Subsecond multichannel magnetic control of select neural circuits in freely moving flies.

Precisely timed activation of genetically targeted cells is a powerful tool for the study of neural circuits and control of cell-based therapies. Magnetic control of cell activity, or 'magnetogenetics', using magnetic nanoparticle heating of temperature-sensitive ion channels enables remote, non-invasive activation of neurons for deep-tissue applications and freely behaving animal studies. However, the in vivo response time of thermal magnetogenetics is currently tens of seconds, which prevents precise temporal modulation of neural activity. Moreover, magnetogenetics has yet to achieve in vivo multiplexed stimulation of different groups of neurons. Here we produce subsecond behavioural responses in Drosophila melanogaster by combining magnetic nanoparticles with a rate-sensitive thermoreceptor (TRPA1-A). Furthermore, by tuning magnetic nanoparticles to respond to different magnetic field strengths and frequencies, we achieve subsecond, multichannel stimulation. These results bring magnetogenetics closer to the temporal resolution and multiplexed stimulation possible with optogenetics while maintaining the minimal invasiveness and deep-tissue stimulation possible only by magnetic control.

Coupling Magnetically Induced Electric Fields to Neurons: Longitudinal and Transverse Activation.

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.

Quasistatic approximation in neuromodulation.

We define and explain the quasistatic approximation (QSA) as applied to field modeling for electrical and magnetic stimulation. Neuromodulation analysis pipelines include discrete stages, and QSA is applied specifically when calculating the electric and magnetic fields generated in tissues by a given stimulation dose. QSA simplifies the modeling equations to support tractable analysis, enhanced understanding, and computational efficiency. The application of QSA in neuro-modulation is based on four underlying assumptions: (A1) no wave propagation or self-induction in tissue, (A2) linear tissue properties, (A3) purely resistive tissue, and (A4) non-dispersive tissue. As a consequence of these assumptions, each tissue is assigned a fixed conductivity, and the simplified equations (e.g., Laplace's equation) are solved for the spatial distribution of the field, which is separated from the field's temporal waveform. Recognizing that electrical tissue properties may be more complex, we explain how QSA can be embedded in parallel or iterative pipelines to model frequency dependence or nonlinearity of conductivity. We survey the history and validity of QSA across specific applications, such as microstimulation, deep brain stimulation, spinal cord stimulation, transcranial electrical stimulation, and transcranial magnetic stimulation. The precise definition and explanation of QSA in neuromodulation are essential for rigor when using QSA models or testing their limits.

Quasistatic approximation in neuromodulation.

We define and explain the quasistatic approximation (QSA) as applied to field modeling for electrical and magnetic stimulation. Neuromodulation analysis pipelines include discrete stages, and QSA is applied specifically when calculating the electric and magnetic fields generated in tissues by a given stimulation dose. QSA simplifies the modeling equations to support tractable analysis, enhanced understanding, and computational efficiency. The application of QSA in neuromodulation is based on four underlying assumptions: (A1) no wave propagation or self-induction in tissue, (A2) linear tissue properties, (A3) purely resistive tissue, and (A4) non-dispersive tissue. As a consequence of these assumptions, each tissue is assigned a fixed conductivity, and the simplified equations (e.g. Laplace's equation) are solved for the spatial distribution of the field, which is separated from the field's temporal waveform. Recognizing that electrical tissue properties may be more complex, we explain how QSA can be embedded in parallel or iterative pipelines to model frequency dependence or nonlinearity of conductivity. We survey the history and validity of QSA across specific applications, such as microstimulation, deep brain stimulation, spinal cord stimulation, transcranial electrical stimulation, and transcranial magnetic stimulation. The precise definition and explanation of QSA in neuromodulation are essential for rigor when using QSA models or testing their limits.

Three novel methods for determining motor threshold with transcranial magnetic stimulation outperform conventional procedures.

