Modeling the effects of electric fields on nerve fibers: influence of tissue electrical properties

The effects of anisotropy and inhomogeneity of the electrical conductivity of extracellular tissue on excitation of nerve fibers by an extracellular point source electrode were determined by computer simulation. Analytical solutions to Poison's equation were used to calculate potentials in anisotropic infinite homogeneous media and isotropic semi-infinite inhomogeneous media, and the net driving function was used to calculate excitation thresholds for nerve fibers. The slope and intercept of the current-distance curve in anisotropic media were power functions of the ratio and product of the orthogonal conductivities, respectively. Excitation thresholds in anisotropic media were also dependent on the orientation of the fibers, and in strongly anisotropic media (sigma z/sigma xy > 4) there were reversals in the recruitment order between different diameter fibers and between fibers at different distances from the electrode. In source-free regions of inhomogeneous media (two regions of differing conductivity separated by a plane boundary), the current-distance relationship of fibers parallel to the interface was dependent only on the average conductivity, whereas in regions containing the source the current-distance relationship was dependent on the individual values of conductivity. Reversals in recruitment order between fibers at different distances from the electrode and between fibers of differing diameter were found in inhomogeneous media. The results of this simulation study demonstrate that the electrical properties of the extracellular medium can have a strong influence on the pattern of neuronal excitation generated by extracellular electric fields, and indicate the importance of tissue electrical properties in interpreting results of studies employing electrical stimulation applied in complex biological volume conductors.