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.     

Selective activation of small motor axons by quasitrapezoidalcurrent pulses

We have found a method to activate electrically smaller nerve fibers without activating larger fibers in the same nerve trunk. The method takes advantage of the fact that action potentials are blocked with less membrane hyperpolarization in larger fibers than in smaller fibers. In our nerve stimulation system, quasitrapezoidal-shaped current pulses were delivered through a tripolar cuff electrode to effect differential block by membrane hyperpolarization. The quasitrapezoidal-shaped pulses with a square leading edge, a 350 microsecond(s) plateau, and an exponential trailing phase ensured the block of propagating action potentials and prevented the occurrence of anodal break excitation. The tripolar cuff electrode design restricted current flow inside the cuff and thus eliminated the undesired nerve stimulation due to a "virtual cathode." Experiments were performed on 13 cats. The cuff electrode was placed on the medial gastrocnemius nerve. Both compound and single fiber action potentials were recorded from L7 ventral root filaments. The results demonstrated that larger alpha motor axons could be blocked at lower current levels than smaller alpha motor axons, and that all alpha fibers could be blocked at lower current levels than gamma fibers. A statistical analysis indicated that the blocking threshold was correlated with the axonal conduction velocity or fiber diameter. This method could be used in physiological experiments and neural prostheses to achieve a small-to-large recruitment order in motor or sensory systems.     

Analysis of magnetic stimulation of a concentric axon in a nervebundle

The authors present an analysis of magnetic stimulation of an axon located at the center of a nerve bundle. A three-dimensional axisymmetric volume conductor model is used to determine the transmembrane potential response along an axon due to induced electric fields produced by a toroidal coil. The authors evaluate four such models of an axon located in: (1) an isotropic nerve bundle with no perineurium, (2) an anisotropic nerve bundle without a perineurium, (3) an isotropic nerve bundle surrounded by a perineurium, and (4) an anisotropic nerve bundle surrounded by a perineurium. The transmembrane polarization computed along an axon for the above four models is compared to that for an axon located in an infinite homogenous medium. These calculations indicate that a nerve bundle with no sheath has little effect on the transmembrane potential. However, the presence of a perineurium around the nerve bundle and anisotropy in the bundle significantly affects the shape of the transmembrane response. Therefore, during magnetic stimulation, nerve bundle anisotropy and the presence of perineurium must be taken into account for calculation of stimulus intensities for threshold excitation     

Focal magnetic stimulation of an axon

The induced electric field produced by a circular coil during magnetic stimulation of an axon is derived from Maxwell's equations. The foci and virtual cathodal and anodal regions are predicted as a function of coil radius and orientation. Two virtual anode and cathode pairs are predicted, one lying outside the coil's perimeter and predominant in the far field, and one lying within the perimeter of the coil which may stimulate the axon when the coil and nerve are in close proximity. When the coil is positioned tangent to the nerve, an orientation commonly used in clinical magnetic stimulation, the foci of the predominant cathode and anode pair are extremely sensitive to changes in coil placement. In addition, the radius of curvature of the activating function, a measure of the size of the virtual cathode at threshold, is predicted to decrease with decreasing coil diameter and distance to the nerve. These predictions may help explain observed variability in measurements of conduction velocity and latency during magnetic stimulation of peripheral axons     

He-Ne 激光对大鼠坐骨神经感觉纤维受损早期轴浆运输作用的研究

大鼠坐骨神经干夹伤后立即用功率密度为42.5 mW/cm~2的 He-Ne 激光照射损伤部位,发现由损伤部位远侧引入的 HRP 经轴浆运输标记同侧腰4～6脊冲经节中的大型冲经元胞体数较对照明显增加(P<0.001)。提示大鼠坐骨神经夹伤早期,激光照射有利于维持冲经中较粗感觉纤维的轴浆运输。     

On the induced electric field gradients in the human body for magnetic stimulation by gradient coils in MRI

Prior theoretical studies indicate that the negative spatial derivative of the electric field induced by magnetic stimulation may be one of the main factors contributing to depolarization of the nerve fiber. This paper studies this parameter for peripheral nerve stimulation (PNS) induced by time-varying gradient fields during MRI scans. The numerical calculations are based on an efficient, quasi-static, finite-difference scheme and an anatomically realistic human, full-body model. Whole-body cylindrical and planar gradient sets in MRI systems and various input signals have been explored. The spatial distributions of the induced electric field and their gradients are calculated and attempts are made to correlate these areas with reported experimental stimulation data. The induced electrical field pattern is similar for both the planar coils and cylindrical coils. This study provides some insight into the spatial characteristics of the induced field gradients for PNS in MRI, which may be used to further evaluate the sites where magnetic stimulation is likely to occur and to optimize gradient coil design.     

