A volume-conduction analysis of magnetic stimulation of peripheral nerves

Magnetic stimulation is a method to study several nervous disorders as well as the intact nervous system in humans. Interest in magnetic stimulation of peripheral nerves has grown rapidly, but difficulties in locating the site of excitation have prevented it from becoming a routine clinical tool. It has been reasoned that the activating function of long and straight nerves is the first spatial derivative of the electric field component parallel to the nerves. Therefore, to predict the site of activation, one has to compute this field feature. We describe here an analytical mathematical model and investigate the influence of volume-conductor shape on the induced field. Predictions of the site of activation are given for typical stimulation coil arrangements and these results are compared with experimental and literature data. Comparisons suggest that the activating function is not simply the spatial gradient of the induced electric field, but that other mechanisms are also involved. The model can be easily utilized in the search for more efficient coil constructions and improved placements with respect to the target nerves.