Spiral waves in two-dimensional models of ventricular muscle: formation of a stationary core.

Previous experimental studies have clearly demonstrated the existence of drifting and stationary electrical spiral waves in cardiac muscle and their involvement in cardiac arrhythmias. Here we present results of a study of reentrant excitation in computer simulations based on a membrane model of the ventricular cell. We have explored in detail the parameter space of the model, using tools derived from previous numerical studies in excitation-dynamics models. We have found appropriate parametric conditions for sustained stable spiral wave dynamics (1 s of activity or approximately 10 rotations) in simulations of an anisotropic (ratio in velocity 4:1) cardiac sheet of 2 cm x 2 cm. Initially, we used a model that reproduced well the characteristics of planar electrical waves exhibited by thin sheets of sheep ventricular epicardial muscle during rapid pacing at a cycle length of 300 ms. Under these conditions, the refractory period was 147 ms; the action potential duration (APD) was 120 ms; the propagation velocity along fibers was 33 cm/s; and the wavelength along fibers was 4.85 cm. Using cross-field stimulation in this model, we obtained a stable self-sustaining spiral wave rotating around an unexcited core of 1.75 mm x 7 mm at a period of 115 ms, which reproduced well the experimental results. Thus the data demonstrate that stable spiral wave activity can occur in small cardiac sheets whose wavelength during planar wave excitation in the longitudinal direction is larger than the size of the sheet. Analysis of the mechanism of this observation demonstrates that, during rotating activity, the core exerts a strong electrotonic influence that effectively abbreviates APD (and thus wavelength) in its immediate surroundings and is responsible for the stabilization and perpetuation of the activity. We conclude that appropriate adjustments in the kinetics of the activation front (i.e., threshold for activation and upstroke velocity of the initiating beat) of currently available models of the cardiac cell allow accurate reproduction of experimentally observed self-sustaining spiral wave activity. As such, the results set the stage for an understanding of functional reentry in terms of ionic mechanisms.     

Short-term cardiac memory and mother rotor fibrillation

Short-term cardiac memory refers to the effects of pacing history on action potential duration (APD). Although the ionic mechanisms for short-term memory occurring over many heartbeats (also called APD accommodation) are poorly understood, they may have important effects on reentry and fibrillation. To explore this issue, we incorporated a generic memory current into the Phase I Luo and Rudy action potential model, which lacks short-term memory. The properties of this current were matched to simulate quantitatively human ventricular monophasic action potential accommodation. We show that, theoretically, short-term memory can resolve the paradox of how mother rotor fibrillation is initiated in heterogeneous tissue by physiological pacing. In simulated heterogeneous two-dimensional tissue and three-dimensional ventricles containing an inward rectifier K(+) current gradient, short-term memory could spontaneously convert multiple wavelet fibrillation to mother rotor fibrillation or to a mixture of both fibrillation types. This was due to progressive acceleration and stabilization of rotors as accumulation of memory shortened APD and flattened APD restitution slope nonuniformly throughout the tissue.     

Transmural action potential and ionic current remodeling in ventricles of failing canine hearts

Heart failure (HF) produces important alterations in currents underlying cardiac repolarization, but the transmural distribution of such changes is unknown. We therefore recorded action potentials and ionic currents in cells isolated from the endocardium, midmyocardium, and epicardium of the left ventricle from dogs with and without tachypacing-induced HF. HF greatly increased action potential duration (APD) but attenuated APD heterogeneity in the three regions. Early afterdepolarizations (EADs) were observed in all cell types of failing hearts but not in controls. Inward rectifier K(+) current (I(K1)) was homogeneously reduced by approximately 41% (at -60 mV) in the three cell types. Transient outward K(+) current (I(to1)) was decreased by 43-45% at +30 mV, and the slow component of the delayed rectifier K(+) current (I(Ks)) was significantly downregulated by 57%, 49%, and 58%, respectively, in epicardial, midmyocardial, and endocardial cells, whereas the rapid component of the delayed rectifier K(+) current was not altered. The results indicate that HF remodels electrophysiology in all layers of the left ventricle, and the downregulation of I(K1), I(to1), and I(Ks) increases APD and favors occurrence of EADs.     

