Reentry In Cardiac Tissue Research Articles

Reentry via high-frequency pacing in a mathematical model for human-ventricular cardiac tissue with a localized fibrotic region

Localized heterogeneities, caused by the regional proliferation of fibroblasts, occur in mammalian hearts because of diseases like myocardial infarction. Such fibroblast clumps can become sources of pathological reentrant activities, e.g., spiral or scroll waves of electrical activation in cardiac tissue. The occurrence of reentry in cardiac tissue with heterogeneities, such as fibroblast clumps, can depend on the frequency at which the medium is paced. Therefore, it is important to study the reentry-initiating potential of such fibroblast clumps at different frequencies of pacing. We investigate the arrhythmogenic effects of fibroblast clumps at high- and low-frequency pacing. We find that reentrant waves are induced in the medium more prominently at high-frequency pacing than with low-frequency pacing. We also study the other factors that affect the potential of fibroblast clumps to induce reentry in cardiac tissue. In particular, we show that the ability of a fibroblast clump to induce reentry depends on the size of the clump, the distribution and percentage of fibroblasts in the clump, and the excitability of the medium. We study the process of reentry in two-dimensional and a three-dimensional mathematical models for cardiac tissue.

Delayed afterdepolarizations generate both triggers and a vulnerable substrate promoting reentry in cardiac tissue

Delayed afterdepolarizations (DADs) have been well characterized as arrhythmia triggers, but their role in generating a tissue substrate vulnerable to reentry is not well understood. The purpose of this study was to test the hypothesis that random DADs can self-organize to generate both an arrhythmia trigger and a vulnerable substrate simultaneously in cardiac tissue as a result of gap junction coupling. Computer simulations in 1-dimensional cable and 2-dimensional tissue models were performed. The cellular DAD amplitude was varied by changing the strength of sarcoplasmic reticulum calcium release. Random DAD latency and amplitude in different cells were simulated using gaussian distributions. Depending on the strength of spontaneous sarcoplasmic reticulum calcium release and other conditions, random DADs in cardiac tissue resulted in the following behaviors: (1) triggered activity (TA); (2) a vulnerable tissue substrate causing unidirectional conduction block and reentry by inactivating sodium channels; (3) both triggers and a vulnerable substrate simultaneously by generating TA in regions next to regions with subthreshold DADs susceptible to unidirectional conduction block and reentry. The probability of the latter 2 behaviors was enhanced by reduced sodium channel availability, reduced gap junction coupling, increased tissue heterogeneity, and less synchronous DAD latency. DADs can self-organize in tissue to generate arrhythmia triggers, a vulnerable tissue substrate, and both simultaneously. Reduced sodium channel availability and gap junction coupling potentiate this mechanism of arrhythmias, which are relevant to a variety of heart disease conditions.

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.

Supernormal Excitability Causes Alternans, Block, Wavebreak and Reentry in Cardiac Tissue

It is well known that alternans can lead to cardiac arrhythmias. Alternans typically occurs in single cells due to voltage or calcium cycling instabilities. We showed in a previous study that alternans can also result from an instability caused by supernormal excitability (negative slope of the conduction velocity (CV) restitution curve), in the absence of voltage or calcium cycling instabilities.In this study, we used computer simulations of cables and two-dimensional domains of Luo-Rudy phase 1 model cells in which supernormal conduction was induced by decreasing the extracellular potassium concentration ([K+]o, 2.0 mmol/L) to explore arrhythmogenesis in the presence of supernormal excitability.Conduction was stable in a homogeneous cable (10 cm long) paced at one end at a basic cycle length (BCL) of 290 ms. However, when a slightly premature stimulus was applied and pacing at BCL was resumed, alternans developed gradually towards the end of the cable. This alternans was caused by supernormal CV restitution. The amplitude of alternans progressively increased until conduction block occurred at approximately 2/3 of the length of the cable.Conduction was also stable in a homogeneous two-dimensional domain (10x10 cm) paced on the left border at BCL=280 ms. However, when a premature pulse was applied at the lower half of the left border and pacing at BCL was resumed, alternans developed in the lower half of the domain via the same mechanism as in the 1D cable, while conduction in the upper half remained stable. This eventually led to conduction block and wavebreak formation in the lower half of the domain, which initiated spiral wave reentry.In conclusion, supernormal excitability represents a novel mechanism of alternans, which can lead to conduction block, wavebreak formation and reentry in cardiac tissue.

