Propagation In Cardiac Muscle Research Articles

Exploring the role of inhibitory coupling in duplex networks**Project supported by the National Natural Science Foundation of China (Grant Nos. 11565005 and 11365003).

The electrical coupling of myocytes and fibroblasts can play a role in inhibiting electrical impluse propagation in cardiac muscle. To understand the function of fibroblast–myocyte coupling in the aging heart, the spiral-wave dynamics in the duplex networks with inhibitory coupling is numerically investigated by the Bär–Eiswirth model. The numerical results show that the inhibitory coupling can change the wave amplitude, excited phase duration and excitability of the system. When the related parameters are properly chosen, the inhibitory coupling can induce local abnormal oscillation in the system and the Eckhaus instability of the spiral wave. For the dense inhibitory network, the maximal decrement (maximal increment) in the excited phase duration can reach 24.3%(13.4%), whereas the maximal decrement in wave amplitude approaches 28.1%. Upon increasing the inhibitory coupling strength, the system excitability is reduced and even completely suppressed when the interval between grid points in the inhibitory network is small enough. Moreover, the inhibitory coupling can lead to richer phase transition scenarios of the system, such as the transition from a stable spiral wave to turbulence and the transition from a meandering spiral wave to a planar wave. In addition, the self-sustaining planar wave, the unique meandering of spiral wave and inward spiral wave are observed. The physical mechanisms behind the phenomena are analyzed.

Role of the intercalated disc in cardiac propagation and arrhythmogenesis.

This review article discusses mechanisms underlying impulse propagation in cardiac muscle with specific emphasis on the role of the cardiac cell-to-cell junction, called the “intercalated disc.”The first part of this review deals with the role of gap junction channels, formed by connexin proteins, as a determinant of impulse propagation. It is shown that, depending on the underlying structure of the cellular network, decreasing the conductance of gap junction channels (so-called “electrical uncoupling”) may either only slow, or additionally stabilize propagation and reverse unidirectional propagation block to bidirectional propagation. This is because the safety factor for propagation increases with decreasing intercellular electrical conductance. The role of heterogeneous connexin expression, which may be present in disease states, is also discussed. The hypothesis that so-called ephaptic impulse transmission plays a role in heart and can substitute for electrical coupling has been revived recently. Whereas ephaptic transmission can be demonstrated in theoretical simulations, direct experimental evidence has not yet been presented. The second part of this review deals with the interaction of three protein complexes at the intercalated disc: (1) desmosomal and adherens junction proteins, (2) ion channel proteins, and (3) gap junction channels consisting of connexins. Recent work has revealed multiple interactions between these three protein complexes which occur, at least in part, at the level of protein trafficking. Such interactions are likely to play an important role in the pathogenesis of arrhythmogenic cardiomyopathy, and may reveal new therapeutic concepts and targets.

Gap-junction channels inhibit transverse propagation in cardiac muscle

The effect of adding many gap-junctions (g-j) channels between contiguous cells in a linear chain on transverse propagation between parallel chains was examined in a 5 × 5 model (5 parallel chains of 5 cells each) for cardiac muscle. The action potential upstrokes were simulated using the PSpice program for circuit analysis. Either a single cell was stimulated (cell A1) or the entire chain was stimulated simultaneously (A-chain). Transverse velocity was calculated from the total propagation time (TPT) from when the first AP crossed a Vm of -20 mV and the last AP crossed -20 mV. The number of g-j channels per junction was varied from zero to 100, 1,000 and 10,000 (Rgj of ∞, 100 MΩ, 10 MΩ, 1.0 MΩ, respectively). The longitudinal resistance of the interstitial fluid (ISF) space between the parallel chains (Rol2) was varied between 200 KΩ (standard value) and 1.0, 5.0, and 10 MΩ. The higher the Rol2 value, the tighter the packing of the chains. It was found that adding many g-j channels inhibited transverse propagation by blocking activation of all 5 chains, unless Rol2 was greatly increased above the standard value of 200 KΩ. This was true for either method of stimulation. This was explained by, when there is strong longitudinal coupling between all 5 cells of a chain awaiting excitation, there must be more transfer energy (i.e., more current) to simultaneously excite all 5 cells of a chain.

Pinning Force in Active Media

Pinning of vortices by defects plays an important role in various physical (superconductivity, superfluidity, etc.) or biological (propagation in cardiac muscle) situations. Which defects act as pinning centers? We propose a way to study this general problem by using an advection field to quantify the attraction between an obstacle and a vortex. A full solution is obtained for the real Ginzburg-Landau equation (RGLE). Two pinning mechanisms are found in excitable media. Our results suggest strong analogies with the RGLE when the heterogeneity is excitable. Unpinning from an unexcitable obstacle is qualitatively harder, resulting in a stronger pinning force. We discuss the implications of our results to control vortices and propose experiments in a chemical active medium and in cardiac tissue.

