Effects of frequency-dependent membrane capacitance on neural excitability

Impact of Extracellular Current Flow on Action Potential Propagation in Myelinated Axons

Myelinated axons conduct action potentials, or spikes, in a saltatory manner. Inward current caused by a spike occurring at one node of Ranvier spreads axially to the next node, which regenerates the spike when depolarized enough for voltage-gated sodium channels to activate, and so on. The rate at which this process progresses dictates the velocity at which the spike is conducted and depends on several factors including axial resistivity and axon diameter that directly affect axial current. Here we show through computational simulations in modified double-cable axon models that conduction velocity also depends on extracellular factors whose effects can be explained by their indirect influence on axial current. Specifically, we show that a conventional double-cable model, with its outside layer connected to ground, transmits less axial current than a model whose outside layer is less absorptive. A more resistive barrier exists when an axon is packed tightly between other myelinated fibers, for example. We show that realistically resistive boundary conditions can significantly increase the velocity and energy efficiency of spike propagation, while also protecting against propagation failure. Certain factors like myelin thickness may be less important than typically thought if extracellular conditions are more resistive than normally considered. We also show how realistically resistive boundary conditions affect ephaptic interactions. Overall, these results highlight the unappreciated importance of extracellular conditions for axon function.

Janus microparticles-based targeted and spatially-controlled piezoelectric neural stimulation via low-intensity focused ultrasound

Electrical stimulation is a fundamental tool in studying neural circuits, treating neurological diseases, and advancing regenerative medicine. Injectable, free-standing piezoelectric particle systems have emerged as non-genetic and wireless alternatives for electrode-based tethered stimulation systems. However, achieving cell-specific and high-frequency piezoelectric neural stimulation remains challenging due to high-intensity thresholds, non-specific diffusion, and internalization of particles. Here, we develop cell-sized 20 μm-diameter silica-based piezoelectric magnetic Janus microparticles (PEMPs), enabling clinically-relevant high-frequency neural stimulation of primary neurons under low-intensity focused ultrasound. Owing to its functionally anisotropic design, half of the PEMP acts as a piezoelectric electrode via conjugated barium titanate nanoparticles to induce electrical stimulation, while the nickel-gold nanofilm-coated magnetic half provides spatial and orientational control on neural stimulation via external uniform rotating magnetic fields. Furthermore, surface functionalization with targeting antibodies enables cell-specific binding/targeting and stimulation of dopaminergic neurons. Taking advantage of such functionalities, the PEMP design offers unique features towards wireless neural stimulation for minimally invasive treatment of neurological diseases.

Modeling ultrasound modulation of neural function in a single cell

Background

Low intensity ultrasound stimulation has been shown to non-invasively modulate neural function in the central nervous system (CNS) and peripheral nervous system (PNS) with high precision. Ultrasound sonication is capable of either excitation or inhibition, depending on the ultrasound parameters used. On the other hand, the mode of interaction of ultrasonic waves with the neural tissue for effective neuromodulation remains ambiguous.

New method

Here within we propose a numerical model that incorporates the mechanical effects of ultrasound stimulation on the Hodgkin-Huxley (HH) neuron by incorporating the relation between increased external pressure and the membrane induced tension, with a stress on the flexoelectric effect on the neural membrane. The external pressure causes an increase in the total tension of the membrane thus affecting the probability of the ion channels being open after the conformational changes that those channels undergo.

Results

The interplay between varying the acoustic intensities and frequencies depicts different action potential suppression rates, whereby a combination of low intensity and low frequency ultrasound sonication proved to be the most effective in modulating neural function.Comparison with Existing Methods: Our method solely depends on the HH model of a single neuron and the linear flexoelectric effect of the dielectric neural membrane, when under an ultrasound-induced mechanical strain, while varying the ion-channels conductances based on different sonication frequencies and intensities. We study the effect of ultrasound parameters on the firing rate, latency, and action potential amplitude of a HH neuron for a better understanding of the neuromodulation modality of ultrasound stimulation (in the continuous and pulsed modes).

