A Note on the Local Current Associated with the Rising Phase of a Propagating Impulse in Nonmyelinated Nerve Fibers

To extend our recent paper dealing with the cable properties and the conduction velocity of nonmyelinated nerve fibers (Bull. Math. Biol. 64, 1069; 2002), the behavior of the local current associated with the rising phase of a propagating action potential is discussed. It is shown that the process of charging the membrane capacity by means of the local current plays a crucial role in determining the velocity of nerve conduction. The symmetry of the local current with respect to the boundary between the resting and active regions of the nerve fiber is emphasized. It is noted that there are several simple quantitative rules governing the intensities of the capacitive, resistive and total membrane currents observed during the rising phase of an action potential.     

The velocity of conduction in nerve fiber and its electric characteristics

The theory developed in this paper shows that the propagation of spike potential along a nerve fiber and the conduction of an electric wave along an inert inorganic conductor follow a common quantitative relationship. This result gives further support to the belief that propagation of excitation is an electrical process. The basic idea of the theory is derived from the consideration that velocity has, by its mathematical definition, a local meaning; conduction in a nerve is completely determined by the local characteristics of the latter, as well as those of the wave. The final formula derived does not make use of any other field of science beyond the fundamental principles of electricity. It gives the conduction velocity in terms of the electric characteristics of the fiber and of the duration of the spike potential. The formula is in agreement with the known dependence of the conduction velocity on various parameters characterizing the axon. The computed velocity agrees with the measured ones on the squid giant axon, crab nerve axon, frog muscle fiber and Nitella cell. The membrane inductance appears as a velocity controling agent which prevents also a possible distortion of the spike potential during conduction. The structural meaning of the electric characteristics of the axon membrane is discussed from the viewpoint of the diffusion theory. A formula for the velocity of spread of the electrotonus is also derived.     

神经传导测定技术对腕管综合征病情评估的价值

目的:近年来腕管综合征发病率逐年升高,然而其慢性、隐匿性不易引起人们的重视,发现时往往已造成较大的危害。本文探讨腕管综合征的神经传导测定对病情评估的临床价值,旨在为患者腕管综合征早期发现和后续治疗提供进一步的临床参考依据。方法:选取我院124例确诊的腕管综合征患者。其中无大鱼际肌萎缩者有64例,并选取平均年龄相近的64例正常人作为对照(组A);有大鱼际肌畏缩者60例,并选取平均年龄相近的60例正常人作为对照(组B)。A、B组均经行神经电图检查,握力测定和两点辨别觉测定,分析神经传导速度改变与感觉、运动功能减退程度的关系。结果:A、B两组患者均有不同程度的神经传导改变:在A组患者神经传导改变中,运动和感觉传导速度(MCV和SCV)轻度下降,运动和感觉电位波幅(CMAP和SNAP)轻度下降,潜伏期(ML)轻度延长;在B组患者神经传导中,运动和感觉传导速度(MCV和SCV)明显下降,运动和感觉电位波幅(CMAP和SNAP)明显下降,潜伏期明显延长。结论:腕管综合征患者不同的临床表现有不同程度的神经电图表现,因此神经电图对神经传导的测定结果对腕管综合征患者的病情有良好的评估价值,值得临床推广。     

Spread of discrete structural changes in synthetic polyanionic gel: a model of propagation of a nerve impulse

Thin fibers of cross-linked polyacrylate gel were prepared by inducing polymerization reaction inside long glass or Tygon tubings. By immersing these gel fibers in salt solutions containing both Ca(2+) and Na(+) at varying ratios, a discontinuous transition from the swollen state to the shrunken was demonstrated. A very sharp boundary was observed between the swollen and shrunken portions of the gel fiber. It was found possible to displace this sharp boundary continuously by application of a weak electric current. Based on the similarity in swelling behavior between nerve fibers and synthetic gel fibers, a non-myelinated nerve fiber carrying an impulse was treated as a cylindrical gel layer consisting of two distinct portions, a swollen (active) portion connected directly to the remaining shrunken (resting) portion. By applying the cable theory to this model of the nerve fiber, mathematical expressions describing the conduction velocity, the maximum rate of potential rise, etc. in terms of the electric parameters of the fiber were derived.     