Dynamical effects of diffusive cell coupling on cardiac excitation and propagation: a simulation study

Cell coupling is considered to be important for cardiac action potential propagation and arrhythmogenesis. We carried out computer simulations to investigate the effects of stimulation strength and cell-to-cell coupling on action potential duration (APD) restitution, APD alternans, and stability of reentry in models of isolated cell, one-dimensional cable, and two-dimensional tissue. Phase I formulation of the Luo and Rudy action potential model was used. We found that stronger stimulation resulted in a shallower APD restitution curve and onset of APD alternans at a faster pacing rate. Reducing diffusive coupling between cells prolonged APD. Weaker diffusive currents along the direction of propagation steepened APD restitution and caused APD alternans to occur at a slower pacing rate in tissue. Diffusive current due to curvature changed APD but had little effect on APD restitution slope and onset of instability. Heterogeneous cell coupling caused APD inhomogeneities in space. Reduction in coupling strength either uniformly or randomly had little effect on the rotation period and stability of a reentry, but random cell decoupling slowed the rotation period and, thus, stabilized the reentry, preventing it from breaking up into multiple waves. Therefore, in addition to its effects on action potential conduction velocity, diffusive cell coupling also affects APD in a rate-dependent manner, causes electrophysiological heterogeneities, and thus modulates the dynamics of cardiac excitation. These effects are brought about by the modulation of ionic current activation and inactivation.     

Electrical refractory period restitution and spiral wave reentry in simulated cardiac tissue

Theoretical and experimental studies have shown that restitution of the cardiac action potential (AP) duration (APD) plays a major role in predisposing ventricular tachycardia to degenerate to ventricular fibrillation, whereas its role in atrial fibrillation is unclear. We used the Courtemanche human atrial cell model and the Luo-Rudy guinea pig ventricular model to compare the roles of electrical restitution in destabilizing spiral wave reentry in simulated two-dimensional homogeneous atrial and ventricular tissue. Because atrial AP morphology is complex, we also validated the usefulness of effective refractory period (ERP) restitution. ERP restitution correlated best with APD restitution at transmembrane potentials greater than or equal to -62 mV, and its steepness was a reliable predictor of spiral wave phenotype (stable, meandering, hypermeandering, and breakup) in both atrial and ventricular tissue. Spiral breakup or single hypermeandering spirals occurred when the slope of ERP restitution exceeded 1 at short diastolic intervals. Thus ERP restitution, which is easier to measure clinically than APD restitution, is a reliable determinant of spiral wave stability in simulated atrial and ventricular tissue.     

Scroll wave dynamics in a three-dimensional cardiac tissue model: roles of restitution, thickness, and fiber rotation

Scroll wave (vortex) breakup is hypothesized to underlie ventricular fibrillation, the leading cause of sudden cardiac death. We simulated scroll wave behaviors in a three-dimensional cardiac tissue model, using phase I of the Luo-Rudy (LR1) action potential model. The effects of action potential duration (APD) restitution, tissue thickness, filament twist, and fiber rotation were studied. We found that APD restitution is the major determinant of scroll wave behavior and that instabilities arising from APD restitution are the main determinants of scroll wave breakup in this cardiac model. We did not see a "thickness-induced instability" in the LR1 model, but a minimum thickness is required for scroll breakup in the presence of fiber rotation. The major effect of fiber rotation is to maintain twist in a scroll wave, promoting filament bending and thus scroll breakup. In addition, fiber rotation induces curvature in the scroll wave, which weakens conduction and further facilitates wave break.     

Postnatal development has a marked effect on ventricular repolarization in mice

To better understand the mechanisms that underlie cardiac repolarization abnormalities in the immature heart, this study characterized and compared K(+) currents in mouse ventricular myocytes from day 1, day 7, day 20, and adult CD1 mice to determine the effects of postnatal development on ventricular repolarization. Current- and patch-clamp techniques were used to examine action potentials and the K(+) currents underlying repolarization in isolated myocytes. RT-PCR was used to quantify mRNA expression for the K(+) channels of interest. This study found that action potential duration (APD) decreased as age increased, with the shortest APDs observed in adult myocytes. This study also showed that K(+) currents and the mRNA relative abundance for the various K(+) channels were significantly greater in adult myocytes compared with day 1 myocytes. Examination of the individual components of total K(+) current revealed that the inward rectifier K(+) current (I(K1)) developed by day 7, both the Ca(2+)-independent transient outward current (I(to)) and the steady-state outward K(+) current (I(ss)) developed by day 20, and the ultrarapid delayed rectifier K(+) current (I(Kur)) did not fully develop until the mouse reached maturity. Interestingly, the increase in I(Kur) was not associated with a decrease in APD. Comparison of atrial and ventricular K(+) currents showed that I(to) and I(Kur) density were significantly greater in day 7, day 20, and adult myocytes compared with age-matched atrial cells. Overall, it appears that, in mouse ventricle, developmental changes in APD are likely attributable to increases in I(to), I(ss), and I(K1), whereas the role of I(Kur) during postnatal development appears to be less critical to APD.     

