Effects of bath resistance on action potentials in the squid giant axon: myocardial implications.

This study presents a simplified version of the quasi-one-dimensional theory (Wu, J., E. A. Johnson, and J. M. Kootsey. 1996. A quasi-one-dimensional theory for anisotropic propagation of excitation in cardiac muscle. Biophys. J. 71:2427-2439) with two components of the extracellular current, along and perpendicular to the axis, and a simulation and its experimental confirmation for the giant axon of the squid. By extending the one-dimensional core conductor cable equations, this theory predicts, as confirmed by the experiment, that the shapes of the intracellular and the extracellular action potentials are related to the resistance of the bath. Such a result was previously only expected by the field theories. The correlation between the shapes of the intracellular and the extracellular potentials of the giant axon of the squid resembles that observed during the anisotropic propagation of excitation in cardiac muscle. Therefore, this study not only develops a quasi-one-dimensional theory for a squid axon, but also provides one possible factor contributing to the anisotropic propagation of action potentials in cardiac muscle.     

An analysis of the relationships between subthreshold electrical properties and excitability in skeletal muscle

Skeletal muscle activation requires action potential (AP) initiation followed by its sarcolemmal propagation and tubular excitation to trigger Ca(2+) release and contraction. Recent studies demonstrate that ion channels underlying the resting membrane conductance (G(M)) of fast-twitch mammalian muscle fibers are highly regulated during muscle activity. Thus, onset of activity reduces G(M), whereas prolonged activity can markedly elevate G(M). Although these observations implicate G(M) regulation in control of muscle excitability, classical theoretical studies in un-myelinated axons predict little influence of G(M) on membrane excitability. However, surface membrane morphologies differ markedly between un-myelinated axons and muscle fibers, predominantly because of the tubular (t)-system of muscle fibers. This study develops a linear circuit model of mammalian muscle fiber and uses this to assess the role of subthreshold electrical properties, including G(M) changes during muscle activity, for AP initiation, AP propagation, and t-system excitation. Experimental observations of frequency-dependent length constant and membrane-phase properties in fast-twitch rat fibers could only be replicated by models that included t-system luminal resistances. Having quantified these resistances, the resulting models showed enhanced conduction velocity of passive current flow also implicating elevated AP propagation velocity. Furthermore, the resistances filter passive currents such that higher frequency current components would determine sarcolemma AP conduction velocity, whereas lower frequency components excite t-system APs. Because G(M) modulation affects only the low-frequency membrane impedance, the G(M) changes in active muscle would predominantly affect neuromuscular transmission and low-frequency t-system excitation while exerting little influence on the high-frequency process of sarcolemmal AP propagation. This physiological role of G(M) regulation was increased by high Cl(-) permeability, as in muscle endplate regions, and by increased extracellular [K(+)], as observed in working muscle. Thus, reduced G(M) at the onset of exercise would enhance t-system excitation and neuromuscular transmission, whereas elevated G(M) after sustained activity would inhibit these processes and thereby accentuate muscle fatigue.     

The propagation potential. An axonal response with implications for scalp-recorded EEG

An electrophysiological response of axons, referred to as the "propagation potential," was investigated. The propagation potential is a sustained voltage that lasts as long as an action potential propagates between two widely spaced electrodes. The sign of the potential depends on the direction of action potential propagation. The electrode towards which the action potential is propagating is positive with respect to the electrode from which it is receding. For normal frog sciatic nerves the magnitude of the propagation potential was 17% of the peak of the extracellular action potential; TEA increased it to 32%. For normal earthworm median or lateral giant fibers it was 30%. A ripple pattern on the propagation potential was attributed to variation in resistance along the length of the worm. Cooling increased the duration of the propagation potential and attenuated the higher frequency components of the ripple pattern. Differential records from two widely spaced intracellular microelectrodes in the same axon differed from the propagation potential. The amplitude of the plateau relative to the peak was smaller, it decreased as the action potential propagated from one electrode site to the other, and the potential did not return to zero as rapidly as for extracellular records. When propagation was blocked by heat, the propagation potential slowly decayed. There was no ripple pattern during the decay. In a volume conductor, electrodes contacting the worm did not show the typical propagation potential, but electrodes located a few centimeters away from the worm did. Simple core-conductor models based on classical action potential theory did not reproduce the propagation potential. More complex, modified core-conductor models were needed to accurately simulate it. The results suggest that long, slowly conducting fibers can contribute to the scalp-recorded EEG.     

