The extracellular potential field of the single active nerve fiber in a volume conductor

The potential field of an active fiber in a uniform medium of infinite extent and within a nerve trunk is calculated from transmembrane potential data. The resulting distributions are given quantitatively. A comparison of both magnitude and field pattern in the nerve trunk and infinite medium environments is made and the effect of interstitial conductivity and nerve trunk diameter on potential magnitudes is considered.     

Augmenting peripheral nerve regeneration using stem cells: A review of current opinion

Outcomes following peripheral nerve injury remain frustratingly poor. The reasons for this are multifactorial, although maintaining a growth permissive environment in the distal nerve stump following repair is arguably the most important. The optimal environment for axonal regeneration relies on the synthesis and release of many biochemical mediators that are temporally and spatially regulated with a high level of incompletely understood complexity. The Schwann cell(SC) has emerged as a key player in this process. Prolonged periods of distal nerve stump denervation, characteristic of large gaps and proximal injuries, have been associated with a reduction in SC number and ability to support regenerating axons. Cell based therapy offers a potential therapy for the improvement of outcomes following peripheral nerve reconstruction. Stem cells have the potential to increase the number of SCs and prolong their ability to support regeneration. They may also have the ability to rescue and replenish populations of chromatolytic and apoptotic neurons following axotomy. Finally, they can be used in non-physiologic ways to preserve injured tissues such as denervated muscle while neuronal ingrowth has not yet occurred. Aside from stem cell type, careful consideration must be given to differentiation status, how stem cells are supported following transplantation and how they will be delivered to the site of injury. It is the aim of this article to review current opinions on the strategies of stem cell based therapy for the augmentation of peripheral nerve regeneration.     

Kinetics of the slow variation of peak sodium current in the membrane of myelinated nerve following changes of holding potential or extracellular pH.

(1) Changes of the holding potential applied to the membrane of myelinated nerve fibres induced slow variations of the peak sodium current, which are super-imposed on the effect of sodium inactivation. (2) These slow variations are transitions between various steady levels of available sodium conductance. Their time course can be described by the function erfc (square root t/tau) where tau is the time and erfc the error function complement. The characteristic time tau lies in the range 2-4 min and depends on the membrane potential. (3) Changes of extracellular pH cause a rapid change of the peak sodium current followed by a slow variation as observed after changes of the holding potential. This slow variation can be prevented by applying simultaneously an appropriate change of the holding potential, e.g. the effect of changing pH from 7.3 to 5.3 is balanced by changing the potential from --70 to --55 mV. (4) The results are interpreted by postulating charged components diffusion slowly within the nodal membrane. Their transverse distribution controls the number of sodium channels available at a given membrane potential. The equivalence between change of pH and voltage is explained by assuming negative fixed charges at the outer surface of the membrane, which are protonated at low pH and thus affect the intrinsic membrane potential. (5) It is concluded that effects which are ascribed to the action of agents on individual sodium channels have to be corrected for variations in the number of available channels if these agents influence the intrinsic membrane potential, e.g. changes of extracellular pH.     

Extracellular currents and potentials of the active myelinated nerve fiber.

This paper is concerned with the accurate and rapid calculation of extracellular potentials and currents from an active myelinated nerve fiber in a volume conductor, under conditions of normal and abnormal conduction. The neuroelectric source for the problem is characterized mathematically by using a modified version of the distributed parameter model of L. Goldman and J. S. Albus (1968, Biophys. J., 8:596-607) for the myelinated nerve fiber. Solution of the partial differential equation associated with the model provides a waveform for the spatial distribution of the transmembrane potential V(z). This model-generated waveform is then used as input to a second model that is based on the principles of electromagnetic field theory, and allows one to calculate easily the spatial distribution for the potential everywhere in the surrounding volume conductor for the nerve fiber. In addition, the field theoretic model may be used to calculate the total longitudinal current in the extracellular medium (I0L(z)) and the transmembrane current per unit length (im(z)); both of these quantities are defined in connection with the well-known core conductor model and associated cable equations in electrophysiology. These potential and current quantities may also be calculated as functions of time and as such, are useful in interpreting measured I0L(t) and im(t) data waveforms. An analysis of the accuracy of conventionally used measurement techniques to determine I0L(t) and im(t) is performed, particularly with regard to the effect of electrode separation distance and size of the volume conductor on these measurements. Also, a simulation of paranodal demyelination at a single node of Ranvier is made and its effects on potential and current waveforms as well as on the conduction process are determined. In particular, our field theoretic model is used to predict the temporal waveshape of the field potentials from the active, non-uniformly conducting nerve fiber in a finite volume conductor.     