Objective. Thresholding of neural responses is central to many applications of transcranial magnetic stimulation (TMS), but the stochastic aspect of neuronal activity and motor evoked potentials (MEPs) challenges thresholding techniques. We analyzed existing methods for obtaining TMS motor threshold and their variations, introduced new methods from other fields, and compared their accuracy and speed.Approach. In addition to existing relative-frequency methods, such as the five-out-of-ten method, we examined adaptive methods based on a probabilistic motor threshold model using maximum-likelihood (ML) or maximuma-posteriori(MAP) estimation. To improve the performance of these adaptive estimation methods, we explored variations in the estimation procedure and inclusion of population-level prior information. We adapted a Bayesian estimation method which iteratively incorporated information of the TMS responses into the probability density function. A family of non-parametric stochastic root-finding methods with different convergence criteria and stepping rules were explored as well. The performance of the thresholding methods was evaluated with an independent stochastic MEP model.Main Results. The conventional relative-frequency methods required a large number of stimuli, were inherently biased on the population level, and had wide error distributions for individual subjects. The parametric estimation methods obtained the thresholds much faster and their accuracy depended on the estimation method, with performance significantly improved when population-level prior information was included. Stochastic root-finding methods were comparable to adaptive estimation methods but were much simpler to implement and did not rely on a potentially inaccurate underlying estimation model.Significance. Two-parameter MAP estimation, Bayesian estimation, and stochastic root-finding methods have better error convergence compared to conventional single-parameter ML estimation, and all these methods require significantly fewer TMS pulses for accurate estimation than conventional relative-frequency methods. Stochastic root-finding appears particularly attractive due to the low computational requirements, simplicity of the algorithmic implementation, and independence from potential model flaws in the parametric estimators.

Responses of model cortical neurons to temporal interference stimulation and related transcranial alternating current stimulation modalities.

Objective.Temporal interference stimulation (TIS) was proposed as a non-invasive, focal, and steerable deep brain stimulation method. However, the mechanisms underlying experimentally-observed suprathreshold TIS effects are unknown, and prior simulation studies had limitations in the representations of the TIS electric field (E-field) and cerebral neurons. We examined the E-field and neural response characteristics for TIS and related transcranial alternating current stimulation modalities.Approach.Using the uniform-field approximation, we simulated a range of stimulation parameters in biophysically realistic model cortical neurons, including different orientations, frequencies, amplitude ratios, amplitude modulation, and phase difference of the E-fields, and obtained thresholds for both activation and conduction block.Main results. For two E-fields with similar amplitudes (representative of E-field distributions at the target region), TIS generated an amplitude-modulated (AM) total E-field. Due to the phase difference of the individual E-fields, the total TIS E-field vector also exhibited rotation where the orientations of the two E-fields were not aligned (generally also at the target region). TIS activation thresholds (75-230 V m-1) were similar to those of high-frequency stimulation with or without modulation and/or rotation. For E-field dominated by the high-frequency carrier and with minimal amplitude modulation and/or rotation (typically outside the target region), TIS was less effective at activation and more effective at block. Unlike AM high-frequency stimulation, TIS generated conduction block with some orientations and amplitude ratios of individual E-fields at very high amplitudes of the total E-field (>1700 V m-1).Significance. The complex 3D properties of the TIS E-fields should be accounted for in computational and experimental studies. The mechanisms of suprathreshold cortical TIS appear to involve neural activity block and periodic activation or onset response, consistent with computational studies of peripheral axons. These phenomena occur at E-field strengths too high to be delivered tolerably through scalp electrodes and may inhibit endogenous activity in off-target regions, suggesting limited significance of suprathreshold TIS.

Optimized monophasic pulses with equivalent electric field for rapid-rate transcranial magnetic stimulation.

