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.     

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.     

Diabetic polyneuropathy. 3. Electroneurographic findings in diabetics and their relationships to age and duration of diabetes

Nerve conduction velocities were determined in patients with diabetes mellitus: motor conduction of the median nerve in 778 patients, sensory conduction of the median nerve in 680 patients and motor conduction of the tibial nerve in 745 patients. In 40.9% out of 778 patients at least one of the three nerve conduction velocities were found within pathological ranges. 30.4% of 227 patients below 19 years of age in whom the duration of the disease did not exceed four years exhibited at least one delayed nerve conduction velocity. Clinical signs of polyneuropathy in children and in adolescents below 19 years of age are rare (0.6%). In contrast delayed nerve conduction velocities were found in 29.4%. Metabolic disturbance of peripheral nerve function is assumed to be responsible in these patients, for angiopathy in children and adolescents is very rare too.     

Changes in interspike interval during propagation: Quantitative description

The intervals between nerve impulses can change substantially during propagation because of conduction velocity aftereffects of previous impulse activity. Effects of such changes on interval histograms and on statistical parameters of spike trains were evaluated for Poisson spike trains and for trains generated by a clock with added random delays. The distribution of short intervals was significantly changed during propagation for these spike trains. Substantial changes in serial correlation coefficients were found in trains with certain initial interval distributions. The relevance of these effects to neural coding is discussed.     

ON THE THEORY OF NERVOUS CONDUCTION

Assuming that the propagation of the nervous impulse consists in the excitation of adjacent regions of the nerve by the action current of the already excited region, exact equations for the velocity of such a propagation are established and integrated. The result depends on the assumptions which we make about the laws of excitation. If Hoorweg''s law is accepted, it is found that the velocity of propagation decreases exponentially with time, and that there is a limiting distance which the impulse will travel and which cannot be exceeded. If however a set of equations proposed by L. Lapique is assumed to govern the process of excitation, we find that the velocity of propagation asymptotically reaches a constant value.     

A fundamental evaluation of the electrical properties and function of cardiac transverse tubules

This work discusses active and passive electrical properties of transverse (T-)tubules in ventricular cardiomyocytes to understand the physiological roles of T-tubules. T-tubules are invaginations of the lateral membrane that provide a large surface for calcium-handling proteins to facilitate sarcomere shortening. Higher heart rates correlate with higher T-tubular densities in mammalian ventricular cardiomyocytes. We assess ion dynamics in T-tubules and the effects of sodium current in T-tubules on the extracellular potential, which leads to a partial reduction of the sodium current in deep segments of a T-tubule. We moreover reflect on the impact of T-tubules on macroscopic conduction velocity, integrating fundamental principles of action potential propagation and conduction. We also theoretically assess how the conduction velocity is affected by different T-tubular sodium current densities. Lastly, we critically assess literature on ion channel expression to determine whether action potentials can be initiated in T-tubules.     

Neural conduction velocity of the human auditory nerve: bipolar recordings from the exposed intracranial portion of the eighth nerve during vestibular nerve section

We measured the conduction velocity of the intracranial portion of the auditory nerve in 3 patients undergoing vestibular nerve section to treat Ménière's disease. The conduction velocity varied from patient to patient, with an average value of 15.1 m/sec. The latency of peak III of the brain-stem auditory evoked potentials (BAEPs) increased by an average of 0.5 msec as a result of exposure of the eighth nerve, and if that increase is assumed to affect the entire length of the auditory nerve (2.6 cm) evenly, then the corrected estimate of conduction velocity would be 22.0 m/sec. Estimates of conduction velocity based on the interpeak latencies of peaks I and II of the BAEP, assuming that peak II is generated by the mid-portion of the intracranial segment of the auditory nerve, yielded similar values of conduction velocities (about 20 m/sec).     

Anisotropic propagation of Ca2+ waves in isolated cardiomyocytes.

Digital imaging microscopy of fluor-3 fluorescence was used to study the propagation of intracellular Ca2+ waves in isolated adult rat cardiomyocytes from 17 to 37 degrees C. Ca2+ waves spread in both transverse and longitudinal direction of a myocyte. Transverse propagation was pronounced in waves starting from a focus at the edge of a myocyte and in waves following an irregular, curved path (spiral waves). For the former type of waves, propagation velocities were determined. Both transverse and longitudinal wave components propagated at constant velocity ranging from 30 to 125 micron/s. Myocytes were anisotropic with respect to wave propagation: waves propagated faster in the longitudinal than in the transverse direction. The ratio between longitudinal and transverse velocity increased from 1.30 at 17 degrees C to 1.55 at 37 degrees C. Apparent activation energies for transverse and longitudinal wave propagation were estimated to be -20 kJ/mol, suggesting that these processes are limited by diffusion of Ca2+. Direction-dependent propagation velocities are interpreted to result from the highly ordered structure of the myocytes, especially from the anisotropic arrangement of diffusion obstacles such as myofilaments and mitochondria.     

