Numerical approaches for dipole modeling in finite element method based source analysis

In EEG/MEG source analysis, a mathematical dipole is widely used as the “atomic” structure of the primary current distribution. When using realistic finite element models for the forward problem, the current dipole introduces a singularity on the right-hand side of the governing differential equation that has to be treated specifically. We evaluated and compared three different numerical approaches, a subtraction method, a direct approach using partial integration and a direct approach using the principle of Saint Venant. Evaluation and comparison were carried out in a four-layer sphere model using quasi-analytical formulas.