Objective.Transcranial magnetic stimulation (TMS) with monophasic pulses achieves greater changes in neuronal excitability but requires higher energy and generates more coil heating than TMS with biphasic pulses, and this limits the use of monophasic pulses in rapid-rate protocols. We sought to design a stimulation waveform that retains the characteristics of monophasic TMS but significantly reduces coil heating, thereby enabling higher pulse rates and increased neuromodulation effectiveness.Approach.A two-step optimization method was developed that uses the temporal relationship between the electric field (E-field) and coil current waveforms. The model-free optimization step reduced the ohmic losses of the coil current and constrained the error of the E-field waveform compared to a template monophasic pulse, with pulse duration as a second constraint. The second, amplitude adjustment step scaled the candidate waveforms based on simulated neural activation to account for differences in stimulation thresholds. The optimized waveforms were implemented to validate the changes in coil heating.Main results.Depending on the pulse duration and E-field matching constraints, the optimized waveforms produced 12%-75% less heating than the original monophasic pulse. The reduction in coil heating was robust across a range of neural models. The changes in the measured ohmic losses of the optimized pulses compared to the original pulse agreed with numeric predictions.Significance.The first step of the optimization approach was independent of any potentially inaccurate or incorrect model and exhibited robust performance by avoiding the highly nonlinear behavior of neural responses, whereas neural simulations were only run once for amplitude scaling in the second step. This significantly reduced computational cost compared to iterative methods using large populations of candidate solutions and more importantly reduced the sensitivity to the choice of neural model. The reduced coil heating and power losses of the optimized pulses can enable rapid-rate monophasic TMS protocols.

Isolating two sources of variability of subcortical stimulation to quantify fluctuations of corticospinal tract excitability.

OBJECTIVE: Investigate the variability previously found with cortical stimulation and handheld transcranial magnetic stimulation (TMS) coils, criticized for its high potential of coil position fluctuations, bypassing the cortex using deep brain electrical stimulation (DBS) of the corticospinal tract with fixed electrodes where both latent variations of the coil position of TMS are eliminated and cortical excitation fluctuations should be absent. METHODS: Ten input-output curves were recorded from five anesthetized cats with implanted DBS electrodes targeting the corticospinal tract. Goodness of fit of regressions with a conventional single variability source as well as a dual variability source model was quantified using a Schwarz Bayesian Information approach to avoid overfitting. RESULTS: Motor evoked potentials (MEPs) through DBS of the corticospinal tract revealed short-term fluctuations in excitability of the targeted neuron pathway reflecting endogenous input-side variability at similar magnitude as TMS despite bypassing cortical networks. CONCLUSION: Input-side variability, i.e., variability resulting in changing MEP amplitudes as if the stimulation strength was modulated, also emerges in electrical stimulation at a similar degree and is not primarily a result of varying stimulation, such as minor coil movements in TMS. More importantly, this variability component is present, although the cortex is bypassed. Thus, it may be of spinal origin, which can include cortical input from spinal projections. Further, the nonlinearity of the compound variability entails complex heteroscedastic non-Gaussian distributions and typically does not allow simple linear averages in statistical analysis of MEPs. As the average is dominated by outliers, it risks bias. With appropriate regression, the net effects of excitatory and inhibitory inputs to the targeted neuron pathways become noninvasively observable and quantifiable. SIGNIFICANCE: The neural responses evoked by artificial stimulation in the cerebral cortex are variable. For example, MEPs in response to repeated presentations of the same stimulus can vary from no response to saturation across trials. Several sources of such variability have been suggested, and most of them may be technical in nature, but localization is missing.

Multichannel power electronics and magnetic nanoparticles for selective thermal magnetogenetics.