Effects of barium and ouabain on electrogenesis in various sites of intact and detubulated skeletal muscle fibers of the frog <Emphasis Type="Italic">R. temporaria</Emphasis>

In loose patch clamp experiments on intact sartorius muscle fibers of the frog Rana temporaria, there have been two types of waveforms of extracellularly recorded action potentials (AP). Responses of the first type (T1AP) consisted of an initial positive phase with a subsequent phase of strong negativity, the latter only in a few cases followed by a weak positive phase. Responses of the second type (T2AP) always had an additional positive phase concluding their waveform. In the detubulated fibers, only T1AP were recorded. Application of Ba²⁺ (10 μM) to the muscle led to a significant increase in the amplitude of the third T2AP phase whereas the T1AP characteristics of both intact and detubulated muscle preparations remained unchanged. In some of the studied intact fibers, after Ba²⁺ or ouabain (50 μM) applied, the latest positive signal phase was replaced by a negative phase. The amplitude of this latest negative phase was increased markedly by highfrequency stimulation. Under the simultaneous action of ouabain and Ba²⁺, there was a summation of their effects. Our results can be tentatively explained by that the T-system of a muscle fiber produces electrical responses substantially differing in their pattern and barium sensitivity from those transmitted across cell membranes. These differences could be resultant from the activity of T-tubular inwardly rectifying potassium channels (K_ir) and that of Na,K-ATPase as they both provide absorption of excessive extracellular potassium.     

Theoretical analysis of the magnetocardiographic pattern for reentry wave propagation in a three-dimensional human heart model

We present a computational study of reentry wave propagation using electrophysiological models of human cardiac cells and the associated magnetic field map of a human heart. We examined the details of magnetic field variation and related physiological parameters for reentry waves in two-dimensional (2-D) human atrial tissue and a three-dimensional (3-D) human ventricle model. A 3-D mesh system representing the human ventricle was reconstructed from the surface geometry of a human heart. We used existing human cardiac cell models to simulate action potential (AP) propagation in atrial tissue and 3-D ventricular geometry, and a finite element method and the Galerkin approximation to discretize the 3-D domain spatially. The reentry wave was generated using an S1-S2 protocol. The calculations of the magnetic field pattern assumed a horizontally layered conductor for reentry wave propagation in the 3-D ventricle. We also compared the AP and magnetocardiograph (MCG) magnitudes during reentry wave propagation to those during normal wave propagation. The temporal changes in the reentry wave motion and magnetic field map patterns were also analyzed using two well-known MCG parameters: the current dipole direction and strength. The current vector in a reentry wave forms a rotating spiral. We delineated the magnetic field using the changes in the vector angle during a reentry wave, demonstrating that the MCG pattern can be helpful for theoretical analysis of reentry waves.     

Electrical Interactions via the Extracellular Potential Near Cell Bodies

Ephaptic interactions between a neuron and axons or dendrites passing by its cell body can be, in principle, more significant than ephaptic interactions among axons in a fiber tract. Extracellular action potentials outside axons are small in amplitude and spatially spread out, while they are larger in amplitude and much more spatially confined near cell bodies. We estimated the extracellular potentials associated with an action potential in a cortical pyramidal cell using standard one-dimensional cable theory and volume conductor theory. Their spatial and temporal pattern reveal much about the location and timing of currents in the cell, especially in combination with a known morphology, and simple experiments could resolve questions about spike initiation. From the extracellular potential we compute the ephaptically induced polarization in a nearby passive cable. The magnitude of this induced voltage can be several mV, does not spread electrotonically, and depends only weakly on the passive properties of the cable. We discuss their possible functional relevance.     