Conclusions

This simulation work confirms the published experimental data that low intensity and low frequency ultrasound sonication has a higher success rate of modulating neural firing.

Optogenetic polymerization and assembly of electrically functional polymers for modulation of single-neuron excitability

Ionic conductivity and membrane capacitance are two foundational parameters that govern neuron excitability. Conventional optogenetics has emerged as a powerful tool to temporarily manipulate membrane ionic conductivity in intact biological systems. However, no analogous method exists for precisely manipulating cell membrane capacitance to enable long-lasting modulation of neuronal excitability. Genetically targetable chemical assembly of conductive and insulating polymers can modulate cell membrane capacitance, but further development of this technique has been hindered by poor spatiotemporal control of the polymer deposition and cytotoxicity from the widely diffused peroxide. We address these issues by harnessing genetically targetable photosensitizer proteins to assemble electrically functional polymers in neurons with precise spatiotemporal control. Using whole-cell patch-clamp recordings, we demonstrate that this optogenetic polymerization can achieve stepwise modulation of both neuron membrane capacitance and intrinsic excitability. Furthermore, cytotoxicity can be limited by controlling light exposure, demonstrating a promising new method for precisely modulating cell excitability.

Effects of waveform shape and electrode material on KiloHertz frequency alternating current block of mammalian peripheral nerve

OBJECTIVES

KiloHertz frequency alternating current waveforms produce conduction block in peripheral nerves. It is not clearly known how the waveform shape affects block outcomes, and if waveform effects are frequency dependent. We determined the effects of waveform shape using two types of electrodes.

MATERIALS AND METHODS

Acute in-vivo experiments were performed on 12 rats. Bipolar electrodes were used to electrically block motor nerve impulses in the sciatic nerve, as measured using force output from the gastrocnemius muscle. Three blocking waveforms were delivered (sinusoidal, square and triangular) at 6 frequencies (10-60 kHz). Bare platinum electrodes were compared with carbon black coated electrodes. We determined the minimum amplitude that could completely block motor nerve conduction (block threshold), and measured properties of the onset response, which is a transient period of nerve activation at the start of block. In-vivo results were compared with computational modeling conducted using the NEURON simulation environment using a nerve membrane model modified for stimulation in the kilohertz frequency range.

RESULTS

For the majority of parameters, in-vivo testing and simulations showed similar results: Block thresholds increased linearly with frequency for all three waveforms. Block thresholds were significantly different between waveforms; lowest for the square waveform and highest for triangular waveform. When converted to charge per cycle, square waveforms required the maximum charge per phase, and triangular waveforms the least. Onset parameters were affected by blocking frequency but not by waveform shape. Electrode comparisons were performed only in-vivo. Electrodes with carbon black coatings gave significantly lower block thresholds and reduced onset responses across all blocking frequencies. For 10 and 20 kHz, carbon black coating significantly reduced the charge required for nerve block.

CONCLUSIONS

We conclude that both sinusoidal and square waveforms at frequencies of 20 kHz or higher would be optimal. Future investigation of carbon black or other high charge capacity electrodes may be useful in achieving block with lower BTs and onsets. These findings will be of importance for designing clinical nerve block systems.

Combining direct current and kilohertz frequency alternating current to mitigate onset activity during electrical nerve block

Objective.

Electrical nerve block offers the ability to immediately and reversibly block peripheral nerve conduction and would have applications in the emerging field of bioelectronics. Two modalities of electrical nerve block have been investigated—kilohertz frequency alternating current (KHFAC) and direct current (DC). KHFAC can be safely delivered with conventional electrodes, but has the disadvantage of having an onset response, which is a period of increased neural activation before block is established and currently limits clinical translation. DC has long been known to block neural conduction without an onset response but creates damaging reactive species. Typical electrodes can safely deliver DC for less than one second, but advances in high capacitance electrodes allow DC delivery up to 10 s without damage. The present work aimed to combine DC and KHFAC into a single waveform, named the combined reduced onset waveform (CROW), which can initiate block without an onset response while also maintaining safe block for long durations. This waveform consists of a short, DC pre-pulse before initiating KHFAC.