Objective.We present a combination of a power electronics system and magnetic nanoparticles that enable frequency-multiplexed magnetothermal-neurostimulation with rapid channel switching between three independent channels spanning a wide frequency range.Approach.The electronics system generates alternating magnetic field spanning 50 kHz to 5 MHz in the same coil by combining silicon (Si) and gallium-nitride (GaN) transistors to resolve the high spread of coil impedance and current required throughout the wide bandwidth. The system drives a liquid-cooled field coil via capacitor banks, forming three series resonance channels which are multiplexed using high-voltage contactors. We characterized the system by the output channels' frequencies, field strength, and switching time, as well as the system's overall operation stability. Using different frequency-amplitude combinations of the magnetic field to target specific magnetic nanoparticles with different coercivity, we demonstrate actuation of iron oxide nanoparticles in all three channels, including a novel nanoparticle composition responding to magnetic fields in the megahertz range.Main results.The system achieved the desired target field strengths for three frequency channels, with switching speed between channels on the order of milliseconds. Specific absorption rate measurements and infrared thermal imaging performed with three types of magnetic nanoparticles demonstrated selective heating and validated the system's intended use.Significance.The system uses a hybrid of Si and GaN transistors in bridge configuration instead of conventional amplifier circuit concepts to drive the magnetic field coil and contactors for fast switching between different capacitor banks. Series-resonance circuits ensure a high output quality while keeping the system efficient. This approach could significantly improve the speed and flexibility of frequency-multiplexed nanoparticle actuation, such as magnetogenetic neurostimulation, and thus provide the technical means for selective stimulation below the magnetic field's fundamental spatial focality limits.

A wireless millimetric magnetoelectric implant for the endovascular stimulation of peripheral nerves.

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.

Simulation of transcranial magnetic stimulation in head model with morphologically-realistic cortical neurons.

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.

Modified cable equation incorporating transverse polarization of neuronal membranes for accurate coupling of electric fields.

OBJECTIVE: We present a theory and computational methods to incorporate transverse polarization of neuronal membranes into the cable equation to account for the secondary electric field generated by the membrane in response to transverse electric fields. The effect of transverse polarization on nonlinear neuronal activation thresholds is quantified and discussed in the context of previous studies using linear membrane models. APPROACH: The response of neuronal membranes to applied electric fields is derived under two time scales and a unified solution of transverse polarization is given for spherical and cylindrical cell geometries. The solution is incorporated into the cable equation re-derived using an asymptotic model that separates the longitudinal and transverse dimensions. Two numerical methods are proposed to implement the modified cable equation. Several common neural stimulation scenarios are tested using two nonlinear membrane models to compare thresholds of the conventional and modified cable equations. MAIN RESULTS: The implementations of the modified cable equation incorporating transverse polarization are validated against previous results in the literature. The test cases show that transverse polarization has limited effect on activation thresholds. The transverse field only affects thresholds of unmyelinated axons for short pulses and in low-gradient field distributions, whereas myelinated axons are mostly unaffected. SIGNIFICANCE: 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.

Experimental Study on Nerve Signals Block for Spasticity Based on Antimissile Strategy.

A method of blocking neural signal for spasticity which is based on the antimissile strategy was proposed. When the pathological nerve action potential signal is detected at the proximal end of the nerve, such a potential signal that is opposite to the signal of the primary neural activity is applied at the distal end of the nerve at a proper delay so as to block the pathological nerve signal. Preliminary tests were performed on toad sciatic nerve-gastrocnemius specimens. Firstly, the effect of the distance between blocking electrodes on the blocking pulse voltage threshold was studied based on the electrical tension induced by the nerve signal on the controlled muscle. Then, the effective parameters of the blocking waveform were studied. Finally, the delay range of the blocking pulse compared to the pathogen action potential was studied. The results showed that in the sciatic nerve-gastrocnemius specimens, the most effective distance between the blocking electrode pairs was 5 mm and the anodic block required an inverted triangle waveform. The voltage threshold of an effective anodic blocking pulse was 1 V and the minimum pulse width was 90 ms. Under the condition of voltage threshold and minimum pulse width, the time shifting value of blocking pulse was greater than 1ms. It is concluded from the study that the spastic action potential caused by the disease can be effectively blocked, and limb muscle spasms can be eliminated under the action of appropriate electrode configuration and blocking signal waveforms.

