Selective stimulation of smaller fibers in a compound nerve trunk with single cathode by rectangular current pulses

Analysis of nerve conduction block induced by direct current

The mechanisms of nerve conduction block induced by direct current (DC) were investigated using a lumped circuit model of the myelinated axon based on Frankenhaeuser-Huxley (FH) model. Four types of nerve conduction block were observed including anodal DC block, cathodal DC block, virtual anodal DC block, and virtual cathodal DC block. The concept of activating function was used to explain the blocking locations and relation between these different types of nerve block. Anodal/cathodal DC blocks occurred at the axonal nodes under the block electrode, while virtual anodal/cathodal DC blocks occurred at the nodes several millimeters away from the block electrode. Anodal or virtual anodal DC block was caused by hyperpolarization of the axon membrane resulting in the failure of activating sodium channels by the arriving action potential. Cathodal or virtual cathodal DC block was caused by depolarization of the axon membrane resulting in inactivation of the sodium channel. The threshold of cathodal DC block was lower than anodal DC block in most conditions. The threshold of virtual anodal/cathodal blocks was about three to five times higher than the threshold of anodal/cathodal blocks. The blocking threshold was decreased with an increase of axonal diameter, a decrease of electrode distance to axon, or an increase of temperature. This simulation study, which revealed four possible mechanisms of nerve conduction block in myelinated axons induced by DC current, can guide future animal experiments as well as optimize the design of electrodes to block nerve conduction in neuroprosthetic applications.

Animal model of the short-term cardiorespiratory effects of intermittent vagus nerve stimulation

PURPOSE

To develop an animal model of the effects of vagus nerve stimulation (VNS) on heart rate and respiration in studies of seizure treatment.

METHODS

Nine rats implanted with ECG, EMG, and VNS electrodes and pulse generator were stimulated with 81 different sets of parameters while they slept in a plethysmographic box.

RESULT

From cardiorespiratory effects of VNS, an index (alpha) was found to distinguish between weak and strong VNS doses. Weak VNS dose induced an increase in respiratory frequency and no significant change in heart rate. The effect of VNS on respiration, similar to that observed in children, can be divided into 3 phases. Strong VNS dose induced a decrease in respiratory frequency concomitant with a decrease in heart rate. Increasing the intensity of the VNS induced a proportional increase in the maximal inspiratory strength.

CONCLUSION

Various VNS parameter settings induce different and concomitant cardiorespiratory variations in conscious sleeping rats. These effects correlate with the intensity of the VNS parameters. Understanding the effects of the intensity of VNS parameters may allow for further optimization of VNS parameters in patients receiving VNS.

Electrode array for reversing the recruitment order of peripheral nerve stimulation: a simulation study

Electrical stimulation of peripheral nerve activates large-diameter fibers before small ones. Previous studies using computer simulations and animal experiments showed that selective activation of small fibers could be achieved using an array of four cathodes and five anodes to reshape the extracellular voltage along the nerve and that the technique was independent of stimulating pulse width. In this simulation study, electrode arrays of 5, 7, 9, and 11 contacts were tested using finite element model of ventral sacral root. Contact separation of the array was 0.75 mm. The 5-contact array activated small axons having internodal distance smaller than contact separation before larger axons (< 7.5 microm in this case). Arrays of 7, 9 and 11 contacts suppressed the excitability of axons having internodal distance close to the intercathodic distance ( approximately 15 microm in this case). The recruitment orders were identical for 50 micros and 200 micros-pulse stimulations. Simulations suggested that electrode arrays of 5 and 7 contacts could be used to achieve selective activation of small axons independently of stimulating pulse width. Arrays of 5 and 7 contacts also decreased the recruitment curve slope to 43% and 72% of the tripolar electrode.

Mechanism of nerve conduction block induced by high-frequency biphasic electrical currents

The mechanisms of nerve conduction block induced by high-frequency biphasic electrical currents were investigated using a lumped circuit model of the myelinated axon based on Frankenhaeuser-Huxley (FH) model or Chiu-Ritchie-Rogart-Stagg-Sweeney (CRRSS) model. The FH model revealed that the constant activation of potassium channels at the node under the block electrode, rather than inactivation of sodium channels, is the likely mechanism underlying conduction block of myelinated axons induced by high-frequency biphasic stimulation. However, the CRRSS model revealed a different blocking mechanism where the complete inactivation of sodium channels at the nodes next to the block electrode caused the nerve conduction block. The stimulation frequencies to observe conduction block in FH model agree with the observations from animal experiments (greater than 6 kHz), but much higher frequencies are required in CRRSS model (greater than 15 kHz). This frequency difference indicated that the constant activation of potassium channels might be the underlying mechanism of conduction block observed in animal experiments. Using the FH model, this study also showed that the axons could recover from conduction block within 1 ms after termination of the blocking stimulation, which also agrees very well with the animal experiments where nerve block could be reversed immediately once the blocking stimulation was removed. This simulation study, which revealed two possible mechanisms of nerve conduction block in myelinated axons induced by high-frequency biphasic stimulation, can guide future animal experiments as well as optimize stimulation waveforms for electrical nerve block in clinical applications.