Closed-loop stimulation of hypoglossal nerve in a dog model of upper airway obstruction

Electrical stimulation of upper airway (UAW) muscles has been under investigation as a treatment method for obstructive sleep apnea (OSA). Particular attention has been given to the electrical activation of the genioglossal muscle, either directly or via the stimulation of the hypoglossal nerve (HG), since the genioglossus is the main tongue protrusor muscle. Regardless of the stimulation site or method, an implantable electrical stimulation device for OSA patients will require a reliable method for detection of obstructive breaths to apply the stimulation when needed. In this paper, we test the hypothesis that the activity of the HG nerve can be used as a feedback signal for closed-loop stimulation of the HG nerve in an animal model of UAW obstruction where a force is applied on the submental region to physically narrow the airways. As an advantage, the method uses a single electrode for both recording and stimulation of the HG nerve. Simple linear filtering techniques were found to be adequate for producing the trigger signal for the electrical stimulation from the HG recordings. Esophageal pressure, which was used to estimate the size of the UAW passage, returned to the preloading values during closed-loop stimulation of the HG nerve. The data demonstrate the feasibility of the closed-loop stimulation of the HG nerve using its activity as the feedback signal.     

Magnetic Measurements of Action Currents in a Single Nerve Axon: A Core-Conductor Model

Measurements have been performed on the medial giant axon of the crayfish in which both microelectrode recordings of the transmembrane action potential and magnetic recordings of the axial, intracellular action current were obtained at a single location along the nerve. This approach is unique because the combination of electric and magnetic techniques allows for independent measurements of transmembrane potential and intracellular current without assumptions regarding membrane capacitance or axonal resistances. The availability of both types of data recorded at a single location on the axon allows the core-conductor model to be solved explicitly for the internal axial resistance of the axon, the membrane capacitance, and the membrane conduction current density without the need to make a series of subthreshold measurements of passive cable properties. The extracellular magnetic measurements can be used both to determine the transmembrane action potential without the need to penetrate the nerve membrane with a microelectrode, and to obtain approximate values for the sodium and potassium peak conductances.     

Magnetic Assembly of a Multifunctional Guidance Conduit for Peripheral Nerve Repair

Nerve growth conduits are designed to support and promote axon regeneration following nerve injuries. Multifunctionalized conduits with combined physical and chemical cues, are a promising avenue aimed at overcoming current therapeutic barriers. However, the efficacious assembly of conduits that promote neuronal growth remains a challenge. Here, a biomimetic regenerative gel is developed, that integrates physical and chemical cues in a biocompatible “one pot reaction” strategy. The collagen gel is enriched with magnetic nanoparticles coated with nerve growth factor (NGF). Then, through a remote magnetic actuation, highly aligned fibrillar gel structure embedded with anisotropically distributed coated nanoparticles, combining multiple regenerating strategies, is obtained. The effects of the multifunctional gels are examined in vitro, and in vivo in a 10-mm rat sciatic nerve injury model. The magneto-based therapeutic conduits demonstrate oriented and directed axonal growth, and improve nerve regeneration in vivo. The study of multifunctional guidance scaffolds that can be implemented efficiently and remotely provides the foundation to a novel therapeutic approach to overcome current medical obstacles for nerve injuries.     

A 3-D differential coil design for localized magnetic stimulation

A novel three-dimensional (3-D) differential coil has been designed for improving the localization of magnetic stimulation. This new coil design consists of a butterfly coil with two additional wing units and an extra bottom unit, both perpendicular to the plane of the butterfly coil. The wing units produce opposite fields to restrict the spread of induced fields while the bottom unit enhances the induced fields at the excitation site. The peak induced field generated by this new design is located at the center of the coil, providing an easy identification of the excitation site. The field localization of the new coil is comparable with that of much smaller coils but with an inductance compatible to current magnetic stimulators. Numerical computations based on the principles of electromagnetic induction and using a human nerve model were performed to analyze the induced fields and the stimulation thresholds of new coil designs. The localization of the coil design was assessed by a half power region (HPR), within which the magnitude of the normalized induced field is greater than 1/square root of 2. The HPR for a 3-D differential coil built is improved (decreased) by a factor of three compared with a standard butterfly coil. Induced fields by this new coil were measured and in agreement with theoretical calculations.     

