Energy considerations in the magnetic (eddy-current) stimulation of tissues

The magnetic field energy and Joule heating required in a coil to induce an electric field pulse are calculated for different geometries of circular coils with rectangular cross section. For a fixed target distance away from the coil, the magnetic field energy takes on a broad minimum when the coil outer radius is between two and five times the target distance. Joule heating in the coil decreases as the radius of the coil increases. Increasing annular width results in a small reduction in field energy and coil Joule heating, and thin coils (small height) reduce the field energy but increase Joule heating. A reasonable compromise between efficiency and coil size results in a coil with an outer diameter that is twice the distance between the coil surface and the underlying tissue to be stimulated and height and annular width that are 0.2 and 0.6 that of the mean radius, respectively. The use of a pair of coplanar coils results in improved efficiency, but placing the coil perpendicular to the skin surface requires additional energy for stimulation