Simulation analysis of conduction block in myelinated axons induced by high-frequency biphasic rectangular pulses

Nerve conduction block induced by high-frequency biphasic rectangular pulses was analyzed using a lumped circuit model of the myelinated axon based on Frankenhaeuser-Huxley (FH) equations. At the temperature of 37 degrees C, axons of different diameters (2-20 microm) can be blocked completely at supra-threshold intensities when the stimulation frequency is above 10 kHz. However, at stimulation frequencies between 6 kHz and 9 kHz, both nerve block and repetitive firing of action potentials can be observed at different stimulation intensities. When the stimulation frequency is below 6 kHz, nerve block does not occur regardless of stimulation intensity. Larger diameter axons have a lower threshold intensity to induce conduction block. When temperature is reduced from 37 degrees C to 20 degrees C, the lowest frequency to completely block large axons (diameters 10-20 microm) decreased from 8 kHz to 4 kHz. This simulation study can guide future animal experiments as well as optimize stimulation waveforms for electrical nerve block in clinical applications.

Electrode Array for Reversing the Recruitment Order of Peripheral Nerve Stimulation: Experimental Studies

One of the most challenging problems in peripheral nerve stimulation is the ability to activate selectively small axons without large ones. Electrical stimulation of peripheral nerve activates large diameter fibers before small ones. Currently available techniques for selective activation of small axons without large ones require long-duration stimulation pulses (>500 micros) and large stimulation amplitude, which shorten battery life of the implanted stimulator and could lead to electrode corrosion. In the current study, the hypothesis that small axons can be recruited before large ones with narrow pulse width (50 micros) using an electrode array was tested in both simulations simulation and experiments in the cat lateral gastrocnemius (LG) model. The LG nerve innervates both LG and soleus muscle groups with axons within 10-13 and 8-12 microm diameter ranges, respectively. A finite element model of LG nerve was constructed and simulations showed that, when activating 40% of LG, a conventional tripolar electrode activated only 9% of soleus whereas the electrode arrays of 5, 7, and 11 contacts activated 39, 46, and 60% of soleus respectively, suggesting that the arrays could activate small axons before fully recruiting large axons. In animal experiments, peak twitch force of LG and soleus were plotted as a function of stimulation amplitude to indicate the recruitment curve. At 40% activation of LG, a conventional tripolar electrode activated only 7% of soleus whereas the electrode arrays of 5, 7, and 11 contacts activated 43, 48, and 72% of soleus respectively. The electrode arrays also decreased significantly the recruitment curve slopes to only 10-20% of the value obtained for the tripolar electrode in both computer simulations and experiments. In conclusion, the 5-, 7-, and 11-contact arrays can be used to reverse the recruitment order of peripheral nerve stimulation with a narrow pulse.

Simulation of nerve block by high-frequency sinusoidal electrical current based on the Hodgkin-Huxley model

Nerve conduction block induced by high-frequency sinusoidal electrical current was simulated using a lumped circuit model of the unmyelinated axon based on Hodgkin-Huxley equations. Axons of different diameters (1-20 microm) can be blocked when the stimulation frequency is above 4 kHz. At higher frequency, a higher stimulation intensity is needed to block nerve conduction. Larger diameter axons have a lower threshold intensity for conduction block. High-frequency sinusoidal electrical currents are less effective in blocking nerve conduction than biphasic square pulses of the same frequency. The activation of potassium channels, rather than inactivation of sodium channels, is the possible mechanism underlying the nerve conduction block of the unmyelinated axon induced by high-frequency biphasic (sinusoidal or square pulse) stimulation. This simulation study, which provides more information about the axonal conduction block induced by high-frequency sinusoidal currents, can guide future animal experiments, as well as optimize stimulation waveforms for electrical nerve block in possible clinical applications.

