Effects of simulated ischemia on spiral wave stability

Arrhythmogenic Potential of Myocardial Edema: The Interstitial Osmolality Induces Spiral Waves and Multiple Excitation Wavelets

Myocardial edema is a common symptom of pathological processes in the heart, causing aggravation of cardiovascular diseases and leading to irreversible myocardial remodeling. Patient-based studies show that myocardial edema is associated with arrhythmias. Currently, there are no studies that have examined how edema may influence changes in calcium dynamics in the functional syncytium. We performed optical mapping of calcium dynamics on a monolayer of neonatal rat cardiomyocytes with Fluo-4. The osmolality of the solutions was adjusted using the NaCl content. The initial Tyrode solution contained 140 mM NaCl (1T) and the hypoosmotic solutions contained 105 (0.75T) and 70 mM NaCl (0.5T). This study demonstrated a sharp decrease in the calcium wave propagation speed with a decrease in the solution osmolality. The successive decrease in osmolality also showed a transition from a normal wavefront to spiral wave and multiple wavelets of excitation with wave break. Our study demonstrated that, in a cellular model, hypoosmolality and, as a consequence, myocardial edema, could potentially lead to fatal ventricular arrhythmias, which to our knowledge has not been studied before. At 0.75T spiral waves appeared, whereas multiple wavelets of excitation occurred in 0.5T, which had not been recorded previously in a two-dimensional monolayer under conditions of cell edema without changes in the pacing protocol.

The electrical restitution of the non-propagated cardiac ventricular action potential

Sudden changes in pacing cycle length are frequently associated with repolarization abnormalities initiating cardiac arrhythmias, and physiologists have long been interested in measuring the likelihood of these events before their manifestation. A marker of repolarization stability has been found in the electrical restitution (ER), the response of the ventricular action potential duration to a pre- or post-mature stimulation, graphically represented by the so-called ER curve. According to the restitution hypothesis (ERH), the slope of this curve provides a quantitative discrimination between stable repolarization and proneness to arrhythmias. ER has been studied at the body surface, whole organ, and tissue level, and ERH has soon become a key reference point in theoretical, clinical, and pharmacological studies concerning arrhythmia development, and, despite criticisms, it is still widely adopted. The ionic mechanism of ER and cellular applications of ERH are covered in the present review. The main criticism on ERH concerns its dependence from the way ER is measured. Over the years, in fact, several different experimental protocols have been established to measure ER, which are also described in this article. In reviewing the state-of-the art on cardiac cellular ER, I have introduced a notation specifying protocols and graphical representations, with the aim of unifying a sometime confusing nomenclature, and providing a physiological tool, better defined in its scope and limitations, to meet the growing expectations of clinical and pharmacological research.

Variability in electrophysiological properties and conducting obstacles controls re-entry risk in heterogeneous ischaemic tissue

Ischaemia, in which inadequate blood supply compromises and eventually kills regions of cardiac tissue, can cause many types of arrhythmia, some life-threatening. A significant component of this is the effects of the resulting hypoxia, and concomitant hyperklaemia and acidosis, on the electrophysiological properties of myocytes. Clinical and experimental data have also shown that regions of structural heterogeneity (fibrosis, necrosis, fibro-fatty infiltration) can act as triggers for arrhythmias under acute ischaemic conditions. Mechanistic models have successfully captured these effects in silico. However, the relative significance of these separate facets of the condition, and how sensitive arrhythmic risk is to the extents of each, is far less explored. In this work, we use partitioned Gaussian process emulation and new metrics for source-sink mismatch that rely on simulations of bifurcating cardiac fibres to interrogate a model of heterogeneous ischaemic tissue. Re-entries were most sensitive to the level of hypoxia and the fraction of non-excitable tissue. In addition, our results reveal both protective and pro-arrhythmic effects of hyperklaemia, and present the levels of hyperklaemia, hypoxia and percentage of non-excitable tissue that pose the highest arrhythmic risks. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

