A numerical meshless particle method in solving the magnetoencephalography forward problem

In this paper, a numerical meshless particle method is presented in order to solve the magnetoencephalography forward problem for analyzing the complex activation patterns in the human brain. The forward problem is devoted to compute the scalp potential and magnetic field distribution generated by a set of current sources representing the neural activity, and in this paper, it has been approached by means of the smoothed particle hydrodynamics method suitably handled. The Poisson equation generated by the quasi-stationary Maxwell’s curl equations, by assuming Neumann boundary conditions has been considered, and the current sources have been simulated by current dipoles. The adopted meshless particle model has provided good results in agreement with the analytical ones and by overcoming the drawback of the mesh generation. The numerical model has been validated, at first, in computing the electric potential and the external magnetic field for a dipole plunged near the upper surface of a homogeneous sphere simulating the human brain. Simulation results obtained by simulating two concentric spheres with different conductivities are also reported. Moreover, in order to better assess the validity of the proposed approach, a realistic human brain cortex model has been also simulated and compared with boundary element method results. A satisfactory agreement has been reached.