Simulations of propagated mouse ventricular action potentials: effects of molecular heterogeneity

The molecular heterogeneity of repolarizing currents produces significant spatial heterogeneity and/or dispersion of repolarization in many mammalian cardiac tissues. Transgenic mice are prominent experimental models for the study of the molecular basis of repolarization and arrhythmias. However, it is debated whether the small mouse heart can sustain physiologically relevant heterogeneity of repolarization. We used a comprehensive model of the mouse action potential (AP) to predict how small a region of the cardiac tissue can maintain spatial gradients of repolarization due to differential expression of channels. Our simulations of a one-dimensional multicellular ring or cable predict that substantial gradients in repolarization and intracellular Ca(2+) concentration transients can be maintained through heterogeneity of expression of K(+) channels in distances of approximately 10 cells that are sufficient to block propagation. The abruptness of expression gradients and the site of stimulation can cause Ca(2+) transient oscillations and affect the stability of Ca(2+) dynamics and AP propagation. Two different mechanisms of instability of AP propagation in one-dimensional cable occur at fast pacing rates. Transitions from periodic activity to alternans or to irregular behavior were observed. Abrupt gradients of channel expression can cause alternans at slower pacing rates than gradual changes. Our simulations demonstrate the importance of incorporating realistic Ca(2+) dynamics and current densities into models of propagated AP. They also emphasize that microscopic aspects of tissue organization are important for predicting large-scale propagation phenomena. Finally, our results predict that the mouse heart should be able to sustain substantial molecularly based heterogeneity of repolarization.     

Propagation through electrically coupled cells. Effects of a resistive barrier

Action potential propagation through cardiac tissue occurs in a spatially inhomogeneous three-dimensional electrical syncytium composed of discrete cells with regional variations in membrane properties and intercellular resistance. In comparison with axons, cardiac tissue presents some differences in the application of core conductor cable theory. We have used analytical and numerical techniques to contrast the propagation of action potentials along nerve axons and along cardiac strands, including an explicit inclusion of cellular anatomical factors (the surface-to-volume ratio), the strand radius, and the regional distribution of longitudinal resistance. A localized decrease in the number of gap junctions will produce a functional resistive barrier, which can lead to unidirectional block of propagation if the tissue on two sides of the barrier in either excitability or passive electrical load. However, in some circumstances, a resistive barrier separating regions of different electrical load can actually facilitate propagation into the region of larger electrical load.     

The cardiac muscle in the pulmonary vein of the rat: A morphological and electrophysiological study

The pulmonary veins of albino Wistar rats were studied by means of light and electron microscopy. The media of larger veins consists of cardiac muscle fibers which extend until the vessels attain about 100 μ in diameter. This coat consists of external longitudinal fibers and internal circular fibers. The vasa vasorum are well developed and the capillaries show pseudofenestrations. The numerous adrenergic and cholinergic nerve endings do not form typical motor end-plates as seen in skeletal muscles. The ultrastructure of these media muscle fibers is similar to that of rat hearts. The smooth muscle layer of larger pulmonary veins is not continuous as it is in smaller veins where it forms cushions. Comparisons of albino rats and other rodents reveal striking differences. Action potential shape and propagation velocity (0.5–1.2 m/s) along the myocardial coat of the pulmonary vein were similar to those observed in the left atrium and so was their sensitivity to locally applied acetylcholine. The physiological direction of propagation in rat pulmonary veins is toward the lung. This finding lends support to the hypothesis of a rhythmic, valve-like action of the striated musculature of the pulmonary venous wall during the systole and a possible role in the capacitance of the pulmonary circulation.     