Delayed activation and retrograde propagation in cardiac muscle: implication of virtual electrode effects.

Point cathodal stimulation of cardiac tissue was shown previously to produce both a dog-bone shaped virtual cathode transverse to the muscle fibers and two longitudinal virtual anodes. We hypothesize that virtual anodes can cause a region of delayed activation, separating two regions of early activation caused by the virtual cathode. Using a high-density electrode array in 42 superfused epicardial slices from 14 canine left ventricles, we observed regions of early and delayed activation and different pathways of retrograde propagation corresponding to the earlier patterns. Retrograde propagation was seen from the transversely located early activation area through areas of delayed activation toward the cathode, and from the early activation area toward the cathode directly. These pathways caused a wide dispersion in the direction of retrograde propagation (2 degrees +/- 31 degrees, n = 179, relative to the fast axis of threshold activation; radial velocity: 0.5 +/- 0.2 m/s, n = 95, in 12 slices from 8 hearts with stimuli of 330 micros, 0.8-30 mA). Delayed activations were observed 0 degrees +/- 6 degrees (n = 32) from the axis in 23 maps (at differing stimulation strengths) recorded in 13 slices from 10 hearts. We conclude that point cathodal stimulation induce delayed activation along the fiber axis and retrograde propagation both along and transverse to the axis.

Role of wavefront curvature in propagation of cardiac impulse.

It is traditionally assumed that impulse propagation in cardiac muscle is determined by the combination of two factors: (1) the active properties of cardiac cell membranes and (2) the passive electrical characteristics of the network formed by cardiac cells. However, advances made recently in the theory of generic excitable media suggest that an additional factor-the geometry of excitation wavefronts -may play an important role. In particular, impulse propagation strongly depends on the wavefront curvature on a small spatial scale. In the heart, excitation wavefronts have pronounced curvatures in several situations including waves initiated by small electrodes, waves emerging from narrow tissue structures, and waves propagating around the sharp edges of anatomical obstacles or around a zone of functional conduction block during spiral wave rotation. In this short review we consider the theoretical background relating impulse propagation to wavefront curvature and we estimate the role of wavefront curvature in electrical stimulation, formation of conduction block, and the dynamic behavior of spiral waves.

A quasi-one-dimensional theory for anisotropic propagation of excitation in cardiac muscle

It has been shown that propagation of excitation in cardiac muscle is anisotropic. Compared to propagation at right angles to the long axes of the fibers, propagation along the long axis is faster, the extracellular action potential (AP) is larger in amplitude, and the intracellular AP has a lower maximum rate of depolarization, a larger time constant of the foot, and a lower peak amplitude. These observations are contrary to the predictions of classical one-dimensional (1-D) cable theory and, thus far, no satisfactory theory for them has been reported. As an alternative description of propagation in cardiac muscle, this study provides a quasi-1-D theory that includes a simplified description of the effects of action currents in extracellular space as well as resistive coupling between surface and deeper fibers in cardiac muscle. In terms of classical 1-D theory, this quasi-1-D theory reveals that the anisotropies in the wave form of the AP arise from modifications in the effective membrane ionic current and capacitance. The theory also shows that it is propagation in the longitudinal, not in the transverse direction that deviates from classical 1-D cable theory.

Directional characteristics of action potential propagation in cardiac muscle. A model study.

Propagation of an elliptic excitation wave front was studied in a two-dimensional model of a thin sheet of cardiac muscle. The sheet model of 2.5 x 10 mm consisted of a set of 100 parallel cables coupled through a regular array of identical transverse resistors. The membrane dynamics was represented by a modified Beeler-Reuter model. We defined the charging factor (CF) to represent by a single number the proportion of input current used to charge the membrane locally below threshold and showed that CF is inversely correlated with the time constant of the foot of the action potential (tau foot) during propagation on a cable. A safety factor of propagation (SF) was also defined for the upstroke of the action potential, with SF directly correlated with the maximum rate of depolarization (Vmax) and, for cablelike propagation, with propagation velocity. Propagation along the principal longitudinal axis of the elliptic wave front is cablelike but, in comparison with a flat wave front, transverse current flow provides a drag effect that somewhat reduces the propagation velocity, Vmax, SF, and CF. With a longitudinal-to-transverse velocity ratio of 3:1 or more, the wave front propagating along the principal transverse axis is essentially flat and is characterized by multiple collisions between successive pairs of input junctions on a given cable; Vmax, SF, and CF are larger than for longitudinal propagation, but CF is no longer correlated with tau foot. There are transient increases in propagation velocity and Vmax with distance from the stimulation site along both principal axes until stablized values are achieved, and a similar transient decrease in tau foot. Away from the principal axes, the action potential characteristics change progressively along the elliptic wave front.(ABSTRACT TRUNCATED AT 250 WORDS)

