Volume conductor model of transcutaneous electrical stimulation with kilohertz signals

A Research Protocol to Study the Priming Effects of Breathing Low Oxygen on Enhancing Training-Related Gains in Walking Function for Persons With Spinal Cord Injury: The BO2ST Trial

Brief episodes of low oxygen breathing (therapeutic acute intermittent hypoxia; tAIH) may serve as an effective plasticity-promoting primer to enhance the effects of transcutaneous spinal stimulation-enhanced walking therapy (WALKtSTIM) in persons with chronic (>1 year) spinal cord injury (SCI). Pre-clinical studies in rodents with SCI show that tAIH and WALKtSTIM therapies harness complementary mechanisms of plasticity to maximize walking recovery. Here, we present a multi-site clinical trial protocol designed to examine the influence of tAIH + WALKtSTIM on walking recovery in persons with chronic SCI. We hypothesize that daily (eight sessions, 2 weeks) tAIH + WALKtSTIM will elicit faster, more persistent improvements in walking recovery than either treatment alone. To test our hypothesis, we are conducting a placebo-controlled clinical trial on 60 SCI participants who randomly receive one of three interventions: tAIH + WALKtSTIM; Placebo + WALKtSTIM; and tAIH + WALKtSHAM. Participants receive daily tAIH (fifteen 90-sec episodes at 10% O2 with 60-sec intervals at 21% O2) or daily placebo (fifteen 90-sec episodes at 21% O2 with 60-sec intervals at 21% O2) before a 45-min session of WALKtSTIM or WALKtSHAM. Our primary outcome measures assess walking speed (10-Meter Walk Test), endurance (6-Minute Walk Test), and balance (Timed Up and Go Test). For safety, we also measure pain levels, spasticity, sleep behavior, cognition, and rates of systemic hypertension and autonomic dysreflexia. Assessments occur before, during, and after sessions, as well as at 1, 4, and 8 weeks post-intervention. Results from this study extend our understanding of the functional benefits of tAIH priming by investigating its capacity to boost the neuromodulatory effects of transcutaneous spinal stimulation on restoring walking after SCI. Given that there is no known cure for SCI and no single treatment is sufficient to overcome walking deficits, there is a critical need for combinatorial treatments that accelerate and anchor walking gains in persons with lifelong SCI.

Trial Registration

ClinicalTrials.gov, NCT05563103.

Modeling the excitation of nerve axons under transcutaneous stimulation

Computational models enable a safe and convenient way to study the excitation of nerve fibers under external stimulation. Contemporary models calculate the electric field distribution from transcutaneous stimulation and the resulting neuronal response separately. This study uses finite element methods to develop a multi-scale model that couples electric fields within macroscopic tissue layers and microscopic nerve fibers in a single-stage computational framework. The model included a triaxial myelinated nerve fiber bundle embedded within a volume conductor of tissue layers to represent the median nerve innervating the forearm muscles. The model captured the excitability of nerve fibers under transcutaneous stimulation and their nerve-tissue interactions to a transient external stimulus. The determinants of the strength-duration curve, rheobase, and chronaxie for the proposed model had close correlations with in-vivo experimentation on human participants. Additionally, the excitability indices for the triaxial myelinated nerve fiber implemented using the finite element method agreed well with experimental data from the literature. The validity of the proposed model encourages its use for applications involving transcutaneous stimulation. Capable of capturing field distribution across realistic morphologies, the model can serve as a testbed to improve stimulation protocols and electrode designs with subject-level specificity.

Spatiotemporal parameters for energy efficient kilohertz-frequency nerve block with low onset response

BACKGROUND

Electrical nerve conduction block has great potential for treatment of disease through reversible and local inactivation of somatic and autonomic nerves. However, the relatively high energy requirements and the presence of undesired excitation at the onset of the kilohertz-frequency (KHF) signals used for block pose obstacles to effective translation. Frequency, electrode geometry, and waveform shape are known to influence block threshold and onset response, but available data provide a limited understanding of how to select these parameters to optimize nerve block.

METHODS

We evaluated KHF nerve block in rat tibial nerve across frequencies (5-60 kHz), electrode geometries (monopolar, bipolar, and tripolar), and waveform shapes. We present a novel Fourier-based method for constructing composite signals that systematically sample the KHF waveform design space.