How different two almost identical action potentials can be: A model study on cardiac repolarization

Spatial heterogeneity in the properties of ion channels generates spatial dispersion of ventricular repolarization, which is modulated by gap junctional coupling. However, it is possible to simulate conditions in which local differences in excitation properties are electrophysiologically silent and only play a role in pathological states. We use a numerical procedure on the Luo-Rudy phase 1 model of the ventricular action potential (AP1) in order to find a modified set of model parameters which generates an action potential profile (AP2) almost identical to AP1. We show that, although the two waveforms elicited from resting conditions as a single AP are very similar and belong to membranes sharing similar passive electrical properties, the modified membrane generating AP2 is a weaker current source than the one generating AP1, has different sensitivity to up/down-regulation of ion channels and to extracellular potassium, and a different electrical restitution profile. We study electrotonic interaction of AP1- and AP2 - type membranes in cell pairs and in cable conduction, and find differences in source-sink properties which are masked in physiological conditions and become manifest during intercellular uncoupling or partial block of ion channels, leading to unidirectional block and spatial repolarization gradients. We provide contour plot representations that summarize differences and similarities. The present report characterizes an inverse problem in cardiac cells, and strengthen the recently emergent notion that a comprehensive characterization and validation of cell models and their components are necessary in order to correctly understand simulation results at higher levels of complexity.     

Rhythms of high-grade block in an ionic model of a strand of regionally ischemic ventricular muscle

Electrical alternans, a beat-to-beat alternation in the electrocardiogram or electrogram, is frequently seen during the first few minutes of acute myocardial ischemia, and is often immediately followed by malignant cardiac arrhythmias such as ventricular tachycardia and ventricular fibrillation. As ischemia progresses, higher-order periodic rhythms (e.g., period-4) can replace the period-2 alternans rhythm. This is also seen in modelling work on a two-dimensional (2-D) sheet of regionally ischemic ventricular muscle. In addition, in the experimental work, ventricular arrhythmias are overwhelmingly seen only after the higher-order rhythms arise. We investigate an ionic model of a strand of ischemic ventricular muscle, constructed as a 3-cm-long 1-D cable with a centrally located 1-cm-long segment exposed to an elevated extracellular potassium concentration ([K(+)](o)). As [K(+)](o) is raised in this "ischemic segment" to represent one major effect of ongoing ischemia, the sequence of rhythms {1:1-->2:2 (alternans)-->2:1} is seen. With further increase in [K(+)](o), one sees higher-order periodic 2N:M rhythms {2:1-->4:2-->4:1-->6:2-->6:1-->8:2-->8:1}. In a 2N:M cycle, only M of the 2N action potentials generated at the proximal end of the cable successfully traverse the ischemic segment, with the remaining ones being blocked within the ischemic segment. Finally, there is a transition to complete block {8:1-->2:0-->1:0} (in an n:0 rhythm, all action potentials die out within the ischemic segment). Changing the length of the ischemic segment results in different rhythms and transitions being seen: e.g., when the ischemic segment is 2 cm long, the period-6 rhythms are not seen; when it is 0.5 cm long, there is a 3:1 rhythm interposed between the 2:1 and 1:0 rhythms. We discuss the relevance of our results to the experimental observations on the higher-order rhythms that presage reentrant ischemic ventricular arrhythmias.     

Increased excitability of acidified skeletal muscle: role of chloride conductance

Generation of the action potentials (AP) necessary to activate skeletal muscle fibers requires that inward membrane currents exceed outward currents and thereby depolarize the fibers to the voltage threshold for AP generation. Excitability therefore depends on both excitatory Na+ currents and inhibitory K+ and Cl- currents. During intensive exercise, active muscle loses K+ and extracellular K+ ([K+]o) increases. Since high [K+]o leads to depolarization and ensuing inactivation of voltage-gated Na+ channels and loss of excitability in isolated muscles, exercise-induced loss of K+ is likely to reduce muscle excitability and thereby contribute to muscle fatigue in vivo. Intensive exercise, however, also leads to muscle acidification, which recently was shown to recover excitability in isolated K(+)-depressed muscles of the rat. Here we show that in rat soleus muscles at 11 mM K+, the almost complete recovery of compound action potentials and force with muscle acidification (CO2 changed from 5 to 24%) was associated with reduced chloride conductance (1731 +/- 151 to 938 +/- 64 microS/cm2, P < 0.01) but not with changes in potassium conductance (405 +/- 20 to 455 +/- 30 microS/cm2, P < 0.16). Furthermore, acidification reduced the rheobase current by 26% at 4 mM K+ and increased the number of excitable fibers at elevated [K+]o. At 11 mM K+ and normal pH, a recovery of excitability and force similar to the observations with muscle acidification could be induced by reducing extracellular Cl- or by blocking the major muscle Cl- channel, ClC-1, with 30 microM 9-AC. It is concluded that recovery of excitability in K(+)-depressed muscles induced by muscle acidification is related to reduction in the inhibitory Cl- currents, possibly through inhibition of ClC-1 channels, and acidosis thereby reduces the Na+ current needed to generate and propagate an AP. Thus short term regulation of Cl- channels is important for maintenance of excitability in working muscle.     