Electric Field Model: An Alternative Mechanism for Cell‐to‐Cell Propagation in Cardiac Muscle and Smooth Muscle

Cardiac muscle and visceral smooth muscle are similar in some regards, in that both tissues are composed of relatively short individual cells that interact in some way to allow the spread of excitation over all or much of the tissue, bringing about a synchronized and nearly simultaneous contraction of the cells to subserve a specific physiologic function. A prevailing view is that these short muscle cells possess low‐resistance interconnections, which allows local‐circuit action current to flow readily from one cell to the next, thereby allowing the propagation of excitation over the entire tissue. The gap junctions, which are observed morphologically, are thought to contain numerous low‐resistance connections. However, gap junctions are not observed in hearts of lower vertebrates or in some visceral smooth muscles. Therefore, the questions arise of what their role is in propagation and whether an alternative mechanism for transfer of excitation from cell to cell might apply in some normal physiologic circumstances and in some pathophysiologic conditions. The case for such an alternative mechanism that is electrical in nature, but does not require low‐resistance connections, is presented here. The arguments in support of low‐resistance coupling in smooth muscle are provided by Alex Bortoff in his accompanying article.

Expanded model of the electric field hypothesis for propagation in cardiac muscle

An electric field model for action potential (AP) propagation between adjoining myocardial cells has been further developed by expanding the model to a strand of 10 cells, increasing the number of active membrane segments per cell, incorporating Beeler-Reuter kinetics, assigning physiologically realistic values to the parameters, and employing a simpler numerical integration scheme. The major assumption is that the pre- and postjunctional membranes are excitable membranes. There is no requirement for a low-resistance coupling between the cells. The electric field that develops in the narrow junctional cleft between cells during the rising phase of the action potential in the prejunctional membrane acts to depolarize the postjunctional membrane to threshold. AP propagation occurred down the strand at a uniform velocity of 32 cm/sec under standard conditions. Propagation was found to be strongly dependent on radial cleft resistance ( R jc ) and the junctional membrane properties. There was an optimal R jc for maximum velocity under any given conditions. However, overall propagation velocity was determined by the AP conduction delay at the junctional clefts. K + accumulation in the clefts was shown to facilitate AP transmission. This model is consistent with many experimental facts concerning propagation in cardiac muscle, including discontinuous conduction, and suggests an alternative mechanism for AP propagation that does not depend on direct current flow between cells.

Simulation of propagation along a cylindrical bundle of cardiac tissue. I. Mathematical formulation

This paper presents a mathematical description based on a three-dimensional model for studying propagation in cardiac muscle. The model makes use of the bidomain concept to construct a representation of a cylindrical, multicellular bundle lying in an extensive volume conductor. The equations for the cylindrical bidomain are derived here for different combinations of boundary conditions and simplifying assumptions. The analysis shows that an analytic model for propagation can be set up if one assumes that the ratio of the intracellular and interstitial bidomain conductivities in the radial and axial direction are the same (i.e., equal anisotropy) and the intracellular radial current density vanishes at the surface. The simulation of this model will be discussed in a subsequent paper. As a point of reference, the classical one-dimensional cable model is also examined and the expressions governing propagation are reformulated to account for the extracellular medium, a factor ignored in most simulation studies.

Effects of increasing intercellular resistance on transverse and longitudinal propagation in sheep epicardial muscle.

Propagation in cardiac muscle is faster in the longitudinal than in the transverse axis of the cells. Yet, as a result of the larger upstroke velocity of action potentials propagating transversely, it has been suggested that longitudinal propagation is more vulnerable to block. To study the relation between conduction velocity and maximal upstroke velocity (Vmax), as well as the time course of conduction delay and block in the transverse vs. longitudinal direction, thin square pieces of sheep epicardial muscle were superfused with the cellular uncoupler heptanol (1.5 mM). Action potentials were recorded with microelectrodes at opposite corners of the preparation while stimulating alternately in the longitudinal or transverse direction with bipolar electrodes located at contralateral corners. In all cases, block occurred more promptly for transverse than for longitudinal propagation. The decrease in conduction velocity was greater than expected for Vmax decay and, in some cases, Vmax increased while conduction velocity decreased. In the presence of high grade conduction impairment, foot potentials appeared and the upstrokes became "notched." We conclude that when intercellular coupling is impaired, transverse propagation is more vulnerable to block, and need not be dependent on changes in Vmax.

The discontinuous nature of electrical propagation in cardiac muscle. Consideration of a quantitative model incorporating the membrane ionic properties and structural complexities. The ALZA distinguished lecture.

