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 magnetoencephalographyforward problem for analyzing the complex activation patterns in the human brain. The forward problem isdevoted to compute the scalp potential and magnetic field distribution generated by a set of current sourcesrepresenting the neural activity, and in this paper, it has been approached by means of the smoothed particlehydrodynamics method suitably handled. The Poisson equation generated by the quasi-stationary Maxwell’s curlequations, by assuming Neumann boundary conditions has been considered, and the current sources have beensimulated by current dipoles. The adopted meshless particle model has provided good results in agreement withthe 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 uppersurface of a homogeneous sphere simulating the human brain. Simulation results obtained by simulating twoconcentric spheres with different conductivities are also reported. Moreover, in order to better assess the validity ofthe proposed approach, a realistic human brain cortex model has been also simulated and compared with boundaryelement method results. A satisfactory agreement has been reached.