Magnetic stimulation of axons in a nerve bundle: Effects of current redistribution in the bundle

Recently, we developed a model of magnetic stimulation of a concentric axon in an anisotropic nerve bundle. In that earlier paper, we considered a single axon surrounded by a nerve bundle represented as a homogeneous anisotropic monodomain medium. In this paper we extend our previous calculations to examine excitation of axons within a nerve bundle without neglecting the presence of other axons in the nerve bundle. A three-dimensional axial symmetry volume conductor model is used to determine the transmembrane potential response along an axon due to induced electric fields produced by a toroidal coil. Our principal objective is to examine the effect of current redistribution to other axons in the bundle on excitation characteristics. We derive the transmembrane potential along an axon for two currently available models of current redistribution: the biodomain model and the spatial-frequency monodomain model. Results indicate that a reduction in the transmembrane potential along an axon due to the presence of other nerve fibers in the bundle is observed. Axons located at the periphery of a nerve bundle have lower thresholds and different excitation sites compared with axons located near the center of a nerve bundle.     

Computational analysis of thresholds for magnetophosphenes

In international guidelines, basic restriction limits on the exposure of humans to low-frequency magnetic and electric fields are set with the objective of preventing the generation of phosphenes, visual sensations of flashing light not caused by light. Measured data on magnetophosphenes, i.e. phosphenes caused by a magnetically induced electric field on the retina, are available from volunteer studies. However, there is no simple way for determining the retinal threshold electric field or current density from the measured threshold magnetic flux density. In this study, the experimental field configuration of a previous study, in which phosphenes were generated in volunteers by exposing their heads to a magnetic field between the poles of an electromagnet, is computationally reproduced. The finite-element method is used for determining the induced electric field and current in five different MRI-based anatomical models of the head. The direction of the induced current density on the retina is dominantly radial to the eyeball, and the maximum induced current density is observed at the superior and inferior sides of the retina, which agrees with literature data on the location of magnetophosphenes at the periphery of the visual field. On the basis of computed data, the macroscopic retinal threshold current density for phosphenes at 20?Hz can be estimated as 10?mA m(-2) (-20%?to + 30%, depending on the anatomical model); this current density corresponds to an induced eddy current of 14 μA (-20%?to + 10%), and about 20% of this eddy current flows through each eye. The ICNIRP basic restriction limit for the induced electric field in the case of occupational exposure is not exceeded until the magnetic flux density is about two to three times the measured threshold for magnetophosphenes, so the basic restriction limit does not seem to be conservative. However, the reasons for the non-conservativeness are purely technical: removal of the highest 1% of electric field values by taking the 99th percentile as recommended by the ICNIRP leads to the underestimation of the induced electric field, and there are difficulties in applying the basic restriction limit for the retinal electric field.     

Action potentials induce uniform calcium influx in mammalian myelinated optic nerves

The myelin sheath enables saltatory conduction by demarcating the axon into a narrow nodal region for excitation and an extended, insulated internodal region for efficient spread of passive current. This anatomical demarcation produces a dramatic heterogeneity in ionic fluxes during excitation, a classical example being the restriction of Na influx at the node. Recent studies have revealed that action potentials also induce calcium influx into myelinated axons of mammalian optic nerves. Does calcium influx in myelinated axons show spatial heterogeneity during nerve excitation? To address this, we analyzed spatial profiles of axonal calcium transients during action potentials by selectively staining axons with calcium indicators and subjected the data to theoretical analysis with parameters for axial calcium diffusion empirically determined using photolysis of caged compounds. The results show surprisingly that during action potentials, calcium influx occurs uniformly along an axon of a fully myelinated mouse optic nerve.     

Rapid penetration of potassium and other salts into the frog tongue papilla.

The permeabilities of the frog tongue epithelium for potassium and other ions during a short time span were investigated electrophysiologically. The fungiform papilla of the bullfrog tongue was suctioned into a U-shaped glass suction electrode, through which Ringer solution was circulated. Compound nerve action potentials were recorded antidromically from the electrode following electrical stimulation of the glossopharyngeal nerve. When more than 5-10 mM potassium salts, 30 mM RbCl, 30 mM CsCl, 0.025 g in dl solution tetrodotoxin, 0.1 g in dl solution lidocaine hydrochloride or 3 g in dl solution ethanol, each of which was dissolved in Ringer solution containing 1.9 mM KCl, were flowed through the suction electrode, only the negative components of action potentials were gradually reduced and finally disappeared. The time needed for 50% reduction of negative components was about 10 sec for 0.1 M potassium salts and longer for the nonelectrolytes. A single suctioned papilla, which was flowed with various test solutions, was stimulated electrically and the change in current threshold of the papillary nerve was measured by recording orthodromic action potentials from the glossopharyngeal nerve. The threshold decreased within 10 sec after 0.05 M BaCl2 was flowed, but increased within 10 sec after 0.1 M KCl was flowed. The reduction of negative components of nerve action potentials may be due to the conduction block induced by potassium and other ions invading to the space around axons terminals. The threshold change also may be induced by the ions reaching the axon. These results suggest that chemical substances can rapidly penetrate the tongue epithelium of the frog, reach the papillary nerve fibers and contribute or modify gustatory informations.     