The propagation of excitation in cardiac muscle has generally been treated as though it occurred in a continuous structure. However, new evidence indicates that propagation in cardiac muscle often displays a discontinuous nature. In this paper, we consider the hypothesis that this previously unrecognized type of propagation is caused by recurrent discontinuities of effective axial resistivity which affect the membrane currents. The major implication is that the combination of discontinuities of axial resistivity at several size scales can produce most currently known cardiac conduction disturbances previously though to require spatial nonuniformities of the membrane properties. At present there is no appropriate model or simulation for propagation in anisotropic cardiac muscle. However, the recent quantitative description of the fast sodium current in voltage-clamped cardiac muscle membrane makes it possible, for the first time, to apply experimentally based quantitative membrane models to propagation in cardiac muscle. The major task now is to account for the functional role of the structural complexities of cardiac muscle. The importance of such a model is that it would establish how the membrane ionic currents and the complexities of cell and tissue structure interact to determine propagation in both normal and abnormal cardiac muscle.

Intercalated discs as a cause for discontinuous propagation in cardiac muscle: a theoretical simulation.

A theoretical model of a cardiac muscle fiber (strand) based on core conductor principles and which includes a periodic intercalated disc structure has been developed. The model allows for examination of the mechanism of electrical propagation in cardiac muscle on a microscopic cell-to-cell level. The results of the model simulations demonstrate the discontinuous nature of electrical propagation in cardiac muscle and the inability of classical continuous cable theory to adequately describe propagation phenomena in cardiac muscle.

The nature of electrical propagation in cardiac muscle

It has long been appreciated that cardiac muscle is composed of individual cells connected by low-resistance connections, but most concepts of cardiac impulse conduction have been based on a simplified model of propagation assuming continuously uniform intracellular resistivity in the direction of propagation. In this article we describe the development of the application of the theory of continuous media to propagation in cardiac muscle and review some of the successes achieved with this theory. New evidence is cited that propagation in cardiac muscle often displays a discontinuous nature. We consider the hypothesis that this previously unrecognized aspect of propagation can be explained by discontinuities in axial resistance related to known structural complexities of cardiac muscle. A major implication is that the combination of discontinuities of effective axial resistivity at several size levels can produce a wide variety of complex abnormalities of propagation, including most currently known cardiac conduction disturbances that have been considered to require spatial nonuniformity of membrane properties.

A model study of the effect of the intercalated discs on discontinuous propagation in cardiac muscle".

There is considerable evidence (1,13,14,22,23) to support the existence of low resistance end-to-end junctions (gap junctions or connexons (10,12,17) which lie in the intercalated discs that make up the associated end-to-end plasma membranes of cardiac muscle cells. Even though these gap junctions are low resistance, they represent a significant discontinuity in the conductive medium. Indeed, while these low resistance contacts are low in the sense of permitting an adequate current to flow and excite the postjunctional cell, an often quoted value for the intercalated disc resistance, 1 ohm-cm2, would be an impediment to axial current flow comparable to the entire myoplasm of the cell. In order to study the effects of these discontinuities due to the intercalated discs on propagation in cardiac muscle a “microscopic” discontinuous cable model which includes the intercalated discs was developed.KeywordsCardiac MuscleConduction VelocitySharp DiscontinuityCable ModelDiscontinuous ModelThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Alteration in sodium channel gate kinetics of the Hodgkin-Huxley equations applied to an electric field model for interaction between excitable cells.

An electric field model for electrical transmission of excitation between adjacent myocardial cells, without the necessity of low-resistance connections between the cells, is further developed. The voltage dependency of the membrane conductances was modeled by the Hodgkin-Huxley equations. A major assumption of the model is that the pre-and postjunctional membranes are excitable. The bulk electrical properties (capacitance, conductivity, etc.) of the junctional membranes may be the same as those of the surface membranes. We showed that a modification of the dynamics of the fast sodium channel gates of the junctional membranes (controlled by the m and h parameters) can be employed as a mechanism to secure propagation of an impulse. The propagation velocity was determined primarily by the dynamics of the junctional membranes, and was essentially independent of the rate of rise of the surface units. Propagation at a constant velocity occurred when the electric field model was expanded to a chain of six cells. Thus, the electric field model, based on closely apposed and excitable junctional membranes, could account for propagation in cardiac muscle, and may apply under various physiological and pathophysiological conditions.

Refractoriness in cardiac muscle.

A preparation consisting of a papillary muscle and attached bundle of Purkinje fibers has been employed to study refractoriness of single cardiac fibers of the dog heart. Transmembrane stimulation of single fibers and records of the transmembrane potential have been used to compare the stimulating efficacy of applied current pulses and normally propagated action potentials. The absolute and effective refractory period and full recovery time of the single cardiac fiber are outlined in a similar manner by both applied cathodal stimuli and the propagated action potential. Two factors, a local response and a change in the local action potential, have been shown to contribute to the latency of response to stimuli applied during the relative refractory period. These studies have also demonstrated a considerable safety factor in propagation in cardiac muscle.