Improved coil design for functional magnetic stimulation of expiratory muscles

Our studies have demonstrated effective stimulation of the expiratory muscles in patients with spinal cord injury (SCI) using functional magnetic stimulation (FMS). The observed contraction of the expiratory muscles and functional improvement of the pulmonary functions make functional magnetic stimulation an appropriate tool for expiratory muscle training. To fully capitalize on the benefits of FMS for expiratory muscle training, this study aimed to optimize the magnetic coils (MCs). The primary goal of this study was to investigate how two parameters of the MC size and winding structure, would affect expiratory muscle training. By varying these parameters, our approach was to conceptualize and evaluate the induced electric field and nerve activation function distributions of six coils, round 9.2, 13.7, and 20 cm, and spiral 9.2-, 13.7-, and 20-cm coils in the computer modeling phase. Round 9.2 cm, spiral 13.7 cm, and spiral 20-cm coils were also evaluated in experimental studies for induced electrical field and in clinical studies of expiratory muscles. Both the computer models and experimental measurements indicated that the spiral 20-cm coil can not only stimulate more expiratory spinal nerves but can also stimulate them more evenly. In addition, coils with larger diameters had better penetration than those with smaller diameters. The clinical results showed that the spiral 20-cm coil produced higher expiratory pressure, flow, and volume in five able-bodied subjects, and it was the coil of choice among the subjects when asked their preferences. In our attempt to optimize MC design for FMS of expiratory muscle training, we followed the designing guidelines set out in our previous study and arrived at a more effective tool.     

Energy-optimal electrical excitation of nerve fibers

We derive, based on an analytical nerve membrane model and optimal control theory of dynamical systems, an energy-optimal stimulation current waveform for electrical excitation of nerve fibers. Optimal stimulation waveforms for nonleaky and leaky membranes are calculated. The case with a leaky membrane is a realistic case. Finally, we compare the waveforms and energies necessary for excitation of a leaky membrane in the case where the stimulation waveform is a square-wave current pulse, and in the case of energy-optimal stimulation. The optimal stimulation waveform is an exponentially rising waveform and necessitates considerably less energy to excite the nerve than a square-wave pulse (especially true for larger pulse durations). The described theoretical results can lead to drastically increased battery lifetime and/or decreased energy transmission requirements for implanted biomedical systems.     

Electronic implementation of a PWM electrical nerve stimulation system for medical treatment of acute and chronic pains

In this paper we will implement a transcutaneous electrical nerve stimulation (TENS) designed for medical applications in order to reduce acute and chronic pains. This procedure uses electrical currents pulses applied on the skin area via electrodes. Two kinds of stimulation are adopted: the peripheral nerve stimulation (PNS) and the spinal cord stimulation (SCS). In either, a small pulse generator sends electrical pulses to the nerves (in PNS stimulation) or to the spinal cord (SCS stimulation). Previous studies on TENS technique showed that the obtained results are not very satisfactory and depend on the patient’s state, condition, age, and stimulation parameters. In order to optimize the conditions and parameters stimulation during treatments, we present in this paper a new strategy called pulse width modulation stimulation (PWM-TENS) based on a parametric computing of frequency, current intensity, pulse duration of stimuli. To implement our approach, we used an embedded platform under Arduino-Uno with five several programs depending on the pain category and according to international medical standards and specifications. The first tests on 15 volunteer patients showed satisfaction ratio (EVA) after 5–12 days and a pain reduction between 80 and 20 after 1 month of stimulation. This result is important because it prolongs the analgesic effect and reduces therapeutic rehabilitation period. The medical aspect of the subject is to have a medical tool that allows objective evaluations for short and medium periods of pain treatments with dynamic evaluation metrics.     

Psychiatry's shocking new tools [brain stimulation techniques]

This paper describes several new brain stimulation techniques for treating patients suffering from severe depression. These techniques involve the use of electronic implants that send signals to specific points of the brain to reduce or eliminate severe chronic depression in some people. They are more effective alternatives to such treatment options as psychiatric counselling as well as drug and electroconvulsive therapy since their effects are longer lasting and they do not cause any side effects. These techniques are: vagus nerve stimulation, repetitive transcranial magnetic stimulation, magnetic seizure therapy, transcranial direct current stimulation, and deep brain stimulation.     

A simulation study of the combined thermoelectric extracellular stimulation of the sciatic nerve of the Xenopus laevis: the localized transient heat block

The electrical behavior of the Xenopus laevis nerve fibers was studied when combined electrical (cuff electrodes) and optical (infrared laser, low power sub-5?mW) stimulations are applied. Assuming that the main effect of the laser irradiation on the nerve tissue is the localized temperature increase, this paper analyzes and gives new insights into the function of the combined thermoelectric stimulation on both excitation and blocking of the nerve action potentials (AP). The calculations involve a finite-element model (COMSOL) to represent the electrical properties of the nerve and cuff. Electric-field distribution along the nerve was computed for the given stimulation current profile and imported into a NEURON model, which was built to simulate the electrical behavior of myelinated nerve fiber under extracellular stimulation. The main result of this study of combined thermoelectric stimulation showed that local temperature increase, for the given electric field, can create a transient block of both the generation and propagation of the APs. Some preliminary experimental data in support of this conclusion are also shown.     

