Simulation analysis of excitation conduction in the heart: Propagation of excitation in different tissues

The normal excitation and conduction in the heart are maintained by the coordination between the dynamics of ionic conductance of each cell and the electrical coupling between cells. To examine functional roles of these two factors, we proposed a spatially-discrete model of conduction of excitation in which the individual cells were assumed isopotential. This approximation was reasoned by comparing the apparent space constant with the measured junctional resistance between myocardial cells. We used the four reconstruction models previously reported for five kinds of myocardial cells. Coupling coefficients between adjacent cells were determined quantitatively from the apparent space constants. We first investigated to what extent the pacemaker activity of the sinoatrial node depends on the number and the coupling coefficient of its cells, by using a one-dimensional model system composed of the sinoatrial node cells and the atrial cells. Extensive computer simulation revealed the following two conditions for the pacemaker activity of the sinoatrial node. The number of the sinoatrial node cells and their coupling coefficients must be large enough to provide the atrium with the sufficient electric current flow. The number of the sinoatrial node cells must be large so that the period of the compound system is close to the intrinsic period of the sinoatrial node cell. In this simulation the same sinoatrial node cells produced action potentials of different shapes depending on where they were located in the sinoatrial node. Therefore it seems premature to classify the myocardial cells only from their waveforms obtained by electrical recordings in the compound tissue. Second, we investigated the very slow conduction in the atrioventricular node compared to, for example, the ventricle. This was assumed to be due to the inherent property of the membrane dynamics of the atrioventricular node cell, or to the small value of the coupling coefficient (weak intercellular coupling), or to the electrical load imposed on the atrioventricular node by the Purkinje fibers, because the relatively small atrioventricular node must provide the Purkinje fibers with sufficient electric current flow. Relative contributions of these three factors to the slow conduction were evaluated using the model system composed of only the atrioventricular cells or that composed of the atrioventricular and Purkinje cells. We found that the weak coupling has the strongest effect. In the model system composed of the atrioventricular cells, the propagation failure was not observed even for very small values of the coupling coefficient.(ABSTRACT TRUNCATED AT 400 WORDS)     

One-Dimensional Mathematical Model of the Atrioventricular Node Including Atrio-Nodal, Nodal, and Nodal-His Cells

Mathematical models are a repository of knowledge as well as research and teaching tools. Although action potential models have been developed for most regions of the heart, there is no model for the atrioventricular node (AVN). We have developed action potential models for single atrio-nodal, nodal, and nodal-His cells. The models have the same action potential shapes and refractoriness as observed in experiments. Using these models, together with models for the sinoatrial node (SAN) and atrial muscle, we have developed a one-dimensional (1D) multicellular model including the SAN and AVN. The multicellular model has slow and fast pathways into the AVN and using it we have analyzed the rich behavior of the AVN. Under normal conditions, action potentials were initiated in the SAN center and then propagated through the atrium and AVN. The relationship between the AVN conduction time and the timing of a premature stimulus (conduction curve) is consistent with experimental data. After premature stimulation, atrioventricular nodal reentry could occur. After slow pathway ablation or block of the L-type Ca²⁺ current, atrioventricular nodal reentry was abolished. During atrial fibrillation, the AVN limited the number of action potentials transmitted to the ventricle. In the absence of SAN pacemaking, the inferior nodal extension acted as the pacemaker. In conclusion, we have developed what we believe is the first detailed mathematical model of the AVN and it shows the typical physiological and pathophysiological characteristics of the tissue. The model can be used as a tool to analyze the complex structure and behavior of the AVN.     

Electrophysiological basis for antiarrhythmic drug action

Arrhythmias result from abnormalities of impulse initiation or impulse conduction or a combination of both. Abnormal impulse initiation results from either automaticity or triggered activity. Automaticity can further be subdivided into (1) automaticity caused by the normal automatic mechanism (a normal property of cardiac cells in the sinus node, in some parts of the atria, in the atrioventricular junctional region, and in the His-Purkinje system) and (2) automaticity caused by an abnormal mechanism (resulting from a decrease in membrane potential of cardiac fibers, which normally have a high level of membrane potential). Triggered activity is caused by afterdepolarizations, which are second depolarizations that occur either during repolarization (referred to as early afterdepolarizations) or after repolarization is complete or nearly complete (referred to as delayed afterdepolarizations). Abnormal impulse conduction results in reentrant excitation. Usually a combination of slowed conduction and unidirectional conduction block provides the conditions necessary for reentry to occur.     