The distribution of membrane current in nerve with longitudinal linearly increasing applied current

The distribution of membrane current in three models of nerve, when a longitudinal, linearly increasing current is applied, is derived. For the simple core conductor model it is shown that, if the region over which such a current is applied is large compared to the space constant of the model, the membrane current in the mid-portion of the region is a constant, independent of the distance, the time following the application of the current, and the impedance of the membrane. The effect of nonlinear membrane electrical properties is discussed. It is further shown that these conclusions apply equally to the case in which the simple model is surrounded by another concentric sheath (the double cable model). In this case the impedance of the sheath does not influence the membrane current in the mid-polar region. Finally, it is shown that the form of the solution for the saltatory model, for this type of applied current, is identical with that for the simple model.     

Non-stationary fluctuation analysis of the Na current in myelinated nerve fibers of Xenopus laevis: experiments and stochastic simulations

Na current fluctuations under voltage-clamp conditions during pulse steps in the potential range from -65 to -30 mV were measured in myelinated nerve fibers of Xenopus laevis. The covariance functions for four consecutive 1 ms intervals were calculated. The time courses of the covariance functions were well fitted with monoexponential functions with time constants between 0.5 and 3 ms, larger at the end of the pulse and larger at more positive potentials. To analyze the underlying channel kinetics we simulated current fluctuations at a step to -35 mV of eight published Na channel models and calculated corresponding covariance functions. None of the models did explain the experimental fluctuation results. We therefore developed a new Na channel model that satisfactorily described the results. Features that distinguished this model from the other tested ones were a slower deactivation rate, and an inactivation transition directly from a closed state.     

Effects of some chemical reagents on sodium current inactivation in myelinated nerve fibers of the frog.

The effect of several chemical reagents on the sodium current was studied in voltage-clamped single nerve fibers of the frog. The oxidants halazone and hypochlorous acid drastically inhibited inactivation. Their effect was similar to that of chloramine T (Wang, 1984a). The curve relating the steady-state inactivation parameter h infinity to the conditioning potential E became nonmonotonic after treatment with the oxidants, i.e., dh infinity/dE greater than 0 for E greater than -20 mV. By contrast, the oxidants periodate, iodate, and hydrogen peroxide (applied for the same time, but at higher concentrations) merely produced a parallel shift of the h infinity(E) curve to more negative values of membrane potential. Diethylpyrocarbonate, a reagent that preferentially modifies histidine groups, had one marked effect: a strong shift of the h infinity(E) curve to more negative values of membrane potential. Almost no effect was observed after application of the tyrosine-reactive reagent N-acetylimidazole. Similarly, the arginine-reactive reagent glyoxal had only minor effects on the Na permeability. The results suggest that methionine is not critically involved in the kinetics of Na current inactivation. Similarly, an essential tyrosine or arginine residue seems to be unavailable to chemical reagents from outside on the frog node of Ranvier. Deduced from the reactivities of (some of) the reagents used, modification of membrane lipids is a tentative explanation for the effects observed on inactivation kinetics.     

The effects of polarizing current on nerve terminal impulses recorded from polymodal and cold receptors in the guinea-pig cornea

It was reported recently that action potentials actively invade the sensory nerve terminals of corneal polymodal receptors, whereas corneal cold receptor nerve terminals are passively invaded (Brock, J.A., S. Pianova, and C. Belmonte. 2001. J. Physiol. 533:493-501). The present study investigated whether this functional difference between these two types of receptor was due to an absence of voltage-activated Na(+) conductances in cold receptor nerve terminals. To address this question, the study examined the effects of polarizing current on the configuration of nerve terminal impulses recorded extracellularly from single polymodal and cold receptors in guinea-pig cornea isolated in vitro. Polarizing currents were applied through the recording electrode. In both receptor types, hyperpolarizing current (+ve) increased the negative amplitude of nerve terminal impulses. In contrast, depolarizing current (-ve) was without effect on polymodal receptor nerve terminal impulses but increased the positive amplitude of cold receptor nerve terminal impulses. The hyperpolarization-induced increase in the negative amplitude of nerve terminal impulses represents a net increase in inward current. In both types of receptor, this increase in inward current was reduced by local application of low Na(+) solution and blocked by lidocaine (10 mM). In addition, tetrodotoxin (1 microM) slowed but did not reduce the hyperpolarization-induced increase in the negative amplitude of polymodal and cold nerve terminal impulses. The depolarization-induced increase in the positive amplitude of cold receptor nerve terminal impulses represents a net increase in outward current. This change was reduced both by lidocaine (10 mM) and the combined application of tetraethylammomium (20 mM) and 4-aminopyridine (1 mM). The interpretation is that both polymodal and cold receptor nerve terminals possess high densities of tetrodotoxin-resistant Na(+) channels. This finding suggests that in cold receptors, under normal conditions, the Na(+) conductances are rendered inactive because the nerve terminal region is relatively depolarized.     

