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 p oint source electrode were determined by computer simulation. Analytical so lutions to Poisson's equation were used to calculate potentials in anisotro pic infinite homogeneous media and isotropic semi-infinite inhomogeneous me dia, and the net driving function was used to calculate excitation threshol ds 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 o rthogonal conductivities, respectively. Excitation thresholds in anisotropi c media were also dependent on the orientation of the fibers, and in strong ly anisotropic media (sigma(z)/sigma(xy) > 4) there were reversals in the r ecruitment order between different diameter fibers and between fibers at di fferent distances from the electrode. In source-free regions of inhomogeneo us media (two regions of differing conductivity separated by a plane bounda ry). the current-distance relationship of fibers parallel to the interface was dependent only on the average conductivity, whereas in regions containi ng the source the current-distance relationship was dependent on the indivi dual, 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 mediu m can have a strong influence on the pattern of neuronal excitation generat ed by extracellular electric fields, and indicate the importance of tissue electrical properties in interpreting results of studies employing electric al stimulation applied in complex biological volume conductors.