Phase-2 reentry in cardiac tissue: Role of the slow calcium pulse

Phase-2 re-entry is thought to underlie many causes of idiopathic ventricular arrhythmias as, for instance, those occurring in Brugada syndrome. In this paper, we study under which circumstances a region of depolarized tissue can re-excite adjacent regions that exhibit shorter action potential duration (APD), eventually inducing reentry. For this purpose, we use a simplified ionic model that reproduces well the ventricular action potential. With the help of this model, we analyze the conditions that lead to very short action potentials (APs), as well as possible mechanisms for re-excitation in a cable. We then study the induction of re-entrant waves (spiral waves) in simulations of AP propagation in the heart ventricles. We show that re-excitation takes place via a slow pulse produced by calcium current that propagates into the region of short APs until it encounters excitable tissue. We calculate analytically the speed of the slow pulse, and also give an estimate of the minimal tissue size necessary for allowing reexcitation to take place.

Effects of fibroblast-myocyte coupling on cardiac conduction and vulnerability to reentry: A computational study

Recent experimental studies have documented that functional gap junctions form between fibroblasts and myocytes, raising the possibility that fibroblasts play roles in cardiac electrophysiology that extend beyond acting as passive electrical insulators. The purpose of this study was to use computational models to investigate how fibroblasts may affect cardiac conduction and vulnerability to reentry under different fibroblast-myocyte coupling conditions and tissue structures. Computational models of two-dimensional tissue with fibroblast-myocyte coupling were developed and numerically simulated. Myocytes were modeled by the phase I of the Luo-Rudy model, and fibroblasts were modeled by a passive model. Besides slowing conduction by cardiomyocyte decoupling and electrotonic loading, fibroblast coupling to myocytes elevates myocyte resting membrane potential, causing conduction velocity to first increase and then decrease as fibroblast content increases, until conduction failure occurs. Fibroblast-myocyte coupling can also enhance conduction by connecting uncoupled myocytes. These competing effects of fibroblasts on conduction give rise to different conduction patterns under different fibroblast-myocyte coupling conditions and tissue structures. Elevation of myocyte resting potential due to fibroblast-myocyte coupling slows sodium channel recovery, which extends postrepolarization refractoriness. Owing to this prolongation of the myocyte refractory period, reentry was more readily induced by a premature stimulation in heterogeneous tissue models when fibroblasts were electrotonically coupled to myocytes compared with uncoupled fibroblasts acting as pure passive electrical insulators. Fibroblasts affect cardiac conduction by acting as obstacles or by creating electrotonic loading and elevating myocyte resting potential. Functional fibroblast-myocyte coupling prolongs the myocyte refractory period, which may facilitate induction of reentry in cardiac tissue with fibrosis.

Effects of early afterdepolarizations on reentry in cardiac tissue: a simulation study

Early afterdepolarizations (EADs) are classically generated at slow heart rates when repolarization reserve is reduced by genetic diseases or drugs. However, EADs may also occur at rapid heart rates if repolarization reserve is sufficiently reduced. In this setting, spontaneous diastolic sarcoplasmic reticulum (SR) Ca release can facilitate cellular EAD formation by augmenting inward currents during the action potential plateau, allowing reactivation of the window L-type Ca current to reverse repolarization. Here, we investigated the effects of spontaneous SR Ca release-induced EADs on reentrant wave propagation in simulated one-, two-, and three-dimensional homogeneous cardiac tissue using a version of the Luo-Rudy dynamic ventricular action potential model modified to increase the likelihood of these EADs. We found: 1) during reentry, nonuniformity in spontaneous SR Ca release related to subtle differences in excitation history throughout the tissue created adjacent regions with and without EADs. This allowed EADs to initiate new wavefronts propagating into repolarized tissue; 2) EAD-generated wavefronts could propagate in either the original or opposite direction, as a single new wave or two new waves, depending on the refractoriness of tissue bordering the EAD region; 3) by suddenly prolonging local refractoriness, EADs caused rapid rotor displacement, shifting the electrical axis; and 4) rapid rotor displacement promoted self-termination by collision with tissue borders, but persistent EADs could regenerate single or multiple focal excitations that reinitiated reentry. These findings may explain many features of Torsades des pointes, such as perpetuation by focal excitations, rapidly changing electrical axis, frequent self-termination, and occasional degeneration to fibrillation.

The Effect of the Fiber Curvature Gradient on Break Excitation in Cardiac Tissue

Break excitation has been hypothesized as a mechanism for the initiation of reentry in cardiac tissue. One way break excitation can occur is by virtual electrodes formed due to a curving fiber geometry. In this article, we are concerned with the relationship between the peak gradient of fiber curvature and the threshold for break stimulation and the initiation of reentry. We calculate the maximum gradient of fiber curvature for different scales of fiber geometry in a constant tissue size (20x20 mm), and also examine the mechanisms by which reentry initiation fails. For small peak gradients, reentry fails because break excitation does not occur. For larger peak gradients, reentry fails because break excitation fails to develop into full-scale reentry. For strong stimuli above the upper limit of vulnerability, reentry fails because the break excitation propagates through the hyperpolarized region and then encounters refractory tissue, causing the wave front to die.