Properties of two human atrial cell models in tissue: restitution, memory, propagation, and reentry

To date, two detailed ionic models of human atrial cell electrophysiology have been developed, the Nygren et al. model (NM) and the Courtemanche et al. model (CM). Although both models draw from similar experimental data, they have vastly different properties. This paper provides the first systematic analysis and comparison of the dynamics of these models in spatially extended systems including one-dimensional cables and rings, two-dimensional sheets, and a realistic three-dimensional human atrial geometry. We observe that, as in single cells, the CM adapts to rate changes primarily by changes in action potential duration (APD) and morphology, while for the NM rate changes affect resting membrane potential (RMP) more than APD. The models also exhibit different memory properties as assessed through S1-S2 APD and conduction velocity (CV) restitution curves with different S1 cycle lengths. Reentrant wave dynamics also differ, with the NM exhibiting stable, non-breaking spirals and the CM exhibiting frequent transient wave breaks. The realistic atrial geometry modifies dynamics in some cases through drift, transient pinning, and breakup. Previously proposed modifications to represent atrial fibrillation-remodeled electrophysiology produce altered dynamics, including reduced rate adaptation and memory for both models and conversion to stable reentry for the CM. Furthermore, proposed variations to the NM to reproduce action potentials more closely resembling those of the CM do not substantially alter the underlying dynamics of the model, so that tissue simulations using these modifications still behave more like the unmodified NM. Finally, interchanging the transmembrane current formulations of the two models suggests that currents contribute more strongly to RMP and CV, intracellular calcium dynamics primarily determine reentrant wave dynamics, and both are important in APD restitution and memory in these models. This finding implies that the formulation of intracellular calcium processes is as important to producing realistic models as transmembrane currents.     

Relevance of ventricular electrical dispersion to arrhythmogenesis in ischemic myocardium--a simulation study

A computer simulation method was used to study the possible role of electrical dispersion induced by regional ischemia in the mechanisms underlying cardiac arrhythmias. Ischemic cells were simulated by considering the three major component conditions of acute ischemia (elevated extracellular K+ concentration, acidosis and anoxia) at the level of ionic currents and ionic concentrations. An ischemic area was introduced into a homogeneous healthy tissue to create a localized inhomogeneity. The constructed models were solved using the operator splitting and adaptive time step methods. The numerical experiments showed that action potential durations (APDs) of ischemic cells did not change with beats of shorter or longer cycle length. The smaller percentage increase of slow component of the delayed rectifier K+ current, I(ks), and smaller outward Na+-Ca2+ exchange current were found to be the ionic mechanisms underlying the decreased rate dependence in ischemic cells. The results suggest that ischemia flattens the APD restitution curve; however, the dispersion of refractory period can be greatly increased by a premature beat in the constructed inhomogeneous sheet. This demonstrates that the dispersion of refractoriness rather than APD by a premature beat contributes to reentrant tachyarrhythmias in the locally ischemic tissue.     

The Contribution of Ionic Currents to Rate-Dependent Action Potential Duration and Pattern of Reentry in a Mathematical Model of Human Atrial Fibrillation

Persistent atrial fibrillation (PeAF) in humans is characterized by shortening of action potential duration (APD) and attenuation of APD rate-adaptation. However, the quantitative influences of particular ionic current alterations on rate-dependent APD changes, and effects on patterns of reentry in atrial tissue, have not been systematically investigated. Using mathematical models of human atrial cells and tissue and performing parameter sensitivity analysis, we evaluated the quantitative contributions to action potential (AP) shortening and APD rate-adaptation of ionic current remodeling seen with PeAF. Ionic remodeling in PeAF was simulated by reducing L-type Ca²⁺ channel current (I_CaL), increasing inward rectifier K⁺ current (I_K1) and modulating five other ionic currents. Parameter sensitivity analysis, which quantified how each ionic current influenced APD in control and PeAF conditions, identified interesting results, including a negative effect of Na⁺/Ca²⁺ exchange on APD only in the PeAF condition. At high pacing rate (2 Hz), electrical remodeling in I_K1 alone accounts for the APD reduction of PeAF, but at slow pacing rate (0.5 Hz) both electrical remodeling in I_CaL alone (-70%) and I_K1 alone (+100%) contribute equally to the APD reduction. Furthermore, AP rate-adaptation was affected by I_Kur in control and by I_NaCa in the PeAF condition. In a 2D tissue model, a large reduction (-70%) of I_CaL becomes a dominant factor leading to a stable spiral wave in PeAF. Our study provides a quantitative and unifying understanding of the roles of ionic current remodeling in determining rate-dependent APD changes at the cellular level and spatial reentry patterns in tissue.     