EFFECTS OF ACUTE GLOBAL ISCHEMIA ON RE-ENTRANT ARRHYTHMOGENESIS: A SIMULATION STUDY

Sudden cardiac death is mainly caused by arrhythmogenesis. For a functional abnormal heart, such as an ischemic heart, the probability of arrhythmia occurring is greatly increased. During myocardial ischemia, re-entry is prone to degenerate into ventricular fibrillation (VF). Therefore it has important meaning to investigate the intricate mechanisms underlying VF under an ischemic condition in order to better facilitate therapeutic interventions. In this paper, to analyze the functional influence of acute global ischemia on cardiac electrical activity and subsequently on re-entrant arrhythmogenesis, we take into account three main pathophysiological consequences of ischemia: hyperkalaemia, acidosis, and anoxia, and develop a 3D human ventricular ischemic model that combines a detailed biophysical description of the excitation kinetics of human ventricular cells with an integrated geometry of human ventricular tissue which incorporates fiber direction anisotropy and the stimulation activation sequence. The results show that under acute global ischemia, the tissue excitability and the slope of ventricular cellular action potential duration restitution (APDR) are greatly decreased. As a result, the complexity of VF activation patterns is reduced. For the three components of ischemia, hyperkalaemia is the dominant contributor to the stability of re-entry under acute global ischemia. Increasing [K+]o acts to prolong the cell refractory period, reduce the tissue excitability and slow the conduction velocity. Our results also show that VF can be eliminated by decreasing cellular excitability, primarily by elevating the concentration value of extracellular K+.

Effect of global cardiac ischemia on human ventricular fibrillation: insights from a multi-scale mechanistic model of the human heart

Acute regional ischemia in the heart can lead to cardiac arrhythmias such as ventricular fibrillation (VF), which in turn compromise cardiac output and result in secondary global cardiac ischemia. The secondary ischemia may influence the underlying arrhythmia mechanism. A recent clinical study documents the effect of global cardiac ischaemia on the mechanisms of VF. During 150 seconds of global ischemia the dominant frequency of activation decreased, while after reperfusion it increased rapidly. At the same time the complexity of epicardial excitation, measured as the number of epicardical phase singularity points, remained approximately constant during ischemia. Here we perform numerical studies based on these clinical data and propose explanations for the observed dynamics of the period and complexity of activation patterns. In particular, we study the effects on ischemia in pseudo-1D and 2D cardiac tissue models as well as in an anatomically accurate model of human heart ventricles. We demonstrate that the fall of dominant frequency in VF during secondary ischemia can be explained by an increase in extracellular potassium, while the increase during reperfusion is consistent with washout of potassium and continued activation of the ATP-dependent potassium channels. We also suggest that memory effects are responsible for the observed complexity dynamics. In addition, we present unpublished clinical results of individual patient recordings and propose a way of estimating extracellular potassium and activation of ATP-dependent potassium channels from these measurements.

Developing a novel comprehensive framework for the investigation of cellular and whole heart electrophysiology in the in situ human heart: historical perspectives, current progress and future prospects

Understanding the mechanisms of fatal ventricular arrhythmias is of great importance. In view of the many electrophysiological differences that exist between animal species and humans, the acquisition of basic electrophysiological data in the intact human heart is essential to drive and complement experimental work in animal and in-silico models. Over the years techniques have been developed to obtain basic electrophysiological signals directly from the patients by incorporating these measurements into routine clinical procedures which access the heart such as cardiac catheterisation and cardiac surgery. Early recordings with monophasic action potentials provided valuable information including normal values for the in vivo human heart, cycle length dependent properties, the effect of ischaemia, autonomic nervous system activity, and mechano-electric interaction. Transmural recordings addressed the controversial issue of the mid myocardial "M" cell. More recently, the technique of multielectrode mapping (256 electrodes) developed in animal models has been extended to humans, enabling mapping of activation and repolarisation on the entire left and right ventricular epicardium in patients during cardiac surgery. Studies have examined the issue of whether ventricular fibrillation was driven by a "mother" rotor with inhomogeneous and fragmented conduction as in some animal models, or by multiple wavelets as in other animal studies; results showed that both mechanisms are operative in humans. The simpler spatial organisation of human VF has important implications for treatment and prevention. To link in-vivo human electrophysiological mapping with cellular biophysics, multielectrode mapping is now being combined with myocardial biopsies. This technique enables region-specific electrophysiology changes to be related to underlying cellular biology, for example: APD alternans, which is a precursor of VF and sudden death. The mechanism is incompletely understood but related to calcium cycling and APD restitution. Multielectrode sock mapping during incremental pacing enables epicardial sites to be identified which exhibit marked APD alternans and sites where APD alternans is absent. Whole heart electrophysiology is assessed by activation repolarisation mapping and analysis is performed immediately on-site in order to guide biopsies to specific myocardial sites. Samples are analysed for ion channel expression, Ca(2+)-handling proteins, gap junctions and extracellular matrix. This new comprehensive approach to bridge cellular and whole heart electrophysiology allowed to identify 20 significant changes in mRNA for ion channels Ca(2+)-handling proteins, a gap junction channel, a Na(+)-K(+) pump subunit and receptors (particularly Kir 2.1) between the positive and negative alternans sites.