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.     

The effect of n-alkanols on the stationary current voltage behavior and action potential of myelinated nerve

Stationary current voltage characteristics and the action potential of single myelinated nerve fibres were measured to examine the effect of $\text{n-}\text{alkanols}$ (methanol to octanol) on the electrophysiological function of the axon membrane. K⁺-depolarized membranes show alkanol-dependent shifts of $\text{V}{}_{\mathrm{<mtext>Tr</mtext>}}$, the membrane transition voltage, whereas in veratridine-depolarized membranes such $\text{V}{}_{\mathrm{<mtext>Tr</mtext>}}\text{-}\text{shifts}$ are not observed. In the latter case, $\text{n-}\text{alkanols}$ reduce both the stationary Na⁺ current and the conductivity step between the high- and low-ohmic conductivity state of the membrane. Action potential amplitude, however, is less affected by the alkanols as is the stationary Na⁺ current. The results are compared with the alkanol-dependent changes of the thermotropic phase transition in phospholipid bilayers.     

Laminar distribution of current sources in the rabbit superior colliculus during optic nerve stimulation

The electric field of evoked potentials developing in the rabbit superior colliculus in response to single electrical stimulation of the optic nerve was investigated. Regions of localization of sources and sinks of synaptic current creating the evoked potential were discovered by the current source density analysis method. Sinks with the shortest latency appeared in the depth of str. griseum superficiale, after which activity created by two dipoles appeared: The sink of one dipole was located in the upper part of str. griseum superficiale, the sink of the other in the lower part. The sinks thus found corresponded in their temporal characteristics and location to the principal components of the combined evoked potential. On the basis of these data the order of activation of the various systems of fibers and synapses responsible for evoked potential formation can be traced.     

The radial decline of nerve impulses in a restricted cylindrical extracellular space

In order to increase the potentials recorded extracellularly from nerve fibres, peripheral nerves are often placed in restricted space with cylindrical geometry. Equations are derived for computing the potentials expected at the surface of the cylinder, based on the potentials at the external surface of a small nerve fibre located on the long axis of the cylinder. These equations are evaluated numerically, using two formulae for a nerve impulse given in the literature. In both cases there is little attenuation for cylinders with radii less than 0.5 mm, but the potential declines approximately as a power of radius b for 1<b<10 mm. Various factors which might affect these results under different experimental conditions are discussed.     

The harvest and clinical application of the superficial peroneal sensory nerve for grafting motor and sensory nerve defects.

Potential donor nerves for autografting are finite and usually limited to cutaneous nerves of the extremities. The superficial peroneal nerve is the major lateral branch of the common peroneal nerve that innervates the peroneus longus and brevis muscles and provides sensation to the lateral aspect of the lower leg and the dorsal foot. It has generally been overlooked as a potential donor of nerve autografts. Cadaver dissections were performed on 10 fresh lower extremity specimens to investigate the anatomic characteristics of the superficial peroneal nerve and to refine a harvesting technique for the nerve. Thirty-one patients underwent nerve grafting of 39 upper and lower extremity nerves using the superficial peroneal donor. There were nine median nerves, four ulnar nerves, two radial nerves, two brachial plexus lesions, 16 digital nerves, and six lower extremity nerves grafted. The superficial peroneal nerve provided a consistently long donor, comparable in length to the sural nerve. The anatomic pattern is consistent, the patient positioning is simple, the surgical harvesting technique is straightforward, and the donor defect is acceptable. The superficial peroneal nerve provides a safe and valuable donor nerve, particularly in cases where multiple or very long nerve grafts are required.     