Cardiac dynamics: a simplified model for action potential propagation

This paper analyzes a new semiphysiological ionic model, used recently to study reexitations and reentry in cardiac tissue [I.R. Cantalapiedra et al, PRE 82 011907 (2010)]. The aim of the model is to reproduce action potencial morphologies and restitution curves obtained, either from experimental data, or from more complex electrophysiological models. The model divides all ion currents into four groups according to their function, thus resulting into fast-slow and inward-outward currents. We show that this simplified model is flexible enough as to accurately capture the electrical properties of cardiac myocytes, having the advantage of being less computational demanding than detailed electrophysiological models. Under some conditions, it has been shown to be amenable to mathematical analysis. The model reproduces the action potential (AP) change with stimulation rate observed both experimentally and in realistic models of healthy human and guinea pig myocytes (TNNP and LRd models, respectively). When simulated in a cable it also gives the right dependence of the conduction velocity (CV) with stimulation rate. Besides reproducing correctly these restitution properties, it also gives a good fit for the morphology of the AP, including the notch typical of phase 1. Finally, we perform simulations in a realistic geometric model of the rabbit’s ventricles, finding a good qualitative agreement in AP propagation and the ECG. Thus, this simplified model represents an alternative to more complex models when studying instabilities in wave propagation.     

Electrophysiological interaction through the interstitial space between adjacent unmyelinated parallel fibers.

The influence of interstitial or extracellular potentials on propagation usually has been ignored, often through assuming these potentials to be insignificantly different from zero, presumably because both measurements and calculations become much more complex when interstitial interactions are included. This study arose primarily from an interest in cardiac muscle, where it has been well established that substantial interstitial potentials occur in tightly packed structures, e.g., tens of millivolts within the ventricular wall. We analyzed the electrophysiological interaction between two adjacent unmyelinated fibers within a restricted extracellular space. Numerical evaluations made use of two linked core-conductor models and Hodgkin-Huxley membrane properties. Changes in transmembrane potentials induced in the second fiber ranged from nonexistent with large intervening volumes to large enough to initiate excitation when fibers were coupled by interstitial currents through a small interstitial space. With equal interstitial and intracellular longitudinal conductivities and close coupling, the interaction was large enough (induced Vm approximately 20 mV peak-to-peak) that action potentials from one fiber initiated excitation in the other, for the 40-microns radius evaluated. With close coupling but no change in structure, propagation velocity in the first fiber varied from 1.66 mm/ms (when both fibers were simultaneously stimulated) to 2.84 mm/ms (when the second fiber remained passive). Although normal propagation through interstitial interaction is unlikely, the magnitudes of the electrotonic interactions were large and may have a substantial modulating effect on function.     

Analytical theory for extracellular electrical stimulation of nerve with focal electrodes. II. Passive myelinated axon.

The cable model of a passive, myelinated fiber is derived using the theory of electromagnetic propagation in periodic structures. The cable may be excited by an intracellular source or by an arbitrary, time-varying, applied extracellular field. When the cable is stimulated by a distant source, its properties are qualitatively similar to an unmyelinated fiber. Under these conditions relative threshold is proportional to the cube of the source distance and inversely proportional to the square of the fiber diameter. Electrical parameters of the model are chosen where possible, from mammalian peripheral nerve and anatomic parameters from cat auditory nerve. Several anatomic representations of the paranodal region are analyzed for their effects on the length and time constants of the fibers. Sensitivity of the model to parameter changes is studied. The linear model reliably predicts the effects of fiber size and electrode-fiber separation on threshold of cat dorsal column fibers to extracellular electrical stimulation.     