Regional differences in APD restitution can initiate wavebreak and re-entry in cardiac tissue: A computational study

BackgroundRegional differences in action potential duration (APD) restitution in the heart favour arrhythmias, but the mechanism is not well understood.MethodsWe simulated a 150 × 150 mm 2D sheet of cardiac ventricular tissue using a simplified computational model. We investigated wavebreak and re-entry initiated by an S1S2S3 stimulus protocol in tissue sheets with two regions, each with different APD restitution. The two regions had a different APD at short diastolic interval (DI), but similar APD at long DI. Simulations were performed twice; once with both regions having steep (slope > 1), and once with both regions having flat (slope < 1) APD restitution.ResultsWavebreak and re-entry were readily initiated using the S1S2S3 protocol in tissue sheets with two regions having different APD restitution properties. Initiation occurred irrespective of whether the APD restitution slopes were steep or flat. With steep APD restitution, the range of S2S3 intervals resulting in wavebreak increased from 1 ms with S1S2 of 250 ms, to 75 ms (S1S2 180 ms). With flat APD restitution, the range of S2S3 intervals resulting in wavebreak increased from 1 ms (S1S2 250 ms), to 21 ms (S1S2 340 ms) and then 11 ms (S1S2 400 ms).ConclusionRegional differences in APD restitution are an arrhythmogenic substrate that can be concealed at normal heart rates. A premature stimulus produces regional differences in repolarisation, and a further premature stimulus can then result in wavebreak and initiate re-entry. This mechanism for initiating re-entry is independent of the steepness of the APD restitution curve.

How the Spatial Frequency of Polarization Influences the Induction of Reentry in Cardiac Tissue

Influences of spatial frequency of polarization. The mechanism by which an electric field induces a rotor during cross-field stimulation of cardiac tissue is not entirely known. Different heterogeneous aspects of cardiac tissue have been offered as possible theories, a prominent one being fiber curvature. The polarization produced when an electric field is applied to a sheet of tissue is varied over many spatial frequencies, depending upon the fiber angle. This article compares the effect of high and low spatial frequencies of polarization on reentry induction. We incorporate a randomized fiber angle geometry into a two-dimensional active cardiac tissue model with unequal anisotropy ratios already exhibiting smooth, curving fibers. We simulate cross-field stimulation to initiate reentry in the tissue model, and compare the electric field thresholds at different S1-S2 intervals for tissue with randomized fiber angles, tissue with a smooth fiber geometry, and tissue with randomized fiber angles plus smooth, curving fibers. The tissue with both small, random fiber angles and curving fibers has a significantly lower threshold for reentry at certain intervals on the strength-interval curve than for the two cases individually. Cardiac tissue exhibiting a random fiber geometry in conjunction with a smooth fiber geometry includes high and low spatial frequencies of polarization that may have an effect on the mechanism for reentry at certain S1-S2 intervals. Low spatial frequency regions of hyperpolarization carve out excitable pathways, and high spatial frequency regions provide the large gradient of transmembrane potential required to initiate break excitation.

Simulation of protective zones during quatrefoil reentry in cardiac tissue.

An S3 stimulus can exert a protective effect by terminating reentry induced by an S2 stimulus. Our goal was to examine the mechanism by which an S3 pulse terminates reentry and the role that virtual electrodes and break excitation play in this process. In our simulation, the bidomain model represents the electrical properties of the tissue and the Beeler-Reuter model represents the membrane kinetics. Quatrefoil reentry is initiated by S1-S2 stimulation, and then a third stimulus S3 is applied at different intervals after S2. All stimuli are applied through the same unipolar electrode. For some S2-S3 intervals, the S2 and S3 wavefronts interact destructively, terminating reentry (protective zones). For other S2-S3 intervals, S2 and S3 wavefronts interact constructively, and reentry continues. Protective zones appear recurrently, with approximately the period of the S2 reentrant circuit. The protective zones are wider for anodal stimulation than for cathodal stimulation. Virtual electrodes, break excitation, and S2-S3 timing all play important roles in determining the electrical response of the tissue.

Effect of fibre rotation on the initiation of re-entry in cardiac tissue.