RESULTS

The lowest frequencies capable of blocking (5-16 kHz) were not the most energy-efficient among the tested frequencies. Further, bipolar cuffs required the largest current and power to block, monopolar cuffs required the lowest current, and both tripolar and monopolar cuffs required the lowest power. Tripolar cuffs produced the smallest onset response across frequencies. Composite signals comprised of a first harmonic sinusoid at fundamental frequency (f0) superposed on a second harmonic sinusoid at 2f0 could block at lower threshold and lower onset response compared to the constituent sinusoids alone. This effect was strongly dependent on the phase of the second harmonic and on the relative amplitudes of the first and second harmonics. This effect was also dependent on electrode geometry: monopolar and tripolar cuffs showed clear composite signal effects in most experiments; bipolar cuffs showed no clear effects in most experiments.

CONCLUSIONS

Our data provide novel information about block threshold and onset response at the boundary of frequencies that can block. Our results also show an interaction between spatial (cuff geometry) and temporal (frequency and waveform shape) parameters. Finally, while previous studies suggested that temporal parameters could reduce onset response only in exchange for increased block threshold (or vice versa), our results show that waveform shape influences KHF response in ways that can be exploited to reduce both energy and onset responses.

Using a high-frequency carrier does not improve comfort of transcutaneous spinal cord stimulation

Objective.Spinal cord neuromodulation has gained much attention for demonstrating improved motor recovery in people with spinal cord injury, motivating the development of clinically applicable technologies. Among them, transcutaneous spinal cord stimulation (tSCS) is attractive because of its non-invasive profile. Many tSCS studies employ a high-frequency (10 kHz) carrier, which has been reported to reduce stimulation discomfort. However, these claims have come under scrutiny in recent years. The purpose of this study was to determine whether using a high-frequency carrier for tSCS is more comfortable at therapeutic amplitudes, which evoke posterior root-muscle (PRM) reflexes.Approach.In 16 neurologically intact participants, tSCS was delivered using a 1 ms long monophasic pulse with and without a high-frequency carrier. Stimulation amplitude and pulse duration were varied and PRM reflexes were recorded from the soleus, gastrocnemius, and tibialis anterior muscles. Participants rated their discomfort during stimulation from 0 to 10 at PRM reflex threshold.Main Results.At PRM reflex threshold, the addition of a high-frequency carrier (0.87 ± 0.2) was equally comfortable as conventional stimulation (1.03 ± 0.18) but required approximately double the charge to evoke the PRM reflex (conventional: 32.4 ± 9.2µC; high-frequency carrier: 62.5 ± 11.1µC). Strength-duration curves for tSCS with a high-frequency carrier had a rheobase that was 4.8× greater and a chronaxie that was 5.7× narrower than the conventional monophasic pulse, indicating that the addition of a high-frequency carrier makes stimulation less efficient in recruiting neural activity in spinal roots.Significance.Using a high-frequency carrier for tSCS is equally as comfortable and less efficient as conventional stimulation at amplitudes required to stimulate spinal dorsal roots.

A partially averaged system to model neuron responses to interferential current stimulation

The interferential current (IFC) therapy is a noninvasive electrical neurostimulation technique intended to activate deep neurons using surface electrodes. In IFC, two independent kilohertz-frequency currents purportedly intersect where an interference field is generated. However, the effects of IFC on neurons within and outside the interference field are not completely understood, and it is unclear whether this technique can reliable activate deep target neurons without side effects. In recent years, realistic computational models of IFC have been introduced to quantify the effects of IFC on brain cells, but they are often complex and computationally costly. Here, we introduce a simplified model of IFC based on the FitzHugh-Nagumo (FHN) model of a neuron. By considering a modified averaging method, we obtain a non-autonomous approximated system, with explicit representation of relevant IFC parameters. For this approximated system we determine conditions under which it reliably approximates the complete FHN system under IFC stimulation, and we mathematically prove its ability to predict nonspiking states. In addition, we perform numerical simulations that show that the interference effect is observed only for a narrow set of IFC parameters and, in particular, for a beat frequency no higher than about 100 [Hz]. Our novel model tailored to the IFC technique contributes to the understanding of neurostimulation modalities using this type of signals, and can have implications in the design of noninvasive electrical stimulation therapies.