家兔离体心脏组织的不应期及房室结的滤波特性

一般认为房室结具有滤波特性,即它能阻止过快或过于提前的心房冲动传到心室。本实验旨在研究家兔离体心脏组织的不应期及房室结的滤波牧场生（ｎ＝１８）。实验中发现：（１）在短基础周期（２００－３００ｍｓ）房室结的相对不应期最长,而在长基础周期（６００,７００ｍｓ）希浦系（ＨｉｓＰｕｒｋｉｎｊｅ ｓｙｔｅｍ）的相对不应期最长;（２）在多种基础周期下,大多数心脏（１６／１８）房室结有效不应期小于心房功能不应期     

Atrioventricular block in low potassium and K dependence of the nodal resting potential

A progressive conduction block leading to atrioventricular dissociation develops in perfused rabbit hearts within 20-30 min of exposure to Krebs containing 0.5 mM potassium (low K). A decrease in potassium permeability resulting in membrane depolarization (as seen in Purkinje fibers) could be responsible for the loss of excitability in nodal cells. We investigated the K dependence of the resting potential and the long-term effects of low K perfusion on the resting and action potentials of nodal cells in rabbit hearts. The resting potential of atrial, atrionodal, and nodal cells varied by 52, 41, and 34 mV per decade of change in Ko within the range of 5-50 mM K. Hyperpolarization of the resting membrane, a progressive decline in action potential amplitude, and a decrease in maximum rate of rise were observed in nodal fibers when exposed to low K. Loss of propagated activity occurred in the middle node within 20-30 min while the cells remained hyperpolarized. There was no evidence of electrogenic Na extrusion and it seems that the low nodal resting potential results from a high resting PNa/PK permeability ratio. The early decrease in rate of rise in low K probably reflects an increase in K-dependent outward currents, whereas the progressive deterioration and final loss of conducted electrical activity may result from an accumulation of internal Na and Ca overload produced by low K inhibition of the Na pump.     

CRH-induced electrical activity and calcium signalling in pituitary corticotrophs

Pituitary corticotroph cells generate repetitive action potentials and associated Ca2+ transients in response to the agonist corticotropin releasing hormone (CRH). There is indirect evidence suggesting that the agonist, by way of complex intracellular mechanisms, modulates the voltage sensitivity of the L-type Ca2+ channels embedded in the plasma membrane. We have previously constructed a Hodgkin-Huxley-type model of this process, which indicated that an increase in the L-type Ca2+ current is sufficient to generate repetitive action potentials (LeBeau et al. (1997). Biophys. J.73, 1263-1275). CRH is also believed to inhibit an inwardly rectifying K+ current. In this paper, we have found that a CRH-induced inhibition of the inwardly rectifying K+ current increases the model action potential firing frequency, [Ca2+]i transients and membrane excitability. This dual modulatory action of CRH on inward rectifier and voltage-gated Ca2+ channels better describes the observed CRH-induced effects. This structural alteration to the model along with parameter changes bring the model firing frequency in line with experimental data. We also show that the model exhibits experimentally observed bursting behaviour, where the depolarization spike is followed by small oscillations in the membrane potential.     

A mathematical model of a myelinated nerve fiber for analysis of impulse conduction mechanisms during the relative refractory period

It was shown by means of a mathematical model of a myelinated nerve fiber (Frankenhaeuser — Huxley) that an increase in threshold and decrease in the amplitude of the action potential (AP) during the relative refractory period are due mainly to sodium inactivation. The contribution of increased potassium permeability to these changes is small, for the chief component of the outgoing ionic current in the node of Ranvier is not the potassium current, but the leak current. Given the ratio between these currents the increase in threshold and graduation of the action potential in the node membrane are less marked than in the membrane of the squid giant axon. At the beginning of the relative refractory period the AP evoked by strong stimulation is conducted only to the next node. Later in the refractory period impulses are conducted incrementally, and the threshold for the spreading impulse is higher than the threshold for spike excitation in the stimulated node. Delay in impulse conduction between refractory nodes leads to the formation of a retrograde depolarization wave. The reasons for differences in the mechanisms of impulse conduction along unmyelinated and myelinated refractory fibers are discussed.Vishnevskii Institute of Surgery, Academy of Medical Sciences of the USSR, Moscow. Translated from Neirofiziologiya, Vol. 4, No. 2, pp. 201–207, March–April, 1972.     

The conducted action potential. Models and comparison to experiments.

