Electric potential and impedance for three-layered spherical volume conductor with spherical bubble with four-electrode system

The model for three-layered spherical volume conductor with eccentric spherical bubble with four-electrode system is built. The three layers respectively denote scalp, skull and brain, and eccentric spherical bubble denotes the pathological region of brain. Starting from Laplace's equation, and according to the boundary conditions at the interface of two adjacent media and the finite conditions at the center of sphere and infinity, analytical solutions of electric potential and impedance are derived. Theoretical values of electric potential are in accordance with the experimental values. There is very little difference between the analytical solution in this paper and the results by Finite element method (FEM). Simulation results show that conductivity and eccentricity changes of spherical bubble affect electric potential largely.