The application of imaginary method in EEG forward question of eccentric spheres models

In this paper, we present a novel method to calculate the scalp potential distribution produced by the inside dipoles of the EEG forward question in detail: imaginary method. Using this method, the eccentric spheres models of the head can be simplified to the homocentric spheres model. The scalp potential distribution of the forward question of EEG of the homocentric spheres model can be solved easily. Using the imaginary method, the influence of the inside eccentric sphere can be replaced by some imaginary dipoles, the imaginary surplus single poles and the fractal single poles as well as fractal dipole. For the question in which the centers of the spheres and the position of the dipole are not in the same line, the analytical solution can be obtained, while the conventional method can only give the analytical solution in the case where all the centers of the spheres and the point of the dipole are in the same line. At last, we validate this method through computer simulation. By comparing the results from the imaginary method, the conventional method and the finite element method FEM (Although FEM can give more precise solution, but it cannot give the analytical solution, which is necessary when solve the reverse question.), the validity of this method is proven