Modulation of axonal excitability mediated by surround electric activity: An intra-axonal study

Summary Intra-axonal recordings were obtained in vitro from frog sciatic nerve axons. Adjusting whole nerve stimulation current to just subthreshold for the impaled axon elicited triphasic threshold changes in that axon. Threshold changes were determined by direct intra-axonal current application. Graded subthreshold depolarizations were present in many axons during the passage of action potentials in surrounding axons. When nerve branches were stimulated and axon recordings were obtained from the main nerve trunk, both branches, the one that activated the impaled axon and the one that did not, elicited threshold changes in the impaled axon. These data indicate on a cellular level that impulse activity in an intact nerve bundle can modulate the excitability of adjacent nonactivated fibers.Supported by the Medical Research Service of the Veterans Administration, a grant from the National Multiple Sclerosis Society (RG 1365), and the Culpeper Foundation     

Double sucrose gap voltage clamp in cardiac muscle

In double sucrose gap voltage clamp experimetns on frog atrial bundles the configuration of membrane current and contraction was used to estimate the quality of voltage control. Attention was focused on possible action potential activity along the test segment in response to depolarizing clamps. At low depolarizations large Na+ inward currents were observed while any tension response was missing. Transmembrane potential threshold for generation of a mechanical response was evaluated from conditioned (attenuated) action potentials. The mechanical threshold determined from action potential measurements was only slightly higher than that determined from step-clamp depolarizations. With clamp potentials below the threshold, then, any action potential activity induced by the inward current phase is expected to be rudimentary.     

Electrical phosphenes: on the influence of conductivity inhomogeneities and small-scale structures of the orbita on the current density threshold of excitation

Electrical and magnetic phosphenes, perceptions of light as a result of non-adequate stimulation of the eye by electrical current or magnetic induction, respectively, are one of the cornerstones to justify limit values for extreme low-frequency fields specified by statutory regulations. However, the mechanism and place of action, as well as the excitation threshold, remain unknown until now. We suggest that the origin of phosphene excitation is the synaptic layer of the eye. The current density threshold value for electrical phosphene excitation was numerically quantified for this area on the basis of a detailed geometrical model in original submillimetre resolution and specifically measured conductivities in the LF range. The threshold values found were 1.8 Am⁻² at 60 Hz and 0.3 Am⁻² at 25 Hz. These values are comparable with values of other excitable tissues. It has been shown that the current density threshold for phosphene generation depends on small-scale structures not taken into account by previous models.     

Ephaptic transmission in squid giant axons.

Some characteristics of ephaptic transmission of action potentials were investigated with squid giant axons. For these studies two isolated axons were placed side by side or, on occasion, a single long axon was looped to form an "ephapse" between the axon trunk and one of its main branches. Extracellular potentials measured adjacent to axons surrounded by a very restricted volume of liquid ranged up to 80 mV in magnitude and had a shape similar to that of the membrane current. Intracellular records of the same axon regions show small voltage deflections; however, the transmembrane voltage (Vm = Vi - Vo) has the appearance of normally propagated action potentials. Ephaptic transmission of action potentials is possible when the ephaptic region is submerged in oil, as well as when the region is immersed in low-calcium solutions. When the speed of the propagated action potential is lowered by replacing the normal artifical seawater (ASW) with low-sodium ASW, some ephaptic effects are enhanced. It is concluded that in regions in which axons are confined by restricted extracellular volume, the large extracellular voltage changes arising during the passage of an action potential in one can cause ephaptic excitation in another.     

