Analysis and Optimisation of Pulse Dynamics for Magnetic Stimulation
  Magnetic stimulation is a standard tool in brain research and many fields of neurology, as well as psychiatry. From a physical perspective, one key aspect of this method is the inefficiency of available setups. Whereas the spatial field properties have been studied rather intensively with coil designs, the dynamics have been neglected almost completely for a long time. Instead, the devices and their technology defined the waveform. Here, an analysis of the waveform space is performed. Based on these data, an appropriate optimisation approach is outlined which makes use of a modern nonlinear axon description of a mammalian motor nerve. The approach is based on a hybrid global-local method; different coordinate systems for describing the continuous waveforms in a limited parameter space are defined for sufficient stability. The results of the numeric setup suggest that there is plenty of room for waveforms with higher efficiency than the traditional shapes. One class of such pulses is analysed further. Although the voltage profile of these waveforms is almost rectangular, the current shape presents distinct characteristics, such as a first phase which precedes the main pulse and decreases the losses. The single representatives, which differ in their maximum voltage shape, are linked by a nonlinear transformation. The main phase, however, seems to scale in time only. 
Stefan M. Goetz, Nam C. Truong, Manuel G. Gerhofer, Thomas Weyh, and   Hans-Georg Herzog
physics.med-ph