Approach.

Simulations of this novel waveform were carried out in the axonal simulation environment NEURON to test feasibility and gain insight into the mechanisms of action. Two sets of acute experiments were then conducted in adult Sprague–Dawley rats to determine the effectiveness of the waveform in mitigating the onset response.

Main results.

The CROW reduced the onset response both in silico and in vivo. The onset area was reduced by over 90% with the tested parameters in the acute experiments. The amplitude of the DC pulse was shown to be particularly important for effective onset mitigation, requiring amplitudes 6–8 times the DC block threshold.

Significance.

This waveform can reliably reduce the onset response due to KHFAC and could allow for wider clinical implementation of electrical nerve block.

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.

A Physical Perspective to the Inductive Function of Myelin-A Missing Piece of Neuroscience

Starting from the inductance in neurons, two physical origins are discussed, which are the coil inductance of myelin and the piezoelectric effect of the cell membrane. The direct evidence of the coil inductance of myelin is the opposite spiraling phenomenon between adjacent myelin sheaths confirmed by previous studies. As for the piezoelectric effect of the cell membrane, which has been well-known in physics, the direct evidence is the mechanical wave accompany with action potential. Therefore, a more complete physical nature of neural signals is provided. In conventional neuroscience, the neural signal is a pure electrical signal. In our new theory, the neural signal is an energy pulse containing electrical, magnetic, and mechanical components. Such a physical understanding of the neural signal and neural systems significantly improve the knowledge of the neurons. On the one hand, we achieve a corrected neural circuit of an inductor-capacitor-capacitor (LCC) form, whose frequency response and electrical characteristics have been validated by previous studies and the modeling fitting of artifacts in our experiments. On the other hand, a number of phenomena observed in neural experiments are explained. In particular, they are the mechanism of magnetic nerve stimulations and ultrasound nerve stimulations, the MRI image contrast issue and Anode Break Excitation. At last, the biological function of myelin is summarized. It is to provide inductance in the process of neural signal, which can enhance the signal speed in peripheral nervous systems and provide frequency modulation function in central nervous systems.

Variable Membrane Dielectric Polarization Characteristic in Individual Live Cells

Investigation of the dielectric properties of cell membranes plays an important role in understanding the biological activities that sustain cellular life and realize cellular functionalities. Herein, the variable dielectric polarization characteristics of cell membranes are reported. In controlling the dielectric polarization of a cell using dielectrophoresis force spectroscopy, different cellular crossover frequencies were observed by modulating both the direction and sweep rate of the frequency. The crossover frequencies were used for the extraction of the variable capacitance, which is involved in the dielectric polarization across the cell membranes. In addition, this variable phenomenon was investigated by examining cells whose membranes were cholesterol-depleted with methyl-β-cyclodextrin, which verified a strong correlation between the variable dielectric polarization characteristics and membrane composition changes. This study presented the dielectric polarization properties in live cells' membranes that can be modified by the regulation of external stimuli and provided a powerful platform to explore cellular membrane dielectric polarization.

Unveiling Stimulation Secrets of Electrical Excitation of Neural Tissue Using a Circuit Probability Theory

Electrical excitation of neural tissue has wide applications, but how electrical stimulation interacts with neural tissue remains to be elucidated. Here, we propose a new theory, named the Circuit-Probability theory, to reveal how this physical interaction happen. The relation between the electrical stimulation input and the neural response can be theoretically calculated. We show that many empirical models, including strength-duration relationship and linear-non-linear-Poisson model, can be theoretically explained, derived, and amended using our theory. Furthermore, this theory can explain the complex non-linear and resonant phenomena and fit in vivo experiment data. In this letter, we validated an entirely new framework to study electrical stimulation on neural tissue, which is to simulate voltage waveforms using a parallel RLC circuit first, and then calculate the excitation probability stochastically.