A TTX-resistant propagating calcium action potential

The cross-commissural (CC) cell in the supraesophageal ganglion of the giant barnacle, Balanus nubilus, was stimulated intrasomatically and antidromically in normal saline and 3 X 10(-7) M tetrodotoxin (TTX) saline. The action potential in normal saline contained both sodium and calcium components, each independently capable of propagation. Evidence that the action potential in TTX saline was calcium dependent included: the amplitude of the spike in TTX saline increased monotonically with increasing calcium; it was blocked by the calcium channel blockers La, Ni, Cd and Co; and equimolar substitution of Ba or Sr for Ca in TTX saline supported regenerative activity. Evidence that the calcium component could propagate alone included: the distance over which the calcium action potential traveled exceeded the space constant of the axon; the biphasic nature of the extracellularly recorded action potential, which propagated to the axon in the nerve root, indicated inward regenerative current was occurring on the axon; electrotonically spread potentials were clearly distinguishable from active regenerative potentials. In addition, optical experiments using the calcium indicator dye arsenazo III (28) showed that the relative magnitude of the calcium signal was not diminished along the axon in TTX saline compared with normal saline. The critical external calcium concentration necessary to support the propagating action potential in TTX saline was estimated to be between 1.25 and 5 mM. To our knowledge, this is the first direct observation of a neuron with sodium and calcium channels of apparently normal kinetics where the calcium component alone can propagate in the absence of an outward current blocker. Our results suggest that there is a greater density of calcium channels on the CC axon than on the axons of other neurons.     

Functional role of low-voltage-activated dihydropyridine-sensitive Ca channels during the action potential in adult rat sensory neurones

Neuronal cell firing is crucial to nerve-nerve communication. The ability to produce consecutive action potentials is related to the activation of inward currents after each upstroke. If fast Na current is indeed responsible for the overshoot, it is still unclear which current drives membrane voltage to the Na threshold. In this study we present evidence that in adult rat sensory neurones a dihydropyridine-sensitive Ca channel exists in addition to the well characterized L-type, or high-threshold Ca channel. During stimulated action potential trains, L-type Ca channels open during the excitation wave, whereas activity of the other dihydropyridine-sensitive Ca channel was observed primarily between action potentials. This second Ca pathway shows remarkably long openings at negative potentials after a series of positive prepulses. The nerve action potential and the repetitive firing work as a physiological Ca channel facilitation mechanism. Therefore, we suggest that this novel Ca conductance provides inward current, between two consecutive action potentials, able to modulate the frequency of neuronal bursts. Received: 3 August 1995/Received after revision: 9 October 1995/Accepted: 10 October 1995     

The basic mechanism for the electrical stimulation of the nervous system

Neural signals can be generated or blocked by extracellular electrodes or magnetic coils. New results about artificial excitation are based on a compartmental model of a target neuron and its equivalent electrical network, as well as on the theory of the generalized activating function. The analysis shows that: (i) in most cases, the origin of artificial excitation is within the axon and the soma is much more difficult to excite; (ii) within the central nervous system, positive and negative threshold currents essentially depend on the position and orientation of the neurons relative to the applied electric field; (iii) in several cases, stimulation with positive currents is easier; and (iv) it should be possible to excite synaptic activity without the generation of propagating action potentials. Furthermore, the theory of the generalized activating function gives hints to understanding the blockage of neural activity.     

Transmembrane potential generated by a magnetically induced transverse electric field in a cylindrical axonal model

During the electrical stimulation of a uniform, long, and straight nerve axon, the electric field oriented parallel to the axon has been widely accepted as the major field component that activates the axon. Recent experimental evidence has shown that the electric field oriented transverse to the axon is also sufficient to activate the axon, by inducing a transmembrane potential within the axon. The transverse field can be generated by a time-varying magnetic field via electromagnetic induction. The aim of this study was to investigate the factors that influence the transmembrane potential induced by a transverse field during magnetic stimulation. Using an unmyelinated axon model, we have provided an analytic expression for the transmembrane potential under spatially uniform, time-varying magnetic stimulation. Polarization of the axon was dependent on the properties of the magnetic field (i.e., orientation to the axon, magnitude, and frequency). Polarization of the axon was also dependent on its own geometrical (i.e., radius of the axon and thickness of the membrane) and electrical properties (i.e., conductivities and dielectric permittivities). Therefore, this article provides evidence that aside from optimal coil design, tissue properties may also play an important role in determining the efficacy of axonal activation under magnetic stimulation. The mathematical basis of this conclusion was discussed. The analytic solution can potentially be used to modify the activation function in current cable equations describing magnetic stimulation.     