Redesigning existing transcranial magnetic stimulation coils to reduce energy: application to low field magnetic stimulation.

OBJECTIVE: To present a systematic framework and exemplar for the development of a compact and energy-efficient coil that replicates the electric field (E-field) distribution induced by an existing transcranial magnetic stimulation coil. APPROACH: The E-field generated by a conventional low field magnetic stimulation (LFMS) coil was measured for a spherical head model and simulated in both spherical and realistic head models. Then, using a spherical head model and spatial harmonic decomposition, a spherical-shaped cap coil was synthesized such that its windings conformed to a spherical surface and replicated the E-field on the cortical surface while requiring less energy. A prototype coil was built and electrically characterized. The effect of constraining the windings to the upper half of the head was also explored via an alternative coil design. MAIN RESULTS: The LFMS E-field distribution resembled that of a large double-cone coil, with a peak field strength around 350 mV m-1 in the cortex. The E-field distributions of the cap coil designs were validated against the original coil, with mean errors of 1%-3%. The cap coil required as little as 2% of the original coil energy and was significantly smaller in size. SIGNIFICANCE: The redesigned LFMS coil is substantially smaller and more energy-efficient than the original, improving cost, power consumption, and portability. These improvements could facilitate deployment of LFMS in the clinic and potentially at home. This coil redesign approach can also be applied to other magnetic stimulation paradigms. Finally, the anatomically-accurate E-field simulation of LFMS can be used to interpret clinical LFMS data.

Analysis of the Peak Resistance Frequency Method.

OBJECTIVE: This study analyzes the peak resistance frequency (PRF) method described by Mercanzini et al., a method that can easily extract the tissue resistance from impedance spectroscopy for many neural engineering applications but has no analytical description thus far. METHODS: Mathematical analyses and computer simulations were used to explore underlying principles, accuracy, and limitations of the PRF method. RESULTS: The mathematical analyses demonstrated that the PRF method has an inherent but correctable deviation dependent on the idealness of the electrode-tissue interface, which is validated by simulations. Further simulations show that both frequency sampling and noise affect the accuracy of the PRF method, and in general, it performs less accurately than least squares methods. However, the PRF method achieves simplicity and reduced measurement and computation time at the expense of accuracy. CONCLUSION: From the qualitative results, the PRF method can work with reasonable precision and simplicity, although its limitation and the idealness of the electrode-tissue interface involved should be taken into consideration. SIGNIFICANCE: This paper provides a mathematical foundation for the PRF method and its practical implementation.

Reduction of edge effect on disk electrodes by optimized current waveform.

Rectangular pulses applied to disk electrodes result in high current density at the edges of the disk, which can lead to electrode corrosion and tissue damage. We explored a method for reducing current density and corrosion, by varying the leading edge of the current pulse. Finite-element modeling and mathematical analysis were used to predict an optimal waveform that reduces current density at the edge while also maintaining short pulse duration. An approximation of the optimized waveform was implemented experimentally and applied to platinum disk electrodes. Surface analysis using energy-dispersive spectroscopy showed significant reduction of corrosion on the periphery of these electrodes after pulsing, compared to those pulsed with the control rectangular waveform.

Reduction of current density at disk electrode periphery by shaping current pulse edges.

Previous studies reveal that the primary distribution of the current density is sharply enhanced at the edge of a disk electrode submerged into a semi-infinite space of conductive solution. The current enhancement will cause the double layer capacitance at the periphery of the electrode to be charged much faster compared to the center, and can also lead to severe corrosion at the edge. While several studies focused on the geometric design of the electrode to reduce this enhancement, we explore the feasibility of achieving similar effect by shaping the edges of the current input. The simulation uses finite element analysis software to solve the system of partial differential equations and results show that the edge enhancement could be greatly reduced without significantly changing the input efficacy of current and/or charge.