Simulation analysis of conduction block in unmyelinated axons induced by high-frequency biphasic electrical currents

Nerve conduction block induced by high-frequency biphasic electrical currents is analyzed using a lumped circuit model of the unmyelinated axon based on Hodgkin-Huxley equations. Axons of different diameters (5-20 microm) can not be blocked completely when the stimulation frequency is between 2 kHz and 4 kHz. However, when the stimulation frequency is above 4 kHz, all axons can be blocked. At high-frequency a higher stimulation intensity is needed to block nerve conduction. The larger diameter axon has a lower threshold intensity for conduction block. The stimulation waveform in which the pulsewidth changes with frequency is more effective in blocking nerve conduction than the waveform in which the pulsewidth is fixed. The activation of potassium channels, rather than inactivation of sodium channels, is the possible mechanism underlying the nerve conduction block of the unmyelinated axon. This simulation study further increases our understanding of axonal conduction block induced by high-frequency biphasic currents, and can guide future animal experiments as well as optimize stimulation waveforms that might be used for electrical nerve block in clinical applications.

Alkanethiolate self-assembled monolayers as functional spacers to resist protein adsorption upon Au-coated nerve microelectrode

Alkanethiolate self-assembled monolayers (SAMs) of varied chain lengths were adsorbed upon Au-coated nerve microelectrodes and employed as protein-resistant spacers. The microelectrode spiraled as a cuff type can be used for restoring motor function via electrical stimulation on the peripheral nerve system; however, an increase of electrode impedance might occur during implantation. In this work, a thin-film SAMs treatment upon Au/polyimide (PI) surface of the microelectrode provided a hydrophobic characteristic, which retarded protein adsorption at the initial stage and subsequent pileup (or thickening) process. The protein-resistant effect exhibited comparable SAMs of different chain lengths adsorbed upon Au/PI surfaces. The increase of electrode impedance as a function of protein deposition time was mainly correlated with the addition of reactance that was associated with the pileup thickness of the deposited protein. Particularly, the SAMs-modified surface was capable to detach a significant portion of the accumulated protein from the protein-deposited SAMs/Au/PI, whereas the protein-deposited layers exhibited firm adhesion upon Au/PI surface. It is therefore very promising to apply thin-film SAMs adsorbed upon Au-coated surface for bioinvasive devices that have the need of functional electrical stimulations or sensing nerve signals during chronic implantation.

Extracellular voltage profile for reversing the recruitment order of peripheral nerve stimulation: a simulation study

Electrical stimulation of peripheral nerve activates large-diameter fibers before small ones. A physiological recruitment order, from small to large-diameter axons, is desirable in many applications. Previous studies using computer simulations showed that selective activation of small fibers could be achieved by reshaping the extracellular voltage profile along the nerve using an array of nine electrodes. In this study, several electrode-array configurations were tested in order to minimize the number of contacts. Electrode arrays of 5, 7, 9, and 11 contacts with 0.75 mm contact separation were performed in computer simulations of dog sacral root (S2). Electrode arrays of 5 and 7 contacts recruited 40% of small axons (<10 microm) when recruiting only 10% of larger axons. Effectiveness of 9- and 11-contact arrays decreased with the presence of epineurium and perineurium. The effectiveness of electrode arrays was independent of stimulation pulsewidth. The biphasic-pulse stimulation with the amplitude of the second phase set as low as possible should be used to prevent the excitation of large axons during the second phase and to minimize the electrode corrosion. Arrays of 5 and 7 contacts also decreased the recruitment curve slope to 26% and 51% of the tripolar electrode, respectively. This modeling study predicts that reversing the recruitment order of peripheral nerve stimulation could be achieved by reshaping the extracellular voltage using electrode arrays of 5 or 7 contacts.

A Novel Electrode Array for Diameter-Dependent Control of Axonal Excitability: A Simulation Study

Electrical extracellular stimulation of peripheral nerve activates the large-diameter motor fibers before the small ones, a recruitment order opposite the physiological recruitment of myelinated motor fibers during voluntary muscle contraction. Current methods to solve this problem require a long-duration stimulus pulse which could lead to electrode corrosion and nerve damage. The hypothesis that the excitability of specific diameter fibers can be suppressed by reshaping the profile of extracellular potential along the axon using multiple electrodes is tested using computer simulations in two different volume conductors. Simulations in a homogenous medium with a nine-contact electrode array show that the current excitation threshold (Ith) of large diameter axons (13-17 microm) (0.6-3.0 mA) is higher than that of small-diameter axons (2-7 microm) (0.4-0.7 mA) with 200-microm axon-electrode distance and 10-micros stimulus pulse. The electrode array is also tested in a three-dimensional finite-element model of the sacral root model of dog (ventral root of S3). A single cathode activates large-diameter axons before activating small axons. However, a nine-electrode array activates 50% of small axons while recruiting only 10% of large ones and activates 90% of small axons while recruiting only 50% of large ones. The simulations suggest that the near-physiological recruitment order can be achieved with an electrode array. The diameter selectivity of the electrode array can be controlled by the electrode separation and the method is independent of pulse width.