外周诱发电位的模型研究

本文根据容积导体中有关动作电位的电生理理论,用三点源模型模拟单根纤维动作电位(SFAP),并假设神经束的复合动作电位(CAP)是由SFAP线性叠加而成,给出了神经束CAP的模型.通过运用上述模型,计算了正常人正中神经纤维传导速度分布,分析了刺激腕部正中神经引导的传感诱发电位(SEP)的N~-_9成分;另外,还得出一些描述此外周传导通路性质的其它参数,如平均传导速度、神经纤维活动最可几传速度分布范围等.此方法可用来研究其它各种外围诱发电位.     

Effect of nonuniform interstitial space properties on impulse propagation: a discrete multidomain model

This work presents a discrete multidomain model that describes ionic diffusion pathways between connected cells and within the interstitium. Unlike classical models of impulse propagation, the intracellular and extracellular spaces are represented as spatially distinct volumes with dynamic/static boundary conditions that electrically couple neighboring spaces. The model is used to investigate the impact of nonuniform geometrical and electrical properties of the interstitial space surrounding a fiber on conduction velocity and action potential waveshape. Comparison of the multidomain and bidomain models shows that although the conduction velocity is relatively insensitive to cases that confine 50% of the membrane surface by narrow extracellular depths (≥2 nm), the action potential morphology varies greatly around the fiber perimeter, resulting in changes in the magnitude of extracellular potential in the tight spaces. Results also show that when the conductivity of the tight spaces is sufficiently reduced, the membrane adjacent to the tight space is eliminated from participating in propagation, and the conduction velocity increases. Owing to its ability to describe the spatial discontinuity of cardiac microstructure, the discrete multidomain can be used to determine appropriate tissue properties for use in classical macroscopic models such as the bidomain during normal and pathophysiological conditions.     

Ionic currents of the nodal membrane underlying the fastest saltatory conduction in myelinated giant nerve fibers of the shrimp Penaeus japonicus.

The myelinated giant nerve fiber of the shrimp, Penaeus japonicus, is known to have the fastest velocity of saltatory impulse conduction among all nerve fibers so far studied, owing to its long distances between nodal regions and large diameter. For a better understanding of the basis of this fast conduction, a medial giant fiber of the ventral nerve cord of the shrimp was isolated, and ionic currents of its presynaptic membrane (a functional node) were examined using the sucrose-gap voltage-clamp method. Inward currents induced by depolarizing voltage pulses had a maximum value of 0.5 microA and a reversal potential of 120 mV. These currents were completely suppressed by tetrodotoxin and greatly prolonged by scorpion toxin, suggesting that they are the Na current. Both activation and inactivation kinetics of the Na current were unusually rapid in comparison with those of vertebrate nodes. According to a rough estimation of the excitable area, the density of Na current reached 500 mA/cm2. In many cases, the late outward currents were induced only by depolarizing pulses larger than 50 mV in amplitude. The slope conductance measured from late currents were mostly smaller than that measured from the Na current, suggesting a low density of K channels in the synaptic membrane. These characteristics are in good harmony with the fact that the presynaptic membrane plays a role as functional node in the fastest impulse conduction of this nerve fiber.     

Evaluation of combined effects of brief electrical stimulation and Schwann-like cells on sciatic nerve injury model

Severe nerve injuries can be treated with electrical stimulation and stem cell therapies, but little is known about the potential benefits of combining these two treatments. In an effort to investigate this combination, we conducted a study to evaluate the effectiveness of electrical stimulation and Schwann-like cell transplantation in female Wistar albino rats. Our study consisted of five groups of rats: a sham group, an injury group, an electrical stimulation group, a Schwann-like cell group, and a combination group. The experimental groups received electrical stimulation, Schwann-like cell transplantation, or both. The animals sciatic function index was evaluated during a 6-week recovery period, and nerve conduction velocity, wet muscle mass, and nerve tissues were also analyzed. The results of the study showed that all experimental groups had a faster functional recovery compared to the injury group, although the difference between groups was not statistically significant. Both the combination group and the Schwann-like cell transplantation group had a higher nerve conduction velocity compared to the other experimental groups. However, there was no significant difference between the combination and Schwann-like cell transplantation groups. Nonetheless, histological analysis showed a better axonal reorganization in the combination group. The study provides preliminary evidence of the potential benefits of combining electrical stimulation and Schwann-like cell transplantation in treating severe nerve injuries. However, further studies with larger sample sizes are needed to confirm these findings and optimize the treatment parameters.     

