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Introduction Accurate modeling of neural activation provides mechanistic understanding of non-invasive brain stimulation and means for optimization of stimulus parameters. The cable equation is commonly used to couple extracellular electric fields to neuronal models. However, its conventional form does not account for some aspects of the neuronal membranes’ response, such as polarization of soma or fibers by transverse electric fields, and has limitations in the theoretical foundation for coupling inductive magnetic stimulation. Until now, the membranes’ detailed interactions with the electric fields could only be modeled by computationally expensive finite element simulation of fine neural structures. Objectives This modeling study incorporates initial polarization into the cable equation to improve the accuracy of estimating neural activation of both electrical and magnetic stimulation. Materials and methods The initial polarization of axon segments and somas was derived analytically and incorporated into the cable equation. Test cases were simulated for neuron models with either linear or nonlinear membrane to evaluate the influence of initial polarization on polarization rate and action potential thresholds. Results Initial polarization can reduce the neural firing threshold by 5–50% for typical axon radii, electrode distances, and pulse widths. Short pulse widths and large electrode distance, such as those in non-invasive stimulation, result in larger decreases in threshold. The depolarization rates of nonlinear membrane models showed that the initial polarization mechanism has activation strength similar to the spatial gradient of the applied field, and contributes significantly to activating the soma and axon initial segment. Initial polarization reduces stimulation thresholds and may potentially shift the spike initiation site from axon terminals to the initial segments. This could be an important effect in transcranial stimulation due to the low spatial gradients of the applied fields. Conclusion Initial polarization may contribute significantly to neural activation. It is captured by the proposed modified cable equation, which could give more accurate estimation of the site and threshold for neural activation with exogenous electric fields. Download : Download high-res image (190KB) Download : Download full-size image

The pulse waveform of transcranial magnetic stimulation (TMS) affects the degree to which various neuronal elements and populations are activated as well as the strength of neuromodulation resulting from repetitive TMS. Conventional TMS devices allow very limited pulse waveform adjustment; therefore we developed TMS devices with controllable pulse parameters (cTMS). So far cTMS has been used, by our and other groups, to study strength-duration curves in motor cortex and the associated neural membrane time constants; pulse-width dependence of motor input–output curves, cortical neuron recruitment, paired-pulse paradigms, and scalp sensation; and pulse-shape dependence of neuromodulatory effects. These studies show that changing the pulse width, shape, and/or direction may alter the neural elements that are preferentially activated in cortex, as evidenced by differences in motor evoked potential latencies and membrane time constants. These parameters also affect the changes of neural excitability resulting from 1 Hz and intermittent theta burst stimulation. For the 1 Hz protocol, the near rectangular cTMS pulses produced stronger inhibition than conventional sinusoidal pulses, with unidirectional cTMS pulses having the strongest effect. As well, cTMS has been used to optimize new repetitive paired-pulse stimulation protocols. cTMS was also used to show that the slope of motor input–output curves depends on pulse width via the same mechanism driving the strength-duration relationship of motor threshold. Finally, the pulse width affects the perceived scalp sensation of TMS, with briefer pulses feeling sharper and slightly more uncomfortable than longer pulses. In parallel with exploring the capabilities afforded by cTMS, we are developing a next generation ultraflexible TMS device called a modular pulse synthesizer (MPS) that would allow the generation of essentially any pulse shape and pulse sequence/train within the energy levels practical for TMS. The development and adoption of cTMS and MPS could enable expanded utilization of the temporal characteristics of TMS as a means of enhancing functional targeting, noninvasive biomarkers, neuromodulatory potency, and tolerability.

Introduction Commercially available transcranial magnetic stimulation (TMS) devices induce electric field (E-field) pulses with damped cosine shape and provide very limited control over the pulse parameters. Furthermore, conventional TMS devices consisting of a single power stage cannot produce rapid bursts ( Objectives To summarize the cTMS3 device capabilities and compare it to conventional TMS and other cTMS devices. Materials and methods The coil current and electric field were measured with a Rogowski current sensor and a search coil, respectively. Results cTMS3 uses a circuit topology with two energy storage capacitors and four controllable switches. It can generate rapid-rate (⩽50 Hz) trains of mono/bi/polyphasic near-rectangular electric field pulses with adjustable amplitude (maximum capacitor voltages of 1 kV and 2.6 kV), pulse width (phase duration of 10 μs to over 200 μs), and directionality (positive/negative phase amplitude ratio range of 1–52). In contrast to earlier cTMS devices, in cTMS3 the pulse phases can assume 4 possible electric field levels, proportional to either of the two capacitor voltages, the capacitor voltage difference, or 0. Thus, cTMS3 can produce waveforms with a staircase shape that can approximate conventional sinusoidal current pulses ( Fig. 1 ). To counteract the loss of capacitor charge in rapid pulse bursts, the pulse width of the second and subsequent pulses can be increased, allowing their stimulation strength to be equal or even higher than the first pulse ( Fig. 2 ). In Fig. 2 , the voltage on the two energy storage capacitors is reduced by 2% and 17%, respectively, after the first pulse, but the second pulse is 67% longer than the first pulse. Consequently, the strength of the second pulse, as measured by modeled neural membrane depolarization (membrane time constant = 196 μs) is 45% higher than the first pulse. Thus, paired-pulse paradigms, where the second pulse can have higher strength than the first pulse, can be implemented. Similarly, increasing the pulse width in a rapid burst of pulses can enable quadripulse stimulation. Conclusions cTMS3 offers flexibility of pulse shape adjustment unparalleled in other available TMS devices. The combination of high energy efficiency of the near rectangular pulses, pulse energy recovery, and pulse width control allow the generation of rapid bursts of pulses with equal or even increasing strength that can implement paired-pulse and quadripulse stimulation. These features could extend the capabilities of TMS as a research and diagnostic tool, and could enable optimization of the stimulus in therapeutic interventions.