Transmural rotation of cardiac fibres can have a big influence on the initiation of re-entry in the heart. However, owing to computational demands, this has not been fully explored in a three-dimensional model of cardiac tissue that has a microscopic description of membrane currents, such as the Luo-Rudy model. Using a previously described model that is computationally fast, re-entry in three-dimensional blocks of cardiac tissue is induced by a cross-shock protocol, and the activity is examined. In the study, the effect of the transmural fibre rotation is ascertained by examining differences between a tissue block with no rotation and ones with 1, 2 and 3 degrees of rotation per fibre layer. The direction of the re-entry is significant in establishing whether or not re-entry can be induced, with clockwise re-entry being easier to initiate. Owing to the rotating anisotropy that results in preferential propagation along the fibre axis, the timing of the second stimulus in the cross-shock protocol has to be changed for different rates of fibre rotation. The fibre rotation either increases or decreases the window of opportunity for re-entry, depending on whether the activation front is perpendicular or parallel to the fibre direction. By varying the transmural extent of the S2, it is found that a deeper stimulus has to be applied to the blocks with fibre rotation to create re-entry. Increasing the transmural resistance also tends to reduce the extent of the S2 required to induce re-entry. Results suggest that increasing fibre rotation reduces the susceptibility of the tissue to re-entry, but that more complex spatiotemporal patterns are possible, e.g. stable figure-of-eight re-entries and transient rotors. Three mechanisms of re-entry annihilation are identified: front catchup, filling of the excitable gap and core wander.

Influence of transmural repolarization gradients on the electrophysiology and pharmacology of ventricular myocardium. Cellular basis for the Brugada and long–QT syndromes

Ventricular myocardium comprises at least three electrophysiologically distinct cell types: epicardial, endocardial and M cells. Epicardial and M cells, but not endocardial cells, display action potentials with a notched or spike–and–dome morphology: the result of a prominent, transient, outward current–mediated phase 1. M cells are distinguished from endocardial and epicardial cells by the ability of their action potential to disproportionately prolong in response to a slowing down of rate and/or in response to agents with class III actions. This intrinsic electrical heterogeneity contributes to the inscription of the electrocardiogram (ECG) as well as to the development of a variety of cardiac arrhythmias. Heterogeneous response of the three cell types to pharmacological agents and/or pathophysiological states results in amplification of intrinsic electrical heterogeneities, thus providing a substrate as well as a trigger for the development of re–entrant arrhythmias, including Torsade de Pointes, commonly associated with the long–QT syndrome (LQTS), and the polymorphic ventricular tachycardia/ventricular fibrillation (VT/VF) encountered in the Brugada syndrome. Despite an abundance of experimental data describing the heterogeneity of cellular electrophysiology that exists across the ventricular wall, relatively few computer models have been developed to investigate the physiological and pathophysiological consequences of such electrical heterogeneity. As computer power increases and numerical algorithms improve, three–dimensional computer models of ventricular conduction that combine physiological membrane kinetics with realistic descriptions of myocardial structure and geometry will become more feasible. With sufficient detail and accuracy, these models should illuminate the complex mechanisms underlying the initiation and maintenance of Torsade de Pointes and other arrhythmias.

Dynamics of action potential head-tail interaction during reentry in cardiac tissue: ionic mechanisms.

In a sufficiently short reentry pathway, the excitation wave front (head) propagates into tissue that is partially refractory (tail) from the previous action potential (AP). We incorporate a detailed mathematical model of the ventricular myocyte into a one-dimensional closed pathway to investigate the effects of head-tail interaction and ion accumulation on the dynamics of reentry. The results were the following: 1) a high degree of head-tail interaction produces oscillations in several AP properties; 2) Ca(2+)-transient oscillations are in phase with AP duration oscillations and are often of greater magnitude; 3) as the wave front propagates around the pathway, AP properties undergo periodic spatial oscillations that produce complicated temporal oscillations at a single site; 4) depending on the degree of head-tail interaction, intracellular [Na(+)] accumulation during reentry either stabilizes or destabilizes reentry; and 5) elevated extracellular [K(+)] destabilizes reentry by prolonging the tail of postrepolarization refractoriness.

Computationally efficient model for simulating electrical activity in cardiac tissue with fiber rotation.