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.     

Ionic currents of the nodal membrane underlying the fastest saltory conduction in myelinated giant nerve fibers of the shrimp Penaeus japonicus

The myelinated giant nerve fiber of the shrimp, Penaeus japonicus, is known to have the fastest velocity of saltatory impulse conduction among all nerve fibers so far studied, owing to its long distances between nodal regions and large diameter. For a better understanding of the basis of this fast conduction, a medial giant fiber of the ventral nerve cord of the shrimp was isolated, and ionic currents of its presynaptic membrane (a functional node) were examined using the sucrose-gap voltage-clamp method. Inward currents induced by depolarizing voltage pulses had a maximum value of 0.5 μA and a reversal potential of 120 mV. These currents were completely suppressed by tetrodotoxin and greatly prolonged by scorpion toxin, suggesting that they are the Na current. Both activation and inactivation kinetics of the Na current were unusually rapid in comparison with those of vertebrate nodes. According to a rough estimation of the excitable area, the density of Na current reached 500 mA/cm². In many cases, the late outward currents were induced only by depolarizing pulses larger than 50 mV in amplitude. The slope conductance measured from late currents were mostly smaller than that measured from the Na current, suggesting a low density of K channels in the synaptic membrane. These characteristics are in good harmony with the fact that the presynaptic membrane plays a role as functional node in the fastest impulse conduction of this nerve fiber.     

Conduction velocities and fiber diameters in a cutaneous nerve of the pigeon

Summary The characteristics of fibers of a cutaneous nerve supplying the wing skin of the pigeon have been investigated with electrophysiological and electron microscopic techniques.Recordings of the compound action potential showed four distinct peaks with conduction velocities of about 30 m/s, 12 m/s, 4 m/s and 0.5 m/s.From electron micrographs both fiber diameters and thickness of myelin sheath were assessed and used as criteria for segregating various fiber populations. Altogether four groups could be discerned: large thickly myelinated fibers, small thickly myelinated fibers, small thinly myelinated fibers, and unmyelinated or C-fibers. The subdivision of the thickly myelinated fibers into two populations is evidenced mainly by corresponding peaks in the compound action potential. The thinly myelinated fibers with a mean diameter of 2 m contributed about 90% of all myelinated fibers in this nerve.When comparing fiber dimensions and conduction velocities of this avian nerve with those of mammalian cutaneous nerves, the lower CV's of avian nerve fibers can be explained by smaller diameters and thinner myelin sheaths.The results of this investigation are a prerequisite for latency considerations in central somatosensory pathways in birds.Abbreviations CAP compound action potential - CV conduction velocity - D fiber diameter - d axon diameter - g ratio d/D - m thickness of myelin sheath     

Action currents, internodal potentials, and extracellular records of myelinated mammalian nerve fibers derived from node potentials.

The potential distribution within the internodal axon of mammalian nerve fibers is derived by applying known node potential waveforms to the ends of an equivalent circuit model of the internode. The complete spatial/temporal profile of action potentials synthesized from the internodal profiles is used to compute the node current waveforn, and the extracellular action potential around fibers captured within a tubular electrode. For amphibia, the results agreed with empirical values. For mammals, the amplitude of the node currents plotted against conduction velocity was fitted by a straight line. The extracellular potential waveform depended on the location of the nodes within the tube. For tubes of length from 2 to 8 internodes, extracellular wave amplitude (mammals) was about one-third of the product of peak node current and tube resistance (center to ends). The extracellular potentials developed by longitudinal and radial currents in an anisotropic medium (fiber bundle) are compared.     