The Na+/K+ pump is an important modulator of refractoriness and rotor dynamics in human atrial tissue

Pharmacological treatment of atrial fibrillation (AF) exhibits limited efficacy. Further developments require a comprehensive characterization of ionic modulators of electrophysiology in human atria. Our aim is to systematically investigate the relative importance of ionic properties in modulating excitability, refractoriness, and rotor dynamics in human atria before and after AF-related electrical remodeling (AFER). Computer simulations of single cell and tissue atrial electrophysiology were conducted using two human atrial action potential (AP) models. Changes in AP, refractory period (RP), conduction velocity (CV), and rotor dynamics caused by alterations in key properties of all atrial ionic currents were characterized before and after AFER. Results show that the investigated human atrial electrophysiological properties are primarily modulated by maximal value of Na(+)/K(+) pump current (G(NaK)) as well as conductances of inward rectifier potassium current (G(K1)) and fast inward sodium current (G(Na)). G(NaK) plays a fundamental role through both electrogenic and homeostatic modulation of AP duration (APD), APD restitution, RP, and reentrant dominant frequency (DF). G(K1) controls DF through modulation of AP, APD restitution, RP, and CV. G(Na) is key in determining DF through alteration of CV and RP, particularly in AFER. Changes in ionic currents have qualitatively similar effects in control and AFER, but effects are smaller in AFER. The systematic analysis conducted in this study unravels the important role of the Na(+)/K(+) pump current in determining human atrial electrophysiology.     

Dynamic changes of cardiac conduction during rapid pacing

Slow conduction and unidirectional conduction block (UCB) are key mechanisms of reentry. Following abrupt changes in heart rate, dynamic changes of conduction velocity (CV) and structurally determined UCB may critically influence arrhythmogenesis. Using patterned cultures of neonatal rat ventricular myocytes grown on microelectrode arrays, we investigated the dynamics of CV in linear strands and the behavior of UCB in tissue expansions following an abrupt decrease in pacing cycle length (CL). Ionic mechanisms underlying rate-dependent conduction changes were investigated using the Pandit-Clark-Giles-Demir model. In linear strands, CV gradually decreased upon a reduction of CL from 500 ms to 230-300 ms. In contrast, at very short CLs (110-220 ms), CV first decreased before increasing again. The simulations suggested that the initial conduction slowing resulted from gradually increasing action potential duration (APD), decreasing diastolic intervals, and increasing postrepolarization refractoriness, which impaired Na(+) current (I(Na)) recovery. Only at very short CLs did APD subsequently shorten again due to increasing Na(+)/K(+) pump current secondary to intracellular Na(+) accumulation, which caused recovery of CV. Across tissue expansions, the degree of UCB gradually increased at CLs of 250-390 ms, whereas at CLs of 180-240 ms, it first increased and subsequently decreased. In the simulations, reduction of inward currents caused by increasing intracellular Na(+) and Ca(2+) concentrations contributed to UCB progression, which was reversed by increasing Na(+)/K(+) pump activity. In conclusion, CV and UCB follow intricate dynamics upon an abrupt decrease in CL that are determined by the interplay among I(Na) recovery, postrepolarization refractoriness, APD changes, ion accumulation, and Na(+)/K(+) pump function.     

Electrophysiological heterogeneity and stability of reentry in simulated cardiac tissue

Generation of wave break is a characteristic feature of cardiac fibrillation. In this study, we investigated how dynamic factors and fixed electrophysiological heterogeneity interact to promote wave break in simulated two-dimensional cardiac tissue, by using the Luo-Rudy (LR1) ventricular action potential model. The degree of dynamic instability of the action potential model was controlled by varying the maximal amplitude of the slow inward Ca(2+) current to produce spiral waves in homogeneous tissue that were either nearly stable, meandering, hypermeandering, or in breakup regimes. Fixed electrophysiological heterogeneity was modeled by randomly varying action potential duration over different spatial scales to create dispersion of refractoriness. We found that the degree of dispersion of refractoriness required to induce wave break decreased markedly as dynamic instability of the cardiac model increased. These findings suggest that reducing the dynamic instability of cardiac cells by interventions, such as decreasing the steepness of action potential duration restitution, may still have merit as an antifibrillatory strategy.     

