A new finite element formulation for the forward problem of electro-magnetic source imaging

The voltage measurements on the scalp and magnetic field measurements near the scalp can be used to compute spatio-temporal evolution of electric currents across the cerebral cortex. Such a representation can be called Electro-Magnetic Source Image. In order to interpret the measured fields accurately, a realistic numerical model of the head should be prepared that includes physical properties and geometry of the individual's head. For that purpose, in this study, Finite Element Method (FEM) is used to solve the scalar potential function. A new FEM formulation is derived that assumes constant current density in isoparametric volume elements. A software is prepared by optimizing the code to run in a PC with 128 MB memory. It is shown that, for a current dipole at 2.5 cm from the origin, the potential distribution can be solved within an accuracy of 0.5% in comparison with the exact solutions, with a mesh of 29001 nodes and 7000 elements. In order to solve the magnetic held, the surface integration tools developed in the same FEM code are used. For the same dipole location the radial magnetic fields are calculated within an accuracy of 2.2%. Obviously, the accuracy in results can be increased by increasing the number of nodes.