Modeling the interactions between stimulation and physiologically induced APs in a mammalian nerve fiber: dependence on frequency and fiber diameter

Electrical stimulation of nerve fibers is used as a therapeutic tool to treat neurophysiological disorders. Despite efforts to model the effects of stimulation, its underlying mechanisms remain unclear. Current mechanistic models quantify the effects that the electrical field produces near the fiber but do not capture interactions between action potentials (APs) initiated by stimulus and APs initiated by underlying physiological activity. In this study, we aim to quantify the effects of stimulation frequency and fiber diameter on AP interactions involving collisions and loss of excitability. We constructed a mechanistic model of a myelinated nerve fiber receiving two inputs: the underlying physiological activity at the terminal end of the fiber, and an external stimulus applied to the middle of the fiber. We define conduction reliability as the percentage of physiological APs that make it to the somatic end of the nerve fiber. At low input frequencies, conduction reliability is greater than 95% and decreases with increasing frequency due to an increase in AP interactions. Conduction reliability is less sensitive to fiber diameter and only decreases slightly with increasing fiber diameter. Finally, both the number and type of AP interactions significantly vary with both input frequencies and fiber diameter. Modeling the interactions between APs initiated by stimulus and APs initiated by underlying physiological activity in a nerve fiber opens opportunities towards understanding mechanisms of electrical stimulation therapies.     

Conduction in bundles of demyelinated nerve fibers: computer simulation

This study presents a model of action potential propagation in bundles of myelinated nerve fibers. The model combines the single-cable formulation of Goldman and Albus (1967) with a basic representation of the ephaptic interaction among the fibers. We analyze first the behavior of the conduction velocity (CV) under the change of the various conductance parameters and temperature. The main parameter influencing the CV is the fast sodium conductance, and the dependence of CV on the temperature is linear up to 30 degrees C. The increase of myelin thickness above its normal value (5 microm) gives a slight increase in CV. The CV of the single fiber decreases monotonically with the disruption of myelin, but the breakdown is abrupt. There is always conduction until the thickness is larger than 2% of its original value, at which with at this point a sharp transition of CV to zero occurs. Also, the increase of temperature can block conduction. At 5% of the original thickness there is still spike propagation, but an increase of 2 degrees C causes conduction block. These results are consistent with clinical observations. Computer simulations are performed to show how the CV is affected by local damage to the myelin sheath, temperature alterations, and increased ephaptic coupling (i.e., coupling of electrical origin due to the electric neutrality of all the nerve) in the case of fiber bundles. The ephaptic interaction is included in the model. Synchronous impulse transmission and the formation of "condensed" pulse states are found. Electric impulses with a delay of 0.5 ms are presented to the system, and the numerical results show that, for increasing coupling, the impulses tend to adjust their speed and become synchronized. Other interesting phenomena are that spurious spikes are likely to be generated when ephaptic interaction is raised and that damaged axons suffering conduction block can be brought into conduction by the normal functioning fibers surrounding them. This is seen also in the case of a large number of fibers (N=500). When all the fibers are stimulated simultaneously, the conduction velocity is found to be strongly dependent on the level of ephaptic coupling and a sensible reduction is observed with respect to the propagation along an isolated axon even for low coupling level. As in the case of three fibers, spikes tend to lock and form collective impulses that propagate slowly in the nerve. On the other hand, if only 10% of fibers are stimulated by an external input, the conduction velocity is only 2% less than that along a single axon. We found a threshold value for the ephaptic coupling such that for lower values it is impossible to recruit the damaged fibers into conduction, for values of the coupling equal to this threshold only one fiber can be restored by the nondamaged fibers, and for values larger than the threshold an increasing number of fibers can return to normal functioning. We get values of the ephaptic coupling such that 25% of axons can be damaged without change of the collective conduction.     

