Analytical solution of electric potential produced by a direct current point source located in a multilayered spherical volume conductor

A general analytical solution is derived for an electric potential produced by a direct current point source located at any position in a multilayered spherical volume conductor. Starting from Poisson's equation, the electric potential whose coefficients are rapidly got in the form of matrix expressions is obtained according to the boundary conditions. Simulation for a four-layered spherical volume conductor denoting the scalp, skull, cerebrospinal fluid and brain tissue proves that electric potential in this paper converges more rapidly in the whole region than that expressed only in spherical harmonics expansion form, and iterative times decrease. Electric potential contour and current streamline figures show that it is important to consider the effect of the low conductivity of skull on electric potential and current flow. The distribution of electric potential on the surface of sphere is discussed, which will be useful in electroencephalography inverse problems, and also in analyzing and interpreting the electric potential measurement.