The distribution of induced currents in magnetic stimulation of the nervous system

Abstract

The spatial distribution of induced currents from the stimulating coil is calculated from a computer model with graphical output. Two configurations of a plane circular coil are considered: parallel to the tissue surface and perpendicular to the surface. The surface is assumed planar and infinite in extent. The tissue is modelled as a uniform, isotropic volume conductor. A quasi-static approximation is made in calculating the electric field. Maps of current density, J, as a function of position, including depth, are shown. In both configurations, J is always parallel to the surface, and is maximum at the surface. There is no perpendicular (vertical) current. For a one-turn 10 cm diameter coil, spaced 1 cm from conducting tissue and parallel to it, with rate of change of current 10⁸ A s^-1, J_max=6.8 A m^-2 (assuming conductivity 0.2 Omega ^-1 m^-1). In the perpendicular configuration J_max=4.1 A m^-2. These results suggest that nerve fibres running parallel to the skin surface are more likely to be stimulated than those running obliquely; and that it is extremely difficult to stimulate nerve fibres running perpendicularly.