Modelling of brain sources using the modified saint Venant's method in FEM resolution of EEG forward problem

In order to reconstruct the electrical brain activities, both the inverse and the forward problems have to be solved. The inverse problem consists of finding brain activities (sources) which are responsible for the measured signals. The forward problem is calculating the potentials at the sensor electrodes placed on the scalp from a given source inside the brain. Its resolution involves models of head and models of sources. The finite-element method (FEM) is investigated in this paper for its ability to model realistic geometry and physical proprieties. However, using this method, the point source introduces singularity in the calculation and impacts the accuracy. Different techniques have been developed to avoid this singularity but the accuracy of the most techniques decrease as the current dipole approaches the interface of different tissues with different conductivities. In this paper, the forward problem is solved by the FEM using a spherical head model and the saint Venant's principle is used to avoid the source's singularity. Near the interface of different brain tissues, a modification on the saint Venant's method is introduced. Simulation results show that this new modification gives good accuracy as compared with the traditional approaches.