Generalized series solution for the induced E-field distribution of slinky-type magnetic stimulators

Magnetic stimulation is a technique to excite biological tissues by means of a time-varying magnetic field. This induced electric field can depolarize the cell membrane so as to evoke an action potential that propagates along neurons, eventually being transmitted to other neurons or to a muscular cell. Design of a magnetic stimulator requires modeling of the impulse propagation along the nerve cell, as well as numerical simulations for coil design optimization to determine adequate excitation levels as well as the degree of focalization on a given target cell. In this paper we report on a new methodology to calculate the stimulation field for the case of the traditional slinky coil geometry, that greatly reduces computation time, thus facilitating simulation studies of the dynamics of electric impulse propagation along a nerve cell.