Simultaneous Information and Power Transfer Using Magnetic Resonance

To deal with the major challenges of embedded sensor networks, we consider the use of magnetic fields as a means of reliably transferring both information and power to embedded sensors. We focus on a power allocation strategy for an orthogonal frequency‐division multiplexing system to maximize the transferred power under the required information capacity and total available power constraints. First, we consider the case of a co‐receiver, where information and power can be extracted from the same signal. In this case, we find an optimal power allocation (OPA) and provide the upper bound of achievable transferred power and capacity pairs. However, the exact calculation of the OPA is computationally complex. Thus, we propose a low‐complexity power reallocation algorithm. For practical consideration, we consider the case of a separated receiver (where information and power are transferred separately through different resources) and propose two heuristic power allocation algorithms. Through simulations using the Agilent Advanced Design System and Ansoft High Frequency Structure Simulator, we validate the magnetic‐inductive channel characteristic. In addition, we show the performances of the proposed algorithms by providing achievable ?‐C regions.     

A stochastic model of the electrically stimulated auditory nerve:single-pulse response

Most models of neural response to electrical stimulation, such as the Hodgkin-Huxley equations, are deterministic, despite significant physiological evidence for the existence of stochastic activity. For instance, the range of discharge probabilities measured in response to single electrical pulses cannot be explained at all by deterministic models. Furthermore, there is growing evidence that the stochastic component of auditory nerve response to electrical stimulation may be fundamental to functionally significant physiological and psychophysical phenomena. In this paper we present a simple and computationally efficient stochastic model of single-fiber response to single biphasic electrical pulses, based on a deterministic threshold model of action potential generation. Comparisons with physiological data from cat auditory nerve fibers are made, and it is shown that the stochastic model predicts discharge probabilities measured in response to single biphasic pulses more accurately than does the equivalent deterministic model. In addition, physiological data show an increase in stochastic activity with increasing pulse width of anodic/cathodic biphasic pulses, a phenomenon not present for monophasic stimuli. These and other data from the auditory nerve are then used to develop a population model of the total auditory nerve, where each fiber is described by the single-fiber model.     

头盔式动态可变多通道经颅磁刺激线圈的设计

为了实现真正意义上的动态可变多通道经颅磁刺激(TMS),首次提出了头盔式网状线圈的设计理念。基于该理念设计的TMS 线圈系统,可以在全头范围内实现多通道经颅磁刺激,而且在线圈定位、分辨率等方面得到极大改善,同时还可以实现刺激部位、面积、方式和强度的实时动态可变性。建立了人体头颅电磁模型来模拟TMS 线圈产生的诱导电流分布,同时还对线圈产生的诱导磁场分布进行了实际测量,模拟与实测结果均与理论值相符,证明了该设计的有效性与可行性。     

Peripheral nerve stimulation by gradient switching fields in magnetic resonance imaging

A heterogeneous model of the human body and the scalar potential finite difference method are used to compute electric fields induced in tissue by magnetic field exposures. Two types of coils are considered that simulate exposure to gradient switching fields during magnetic resonance imaging (MRI). These coils producing coronal (y axis) and axial (z axis) magnetic fields have previously been used in experiments with humans.The computed fields can, therefore, be directly compared to human response data. The computed electric fields in subcutaneous fat and skin corresponding to peripheral nerve stimulation (PNS) thresholds in humans in simulated MRI experiments range from 3.8 to 5.8 V/m for the fields exceeded in 0.5% of tissue volume (skin and fat of the torso). The threshold depends on coil type and position along the body, and on the anatomy and resolution of the human body model. The computed values are in agreement with previously established thresholds for neural stimulation.     

Analysis of efficiency of magnetic stimulation

Magnetic stimulation can activate excitable tissues noninvasively. However, this method requires high energy to operate and can produce equipment heat that leads to inefficient stimulation. In this study, a comprehensive optimization of efficiency for magnetic stimulation has been conducted. A total of 16 781 coil designs were tested in order to determine the optimal coil geometry and inductance for neural excitation. Induced electric fields were calculated to find the optimal stimulation site (OSS) of a given coil. The threshold energy of a magnetic pulse for neural excitation was then calculated based on the transmembrane responses of a nerve model. Simulation results show that there exists an optimal inductance, as a consequence of an optimal pulse duration, corresponding to a minimum threshold energy. A longer pulse width is required to obtain the maximum efficiency for axons with slower membrane dynamics, a longer coil-to-fiber distance, and greater values of resistance (R) and capacitance (C) of the resistance-inductance-capacitance circuit. The optimal geometry features a minimum coil height, suggesting a flat coil design for optimal efficiency. The dimension of the optimal coil design increases with the coil-to-fiber distance. Moreover, the cloverleaf design achieves the highest efficiency for infinitely long fibers whereas the butterfly design is optimal for terminating or bending fibers.