Augmented Transcutaneous Stimulation Using an Injectable Electrode: A Computational Study

Minimally invasive neuromodulation technologies seek to marry the neural selectivity of implantable devices with the low-cost and non-invasive nature of transcutaneous electrical stimulation (TES). The Injectrode® is a needle-delivered electrode that is injected onto neural structures under image guidance. Power is then transcutaneously delivered to the Injectrode using surface electrodes. The Injectrode serves as a low-impedance conduit to guide current to the deep on-target nerve, reducing activation thresholds by an order of magnitude compared to using only surface stimulation electrodes. To minimize off-target recruitment of cutaneous fibers, the energy transfer efficiency from the surface electrodes to the Injectrode must be optimized. TES energy is transferred to the Injectrode through both capacitive and resistive mechanisms. Electrostatic finite element models generally used in TES research consider only the resistive means of energy transfer by defining tissue conductivities. Here, we present an electroquasistatic model, taking into consideration both the conductivity and permittivity of tissue, to understand transcutaneous power delivery to the Injectrode. The model was validated with measurements taken from (n = 4) swine cadavers. We used the validated model to investigate system and anatomic parameters that influence the coupling efficiency of the Injectrode energy delivery system. Our work suggests the relevance of electroquasistatic models to account for capacitive charge transfer mechanisms when studying TES, particularly when high-frequency voltage components are present, such as those used for voltage-controlled pulses and sinusoidal nerve blocks.

Parameterization of physical properties of layered body structure into equivalent circuit model

Background

This study presents a novel technique to develop an equivalent circuit model (ECM) for analyzing the responses of the layered body structure to transcutaneous electrical nerve stimulation (TENS) by parameterizing electrical and geometrical properties.Many classical ECMs are non-parametric because of the difficulty in projecting intrapersonal variability in the physical properties into ECM. However, not considering the intrapersonal variability hampers patient-specifically analyzing the body response to TENS and personal optimization of TENS parameter design. To overcome this limitation, we propose a tissue property-based (TPB) approach for the direct parameterization of the physical properties in the layered body structure and thus enable to quantify the effects of intrapersonal variability.

Results

The proposed method was first validated through in vitro phantom studies and then was applied in-vivo to analyze the TENS on the forearm. The TPB-ECM calculated the impedance network in the forearm and corresponding responses to TENS. In addition, the modelled impedance was in good agreement with well-known impedance properties that have been achieved empirically.

Conclusions

The TPB approach uses the parameterized circuit components compared to non-parametric conventional ECMs, thus overcoming the intrapersonal variability problem of the conventional ECMs. Therefore, the TPB-ECM has a potential for widely-applicable TENS analysis and could provide impactful guidance in the TENS parameter design.

Supplementary Information

The online version contains supplementary material available at (10.1186/s42490-021-00054-8).

Kilohertz-frequency stimulation of the nervous system: A review of underlying mechanisms

BACKGROUND

Electrical stimulation in the kilohertz-frequency range has gained interest in the field of neuroscience. The mechanisms underlying stimulation in this frequency range, however, are poorly characterized to date.

OBJECTIVE/HYPOTHESIS

To summarize the manifold biological effects elicited by kilohertz-frequency stimulation in the context of the currently existing literature and provide a mechanistic framework for the neural responses observed in this frequency range.

METHODS

A comprehensive search of the peer-reviewed literature was conducted across electronic databases. Relevant computational, clinical, and mechanistic studies were selected for review.

RESULTS

The effects of kilohertz-frequency stimulation on neural tissue are diverse and yield effects that are distinct from conventional stimulation. Broadly, these can be divided into 1) subthreshold, 2) suprathreshold, 3) synaptic and 4) thermal effects. While facilitation is the dominating mechanism at the subthreshold level, desynchronization, spike-rate adaptation, conduction block, and non-monotonic activation can be observed during suprathreshold kilohertz-frequency stimulation. At the synaptic level, kilohertz-frequency stimulation has been associated with the transient depletion of the available neurotransmitter pool - also known as synaptic fatigue. Finally, thermal effects associated with extrinsic (environmental) and intrinsic (associated with kilohertz-frequency stimulation) temperature changes have been suggested to alter the neural response to stimulation paradigms.

CONCLUSION

The diverse spectrum of neural responses to stimulation in the kilohertz-frequency range is distinct from that associated with conventional stimulation. This offers the potential for new therapeutic avenues across stimulation modalities. However, stimulation in the kilohertz-frequency range is associated with distinct challenges and caveats that need to be considered in experimental paradigms.