Substance P-, CGRP- and NPY-immunoreactive nerve fibers in rat sciatic nerve-end neuromas

Substance P (SP)-, calcitonin gene-related peptide (CGRP)- and neuropeptide Y (NPY)-immunoreactive nerve fibers were examined in experimental sciatic nerve-end neuromas in the rat with immunohistochemical techniques. At 1-3 days after nerve ligation and section of the sciatic nerve there was an accumulation of SP-like immunoreactivity (SP-LI). Six days after the lesion there was, however, a marked reduction and the neuromas remained virtually depleted from SP-LI at survival times between 8 days and 3 months. CGRP-LI was strong at 1-5 days post-operatively. By 8 days, CGRP-LI was reduced, but a large number of axons were still immunoreactive, and remained immunolabelled up to 3 months. CGRP-LI nerve fibers formed endbulbs, and appeared to grow in both anterograde and retrograde directions. Fine fibers sprouts were first observed at 8 days, but preterminal branching in neuromas aged less than a month was uncommon. At early stages (1-3 days) after ligation, there was a marked accumulation of NPY-LI proximal to the nerve constriction. NPY-LI was reduced from 5 days and on, but many fibers remained NPY-positive and their growth pattern through proximal and distal neuroma segments could be determined. The present results thus may indicate a differential effect of nerve injury on neuropeptide expression: immunohistochemically detectable SP-LI rapidly disappears from sciatic nerve fibers trapped in nerve-end neuromas, but CGRP-LI and NPY-LI remain and are useful as neuroanatomical markers for two subclasses of sprouting axons. Furthermore, the findings suggest that both CGRP and NPY, but not SP, could be involved in ectopic electrical activity in experimental neuromas.     

Comparison of ion current noise predicted from different models of the sodium channel gating mechanism in nerve membrane

Summary The theoretical power density spectrumS(f) of ion current noise is calculated from several models of the sodium channel gating mechanism in nerve membrane. Sodium ion noise experimental data from the frog node of Ranvier [Conti, F.,et al. (1976),J. Physiol. (London) 262:699] is used as a test of the theoretical results. The motivation for recent modeling has been evidence for a coupling between sodium activation and inactivation from voltage clamp data. The two processes are independent of one another in the Hodgkin and Huxley (HH) model [Hodgkin, A.L., Huxley, A.F. (1952),J. Physiol. (London) 117:500] The noise data is consistent with HH, as noted by Contiet al. (1976). The theoretical results given here appear to indicate that only one case of coupling models is also consistent with the noise data.     

Semi-excitation in nerve and electric nerve model (ENM) (author's transl)]

The "semi-excitation" is an excitation (like phenomenon) found by the authors, first in ENM and then in nerve during observation of the action potential and impedance decrease associated with excitation. The phenomenon was further investigated in relation to the action potential and impedance decrease (for AC of 13 kHz) of the stimulated site on the sciatic nerve and ENM. The nature of the phenomenon was the following. 1. The configuration of the action potential and impedance decrease were almost the same as that of the (complete) excitation, but the durations of the potential change (plateau) and impedance decrease depended on entirely to the duration of stimulating current. 2. Submaximum amplitude of action potential and impedance decrease were graded by the intensity of the stimulating current, but the threshold of this excitation was found. 3. During or after the semi-excitation, absolute or relative refractory period was not found. 4. Both in nerve and ENM, transition from complete excitation to semi-excitation or vice versa was observed. 5. Semi-excitation was found to occurr in the state of reduced membrane potential of the nerve and ENM.     

The role of slow potassium current in phenomena of voltage-dependent action of 4-aminopyridine in amphibian myelinated nerve fibres

