Background: Transcranial magnetic stimulation (TMS) enables non-invasive modulation of brain activity with both clinical and research applications, but fundamental questions remain about the neural types and elements TMS activates and how stimulation parameters affect the neural response. Objective: To develop a multi-scale computational model to quantify the effect of TMS parameters on the direct response of individual neurons. Methods: We integrated morphologically-realistic neuronal models with TMS-induced electric fields computed in a finite element model of a human head to quantify the cortical response to TMS with several combinations of pulse waveforms and current directions. Results: TMS activated with lowest intensity intracortical axonal terminations in the superficial gyral crown and lip regions. Layer 5 pyramidal cells had the lowest thresholds, but layer 2/3 pyramidal cells and inhibitory basket cells were also activated at most intensities. Direct activation of layers 1 and 6 was unlikely. Neural activation was largely driven by the field magnitude, rather than the field component normal to the cortical surface. Varying the induced current direction caused a waveform-dependent shift in the activation site and provided a potential mechanism for experimentally observed differences in thresholds and latencies of muscle responses. Conclusions: This biophysically-based simulation provides a novel method to elucidate mechanisms and inform parameter selection of TMS and other cortical stimulation modalities. It also serves as a foundation for more detailed network models of the response to TMS, which may include endogenous activity, synaptic connectivity, inputs from intrinsic and extrinsic axonal projections, and corticofugal axons in white matter.

Transcranial magnetic stimulation (TMS) enables non-invasive modulation of brain activity with both clinical and research applications, but fundamental questions remain about the neural types and elements it activates and how stimulation parameters affect the neural response. We integrated detailed neuronal models with TMSinduced electric fields in the human head to quantify the effects of TMS on cortical neurons. TMS activated with lowest intensity layer 5 pyramidal cells at their intracortical axonal terminations in the superficial gyral crown and lip regions. Layer 2/3 pyramidal cells and inhibitory basket cells may be activated too, whereas direct activation of layers 1 and 6 was unlikely. Neural activation was largely driven by the field magnitude, contrary to theories implicating the field component normal to the cortical surface. Varying the induced current's direction caused a waveform-dependent shift in the activation site and provided a mechanistic explanation for experimentally observed differences in thresholds and latencies of muscle responses. This biophysically-based simulation provides a novel method to elucidate mechanisms and inform parameter selection of TMS and other forms of cortical stimulation.

Implantable bioelectronic devices for the simulation of peripheral nerves could be used to treat disorders that are resistant to traditional pharmacological therapies. However, for many nerve targets, this requires invasive surgeries and the implantation of bulky devices (about a few centimetres in at least one dimension). Here we report the design and in vivo proof-of-concept testing of an endovascular wireless and battery-free millimetric implant for the stimulation of specific peripheral nerves that are difficult to reach via traditional surgeries. The device can be delivered through a percutaneous catheter and leverages magnetoelectric materials to receive data and power through tissue via a digitally programmable 1 mm × 0.8 mm system-on-a-chip. Implantation of the device directly on top of the sciatic nerve in rats and near a femoral artery in pigs (with a stimulation lead introduced into a blood vessel through a catheter) allowed for wireless stimulation of the animals’ sciatic and femoral nerves. Minimally invasive magnetoelectric implants may allow for the stimulation of nerves without the need for open surgery or the implantation of battery-powered pulse generators.

The modified cable equation captures the membrane's behavior on different time scales and models more accurately the coupling between electric fields and neurons. It addresses the limitations of the conventional cable equation and allows sound theoretical interpretations. The implementation provides simple methods that are compatible with current simulation approaches to study the effect of transverse polarization on nonlinear membranes. The minimal influence by transverse polarization on axonal activation thresholds for the nonlinear membrane models indicates that predictions of stronger effects in linear membrane models with a fixed activation threshold are inaccurate. Thus, the conventional cable equation works well for most neuroengineering applications, and the presented modeling approach is well suited to address the exceptions.

We present a theory and computational models to couple the electric field induced by magnetic stimulation to neuronal membranes. Based on the characteristics of magnetically induced electric fields and the modified cable equation that we developed previously, quasipotentials are derived as a simple and accurate approximation for coupling of the electric fields to neurons. The conventional and modified cable equations are used to simulate magnetic stimulation of long peripheral nerves by circular and figure-8 coils. Activation thresholds are obtained over a range of lateral and vertical coil positions for two nonlinear membrane models representing unmyelinated and myelinated straight axons and also for undulating myelinated axons. For unmyelinated straight axons, the thresholds obtained with the modified cable equation are significantly lower due to transverse polarization, and the spatial distributions of thresholds as a function of coil position differ significantly from predictions by the activating function. However, the activation thresholds of unmyelinated axons obtained with either cable equation are very high and beyond the output capabilities of conventional magnetic stimulators. For myelinated axons, threshold values are similar for both cable equations and within the range of magnetic stimulators. Whereas the transverse field contributes negligibly to the activation thresholds of myelinated fibers, axonal undulation can significantly increase or decrease thresholds depending on coil position. The analysis provides a rigorous theoretical foundation and implementation methods for the use of the cable equation to model neuronal response to magnetically induced electric fields. Experimentally observed stimulation with the electric fields perpendicular to the nerve trunk cannot be explained by transverse polarization and is likely due to nerve fiber undulation and other geometrical inhomogeneities.