Analytical solution of electric potential produced by a direct current point source located in a multilayered spherical volume conductor
分层球形导体中任意位置直流电流元产生电位的解析解

A general analytical solution is derived for an electric potential produced by a direct current point source located at any position in a multilayered spher ical 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 whol e region than that expressed only in spherical harmonics expansion form, and ite rative times decrease. Electric potential contour and current streamline figur es show that it is important to consider the effect of the low conductivity of s kull on electric potential and current flow. The distribution of electric potent ial on the surface of sphere is discussed, which will be useful in electroenceph alography inverse problems, and also in analyzing and interpreting the electric potential measurement.