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.     

Frequency Distribution of F-Latencies (DFL) has Physiological Significance and Gives Distribution of Conduction Velocity (DCV) of Motor Nerve Fibres With Implications for Diagnosis

On electrical stimulation of a peripheral motor nerve, a delayed and reduced F-response is obtained, which is known to occur due to random backfiring of a few percent of the motor nerve fibres at the spinal end after antidromic conduction. F-latencies obtained from multiple stimulations vary in latency, size and shape because of this randomness. We hypothesised that, being a random process, recruitment of fibres for F-response would depend on the distribution of conduction velocity (DCV) for motor nerve fibres directly, and therefore, a frequency distribution of F-latencies (DFL) from such multiple F-responses would be an approximate mirror image of DCV, latency being inversely proportional to velocity. First, obtaining DFL from many human subjects, we have shown that this is a reproducible parameter for a nerve trunk of a subject, and hence reveals a new physiological phenomenon. DFL has a single peaked distribution, which is also expected for the DCV of a normal healthy motor nerve. To validate its hypothesised relationship to DCV further, DFLs were obtained from both median nerves of patients with unilateral carpal tunnel syndrome (CTS). The patterns of DFL from both sides remained almost the same except for a delay shift equal to that in between the two M-responses, which lends support to this hypothesis. DFL, and DCV as its suggested mirror image, appear to change systematically with certain known disorders such as cervical spondylosis, even at a subclinical stage, which needs further study. This also indicates that DFL may become a new and improved investigative diagnostic tool in neurophysiology.     

Microdomain Effects on Transverse Cardiac Propagation

The effect of gap junctional coupling, sodium ion channel distribution, and extracellular conductivity on transverse conduction in cardiac tissue is explored using a microdomain model that incorporates aspects of the inhomogeneous cellular structure. The propagation velocities found in our model are compared to those in the classic bidomain model and indicate a strong ephaptic microdomain contribution to conduction depending on the parameter regime. We show that ephaptic effects can be quite significant in the junctional spaces between cells, and that the cell activation sequence is modified substantially by these effects. Further, we find that transverse propagation can be maintained by ephaptic effects, even in the absence of gap junctional coupling. The mechanism by which this occurs is found to be cablelike in that the junctional regions act like inverted cables. Our results provide insight into several recent experimental studies that indirectly indicate a mode of action potential propagation that does not rely exclusively on gap junctions.     

Microdomain Effects on Transverse Cardiac Propagation

The effect of gap junctional coupling, sodium ion channel distribution, and extracellular conductivity on transverse conduction in cardiac tissue is explored using a microdomain model that incorporates aspects of the inhomogeneous cellular structure. The propagation velocities found in our model are compared to those in the classic bidomain model and indicate a strong ephaptic microdomain contribution to conduction depending on the parameter regime. We show that ephaptic effects can be quite significant in the junctional spaces between cells, and that the cell activation sequence is modified substantially by these effects. Further, we find that transverse propagation can be maintained by ephaptic effects, even in the absence of gap junctional coupling. The mechanism by which this occurs is found to be cablelike in that the junctional regions act like inverted cables. Our results provide insight into several recent experimental studies that indirectly indicate a mode of action potential propagation that does not rely exclusively on gap junctions.     

Optimal Velocity and Safety of Discontinuous Conduction through the Heterogeneous Purkinje-Ventricular Junction

Slow and discontinuous wave conduction through nonuniform junctions in cardiac tissues is generally considered unsafe and proarrythmogenic. However, the relationships between tissue structure, wave conduction velocity, and safety at such junctions are unknown. We have developed a structurally and electrophysiologically detailed model of the canine Purkinje-ventricular junction (PVJ) and varied its heterogeneity parameters to determine such relationships. We show that neither very fast nor very slow conduction is safe, and there exists an optimal velocity that provides the maximum safety factor for conduction through the junction. The resultant conduction time delay across the PVJ is a natural consequence of the electrophysiological and morphological differences between the Purkinje fiber and ventricular tissue. The delay allows the PVJ to accumulate and pass sufficient charge to excite the adjacent ventricular tissue, but is not long enough for the source-to-load mismatch at the junction to be enhanced over time. The observed relationships between the conduction velocity and safety factor can provide new insights into optimal conditions for wave propagation through nonuniform junctions between various cardiac tissues.     