Human ventricular fibrillation during global ischemia and reperfusion: paradoxical changes in activation rate and wavefront complexity

BACKGROUND

Ischemic ventricular fibrillation in experimental models has been shown to progress through a series of stages. Progression of ischemic VF in the in vivo human heart has not been determined.

METHODS AND RESULTS

We studied 10 patients undergoing cardiac surgery. Ventricular fibrillation was induced by burst pacing. After 30 seconds, global myocardial ischemia was induced by aortic cross-clamp and maintained for 2.5 minutes, followed by coronary reflow. Epicardial activity was sampled (1 kHz) with a sock that contained 256 unipolar contact electrodes. Dominant frequencies were calculated with a fast Fourier transform with a moving window. The locations of phase singularities and activation wavefronts were identified at 10-ms intervals. Preischemic (perfused) ventricular fibrillation was maintained by a disorganized mix of large and small wavefronts. During global myocardial ischemia, mean dominant frequencies decreased from 6.4 to 4.7 Hz at a rate of -0.011±0.002 Hz s(-1) (P<0.001) and then increased rapidly to 7.4 Hz within 30 seconds of reflow. In contrast, the average number of epicardial phase singularities increased during ischemia from 7.7 to 9.7 at a rate of 0.013±0.005 phase singularities per second (P<0.01) and remained unchanged during reflow, at 10.3. The number of wavefronts showed a similar time course to the number of phase singularities.

CONCLUSIONS

In human ventricular fibrillation, we found an increase in complexity of electric activation patterns during global myocardial ischemia, and this was not reversed during reflow despite an increase in activation rate.

Computing the stability of steady-state solutions of mathematical models of the electrical activity in the heart

Instabilities in the electro-chemical resting state of the heart can generate ectopic waves that in turn can initiate arrhythmias. We derive methods for computing the resting state for mathematical models of the electro-chemical process underpinning a heartbeat, and we estimate the stability of the resting state by invoking the largest real part of the eigenvalues of a linearized model. The implementation of the methods is described and a number of numerical experiments illustrate the feasibility of the methods. In particular, we test the methods for problems where we can compare the solutions with analytical results, and problems where we have solutions computed by independent software. The software is also tested for a fairly realistic 3D model.

A note on a method for determining advantageous properties of an anti-arrhythmic drug based on a mathematical model of cardiac cells

Regional hyperkalemia during acute ischemia may provoke cardiac arrhythmias such as ventricular fibrillation. Despite intense research efforts over the last decades, the problem of finding an efficient anti-arrhythmic drug without dangerous side effects is still open. One approach to analyze the effect of anti-arrhythmic drugs is to do simulations based on mathematical models of collections of cardiomyocytes. Such simulations have recently illuminated the pro-arrhythmic capability of well-established anti-arrhythmic drugs. The purpose of the present note is to introduce a method intended for computing advantageous properties of an anti-arrhythmic drug. For a given model of a normal and an ischemic cell, we introduce a drug as a vector of non-negative real numbers whose components are multiplied by individual terms representing specific ionic currents. The drug vector is computed such that the action potentials of the resulting drugged cells are as close as possible to the action potential of a normal (not drugged) cell. Numerical simulations based on the Luo-Rudy I model and the Hund-Rudy model show that the classical shortened action potential obtained due to hyperkalemia is prolonged by using the drug computed by this method. Furthermore, for both models a 2D collection of spatially coupled ischemic cells give arrhythmogenic solutions before the drug is applied, and stable solutions after the drug is applied. It is emphasized that we do not address the possibility of realizing a drug with the properties computed in this note.

Intracoronary infusion of catecholamines causes focal arrhythmias in pigs

BACKGROUND

Acute ischemia causes myriad changes including increased catecholamines. We tested the hypothesis that elevated catecholamines alone are arrhythmogenic.