Non-monotonic kilohertz frequency neural block thresholds arise from amplitude- and frequency-dependent charge imbalance

Reversible block of nerve conduction using kilohertz frequency electrical signals has substantial potential for treatment of disease. However, the ability to block nerve fibers selectively is limited by poor understanding of the relationship between waveform parameters and the nerve fibers that are blocked. Previous in vivo studies reported non-monotonic relationships between block signal frequency and block threshold, suggesting the potential for fiber-selective block. However, the mechanisms of non-monotonic block thresholds were unclear, and these findings were not replicated in a subsequent in vivo study. We used high-fidelity computational models and in vivo experiments in anesthetized rats to show that non-monotonic threshold-frequency relationships do occur, that they result from amplitude- and frequency-dependent charge imbalances that cause a shift between kilohertz frequency and direct current block regimes, and that these relationships can differ across fiber diameters such that smaller fibers can be blocked at lower thresholds than larger fibers. These results reconcile previous contradictory studies, clarify the mechanisms of interaction between kilohertz frequency and direct current block, and demonstrate the potential for selective block of small fiber diameters.

Role of skin tissue layers and ultra-structure in transcutaneous electrical stimulation including tDCS

BACKGROUND

During transcranial electrical stimulation (tES), including transcranial direct current stimulation (tDCS) and transcranial alternating current stimulation (tACS), current density concentration around the electrode edges that is predicted by simplistic skin models does not match experimental observations of erythema, heating, or other adverse events. We hypothesized that enhancing models to include skin anatomical details, would alter predicted current patterns to align with experimental observations.

METHOD

We develop a high-resolution multi-layer skin model (epidermis, dermis, and fat), with or without additional ultra-structures (hair follicles, sweat glands, and blood vessels). Current flow patterns across each layer and within ultra-structures were predicted using finite element methods considering a broad range of modeled tissue parameters including 78 combinations of skin layer conductivities (S m^-1): epidermis (standard: 1.05 × 10^-5; range: 1.05 × 10^-6 to 0.465); dermis (standard: 0.23; range: 0.0023 to 23), fat (standard: 2 × 10^-4; range: 0.02 to 2 × 10^-5). The impact of each ultra-structures in isolation and combination was evaluated with varied basic geometries. An integrated final model is then developed.

RESULTS

Consistent with prior models, current flow through homogenous skin was annular (concentrated at the electrode edges). In multi-layer skin, reducing epidermis conductivity and/or increasing dermis conductivity decreased current near electrode edges, however no realistic tissue layer parameters produced non-annular current flow at both epidermis and dermis. Addition of just hair follicles, sweat glands, or blood vessels resulted in current peaks around each ultrastructure, irrespective of proximity to electrode edges. Addition of only sweat glands was the most effective approach in reducing overall current concentration near electrode edges. Representation of blood vessels resulted in a uniform current flow across the vascular network. Finally, we ran the first realistic model of current flow across the skin.

CONCLUSION

We confirm prior models exhibiting current concentration near hair follicles or sweat glands, but also exhibit that an overall annular pattern of current flow remains for realistic tissue parameters. We model skin blood vessels for the first time and show that this robustly distributes current across the vascular network, consistent with experimental erythema patterns. Only a state-of-the-art precise model of skin current flow predicts lack of current concentration near electrode edges across all skin layers.

Quantitative comparisons of block thresholds and onset responses for charge-balanced kilohertz frequency waveforms

OBJECTIVE

There is growing interest in delivering kilohertz frequency (KHF) electrical signals to block conduction in peripheral nerves for treatment of various diseases. Previous studies used different KHF waveforms to achieve block, and it remains unclear how waveform affects nerve block parameters.

APPROACH

We quantified the effects of waveform on KHF block of the rat tibial nerve in vivo and in computational models. We compared block thresholds and onset responses across current-controlled sinusoids and charge-balanced rectangular waveforms with different asymmetries and duty cycles.

MAIN RESULTS

Sine waves had higher block thresholds than square waves, but used less power at block threshold. Block threshold had an inverse relationship with duty cycle of rectangular waveforms irrespective of waveform asymmetry. Computational model results were consistent with relationships measured in vivo, although the models underestimated the effect of duty cycle on increasing thresholds. The axonal membrane substantially filtered waveforms, the filter transfer function was strikingly similar across waveforms, and filtering resulted in post-filtered rms block thresholds that were approximately constant across waveforms in silico and in vivo. Onset response was not consistently affected by waveform shape, but onset response was smaller at amplitudes well above block threshold. Therefore, waveforms with lower block thresholds (e.g. sine waves or square waves) could be more readily increased to higher amplitudes relative to block threshold to reduce onset response. We also observed a reduction in onset responses across consecutive trials after initial application of supra-block threshold amplitudes.