Transverse propagation in an expanded PSpice model for cardiac muscle with gap-junction ion channels

Transverse propagation was previously found to occur in a two-dimensional model of cardiac muscle using the PSpice software program for electronic circuit design and analysis. Longitudinal propagation within each chain, and transverse propagation between parallel chains, occurred even when there were no gap-junction (g-j) channels inserted between the simulated myocardial cells either longitudinally or transversely. In those studies, there were pronounced edge (boundary) effects and end-effects even within single chains. Transverse velocity increased with increase in model size. The present study was performed to examine boundary effects on transverse propagation velocity when the length of the chains was held constant at 10 cells and the number of parallel chains was varied from 3 to 5, to 7, to 10, and to 20. The number of g-j channels was either zero, both longitudinally and transversely (0/0), or 100/100. Some experiments were also made at 100/0, 1/1, and 10/10. Transverse velocity and overall velocity (both longitudinal and transverse components) was calculated from the measured total propagation time (TPT), i.e., the elapsed time between when the first action potential (AP) and the last AP crossed the zero potential level. The transverse g-j channels were placed only at the ends of each chain, such that propagation would occur in a zigzag pattern. Electrical stimulation was applied intracellularly between cells A1 and A2. It was found that, with no g-j channels (0/0), overall velocity increased almost linearly when more and more chains were placed in parallel. In contrast, with many g-j channels (100/100), there was a much flatter relationship between overall velocity and number of parallel chains. The difference in velocities with 0/0 channels and 100/100 channels was reduced as the number of chains was increased. In conclusion, edges have important effects on propagation velocity (overall and transverse) in cardiac muscle simulations.     

Electrical impedance tomography imaging using a priori ultrasound data

Transverse propagation was previously found to occur in a two-dimensional model of cardiac muscle using the PSpice software program for electronic circuit design and analysis. Longitudinal propagation within each chain, and transverse propagation between parallel chains, occurred even when there were no gap-junction (g-j) channels inserted between the simulated myocardial cells either longitudinally or transversely. In those studies, there were pronounced edge (boundary) effects and end-effects even within single chains. Transverse velocity increased with increase in model size. The present study was performed to examine boundary effects on transverse propagation velocity when the length of the chains was held constant at 10 cells and the number of parallel chains was varied from 3 to 5, to 7, to 10, and to 20. The number of g-j channels was either zero, both longitudinally and transversely (0/0), or 100/100. Some experiments were also made at 100/0, 1/1, and 10/10. Transverse velocity and overall velocity (both longitudinal and transverse components) was calculated from the measured total propagation time (TPT), i.e., the elapsed time between when the first action potential (AP) and the last AP crossed the zero potential level. The transverse g-j channels were placed only at the ends of each chain, such that propagation would occur in a zigzag pattern. Electrical stimulation was applied intracellularly between cells A1 and A2. It was found that, with no g-j channels (0/0), overall velocity increased almost linearly when more and more chains were placed in parallel. In contrast, with many g-j channels (100/100), there was a much flatter relationship between overall velocity and number of parallel chains. The difference in velocities with 0/0 channels and 100/100 channels was reduced as the number of chains was increased. In conclusion, edges have important effects on propagation velocity (overall and transverse) in cardiac muscle simulations.     

An analytical study of the physiology and pathology of the propagation of cardiac action potentials

Many cardiac diseases are caused by the abnormal propagation of electrical waves. Previous experimental and modelling work is reviewed, then a detailed study of the mathematics of cardiac propagation is presented. Pathologies are examined in the context of the models by varying parameters in the models to mimic different pathological states. Ionic models of cells are simplified to form analytically tractable models of the propagation of electrical cardiac waves. The roles that sodium channel activation and inactivation play in determining the conduction velocity are studied in detail, and the roles of resting potential currents in conduction block are calculated. The effect of curvature on the conduction velocity is examined, and the conditions in which curvature leads to conduction block and fibrillation are discussed. Hyperkalaemia (important during ischaemia) is modelled, and the model correctly describes the bi-phasic relation between propagation velocity and extracellular potassium.     

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.     

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。     

Slowing of Motor Nerve Conduction Velocity in Streptozotocin-induced Diabetic Rats is Preceded by Impaired Vasodilation in Arterioles that Overlie the Sciatic Nerve

Diabetes mellitus produces marked abnormalities in motor nerve conduction, but the mechanism is not clear. In the present study we hypothesized that in the streptozotocin (STZ)-induced diabetic rat impaired vasodilator function in arterioles that provide circulation to the region of the sciatic nerve is associated with reduced endoneural blood flow (EBF) and that these defects precede slowing of motor nerve conduction velocity, and thereby may contribute to nerve dysfunction. As early as three days after the induction of diabetes endoneural blood flow was reduced in the STZ-induced diabetic rat. Furthermore, after 1 week of diabetes acetylcholine- induced vasodilation was found to be impaired. This was accompanied by an increase in the superoxide level in arterioles that provide circulation to the region of the sciatic nerve as well as changes in the level of other markers of oxidative stress including an increase in serum levels of thiobarbituric acid reactive substances and a decrease in lens glutathione level. In contrast to the vascular related changes that occur within 1 week of diabetes, motor nerve conduction velocity and sciatic nerve Na⁺/k⁺ ATPase activity were significantly reduced following 2 and 4 weeks of diabetes, respectively. These studies demonstrate that changes in vascular function in the STZ-induced diabetic rat precede the slowing of motor nerve conduction velocity (MNCV) and are accompanied by an increase in superoxide levels in arterioles that provide circulation to the region of the sciatic nerve.