Regulation of voltage-dependent excitatory responses to alpha,beta-methylene ATP, ATP and non-adrenergic nerve stimulation by dihydropyridines in the guinea-pig vas deferens

Simultaneous recordings of mechanical and intracellular electrical activity were obtained from the guinea-pig vas deferens, where nerve stimulation, ATP and the stable nucleotide analogue alpha,beta-methylene ATP elicited excitatory responses. Excitatory junction potentials and action potentials were elicited by low-frequency (trains of pulses, generally less than or equal to 2 Hz) field stimulation. alpha,beta-Methylene ATP and ATP elicited only concentration-dependent depolarizations at low concentrations, while higher concentrations elicited a superimposed action potential discharge which was accompanied by mechanical contraction. The voltage threshold at which action potential discharge was initiated by these three stimuli was about -45 mV (resting membrane potential averaged -66 mV). Action potential discharges and contractile responses were antagonized by nifedipine and augmented by Bay K 8644 at concentrations (1 and 0.5 microM, respectively) which exhibited only small effects on either excitatory junction potential amplitudes or nucleotide-induced depolarizations. Bay K 8644 enhanced and nifedipine antagonized the repolarization (rectification) phase of action potential discharge elicited by nerve stimulation and drugs; after-hyperpolarizations were prominent in the presence of Bay K 8644 (0.1-5 microM). Excitatory junction potentials were antagonized after exposure to alpha,beta-methylene ATP. This antagonistic effect of alpha,beta-methylene ATP was also observed following depolarizations elicited in the absence and presence of nifedipine (1 microM). Noradrenaline was approximately 50-100 times less potent than alpha,beta-methylene ATP in eliciting action potential discharge and contraction. It was only when a high concentration of noradrenaline was used (about 60-100 microM) that the noradrenaline-induced depolarization attained the voltage threshold for action potential initiation. These results illustrate the similarity of the electrical components which underlie excitation by nerve stimulation and adenine nucleotides in the vas deferens, and demonstrate the ability of dihydropyridines to regulate voltage-dependent events associated with both the generation and inactivation of muscle action potentials. These are probably voltage-dependent calcium currents and calcium-activated potassium currents, respectively. Neither excitatory junction potentials nor the mechanism of desensitization of the ATP purinoceptor by alpha,beta-methylene ATP involve voltage-dependent calcium channels.     

Isolation of Toxins from Buthus Occitanus Sp. Scorpion and Their Action on Excitability of Myelinated Nerve

A series of short neurotoxins (molecular weight 3500-5000 D) was isolated from Vietnamese scorpion B. occitanus sp. All these toxins blocked generation of action potentials (this effect depended on their molecular weight), but did not change conduction velocity and excitation threshold of the nerve.     

Effects of time-varying electromagnetic fields on K+ (Rb+) fluxes and surface charge of HeLa cells.

The magnetic flux density was varied intermittently from 0.35 to 1.77T and from 0.07 to 1.54 or 1.77T by manual and automatic switchings, respectively, of the power source of an electromagnet. The durations of the "switching-on time" and "-off time" were varied but kept equal. An electric eddy current induced in the culture medium by changes in the magnetic flux density was simulated. When the durations were shorter than 10s, ouabain-sensitive Rb+ influx (active K+ influx) into cultured HeLa cells was significantly inhibited, but the ouabain-insensitive Rb+ influx (passive K+ influx) was not influenced significantly. Inhibition of active Rb+ influx increased with time during exposure for 2 h. Conversely, K+ efflux from the cells was significantly stimulated by the exposure. Microfluorometric examinations of cells loaded with the fluorescent pH indicator 4-heptadecyl-7-hydroxycoumarin (6 microM) and the membrane potential indicator diS-C3-(5) (1 microM) suggested increase in the negative charge on the cell surface during exposure. The observed changes in the K+ (Rb+) fluxes would be related to change in the electric properties of the cell surface caused by exposure to intermittent electromagnetic fields.     

Effects of tubocurarine and eserine on the axon-Schwann cell relationship in the squid nerve fibre

The effects of eserine and D-tubocurarine on the axon and Schwann cell membrane potentials have been studied in the giant nerve fibre of the squid.1. The addition of eserine at concentrations of up to 10(-4)M to the external sea-water medium has no appreciable effects on either the Schwann cell electrical potential of unstimulated nerve fibres or on the resting and action potentials of the axon.2. However, eserine at a concentration of 10(-9)M prolongs the long-lasting Schwann cell hyperpolarizations which follow the conduction of impulse trains by the axon.3. Higher concentrations of eserine (10(-7), 10(-4)M) decrease and block the long-lasting effects of nerve impulse train conduction.4. D-tubocurarine at concentrations of up to 10(-5)M has no appreciable effect on the resting and action potentials of the axon.5. However, D-tubocurarine at a concentration of 10(-9)M blocks completely the hyperpolarizing effects of nerve impulse trains on the Schwann cell electrical potential.6. In addition to its blocking action, D-tubocurarine induces transient hyperpolarizations in the Schwann cells of unstimulated nerve fibres both in intact fibres and in slitted preparations.7. These findings suggest that a cholinergic system, which may be located at the axon-Schwann cell boundary, is involved in the genesis of the long-lasting Schwann cell hyperpolarization caused by the conduction of nerve impulse trains by the axon.     