Regional increase of extracellular potassium leads to electrical instability and reentry occurrence through the spatial heterogeneity of APD restitution

The heterogeneities of electrophysiological properties of cardiac tissue are the main factors that control both arrhythmia induction and maintenance. Although the local increase of extracellular potassium ([K(+)](o)) due to coronary occlusion is a well-established metabolic response to acute ischemia, the role of local [K(+)](o) heterogeneity in phase 1a arrhythmias has yet to be determined. In this work, we created local [K(+)](o) heterogeneity and investigated its role in fast pacing response and arrhythmia induction. The left marginal vein of a Langendorff-perfused rabbit heart was cannulated and perfused separately with solutions containing 4, 6, 8, 10, and 12 mM of K(+). The fluorescence dye was utilized to map the voltage distribution. We tested stimulation rates, starting from 400 ms down to 120 ms, with steps of 5-50 ms. We found that local [K(+)](o) heterogeneity causes action potential (AP) alternans, 2:1 conduction block, and wave breaks. The effect of [K(+)](o) heterogeneity on electrical stability and vulnerability to arrhythmia induction was largest during regional perfusion with 10 mM of K(+). We detected three concurrent dynamics: normally propagating activation when excitation waves spread over tissue perfused with normal K(+), alternating 2:2 rhythm near the border of [K(+)](o) heterogeneity, and 2:1 aperiodicity when propagation was within the high [K(+)](o) area. [K(+)](o) elevation changed the AP duration (APD) restitution and shifted the restitution curve toward longer diastolic intervals and shorter APD. We conclude that spatial heterogeneity of the APD restitution, created with regional elevation of [K(+)](o), can lead to AP instability, 2:1 block, and reentry induction.     

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.     

Electrical remodeling in a canine model of ischemic cardiomyopathy

The nature of electrical remodeling in a canine model of ischemic cardiomyopathy (ICM; induced by repetitive intracoronary microembolizations) that exhibits spontaneous ventricular tachycardia is not entirely clear. We used the patch-clamp technique to record action potentials and ionic currents of left ventricular myocytes isolated from the region affected by microembolizations. We also used the immunoblot technique to examine channel subunit expression in adjacent affected tissue. Ventricular myocytes and tissue isolated from the corresponding region of normal hearts served as control. ICM myocytes had prolonged action potential duration (APD) and more pronounced APD dispersion. Slow delayed rectifier current (I(Ks)) was reduced at voltages positive to 0 mV, along with a negative shift in its voltage dependence of activation. Immunoblots showed that there was no change in KCNQ1.1 (I(Ks) pore-forming or alpha-subunit), but KCNE1 (I(Ks) auxiliary or beta-subunit) was reduced, and KCNQ1.2 (a truncated KCNQ1 splice variant with a dominant-negative effect on I(Ks)) was increased. Transient outward current (I(to)) was reduced, along with an acceleration of the slow phase of recovery from inactivation. Immunoblots showed that there was no change in Kv4.3 (alpha-subunit of fast-recovering I(to) component), but KChIP2 (beta-subunit of fast-recovering component) and Kv1.4 (alpha-subunit of slow-recovering component) were reduced. Inward rectifier current was reduced. L-type Ca current was unaltered. The immunoblot data provide mechanistic insights into the observed changes in current amplitude and gating kinetics of I(Ks) and I(to). We suggest that these changes, along with the decrease in inward rectifier current, contribute to APD prolongation in ICM hearts.     

Effects of Na(+) and K(+) channel blockade on vulnerability to and termination of fibrillation in simulated normal cardiac tissue

Na(+) and K(+) channel-blocking drugs have anti- and proarrhythmic effects. Their effects during fibrillation, however, remain poorly understood. We used computer simulation of a two-dimensional (2-D) structurally normal tissue model with phase I of the Luo-Rudy action potential model to study the effects of Na(+) and K(+) channel blockade on vulnerability to and termination of reentry in simulated multiple-wavelet and mother rotor fibrillation. Our main findings are as follows: 1) Na(+) channel blockade decreased, whereas K(+) channel blockade increased, the vulnerable window of reentry in heterogeneous 2-D tissue because of opposing effects on dynamical wave instability. 2) Na(+) channel blockade increased the cycle length of reentry more than it increased refractoriness. In multiple-wavelet fibrillation, Na(+) channel blockade first increased and then decreased the average duration or transient time () of fibrillation. In mother rotor fibrillation, Na(+) channel blockade caused peripheral fibrillatory conduction block to resolve and the mother rotor to drift, leading to self-termination or sustained tachycardia. 3) K(+) channel blockade increased dynamical instability by steepening action potential duration restitution. In multiple-wavelet fibrillation, this effect shortened because of enhanced wave instability. In mother rotor fibrillation, this effect converted mother rotor fibrillation to multiple-wavelet fibrillation, which then could self-terminate. Our findings help illuminate, from a theoretical perspective, the possible underlying mechanisms of termination of different types of fibrillation by antiarrhythmic drugs.     

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.