The need to correctly predict the voltage across terminals of mm-sized coils, with ferrite core, to be employed for magnetic stimulation of the peripheral neural system is the motivation for this work. In such applications, which rely on a capacitive discharge on the coil to realise a transient voltage curve of duration and strength suitable for neural stimulation, the correct modelling of the non-linearity of the ferrite core is critical. A demonstration of how a finite-difference model of the considered coils, which include a model of the current-controlled inductance in the coil, can be used to correctly predict the time-domain voltage waveforms across the terminals of a test coil is presented. Five coils of different dimensions, loaded with ferrite cores, have been fabricated and tested: the measured magnitude and width of the induced pulse are within 10% of simulated values.
Introduction:Magnetic fields cover an important role in several biomedical devices and diagnostic equipment. From the point of view of neurostimulation, transcranial magnetic stimulation (TMS) is one of the non-invasive techniques for the stimulation of the central nervous system. It uses time-varying magnetic fields to induce eddy currents in the tissue and elicit neural stimulation [1]. Compared with an electrical stimulator, a magnetic neurostimulator can provide reliable stimulation over long periods because of its contactless stimulation mechanism. In the literature, several approaches have been considered to employ magnetic core-based coils to generate high induced electric fields using small dimension coils (diameter 4-12 mm) [1, 2] and large TMS coils (diameter 10 cm) [3]. Traditionally, these designs use expensive magnetic cores with high permeability (μ r ∼20 000) and high magnetic field saturation (∼2 T). Despite the advances in the use and analysis of relatively large coils for neurostimulation, external to the human body, the development of small coils for possible implantation still faces significant challenges. Among these challenges, the behaviour of small ferrite-loaded coils to be used in implants and, in particular, the effect of saturation on the waveform of these neurostimulators have not been well studied.Most magnetic materials (iron, ferrite) are non-linear and dispersive. Their relative magnetic permeability (μ r ) varies with the applied magnetic field intensity (H) and operating frequency. Due to changes in μ r with respect to field intensity, inductors with a magnetic core may show a non-linear inductance as a function of the applied current. In the case of small sized, ferrite-loaded coils for neurostimulation a linear inductor model is no longer valid [4], and the correct prediction of the non-linear effect in the inductor is critical in determining the potential effectiveness of these coils for magnetic stimulation. In fact, for magnetic stimulation, the calculation of electric field distributions (spatial and temporal) in the proximal region of the stimulus coil is required to predict the stimulation site...