Analysis of efficiency of magnetic stimulation

Magnetic stimulation can activate excitable tissues noninvasively. However, this method requires high energy to operate and can produce equipment heat that leads to inefficient stimulation. In this study, a comprehensive optimization of efficiency for magnetic stimulation has been conducted. A total of 16,781 coil designs were tested in order to determine the optimal coil geometry and inductance for neural excitation. Induced electric fields were calculated to find the optimal stimulation site (OSS) of a given coil. The threshold energy of a magnetic pulse for neural excitation was then calculated based on the transmembrane responses of a nerve model. Simulation results show that there exists an optimal inductance, as a consequence of an optimal pulse duration, corresponding to a minimum threshold energy. A longer pulse width is required to obtain the maximum efficiency for axons with slower membrane dynamics, a longer coil-to-fiber distance, and greater values of resistance (R) and capacitance (C) of the resistance-inductance-capacitance circuit. The optimal geometry features a minimum coil height, suggesting a flat coil design for optimal efficiency. The dimension of the optimal coil design increases with the coil-to-fiber distance. Moreover, the cloverleaf design achieves the highest efficiency for infinitely long fibers whereas the butterfly design is optimal for terminating or bending fibers.