METHODS AND RESULTS

A 504 electrode sock was placed over both ventricles in six open-chest pigs. During control infusion of saline through a catheter in the left anterior descending coronary artery (LAD), no sustained arrhythmias occurred, and the refractory period estimated by the activation recovery interval (ARI) was 175 +/- 14 ms in the LAD bed below the catheter. After infusion of isoproterenol at 0.1 microg/kg/min through the catheter, the ARI in this bed was significantly reduced to 109 +/- 10 ms. A sharp gradient of refractoriness of 43 +/- 10 ms was at the border of the perfused bed. Sustained monomorphic ventricular tachycardia occurred after drug infusion in the perfused bed or near its boundary in all animals with a cycle length of 329 +/- 26 ms and a focal origin. The maximum slope of the ARI restitution curve at the focal origins of the tachyarrhythmias was always <1 (0.62 +/- 0.15). Similar results with a focal arrhythmia origin occurred in two additional pigs in which intramural mapping was performed with 36 plunge needle electrodes in the left ventricular perfused bed.

CONCLUSION

Regional elevation of a catecholamine, which is one of the alterations produced by acute ischemia, can by itself cause tachyarrhythmias. These arrhythmias are closely associated with a shortened refractory period and a large gradient of the spatial distribution of refractoriness but not with a steep restitution curve.

Negative filament tension in the Luo-Rudy model of cardiac tissue

Scroll waves are vortices that occur in three-dimensional excitable media. Scroll waves have been observed in a variety of systems including cardiac tissue, where they are associated with cardiac arrhythmias. The disorganization of scroll waves into chaotic behavior is thought to be the mechanism of ventricular fibrillation, which lethality is widely known. One of the possible mechanisms of scroll wave instability is negative filament tension, which was studied theoretically using low-dimensional models of excitable medium. In this article we perform a numerical study of negative filament tension using the Luo-Rudy phase 1 model, which is widely used in cardiac electrophysiology. We show that this instability exists in this model, study its manifestation and discuss its relation to cardiac arrhythmogenesis.

Cell model for efficient simulation of wave propagation in human ventricular tissue under normal and pathological conditions

In this paper, we formulate a model for human ventricular cells that is efficient enough for whole organ arrhythmia simulations yet detailed enough to capture the effects of cell level processes such as current blocks and channelopathies. The model is obtained from our detailed human ventricular cell model by using mathematical techniques to reduce the number of variables from 19 to nine. We carefully compare our full and reduced model at the single cell, cable and 2D tissue level and show that the reduced model has a very similar behaviour. Importantly, the new model correctly produces the effects of current blocks and channelopathies on AP and spiral wave behaviour, processes at the core of current day arrhythmia research. The new model is well over four times more efficient than the full model. We conclude that the new model can be used for efficient simulations of the effects of current changes on arrhythmias in the human heart.

Reentry wave formation in excitable media with stochastically generated inhomogeneities

Clinical research shows that the frequency of arrhythmia events depends on the number and area of the border zones of infarct scars. We investigate the possibility that arrhythmia is initiated by reentry waves generated by the inhomogeneity of conduction velocity at the border zone. The interaction of a plane wave with a spatially extended inhomogeneity is simulated in the FitzHugh- Nagumo model. The inhomogeneity is introduced into the model by modifying the spatial dependence of the diffusion coefficient in a stochastic manner. This results in a rich variety of spatial distributions of conductivity. A plane wave propagating through such a system may break up on the regions with low conductivity and produce numerous spiral waves. The frequency of reentry wave formation is studied as a function of the parameters of the inhomogeneity generation algorithm. Three main scenarios of reentry wave formation were found: unidirectional block, main wave-wavelet collision, and wave break up during collision, on a region in which a conduction velocity gradient occurs. These scenarios are likely candidates for the mechanisms of arrhythmia initiation in a damaged tissue, e.g., the border zone of an infarct scar.

Coexistence of Two Types of Ventricular Fibrillation During Acute Regional Ischemia in Rabbit Ventricle

INTRODUCTION

We previously reported that a normal ventricle can demonstrate two types of ventricular fibrillation (VF), depending on the underlying electrophysiologic characteristics at the time of VF induction. We hypothesize that the two types of VF can coexist in acutely ischemic ventricles.