New currents in electrical stimulation of excitable tissues

Electric fields can stimulate excitable tissue by a number of mechanisms. A uniform long, straight peripheral axon is activated by the gradient of the electric field that is oriented parallel to the fiber axis. Cortical neurons in the brain are excited when the electric field, which is applied along the axon-dendrite axis, reaches a particular threshold value. Cardiac tissue is thought to be depolarized in a uniform electric field by the curved trajectories of its fiber tracts. The bidomain model provides a coherent conceptual framework for analyzing and understanding these apparently disparate phenomena. Concepts such as the activating function and virtual anode and cathode, as well as anode and cathode break and make stimulation, are presented to help explain these excitation events in a unified manner. This modeling approach can also be used to describe the response of excitable tissues to electric fields that arise from charge redistribution (electrical stimulation) and from time-varying magnetic fields (magnetic stimulation) in a self-consistent manner. It has also proved useful to predict the behavior of excitable tissues, to test hypotheses about possible excitation mechanisms, to design novel electrophysiological experiments, and to interpret their findings.

Analysis of a linear model for electrical stimulation of axons--critical remarks on the "activating function concept"

A comprehensive description of a linear model of an axon of infinite length exposed to an external voltage is presented. The steady-state transmembrane potential is derived as a function proportional to the convolution product of the second spatial difference sn of the external potential (the "activating function") and the impulse response psin of a spatial low-pass filter. The impulse response psin represents the influence of the axon and is fully characterized by the axon's length constant lambda. A closed-form solution of the cable equation can be given in the spatial Fourier domain. Due to a "spectral acceleration effect", the overall transmembrane potential approximates the steady-state considerably faster than an exponential with the axon's membrane time constant tau. The effect is increasingly pronounced, the smaller the distance between the electrode and the axon. Regarding myelinated fibers and practically relevant electrode/axon distances and pulse widths, the transmembrane potential at the end of a stimulation pulse can be substantially better approximated by the steady-state condition than by the initial response as claimed by the "activating function concept." Quantitative limits for the range of validity of the activating function concept are derived.

Multimicroelectrode stimulation within the cat L6 spinal cord: influences of electrode combinations and stimulus interleave time on knee joint extension torque

During multimicroelectrode stimulation within the cat L6 spinal cord, the number of electrodes activated, their separation distance, and the stimulus interleave time all influenced isometric knee joint extension torque. The torque evoked by stimulation with a three electrode combination could be enhanced or suppressed when compared with that evoked by single or paired electrode stimulation. A similar difference was noted when comparing two electrode combination versus single electrode stimulation. Relative fatigue was not improved significantly by interleaving the stimuli from two or three microelectrodes. Compared with the extension torque response evoked by noninterleaved stimulation, torque evoked by interleaved stimulation with the two microelectrode combination was decreased when the electrode distance was 2.0 mm or less and increased when the electrode distance was 3.0 mm. Designing an optimal stimulation strategy for multimicroelectrode spinal cord stimulation will be challenging and complex if a suppression effect among these electrodes is to be avoided. To reduce muscle fatigue, an asynchronous, interleaved strategy of stimulation may be required.

Isometric torque about the knee joint generated by microstimulation of the cat L6 spinal cord

Isometric torque was generated about the knee joint by microstimulation of the cat L6 spinal cord using a single microelectrode. The torque responses varied with microstimulation location. Appreciable extension torque was generated by microstimulation in ventrolateral locations of the L6 spinal cord. Stimulation parameters (intensity, frequency and pulse-width) also influenced the extension torque. Specific stimulation parameters (100 microA intensity, 40 Hz frequency and 0.20 ms pulse-width) appear best suited for mapping the spinal cord based on knee joint torque responses. Low levels of cocontraction of the extensor and flexor could be achieved when extension torque was produced, but also varied with the stimulation locations. There are locations in the L6 ventral horn where microstimulation could evoke sustained extension for at least 4 min with only a slight change in torque. This study suggests the possibility of restoring lower limb function in patients with spinal cord injury above the lumbar level.