Propagation of the action potential is a complex process, and the relationships among the various factors involved in conduction have not been clear. We use three mathematical models of uniform conduction in a cable to clarify some of these relationships. One model is newly derived here, and two have been previously derived by Hunter et al. (1975, Prog. Biophys. Mol. Biol., 30:99-144). These models were able to simulate individual experimental action potential upstrokes previously obtained (Walton and Fozzard, 1983, Biophys. J., 44:1-8). The models were then utilized to provide relationships between measures of conduction. Among these were that maximal upstroke velocity (Vmax) is directly proportional to peak inward ionic current normalized by capacitance that is filled during the upstroke (I/Cf), and that conduction velocity was directly related to the square root of either Vmax or I/Cf. These relationships were shown to be model independent and to predict the experimental results, thus providing validated quantitative relationships that were not discernible through use of experimental data alone. The concept of safety factor was considered and a parameter was proposed that may be related to safety factor.     

Slow Conduction in Cardiac Muscle: A Biophysical Model

Mechanisms of slow conduction in cardiac muscle are categorized and the most likely identified. Propagating action potentials were obtained experimentally from a synthetically grown strand of cardiac muscle (around 50 μm by 30 mm) and theoretically from a one-dimensional cable model that incorporated varying axial resistance and membrane properties along its length. Action potentials propagated at about 0.3 m/s, but in some synthetic strands there were regions (approximately 100 μm in length) where the velocity decreased to 0.002 m/s. The electrophysiological behavior associated with this slow conduction was similar to that associated with slow conduction in naturally occurring cardiac muscle (notches, Wenckebach phenomena, and block). Theoretically, reasonable changes in specific membrane capacitance, membrane activity, and various changes in geometry were insufficient to account for the observed slow conduction velocities. Conduction velocities as low as 0.009 m/s, however, could be obtained by increasing the resistance (r_i) of connections between the cells in the cable; velocities as low as 0.0005 m/s could be obtained by a further increase in r_i made possible by a reduction in membrane activity by one-fourth, which in itself decreased conduction velocity by only a factor of 1/1.4. As a result of these findings, several of the mechanisms that have been postulated, previously, are shown to be incapable of accounting for delays such as those which occur in the synthetic strand as well as in the atrioventricular (VA) node.     

Cholinergic modulation of activation sequence in the atrial myocardium of non-mammalian vertebrates

Cholinergic changes of electric activity were studied in isolated atrium preparations from fishes (cod and carp), amphibians (frog) and reptilians (lizard) using the microelectrode technique and high-resolution optical mapping. Perfusion of isolated atrium with acetylcholine (10^? 6–5 · 10^? 5 M) caused gradual suppression of action potential generation and, eventually, completely blocked the excitation in a part of the preparation. Other regions of atrium, situated close to the sinoatrial and atrioventricular junctions, remained excitable. Such cholinergic suppression of electric activity was observed in the atrial myocardium of frog and in both fish species, but not in reptilians. Ba²⁺ (10^? 4 M), which blocks the acetylcholine-dependent potassium current (I_KACh), prevented cholinergic reduction of action potential amplitude. In several preparations of frog atrium, cholinergic suppression of excitation coincided with episodes of atrial fibrillation. We conclude that the phenomenon of cholinergic suppression of electric activity is typical for atria of fishes and amphibians. It is likely to be caused by I_KACh activation and may be important for initiation of atrial arrhythmias.     

The sinoatrial ring bundle: a cardiac neural communication system?

The sinoatrial ring bundle (SARB), was originally described as a "whitish bundle of tissue which describes an almost complete loop around the two venae cavae and the coronary sinus" in the adult rabbit heart (Paes de Carvalho et al., 1959). The histologically and electrophysiologically differentiated structure, derived from the embryonic venous valves, was suitably placed for rapid conduction from sinoatrial (SA) to atrioventricular (AV) node, but no evidence was found for this role. Today, the function of the SARB remains obscure. Cholinesterase/silver staining reveals the neural pattern associated with the SARB and suggests a function. Throughout its extent, the SARB contains a bundle of parallel muscle fibers and accompanying long nerves. The nerves distribute to structures at either side of the loop: superolaterally to pectinate muscle and inferomedially to the region of the AV node. Along the curve of the right SARB, the nerves contribute to a dense neural plexus with nerves coiled around muscle. The plexus communicates with the nearby SA node and with the ganglia inferior to the node near the inferior vena cava. The morphological pattern of neural elements is suitably organized to suggest tension monitoring and internodal, neural communication.     