Anatomical and technical factors affecting the neural response to epidural spinal cord stimulation

OBJECTIVE

Spinal cord stimulation (SCS) is a common neurostimulation therapy to treat chronic pain. Computational models represent a valuable tool to study the potential mechanisms of action of SCS and to optimize the design and implementation of SCS technologies. However, it is imperative that these computational models include the appropriate level of detail to accurately predict the neural response to SCS and to correlate model predictions with clinical outcomes. Therefore, the goal of this study was to investigate several anatomic and technical factors that may affect model-based predictions of neural activation during thoracic SCS.

APPROACH

We developed computational models that consisted of detailed finite element models of the lower thoracic spinal cord, surrounding tissues, and implanted SCS electrode arrays. We positioned multicompartment models of sensory axons within the spinal cord to calculate the activation threshold for each sensory axon. We then investigated how activation thresholds changed as a function of several anatomical variables (e.g. spine geometry, dorsal rootlet anatomy), stimulation type (i.e. voltage-controlled vs. current-controlled), electrode impedance, lead position, lead type, and electrical properties of surrounding tissues (e.g. dura conductivity, frequency-dependent conductivity).

MAIN RESULTS

Several anatomic and modeling factors produced significant percent differences or errors in activation thresholds. Rostrocaudal positioning of the cathode with respect to the vertebrae had a large effect (up to 32%) on activation thresholds. Variability in electrode impedance produced significant changes in activation thresholds for voltage-controlled stimulation (38% to 51%), but had little effect on activation thresholds for current-controlled stimulation (less than 13%). Changing the dura conductivity also produced significant differences in activation thresholds.

SIGNIFICANCE

This study demonstrates several anatomic and technical factors that can affect the neural response to SCS. These factors should be considered in clinical implementation and in future computational modeling studies of thoracic SCS.

Genetically targeted chemical assembly of functional materials in living cells, tissues, and animals

The structural and functional complexity of multicellular biological systems, such as the brain, are beyond the reach of human design or assembly capabilities. Cells in living organisms may be recruited to construct synthetic materials or structures if treated as anatomically defined compartments for specific chemistry, harnessing biology for the assembly of complex functional structures. By integrating engineered-enzyme targeting and polymer chemistry, we genetically instructed specific living neurons to guide chemical synthesis of electrically functional (conductive or insulating) polymers at the plasma membrane. Electrophysiological and behavioral analyses confirmed that rationally designed, genetically targeted assembly of functional polymers not only preserved neuronal viability but also achieved remodeling of membrane properties and modulated cell type-specific behaviors in freely moving animals. This approach may enable the creation of diverse, complex, and functional structures and materials within living systems.

Perineuronal nets decrease membrane capacitance of peritumoral fast spiking interneurons in a model of epilepsy

Brain tumor patients commonly present with epileptic seizures. We show that tumor-associated seizures are the consequence of impaired GABAergic inhibition due to an overall loss of peritumoral fast spiking interneurons (FSNs) concomitant with a significantly reduced firing rate of those that remain. The reduced firing is due to the degradation of perineuronal nets (PNNs) that surround FSNs. We show that PNNs decrease specific membrane capacitance of FSNs permitting them to fire action potentials at supra-physiological frequencies. Tumor-released proteolytic enzymes degrade PNNs, resulting in increased membrane capacitance, reduced firing, and hence decreased GABA release. These studies uncovered a hitherto unknown role of PNNs as an electrostatic insulator that reduces specific membrane capacitance, functionally akin to myelin sheaths around axons, thereby permitting FSNs to exceed physiological firing rates. Disruption of PNNs may similarly account for excitation-inhibition imbalances in other forms of epilepsy and PNN protection through proteolytic inhibition may provide therapeutic benefits.