METHODS AND RESULTS

Optical mapping studies were performed with di-4ANEPPS in 15 Langendorff-perfused rabbit hearts. Coronary artery branches were ligated to create regional ischemia in 10 hearts. Action potential duration measured to 50% repolarization (APD50) during ischemia showed an area with uniformly shortened APD50 (zone 1), an area with normal or lengthened APD50 (zone 3), and an area in between with an APD50 gradient (zone 2). Ischemia flattened APD restitution (APDR) slope and reduced conduction velocity in zone 1, creating a condition for type II VF. APDR steepened and the conduction velocity changed little in the nonischemic zone (zone 3), creating a condition for type I VF. During induced VF, the dominant frequency in zones 2 and 3 progressively increased after ischemia onset. The dominant frequency in zone 1 (ischemic zone) first decreased and then slightly increased but typically remained less than the dominant frequency in zone 3. The number of wavebreaks increased with time in all three zones (baseline: 4.3 +/- 1.5; 30 min: 11.7 +/- 5.6; 60 min: 15.6 +/- 11 per frame; P < 0.01).

CONCLUSION

Two types of VF can coexist during acute regional ischemia. Both ischemic and nonischemic regions develop proarrhythmic changes during regional ischemia, thus contributing to increased ventricular vulnerability to VF and sudden death during acute coronary occlusion.

Effects of Na+ channel and cell coupling abnormalities on vulnerability to reentry: a simulation study

The role of dynamic instabilities in the initiation of reentry in diseased (remodeled) hearts remains poorly explored. Using computer simulations, we studied the effects of altered Na+ channel and cell coupling properties on the vulnerable window (VW) for reentry in simulated two-dimensional cardiac tissue with and without dynamic instabilities. We related the VW for reentry to effects on conduction velocity, action potential duration (APD), effective refractory period dispersion and restitution, and concordant and discordant APD alternans. We found the following: 1) reduced Na+ current density and slowed recovery promoted postrepolarization refractoriness and enhanced concordant and discordant APD alternans, which increased the VW for reentry; 2) uniformly reduced cell coupling had little effect on cellular electrophysiological properties and the VW for reentry. However, randomly reduced cell coupling combined with decoupling promoted APD dispersion and alternans, which also increased the VW for reentry; 3) the combination of decreased Na+ channel conductance, slowed Na+ channel recovery, and cellular uncoupling synergistically increased the VW for reentry; and 4) the VW for reentry was greater when APD restitution slope was steep than when it was flat. In summary, altered Na+ channel and cellular coupling properties increase vulnerability to reentrant arrhythmias. In remodeled hearts with altered Na+ channel properties and cellular uncoupling, dynamic instabilities arising from electrical restitution exert important influences on the VW for reentry.

A model for human ventricular tissue

The experimental and clinical possibilities for studying cardiac arrhythmias in human ventricular myocardium are very limited. Therefore, the use of alternative methods such as computer simulations is of great importance. In this article we introduce a mathematical model of the action potential of human ventricular cells that, while including a high level of electrophysiological detail, is computationally cost-effective enough to be applied in large-scale spatial simulations for the study of reentrant arrhythmias. The model is based on recent experimental data on most of the major ionic currents: the fast sodium, L-type calcium, transient outward, rapid and slow delayed rectifier, and inward rectifier currents. The model includes a basic calcium dynamics, allowing for the realistic modeling of calcium transients, calcium current inactivation, and the contraction staircase. We are able to reproduce human epicardial, endocardial, and M cell action potentials and show that differences can be explained by differences in the transient outward and slow delayed rectifier currents. Our model reproduces the experimentally observed data on action potential duration restitution, which is an important characteristic for reentrant arrhythmias. The conduction velocity restitution of our model is broader than in other models and agrees better with available data. Finally, we model the dynamics of spiral wave rotation in a two-dimensional sheet of human ventricular tissue and show that the spiral wave follows a complex meandering pattern and has a period of 265 ms. We conclude that the proposed model reproduces a variety of electrophysiological behaviors and provides a basis for studies of reentrant arrhythmias in human ventricular tissue.