Acceleratory nervous regulation of juvenile myogenic hearts in the isopod crustacean Ligia exotica

We examined regulation of the myogenic heart by two identified cardioacceleratory neurons (CA1, CA2) in early juveniles of the isopod Ligia exotica. Repetitive stimulation of either the CA1 or CA2 axon increased the frequency and plateau amplitude of the action potential and decreased the maximum hyperpolarization of the cardiac muscle. These effects were larger with increasing stimulus frequency. The rate of increase in the frequency caused by CA1 stimulation was significantly larger than that by CA2. No impulse activity of the cardiac ganglion was induced by acceleratory nerve stimulation. The frequency of the muscle activity was decreased by injection of a hyperpolarizing current into the muscle during stimulation of the acceleratory nerve. In a quiescent heart, acceleratory nerve stimulation caused an overall depolarization in the muscle membrane and the amplitude of the depolarization induced by CA1 stimulation was significantly larger than that by CA2. These results suggest that CA1 and CA2 neurons regulate the myogenic heart affecting directly the cardiac muscle; the CA1 neuron produces more potent effects than does the CA2 neuron.     

Amplitude-related characteristics of motor unit and M-wave potentials during fatigue. A simulation study using literature data on intracellular potential changes found in vitro.

To realize possible reasons for changes in EMG amplitude characteristics with fatigue, we analyzed motor unit potentials (MUPs) and M-waves under simultaneous variations of the intracellular action potential (IAP) amplitude, duration, and shape as well as of the muscle fiber propagation velocity and desynchronization in activation of individual muscle fibers. Analysis was performed through computer simulation of MUPs and M-waves detected at different distances from active fibers in infinite anisotropic volume conductor. Changes in the IAP spike and negative after-potential were taken from in vitro experiments reported in the literature. It was shown that the amplitudes of MUP and M-wave detected simultaneously at different distances could decrease close to the active fibers, be almost unchanged at middle distances, and increase far from the fibers even under IAP amplitude decreasing. This reflected the distance-dependent effects of changes in the IAP profile along the fiber. Electrode position affected sensitivity of MUP and M-wave durations to changes in the IAP duration and propagation velocity. Thus, the signal area and RMS depended on electrode position and could change with fatigue in a way different from that of signal amplitude. The results can help to avoid misleading interpretation of EMG changes.     

The functional motility of motor units of the gastrocnemius and soleus muscles in the rat under indirect stimulation depending on the stimulus frequency]

With increasing pulse rate (up to 150 square pulses/sec) applied for 1 second at the gastrocnemius and soleus muscle the amplitude of electromyographic response was found to decrease. An amplitude decrease of sum action potentials (AP) recorded from the muscle surface occurred already at pulse rates below 100 pulses/sec. For the gastrocnemius muscle, this amplitude fall in the medium pulse-rate region can be described by the relation: amplitude = -log-pulse rate. At the soleus muscle, the amplitude fall is shifted towards the higher frequencies. After intensive swimming of the animal the amplitude depression of AP at the gastrocnemius muscle occurs already at a lower rate, and departs from the aforementioned relation. The causes are looked for in the differential properties of the various muscle fibres.     

Effect of calmidazolium (R 24571) on the electrical and contractile properties of smooth muscle cells in the guinea pig ureter

Calmidazolium in macromolecular concentrations inhibited the electric and contractile activity of smooth muscle cells (SMC). The concentrations causing a 50% inhibition of oscillations on the action potential (AP) plate were equal to 1 X 10(-6) microM, AP amplitude was 3 X 10(-6) microM and contraction amplitude was 1 X 10(-6) microM. Calcium ionophore A 23187/8 X 10(-7) microM, added to the normal Krebs solution, decreased rapid AP components amplitude and increased the contraction power of the isolated SMC strip by 62 +/- 9%. A 23187, though to a lesser extent, increased smooth muscle contractions during the action of calmidazolium. With combined use of A 23187 and calmidazolium, rapid AP components were depressed to a greater extent than each of them taken separately. The data obtained point to the presence of calmodulin or similar protein in SMC of the calcium channels.