Muscle compound motor action potentials from esophago-vertebral electrical stimulation of the spinal cord in the normal awake man

In 15 normal alert subjects, electrical stimulation of the spinal cord at various levels by a nasopharyngeal probe (cathode) and a vertebral surface electrode (anode) was performed with different orientation of the stimulating dipole. Maximum spinal cord compound motor action potentials (SCCMAPmax) simultaneously recorded from homologous muscles of the upper arm of both sides were not significantly different in amplitude and latency. By stimulating the spinal cord at the cervico-dorsal level it was possible to obtain simultaneous recordings of SCCMAP from muscles of the upper and lower limbs and trunk at a stimulus intensity of 50-70 mA. Stimulating the spinal cord and the peripheral nerve at Erb's point it was also possible to calculate motor propagation velocity of the peripheral nerve of limb-girdle muscles. Central latency of the F wave exceeded by 0.5 to 0.7 ms that of the SCCMAP, suggesting that esophago-vertebral stimulation is able to directly excite the motor neurons. By threshold current intensity, it is possible to obtain a threshold SCCMAP (SCCMAPth) of the same latency as SCCMAPmax and different in shape, duration and amplitude from the CMAP obtained by cortical stimulation with threshold magnetic stimuli. SCCMAPth was different in shape from the motor unit action potential activated at weak voluntary effort, SCCMAPth latency and amplitude were unchanged after voluntary homo- and contralateral activation.     

Decremental Conduction,in Normal Human Nerves Subjected to Ischemia?

The effect of ischemia on the maximal orthodromic sensory and motor nerve conduction was studied in the digit 1-elbow segment of the median nerve in 24 normal subjects. Action potentials were recorded at 2, 3 or 4 sites along the nerve. The latency of the potentials increased as a function of the duration of ischemia and of the distance from the point of stimulation. The earliest indication of an impaired nerve function was a decrease in the sensory action potential amplitude. During ischemia the length of the nerve segment, through which the potential was propagated, gradually became shortened. This was seen in sensory as well as in motor nerves. The sensory threshold to electrical stimuli (digit 3) had a two-phasic course: During 15 min of ischemia it was almost stationary despite a severe reduction of the conduction velocity and of the potential amplitude. Then a rapid increase took place, coincicling with the extinction of the potential recorded at the elbow just below the occlucling cuff. The conduction parameters were normalized shortly after reestablishment of the circulation in the arm. The results indicate that action potentials become conducted with decrement during ischemia.     

Effect of subcutaneous fat thickness and surface electrode configuration during neuromuscular electrical stimulation

The effect of subcutaneous fat thickness, electrode size and inter-electrode distance on the minimum stimulus current necessary for fiber excitation was examined in an attempt to improve the efficacy of neuromuscular electrical stimulation (NMES) in obese populations. A three-dimensional finite element model of the human thigh was developed and used to calculate the potential along a myelinated nerve fiber due to NMES. The activating function was used to examine alterations in the excitation of the fiber due to fat thickness, electrode size and inter-electrode distance. The finite element model was coupled to a neural model to examine the stimulus current required for action potential propagation. The stimulus current required to evoke 10% of the maximum M-wave amplitude was measured experimentally. Both experimental and modeling studies indicated that the stimulus current required to reach the threshold for muscle activation increased with fat thickness, electrode size, and inter-electrode distance. However, as fat thickness increased, the threshold for muscle activation became less sensitive to inter-electrode distance and electrode size. These results suggest that by using larger electrodes above regions of high subcutaneous fat thickness, the efficacy of NMES could be maintained while reducing the current density at the skin and the associated subject discomfort.     

Is action potential threshold lowest in the axon?

Action potential threshold is thought to be lowest in the axon, but when measured using conventional techniques, we found that action potential voltage threshold of rat cortical pyramidal neurons was higher in the axon than at other neuronal locations. In contrast, both current threshold and voltage threshold of the isolated somato-dendritic spike were substantially higher at the soma. These data indicate that action potential threshold is indeed lowest in the axon.