A Meshfree Solver for the MEG Forward Problem

Non-invasive estimation of brain activity via magnetoencephalography (MEG) involves an inverse problem whose solution requires an accurate and fast forward solver. To this end, we propose the method of fundamental solutions as a meshfree alternative to the boundary element method (BEM). The solution of the MEG forward problem is obtained, via the method of particular solutions, by numerically solving a boundary value problem for the electric scalar potential, derived from the quasi-stationary approximation of Maxwell's equations. The magnetic field is then computed by the Biot-Savart law. Numerical experiments have been carried out in a realistic single-shell head geometry. The proposed solver is compared with a state-of-the-art BEM solver. A good agreement and a reduced computational load show the attractiveness of the meshfree approach.