Stimulation Strategies for Tinnitus Suppression in a Neuron Model

Tinnitus is a debilitating perception of sound in the absence of external auditory stimuli. It may have either a central or a peripheral origin in the cochlea. Experimental studies evidenced that an electrical stimulation of peripheral auditory fibers may alleviate symptoms but the underlying mechanisms are still unknown. In this work, a stochastic neuron model is used, that mimics an auditory fiber affected by tinnitus, to check the effects, in terms of firing reduction, of different kinds of electric stimulations, i.e., continuous wave signals and white Gaussian noise. Results show that both white Gaussian noise and continuous waves at tens of kHz induce a neuronal firing reduction; however, for the same amplitude of fluctuations, Gaussian noise is more efficient than continuous waves. When contemporary applied, signal and noise exhibit a cooperative effect in retrieving neuronal firing to physiological values. These results are a proof of concept that a combination of signal and noise could be delivered through cochlear prosthesis for tinnitus suppression.

Adaptive Estimation of the Neural Activation Extent in Computational Volume Conductor Models of Deep Brain Stimulation

OBJECTIVE

The aim of this study is to propose an adaptive scheme embedded into an open-source environment for the estimation of the neural activation extent during deep brain stimulation and to investigate the feasibility of approximating the neural activation extent by thresholds of the field solution.

METHODS

Open-source solutions for solving the field equation in volume conductor models of deep brain stimulation and computing the neural activation are embedded into a Python package to estimate the neural activation dependent on the dielectric tissue properties and axon parameters by employing a spatially adaptive scheme. Feasibility of the approximation of the neural activation extent by field thresholds is investigated to further reduce the computational expense.

RESULTS

The varying extents of neural activation for different patient-specific dielectric properties were estimated with the adaptive scheme. The results revealed the strong influence of the dielectric properties of the encapsulation layer in the acute and chronic phase after surgery. The computational time required to determine the neural activation extent in each studied model case was substantially reduced.

CONCLUSION

The neural activation extent is altered by patient-specific parameters. Threshold values of the electric potential and electric field norm facilitate a computationally efficient method to estimate the neural activation extent.

SIGNIFICANCE

The presented adaptive scheme is able to robustly determine neural activation extents and field threshold estimates for varying dielectric tissue properties and axon diameters while substantially reducing the computational expense.

Induced mitochondrial membrane potential for modeling solitonic conduction of electrotonic signals

A cable model that includes polarization-induced capacitive current is derived for modeling the solitonic conduction of electrotonic potentials in neuronal branchlets with microstructure containing endoplasmic membranes. A solution of the nonlinear cable equation modified for fissured intracellular medium with a source term representing charge ‘soakage’ is used to show how intracellular capacitive effects of bound electrical charges within mitochondrial membranes can influence electrotonic signals expressed as solitary waves. The elastic collision resulting from a head-on collision of two solitary waves results in localized and non-dispersing electrical solitons created by the nonlinearity of the source term. It has been shown that solitons in neurons with mitochondrial membrane and quasi-electrostatic interactions of charges held by the microstructure (i.e., charge ‘soakage’) have a slower velocity of propagation compared with solitons in neurons with microstructure, but without endoplasmic membranes. When the equilibrium potential is a small deviation from rest, the nonohmic conductance acts as a leaky channel and the solitons are small compared when the equilibrium potential is large and the outer mitochondrial membrane acts as an amplifier, boosting the amplitude of the endogenously generated solitons. These findings demonstrate a functional role of quasi-electrostatic interactions of bound electrical charges held by microstructure for sustaining solitons with robust self-regulation in their amplitude through changes in the mitochondrial membrane equilibrium potential. The implication of our results indicate that a phenomenological description of ionic current can be successfully modeled with displacement current in Maxwell’s equations as a conduction process involving quasi-electrostatic interactions without the inclusion of diffusive current. This is the first study in which solitonic conduction of electrotonic potentials are generated by polarization-induced capacitive current in microstructure and nonohmic mitochondrial membrane current.

Modeling the response of small myelinated axons in a compound nerve to kilohertz frequency signals

OBJECTIVE

There is growing interest in electrical neuromodulation of peripheral nerves, particularly autonomic nerves, to treat various diseases. Electrical signals in the kilohertz frequency (KHF) range can produce different responses, including conduction block. For example, EnteroMedics' vBloc® therapy for obesity delivers 5 kHz stimulation to block the abdominal vagus nerves, but the mechanisms of action are unclear.