Wavebreak formation during ventricular fibrillation in the isolated, regionally ischemic pig heart

Both fixed and dynamic heterogeneities were implicated in the mechanism of wavebreak (WB) generation during ventricular fibrillation (VF). However, their relative roles remain unclear. We hypothesized that during ischemic VF, the WBs are produced primarily because of a fixed heterogeneity; namely, the gradient of refractoriness across the ischemic border zone (BZ). Ischemia was induced in 15 isolated blood-perfused hearts by occluding the left anterior descending coronary artery. Simultaneous video imaging (approximately 32x32 mm2) of Di-4-ANEPPS fluorescence in the ischemic zone (IZ), the BZ, and the nonischemic zone (NIZ) was performed. Dominant-frequency maps were constructed to assess gradients of refractoriness during VF. We used singularity points analysis to quantify the incidence of WBs per square centimeter per second. During preischemic VF, the distribution of WBs was relatively uniform. Ischemia caused an increase of WBs in the BZ (from 6.2+/-2.8 to 10.8+/-4.0) and a decrease of WBs in the IZ (from 5.8+/-2.8 to 2.8+/-1.4), without a significant change in NIZ (from 6.4+/-2.3 to 4.1+/-1.7). This finding is fully consistent with the dominant-frequency distribution during ischemic VF: the average dominant frequency was significantly slower in IZ than in NIZ (7.8+/-0.7 versus 10.1+/-1.0 Hz), suggesting a large gradient in refractory periods across the BZ. We concluded that acute regional ischemia plays a dual role in the maintenance of VF, decreasing the incidence of WB in the IZ while increasing it in the BZ. This suggests a predominant role of fixed heterogeneities in the formation of WB during VF in acute regional ischemia.

Termination of reentry in an inhomogeneous ring of model cardiac cells

Reentrant waves propagating in a ring or annulus of excitable media are a model of the basic mechanism underlying a major class of irregular cardiac rhythms known as anatomical reentry. Such reentrant waves are terminated by rapid electrical stimulation (pacing) from an implantable device. Because the mechanisms of such termination are poorly understood, we study pacing of anatomical reentry in a one-dimensional ring of model cardiac cells. For realistic off-circuit pacing, our model-independent results suggest that circuit inhomogeneities, and the electrophysiological dynamical changes they introduce, may be essential for terminating reentry in some cases.

Critical role of inhomogeneities in pacing termination of cardiac reentry

Reentry around nonconducting ventricular scar tissue, a cause of lethal arrhythmias, is typically treated by rapid electrical stimulation from an implantable cardioverter defibrillator. However, the dynamical mechanisms of termination (success and failure) are poorly understood. To elucidate such mechanisms, we study the dynamics of pacing in one- and two-dimensional models of anatomical reentry. In a crucial realistic difference from previous studies of such systems, we have placed the pacing site away from the reentry circuit. Our model-independent results suggest that with such off-circuit pacing, the existence of inhomogeneity in the reentry circuit is essential for successful termination of tachycardia under certain conditions. Considering the critical role of such inhomogeneities may lead to more effective pacing algorithms. (c) 2002 American Institute of Physics.

Frequency analysis of ventricular fibrillation in Swine ventricles

It has been suggested from frequency analysis that cardiac fibrillation is driven by stable intramural reentry, with wavebreak occurring due to failure of 1:1 propagation. We tested this hypothesis with a combined experimental and theoretical approach. Optical mapping was performed on epicardial, endocardial, and transmural cut surfaces of fibrillating swine ventricles. Wavelets were characterized, the frequency content of optical signals analyzed, and space-time plots (STPs) constructed to detect Wenckebach-like conduction. The findings were compared with simulations in 2D and 3D cardiac tissue using the Luo-Rudy action potential model. The incidence of reentry in the cut transmural surface (11.8% in right ventricle, 14.3% in left ventricle) was similar to that on the endocardial surface (13.1%, P=NS) but greater than on the epicardial surface (7.7%, P<0.01). Frequency spectra of optically recorded membrane voltage were organized into spatial domains with the same dominant frequency, but these domains were nonstationary. In STPs, pseudo-2:1 conduction block was caused by double potentials arising when reentry occurred on the recording site rather than true Wenckebach conduction. The latter was observed in 11 of 166 STPs but did not occur at borders of high-to-low frequency domains. In simulations, similar findings were obtained when action potential duration (APD) restitution slope was steep. Stationary dominant frequency domains with Wenckebach conduction patterns were observed only in the presence of shallow APD restitution slope and marked nonuniform tissue heterogeneity. In conclusion, stable intramural reentry as the engine of fibrillation was not observed. Our findings support the idea that dynamic wavebreak plays a fundamental role in the generation and maintenance of ventricular fibrillation.