Cytofluorometric nuclear DNA determinations on the atrioventricular nodal cells in human hearts

In the human heart, it is well known that the polyploidization of working heart-muscle cells increases in proportion to increases in heart weight, but there has been no investigation of the process of polyploidization in the specialized heart-muscle cells of the cardiac conduction system which have a nerve-like function. In order to investigate the process of polyploidization in these cells, the nuclear DNA content of atrioventricular nodal cells was measured using cytofluorometry. Tissue samples taken from autopsied hearts without arrhythmias were embedded in paraffin blocks after Carnoy fixation. Blocks containing the atrioventricular conduction system were cut according to the serial sectioning method of Lev et al. The compact atrioventricular nodes were removed from thick paraffin sections (150 micron) under a stereomicroscope. The cells were then isolated by enzyme digestion and ultrasonic treatment. Smears of the isolated cells were double stained with azocarmin-G and acriflavine-Feulgen. Cytofluorometric DNA determinations of the DNA content of atrioventricular nodal cells were performed. Atrioventricular nodes were found to be composed of a large number of diploid cells and a small number of tetraploid cells. No octaploid cells were found. These findings reveal that the process of polyploidization in atrioventricular nodal cells is different from that found in working heart-muscle cells.     

Cardiac conducting system of Gallus domesticus with special reference to the atrial bundles

Gross anatomy and histology of the cardiac conducting system of Gallus domesticus has been studied. Detailed histology of the atrium revealed for the first time, in the avian heart, the presence of three atrial bundles which communicate between the sinuatrial node and the atrioventricular node. Purkinje fibres in the subendocardium of the right atrium are observed. An atrioventricular segment comprising of the posterior end of the interatrial septum and the atrioventricular nodal region has been reported in which the three atrial bundles converge. The role of the atrial bundles in the cardiac contraction has been discussed.     

Subtle Paranodal Injury Slows Impulse Conduction in a Mathematical Model of Myelinated Axons

This study explores in detail the functional consequences of subtle retraction and detachment of myelin around the nodes of Ranvier following mild-to-moderate crush or stretch mediated injury. An equivalent electrical circuit model for a series of equally spaced nodes of Ranvier was created incorporating extracellular and axonal resistances, paranodal resistances, nodal capacitances, time varying sodium and potassium currents, and realistic resting and threshold membrane potentials in a myelinated axon segment of 21 successive nodes. Differential equations describing membrane potentials at each nodal region were solved numerically. Subtle injury was simulated by increasing the width of exposed nodal membrane in nodes 8 through 20 of the model. Such injury diminishes action potential amplitude and slows conduction velocity from 19.1 m/sec in the normal region to 7.8 m/sec in the crushed region. Detachment of paranodal myelin, exposing juxtaparanodal potassium channels, decreases conduction velocity further to 6.6 m/sec, an effect that is partially reversible with potassium ion channel blockade. Conduction velocity decreases as node width increases or as paranodal resistance falls. The calculated changes in conduction velocity with subtle paranodal injury agree with experimental observations. Nodes of Ranvier are highly effective but somewhat fragile devices for increasing nerve conduction velocity and decreasing reaction time in vertebrate animals. Their fundamental design limitation is that even small mechanical retractions of myelin from very narrow nodes or slight loosening of paranodal myelin, which are difficult to notice at the light microscopic level of observation, can cause large changes in myelinated nerve conduction velocity.     

Initiation and abolition of the action potential of a single node of Ranvier

1. Using single node preparations of the bull frog or the toad, observations were made on the variation of the voltage across the nodal membrane under various experimental conditions. 2. The time constant of the variation in the membrane voltage caused by a long subthreshold rectangular pulse was of the order of 0.1 msec. 3. The action potential was initiated when the potential inside the node was raised stimulating pulses above a threshold level of approximately 15 mv. for a node in normal Ringer; it was greater in a relatively refractory node and in a partially narcotized node. 4. The variation of the membrane voltage caused by long stimulating pulses of subrheobasic strengths was in general proportional to the strength of the applied pulse. A non-linear behavior of the membrane voltage was observed with barely subthreshold stimulating pulses. 5. The early portion of the action potential of a node was not modified by a direct current which was strong enough to produce measurable potential changes (IR drops) across the resting membrane. 6. A strong pulse of inward current applied to the node during activity abolished the portion of the action potential following the pulse in all-or-none manner. 7. There was no refractory period after a response abolished in its early phase. Following a response abolished later, the recovery in the spike height started from the level of the action potential at the time of abolition. 8. Initiation and abolition of action potentials at a single node are interpreted as "transitions" between the two "equilibrium potential levels" at the node.     