The mechanism underlying the voltage-dependent action of 4-aminopyridine (4-AP) is investigated in experiments on amphibian myelinated nerve fibres (Rana ridibunda Pallas) by way of extracellular recording of electrical activity and using activators of potassium current (potassium-free solution and nitric oxide NO) and inhibitors of sodium current (tetrodotoxin). Measurement of action potential (AP) areas was used to evaluate the extent of general membrane depolarization during the activity of nerve fibres. Tetrodotoxin-induced decrease in general membrane depolarization (when the action potential amplitude was reduced by less than 20%) leads to an increase in the duration of depolarizing after-potential (DAP). This supports the dependence of time course of DAP in the presence of 4-AP on ratio of fast and slow potassium channels. In the absence of 4-AP, potassium-free solution and NO increase the potassium current through fast potassium channels (decreasing AP duration, reducing DAP and sometimes producing fast hyperpolarizing after-potential (HAP) after shortened AP), and in the presence of 4-AP these activators increase potassium current through unblocked slow potassium channels (making the development of slow HAP induced by 4-AP more rapid). The increase of slow HAP induced by 4-AP under the influence of potassium-free solution with NO supports the idea that slow HAP is due to activation of slow potassium channels and argues against the notion of removal of block of fast potassium channels. All analyzed phenomena of voltage-dependent action of 4-AP in amphibian myelinated nerve fibers can be accounted for by the activation of slow potassium current produced by membrane depolarization and a decrease of the amount of fast potassium channels involved in the membrane repolarization.     

Parameter estimation in Hodgkin-Huxley-Type equations for membrane action potentials in nerve and heart muscle

A method is presented which renders parameter estimation possible in systems of non-linear differential equations where normally no solution exists in terms of analytic functions and which have to be solved numerically. The method uses the concept of sensitivity equations. Two examples are given, taking mathematical models for membrane action potentials in nerve and heart muscle by Hodgkin and Huxley and by Beeler and Reuter. The model equations together with the corresponding system of sensitivity equations are given, which are necessary to estimate maximum conductivity coefficients defining the interactions of different ionic current components. A computer program is described and results of action potential numerical analysis are presented using simulated data. It can be seen, that even with superimposed simulated noise the real parameter values are estimated in an excellent manner. The method can be used to interpret observed changes in action potential time courses under physiological and pharmacological conditions.     

Rate of excitation propagation in a reduced Hodgkins-Huxley model. II. Slow relaxation of the sodium current]

The influence of sodium current activation on the value of nerve excitation conduction velocity is investigated on the basis of Hodgkin-Huxley model. The potassium activation and sodium inactivation are considered as slow processes which do not develop to an appreciable extent in the region of conduction velocity formation. The system of equations was derived and solved analytically after neglecting the dependency of sodium relaxation time on potential; the approximation of steady-state sodium activation was also used with the help of Hevyside function. The algebraic equation for conduction velocity was obtained; its solution has a simple analytical form in two limits of rapid and slow sodium current relaxation. The comparison with the experimental data has shown that at not very high temperatures the slow (compared to the potential dynamics) sodium current relaxation approximation is more appropriate. The dependency of impulse velocity on capacitance and conductance of the fiber was analyzed.     

The slow inward current, isi, in the rabbit sino-atrial node investigated by voltage clamp and computer simulation

The properties of the slow inward current, isi, in the sino-atrial (s.a.) node of the rabbit have been investigated using two microelectrodes to apply voltage clamp to small, spontaneously beating, preparations. Many of the experimental results can be closely simulated using the computer model of s.a. node electrical activity (Noble & Noble 1984) which has been developed from models of Purkinje fibre activity (Noble 1962; DiFrancesco & Noble 1984). Comparison of the computed reconstructions with experimental results provides a test of the validity of the modelling. Experiments using paired depolarizing clamp pulses show that inactivation of isi is calcium-entry dependent although, unlike the inactivation of Ca2+ currents in some other systems, it also shows some voltage-dependence. Re-availability (recovery from inactivation) of isi in s.a. node is much slower than inactivation at the same potential, showing that isi is not controlled by a single first order process. This very slow recovery from inactivation of isi in the s.a. node and the slow time course of its activation and inactivation at voltages near threshold (-40 to -50 mV) can be closely modelled by assuming that there are two components of 'total isi': a fast inward current, iCa,f' representing the 'gated' fraction and a second, slower, inward current component, iNaCa which, we propose, is caused by the sodium-calcium exchange that ensues when the initial Ca2+ -entry triggers the release of stored intracellular Ca2+. When repetitive trains of clamp pulses are given, a 'staircase' of isi magnitude is seen which can be increasing ('positive') or decreasing ('negative') according to the potential level and frequency of the pulse train given. When computer reconstructions of such staircases are made, it is found that the positive staircases (which, in contrast to negative staircases, imply that more complex processes than simple inactivation are present) can be closely simulated by a model which incorporates slower processes (suggested Na-Ca exchange current) in the total isi in addition to the gated current component.(ABSTRACT TRUNCATED AT 400 WORDS)