin and symmetric BEM approaches in a realistic 3-shell EEG/MEG model. The results show that the LGISA is a state-of-the-art method for EEG/MEG forward modeling: the ISA formulation increases the accuracy and decreases the computational load. Contrary to some earlier studies, the results show that the ISA increases the accuracy also in the computation of magnetic fields.