Parasympathetic control of the heart. II. A novel interganglionic intrinsic cardiac circuit mediates neural control of heart rate.

Intracardiac pathways mediating the parasympathetic control of various cardiac functions are incompletely understood. Several intracardiac ganglia have been demonstrated to potently influence cardiac rate [the sinoatrial (SA) ganglion], atrioventricular (AV) conduction (the AV ganglion), or left ventricular contractility (the cranioventricular ganglion). However, there are numerous ganglia found throughout the heart whose functions are poorly characterized. One such ganglion, the posterior atrial (PA) ganglion, is found in a fat pad on the rostral dorsal surface of the right atrium. We have investigated the potential impact of this ganglion on cardiac rate and AV conduction. We report that microinjections of a ganglionic blocker into the PA ganglion significantly attenuates the negative chronotropic effects of vagal stimulation without significantly influencing negative dromotropic effects. Because prior evidence indicates that the PA ganglion does not project to the SA node, we neuroanatomically tested the hypothesis that the PA ganglion mediates its effect on cardiac rate through an interganglionic projection to the SA ganglion. Subsequent to microinjections of the retrograde tracer fast blue into the SA ganglion, >70% of the retrogradely labeled neurons found within five intracardiac ganglia throughout the heart were observed in the PA ganglion. The neuroanatomic data further indicate that intraganglionic neuronal circuits are found within the SA ganglion. The present data support the hypothesis that two interacting cardiac centers, i.e., the SA and PA ganglia, mediate the peripheral parasympathetic control of cardiac rate. These data further support the emerging concept of an intrinsic cardiac nervous system.     

A model of slow conduction in bullfrog atrial trabeculae.

The success or failure of the propagation of electrical activity in cardiac tissue is dependent on both cellular membrane characteristics and intercellular coupling properties. This paper considers a linear arrangement of individual bullfrog atrial cells that are resistively coupled end to end to form a cylindrical strand. The strand, in turn, is encased by an endothelial sheath that provides a restricted extracellular space and an ion diffusion barrier to the outer bathing medium. This encased strand serves as an idealized model of an atrial trabeculum. Excitable membrane characteristics of the atrial cell are specified in terms of a Hodgkin-Huxley type of model that is quantitatively based on single-microelectrode voltage clamp data from bullfrog atrial myocytes. This membrane model can simulate the behavior of normal cells as well as of ischemic cells that exhibit depressed electrophysiological behavior (e.g., decreased resting potential, upstroke velocity, peak height, and action potential duration). Depressed activity can be easily simulated with variation of a single model parameter, the gain of the Na+/K+ pump current (INaK). Intercellular coupling properties are specified in terms of a lumped resistive T-type network between adjacent cells. The atrial strand model provides a means for studying the theoretical aspects of slow conduction in a "hybrid" strand that consists of a central region of cells having abnormal membrane or coupling properties, flanked on either side by normal atrial cells. Both uniform and discontinuous conduction are simulated by means of appropriate changes in the coupling resistance between cells. In addition, by varying either the degree of depressed electrical activity or the intercalated disc resistance in the central zone of the strand, slow conduction or complete conduction block in that region is demonstrated. Since the cellular model used in this study is based on experimental data and closely mimics both the atrial action potential and the underlying membrane currents, it has the potential to (1) accurately represent the current and voltage wave-forms occurring in the region of intercalated discs and (2) provide detailed information regarding the mechanisms in intercellular current spread in the region of slow conduction.     

The effect of mebudipine and dibudipine, two new Ca2+ channel blockers, in comparison with nifedipine on Ca2+ spikes of F1 neuronal soma membrane in Helix aspersa

Mebudipine and dibudipine are two new dihydropyridine (DHP) Ca2+ channel blockers that have been synthesized by Mahmoudian et al. (1997). In previous studies, they showed considerable relaxant effect on vascular and ileal smooth muscles. These two compounds also reduced the contraction force of rat left atrium (20, 22). In the present study, we attempted to compare the inhibitory actions of these new DHPs and nifedipine on the high threshold Ca2+ spikes of F1 neuronal soma membrane in the subesophageal ganglia of Helix aspersa, using current-clamp method. At a concentration of 1 microM, two new DHP compounds (mebudipine and dibudipine) were tested for their L-type Ca2+ channel blocker activity. Both compounds reversibly reduced the peak amplitude of action potential and after hyperpolarization potential and markedly decreased the duration of Ca2+ spikes. The most potent of these DHPs was mebudipine. Neither the two new DHPs nor nifedipine changed the resting membrane potential in a statistically significant way.