APPROACH

We developed a two-part computational model, coupling a 3D finite element model of a cuff electrode around the human abdominal vagus nerve with biophysically-realistic electrical circuit equivalent (cable) model axons (1, 2, and 5.7 µm in diameter). We developed an automated algorithm to classify conduction responses as subthreshold (transmission), KHF-evoked activity (excitation), or block. We quantified neural responses across kilohertz frequencies (5-20 kHz), amplitudes (1-8 mA), and electrode designs.

MAIN RESULTS

We found heterogeneous conduction responses across the modeled nerve trunk, both for a given parameter set and across parameter sets, although most suprathreshold responses were excitation, rather than block. The firing patterns were irregular near transmission and block boundaries, but otherwise regular, and mean firing rates varied with electrode-fibre distance. Further, we identified excitation responses at amplitudes above block threshold, termed 're-excitation', arising from action potentials initiated at virtual cathodes. Excitation and block thresholds decreased with smaller electrode-fibre distances, larger fibre diameters, and lower kilohertz frequencies. A point source model predicted a larger fraction of blocked fibres and greater change of threshold with distance as compared to the realistic cuff and nerve model.

SIGNIFICANCE

Our findings of widespread asynchronous KHF-evoked activity suggest that conduction block in the abdominal vagus nerves is unlikely with current clinical parameters. Our results indicate that compound neural or downstream muscle force recordings may be unreliable as quantitative measures of neural activity for in vivo studies or as biomarkers in closed-loop clinical devices.

The development and modelling of devices and paradigms for transcranial magnetic stimulation

Magnetic stimulation is a non-invasive neurostimulation technique that can evoke action potentials and modulate neural circuits through induced electric fields. Biophysical models of magnetic stimulation have become a major driver for technological developments and the understanding of the mechanisms of magnetic neurostimulation and neuromodulation. Major technological developments involve stimulation coils with different spatial characteristics and pulse sources to control the pulse waveform. While early technological developments were the result of manual design and invention processes, there is a trend in both stimulation coil and pulse source design to mathematically optimize parameters with the help of computational models. To date, macroscopically highly realistic spatial models of the brain, as well as peripheral targets, and user-friendly software packages enable researchers and practitioners to simulate the treatment-specific and induced electric field distribution in the brains of individual subjects and patients. Neuron models further introduce the microscopic level of neural activation to understand the influence of activation dynamics in response to different pulse shapes. A number of models that were designed for online calibration to extract otherwise covert information and biomarkers from the neural system recently form a third branch of modelling.

Higher-order power harmonics of pulsed electrical stimulation modulates corticospinal contribution of peripheral nerve stimulation

It is well established that electrical-stimulation frequency is crucial to determining the scale of induced neuromodulation, particularly when attempting to modulate corticospinal excitability. However, the modulatory effects of stimulation frequency are not only determined by its absolute value but also by other parameters such as power at harmonics. The stimulus pulse shape further influences parameters such as excitation threshold and fiber selectivity. The explicit role of the power in these harmonics in determining the outcome of stimulation has not previously been analyzed. In this study, we adopted an animal model of peripheral electrical stimulation that includes an amplitude-adapted pulse train which induces force enhancements with a corticospinal contribution. We report that the electrical-stimulation-induced force enhancements were correlated with the amplitude of stimulation power harmonics during the amplitude-adapted pulse train. In an exploratory analysis, different levels of correlation were observed between force enhancement and power harmonics of 20–80 Hz (r = 0.4247, p = 0.0243), 100–180 Hz (r = 0.5894, p = 0.0001), 200–280 Hz (r = 0.7002, p < 0.0001), 300–380 Hz (r = 0.7449, p < 0.0001), 400–480 Hz (r = 0.7906, p < 0.0001), 500–600 Hz (r = 0.7717, p < 0.0001), indicating a trend of increasing correlation, specifically at higher order frequency power harmonics. This is a pilot, but important first demonstration that power at high order harmonics in the frequency spectrum of electrical stimulation pulses may contribute to neuromodulation, thus warrant explicit attention in therapy design and analysis.

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.