Frequency-related effects in the optimization of coils for the magnetic stimulation of the nervous system

Magnetic stimulation of the nervous system is a non-invasive technique with a large number of applications in neurological diagnosis, brain research, and, recently, therapy. New applications require engineering modifications in order to decrease power consumption and coil heating. This can be accomplished by optimized coils with minimized resistance. In this study the influence of some frequency-related effects (skin and proximity effect) on the coil resistance will be discussed, together with the role played by wire shape, wire section, and twisting effect. The results show that the coil resistance increases with frequency. As an example, for a 20-mm2 circular wire section, the skin effect in the typical frequency range of magnetic stimulator devices (2-4 kHz) increases the coil resistance up to about 45% with respect to its dc value. Moreover, the influence of the frequency is lower for flat wire sections and reasonably small helix twist angle of the coil.