Cylindrical tissue model for magnetic field stimulation of neurons: effects of coil geometry

An analytical solution for the electric field induced in a homogeneous cylindrical conductor under quasi-static conditions from current in a coil is used to model peripheral nerve stimulation with magnetic fields. A variety of coil geometries is analyzed in terms of the spatial derivative of the induced electric field along a long straight nerve, parallel to the axis, in a human-arm model. The results of these computations are found to be in general agreement with conclusions regarding the optimization of stimulating coils derived from analyses of the semi-infinite tissue model. The differences and their physical basis are pointed out.