In this paper a multisphere particle method is developed to estimate the solution of the Poisson's equation with Neumann boundary conditions describing the neuronal human brain activity. The partial differential equations governing the relationships between neural current sources and the data produced by neuroimaging technique, are able to compute the scalp potential and magnetic field distributions generated by the neural activity. A numerical approach is proposed with current dipoles as current sources and going on in the computation by avoiding the mesh construction. The current dipoles are into an homogeneous spherical domain modeling the head and the computational approach is extended to multilayered configuration with different conductivities. A good agreement of the numerical results is shown compared for the first time with the analytical ones.
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