Transmural rotation of cardiac fibers may have a large influence on the initiation, stabilization, and termination of several life threatening cardiac arrhythmias. However, three-dimensional modeling of reentry in cardiac tissue is computationally demanding, as a tissue on the order of centimeters in size must be used to sustain reentry and several seconds must be simulated. Numerical accuracy requires time steps on the order of microseconds and spatial discretization on the order of microns. Consequently, the resultant numerical systems are extremely large. In this article, a computationally efficient model of a three-dimensional block of cardiac tissue with fiber rotation is presented. Computational speedup is achieved by using a discrete cable model which allowed for system order reduction, and also by using a scheme for tracking the activation wave front which identified regions requiring integration with a small time step. Simulating 1.2 s of activity of the approximately 2 x 10(6) cells constituting a block measuring 2.0 x 4.0 x 0.29 cm was performed in 26 h. Effects of model parameters on performance are discussed. The effect of fiber rotation on the spread of electrical activity after point source stimulation and a cross shock protocol is clearly demonstrated.

The induction of reentry in cardiac tissue. The missing link: How electric fields alter transmembrane potential.

This review examines the initiation of reentry in cardiac muscle by strong electric shocks. Specifically, it concentrates on the mechanisms by which electric shocks change the transmembrane potential of the cardiac membrane and create the physiological substrate required by the critical point theory for the initiation of rotors. The mechanisms examined include (1) direct polarization of the tissue by the stimulating current, as described by the one-dimensional cable model and its two- and three-dimensional extensions, (2) the presence of virtual anodes and cathodes, as described by the bidomain model with unequal anisotropy ratios of the intra- and extracellular spaces, (3) polarization of the tissue due to changing orientation of cardiac fibers, and (4) polarization of individual cells or groups of cells by the electric field ("sawtooth potential"). The importance of these mechanisms in the initiation of reentry is examined in two case studies: the induction of rotors using successive stimulation with a unipolar electrode, and the induction of rotors using cross-field stimulation. These cases reveal that the mechanism by which a unipolar stimulation induces arrhythmias can be explained in the framework of the bidomain model with unequal anisotropy ratios. In contrast, none of the examined mechanisms provide an adequate explanation for the induction of rotors by cross-field stimulation. Hence, this study emphasizes the need for further experimental and theoretical work directed toward explaining the mechanism of field stimulation. (c) 1998 American Institute of Physics.

The vulnerable window for unidirectional block in cardiac tissue: characterization and dependence on membrane excitability and intercellular coupling.

Unidirectional block is a requisite event in the initiation of reentry in cardiac tissue, but its initiation and behavior in the presence of tissue pathologies remain poorly understood. Previous experimental and theoretical reports on vulnerability to unidirectional block under conditions of reduced cellular coupling and reduced membrane excitability have varied due to differences in experimental and simulation protocols. We have addressed the issue of vulnerability to unidirectional block using the recent Luo-Rudy membrane model and computer simulations of propagation in a one-dimensional cardiac fiber. The vulnerable window (VW) of unidirectional block from premature stimulation is expressed in units of time, VWtime, and as a range of membrane potentials at the stimulus site, VWpot. VWpot and VWtime were quantified over a range of membrane excitability and gap junction resistances (intercellular coupling). With normal membrane excitability and intercellular coupling, VWpot and VWtime were small (VWpot = 0.44 mV, VWtime = 0.39 msec). A uniform reduction (0.25x) in the degree of intercellular coupling increased VWtime and VWpot by factors of 3.6 and 4.7, respectively, whereas a uniform decrease (0.25x) in membrane excitability (same resulting velocity) increased VWtime by only a factor of 0.4 and decreased VWpot to negligible levels. When inhomogeneities in fiber properties were introduced (intercellular coupling and membrane excitability), VWtime increased more due to inhomogeneity in membrane excitability (VWtime = 4.5 msec) than to inhomogeneity in intercellular coupling (VWtime = 1.5 msec). The simulations also clarify the dependence of the VW on the dimensions of the stimulating electrode. The length of the stimulating electrode added a factor, equal to the propagation time across the electrode length, to the intrinsic VW of the fiber. VWpot and VWtime are both important parameters for quantifying vulnerability to unidirectional block. In an environment with uniform distribution of fiber and membrane properties, reduced intercellular coupling has a greater effect on the VW than reduced membrane excitability. Inhomogeneous reduction of membrane excitability can significantly enhance vulnerability to unidirectional block, much more so than inhomogeneous reduction of intercellular coupling. Theoretically, stimulation at a point should be used to define the VW. Finite electrode dimensions introduce a geometrical factor that affects the measurement of the VW.

A computer model of re-entry in cardiac tissue

This paper describes the use of a computer model to investigate the nature of impulse propagation and the mechanisms of electrical instability which precipitate ventricular arrhythmias. The model provides the opportunity for a systematic analysis of the conditions of cardiac conduction under controlled conditions. From the simulation studies performed it is found that the most critical parameter which influences re-entry circuit formation is the ratio of exited to refractory duration.