The effect of temperature on a simulated systematically paranodally demyelinated nerve fiber

The temperature dependence (from 10° to 50°C) of the intracellular action potentials' parameters as well as of the ionic currents' kinetics in normal and demyelinated nerve fiber is studied. The simulation of the conduction in the normal fiber is based on the Frankenhaeuser and Huxley (1964) and Goldman and Albus (1968) equations, while in the case of a demyelinated fiber according to the same equations modified by Stephanova (1988). The temperature coefficients (Q ₁₀) for the rate constants as well as for the sodium and potassium permeabilities are introduced. It is shown that increased temperature blocks conduction in the simulated demyelinated fiber at temperatures much lower than the blocking temperature for the normal fiber. When temperature is increased, the amplitude as well as the wavelength and the asymmetry of the potential decrease. The relationship between conduction velocity and temperature is non-linear. The velocity increases when the temperature approaches the blocking temperature, after which abruptly drops. At a given degree of demyelination with increasing temperatures, the ionic currents' flow and the membrane conduction respectively increase, but, at lower temperatures, when the degree of the demyelination is increased, the conduction is blocked.     

Changes in the electrical activity of the rabbit proximal colon in vivo by stimulation of the vagus and splanchnic nerves]

1. Using extracellular electrodes placed on the serosa, we recorded the modifications of the electrical activity of the colonic muslce fibers caused by the stimulation of vagal and splanchnic nerve fibers. 2. Vagal stimulation produces two types of junction potentials: excitatory junction potentials (EJPs) and inhibitory junction potentials (IJPs). The IJPs are elicited by stimulation of vagal fibers which innervate intramural non-adrenergic inhibitory neurons. 3. The conduction velocity of the nerve impulse along the vagal pre-ganglionic fibers is 1.01 m/sec for excitatory fibers and 0.5. m/sec for inhibitory fibers. 4. Splanchnic fiber stimulation causes EJP disappearance, blocking transmission between preganglionic fibers and intramural excitatory neurons, and a decrease in IJP amplitude that most likely indicates a previous hyperpolarization of the smooth muscle. 5. IJP persistence during splanchnic stimulation proves that sympathetic inhibition does not modify the transmission of the vagal influx onto the non-adrenergic inhibitory neurons of the intramural plexuses. 6. Through a comparative study of proximal and distal colonic innervation, we are able to show that there is a similar organization of both regions, that is a double inhibitory innervation: an adrenergic one of a sympathetic origin, and a non adrenergic one of a parasympathetic origin.     

Action potential of the Garfish non-myelinated olfactory nerve.

The interesting Garfish olfactory nerve has been described by D. Easton (6). His structural analysis of the preparation shows homogeneous, uniform diametered axons measuring about 0.24 microns. The present study is an attempt to characterize its electrical and ionic property. The duration of the extracellularly measured action potential is about 60 msec at 20°C and increases to about 500 msec at 5°C, a time dispersion of about 8X. The conduction velocity varies from 20 cm/sec at 20°C to 4 cm/sec at 0°C. Recordings from small isolated fiber bundles have been shown to be viable. Reduction of sodium concentration to 5 mM in the external medium annihilates the A.P. response. Increase in external potassium concentration to about 16 mM makes the nerve inexcitable.     

TOCP对鸡迷走神经不同纤维成份传导速度和兴奋性的影响

对磷酸三邻甲苯醋(TOCP)染毒母鸡进行迷走神经不同纤维成份传导速度和兴奋性测定,发现实验组动物在染毒后14天迷走神经第5波(类似于C纤维)传导速度减慢30%,染毒后21天时减慢52%,并出现迷走神经各波兴奋性显著降低.实验结果说明,TOCP所致迟发性神经病可损害与内脏活动有关的迷走神经.     

A study of conduction velocity in nonmyelinated nerve fibers.

By treating a nonmyelinated nerve fiber as a continuous cable consisting of three distinct zones (Resting, transitional, and excited), the following mathematical expression was derived: (formula: see text) where v is the conduction velocity, d the diameter of the fiber, R the resistance of the membrane of unit area at the peak of excitation, rho the resistivity of the medium inside the fiber, and C the capacity of membrane per unit area. The validity of this expression was demonstrated by using squid giant nerve fibers intracellularly perfused with dilute salt solutions. The relationship between these results and previous theories and experiments on conduction velocity is discussed.