SIGNIFICANCE

Waveform had substantial effects on block thresholds, and the amplitude relative to block threshold had substantial effects on onset response. These data inform choice of waveform in subsequent studies and clinical applications, enhance effective use of block in therapeutic applications, and facilitate the design of parameters that achieve block with minimal onset responses.

A simulation environment for studying transcutaneous electrotactile stimulation

Transcutaneous electrical nerve stimulation (TENS) allows the artificial excitation of nerve fibres by applying electric-current pulses through electrodes on the skin's surface. This work involves the development of a simulation environment that can be used for studying transcutaneous electrotactile stimulation and its dependence on electrode layout and excitation patterns. Using an eight-electrode array implementation, it is shown how nerves located at different depths and with different orientations respond to specific injected currents, allowing the replication of already reported experimental findings and the creation of new hypotheses about the tactile sensations associated with certain stimulation patterns. The simulation consists of a finite element model of a human finger used to calculate the distribution of the electric potential in the finger tissues neglecting capacitive effects, and a cable model to calculate the excitation/inhibition of action potentials in each nerve.

Nerve excitation using an amplitude-modulated signal with kilohertz-frequency carrier and non-zero offset

BACKGROUND

Incorporating kilohertz-frequency signals in transcutaneous electrical stimulation has been proposed as a means to overcome the impedance of the skin, thereby reaching deeper nerves. In particular, a transdermal amplitude modulated signal (TAMS), composed of a 210 kHz non-zero offset carrier modulated by rectangular pulses, was introduced recently for the treatment of overactive bladder. However, the contribution of the components of TAMS to nerve fiber activation has not been quantified.

METHODS

We conducted in vivo experiments and applied direct stimulation to the sciatic nerve of cats and rats. We measured electromyogram and compound action potential activity evoked by pulses, TAMS and modified versions of TAMS in which we varied the size of the carrier.

RESULTS

Nerve fiber activation using TAMS showed no difference with respect to activation with conventional pulse for carrier frequencies of 20 kHz and higher, regardless the relative amplitude of the carrier. For frequencies lower than 20 kHz, the offset needed to generate half of the maximal evoked response decreased significantly with respect to the pulse. Results of simulations in a computational model of nerve fiber stimulation using the same stimulation waveforms closely matched our experimental measurements.

CONCLUSION

Taken together, these results suggest that a TAMS with carrier frequencies >20 kHz does not offer any advantage over conventional pulses, even with larger amplitudes of the carrier, and this has implications for design of waveforms for efficient and effective transcutaneous stimulation.

Effects of frequency-dependent membrane capacitance on neural excitability

OBJECTIVE

Models of excitable cells consider the membrane specific capacitance as a ubiquitous and constant parameter. However, experimental measurements show that the membrane capacitance declines with increasing frequency, i.e., exhibits dispersion. We quantified the effects of frequency-dependent membrane capacitance, c(f), on the excitability of cells and nerve fibers across the frequency range from dc to hundreds of kilohertz.

APPROACH

We implemented a model of c(f) using linear circuit elements, and incorporated it into several models of neurons with different channel kinetics: the Hodgkin-Huxley model of an unmyelinated axon, the McIntyre-Richardson-Grill (MRG) of a mammalian myelinated axon, and a model of a cortical neuron from prefrontal cortex (PFC). We calculated thresholds for excitation and kHz frequency conduction block, the conduction velocity, recovery cycle, strength-distance relationship and firing rate.

MAIN RESULTS

The impact of c(f) on activation thresholds depended on the stimulation waveform and channel kinetics. We observed no effect using rectangular pulse stimulation, and a reduction for frequencies of 10 kHz and above using sinusoidal signals only for the MRG model. c(f) had minimal impact on the recovery cycle and the strength-distance relationship, whereas the conduction velocity increased by up to 7.9% and 1.7% for myelinated and unmyelinated fibers, respectively. Block thresholds declined moderately when incorporating c(f), the effect was greater at higher frequencies, and the maximum reduction was 11.5%. Finally, c(f) marginally altered the firing pattern of a model of a PFC cell, reducing the median interspike interval by less than 2%.

SIGNIFICANCE

This is the first comprehensive analysis of the effects of dispersive capacitance on neural excitability, and as the interest on stimulation with kHz signals gains more attention, it defines the regions over which frequency-dependent membrane capacitance, c(f), should be considered.