Action potential duration dispersion and alternans in simulated heterogeneous cardiac tissue with a structural barrier

Structural barriers to wave propagation in cardiac tissue are associated with a decreased threshold for repolarization alternans both experimentally and clinically. Using computer simulations, we investigated the effects of a structural barrier on the onset of spatially concordant and discordant alternans. We used two-dimensional tissue geometry with heterogeneity in selected potassium conductances to mimic known apex-base gradients. Although we found that the actual onset of alternans was similar with and without the structural barrier, the increase in alternans magnitude with faster pacing was steeper with the barrier--giving the appearance of an earlier alternans onset in its presence. This is consistent with both experimental structural barrier findings and the clinical observation of T-wave alternans occurring at slower pacing rates in patients with structural heart disease. In ionically homogeneous tissue, discordant alternans induced by the presence of the structural barrier arose at intermediate pacing rates due to a source-sink mismatch behind the barrier. In heterogeneous tissue, discordant alternans occurred during fast pacing due to a barrier-induced decoupling of tissue with different restitution properties. Our results demonstrate a causal relationship between the presence of a structural barrier and increased alternans magnitude and action potential duration dispersion, which may contribute to why patients with structural heart disease are at higher risk for ventricular tachyarrhythmias.     

Spatially Discordant Repolarization Alternans in the Absence of Conduction Velocity Restitution

Spatially discordant alternans (SDA) of action potential duration (APD) has been widely observed in cardiac tissue and is linked to cardiac arrhythmogenesis. Theoretical studies have shown that conduction velocity restitution (CVR) is required for the formation of SDA. However, this theory is not completely supported by experiments, indicating that other mechanisms may exist. In this study, we carried out computer simulations using mathematical models of action potentials to investigate the mechanisms of SDA in cardiac tissue. We show that when CVR is present and engaged, such as fast pacing from one side of the tissue, the spatial pattern of APD in the tissue undergoes either spatially concordant alternans or SDA, independent of initial conditions or tissue heterogeneities. When CVR is not engaged, such as simultaneous pacing of the whole tissue or under normal/slow heart rates, the spatial pattern of APD in the tissue can have multiple solutions, including spatially concordant alternans and different SDA patterns, depending on heterogeneous initial conditions or pre-existing repolarization heterogeneities. In homogeneous tissue, curved nodal lines are not stable, which either evolve into straight lines or disappear. However, in heterogeneous itssue, curved nodal lines can be stable, depending on their initial locations and shapes relative to the structure of the heterogeneity. Therefore, CVR-induced SDA and non-CVR-induced SDA exhibit different dynamical properties, which may be responsible for the different SDA properties observed in experimental studies and arrhythmogenesis in different clinical settings.     

L-type Ca2+ channel mutations and T-wave alternans: a model study

A number of mutations have been linked to diseases for which the underlying mechanisms are poorly understood. An example is Timothy Syndrome (TS), a multisystem disorder that includes severe cardiac arrhythmias. Here we employ theoretical simulations to examine the effects of a TS mutation in the L-type Ca(2+) channel on cardiac dynamics over multiple scales, from a gene mutation to protein, cell, tissue, and finally the ECG, to connect a defective Ca(2+) channel to arrhythmia susceptibility. Our results indicate that 1) the TS mutation disrupts the rate-dependent dynamics in a single cardiac cell and promotes the development of alternans; 2) in coupled tissue, concordant alternans is observed at slower heart rates in mutant tissue than in normal tissue and, once initiated, rapidly degenerates into discordant alternans and conduction block; and 3) the ECG computed from mutant-simulated tissue exhibits prolonged QT intervals at physiological rates and with small increases in pacing rate, T-wave alternans, and alternating T-wave inversion. At the cellular level, enhanced Ca(2+) influx due to the TS mutation causes electrical instabilities. In tissue, the interplay between faulty Ca(2+) influx and steep action potential duration restitution causes arrhythmogenic discordant alternans. The prolongation of action potentials causes spatial dispersion of the Na(+) channel excitability, leading to inhomogeneous conduction velocity and large action potential spatial gradients. Our model simulations are consistent with the ECG patterns from TS patients, which suggest that the TS mutation is sufficient to cause the clinical phenotype and allows for the revelation of the complex interactions of currents underlying it.     

Qualitative modeling of mechanoelectrical feedback in a ventricular cell

Mechanical changes in the heart muscle can influence its electrical properties through a process called mechanoelectrical feedback (MEF). This feedback can operate via changes in calcium dynamics during the cross-bridge cycle or via mechanosensitive (stretch-activated) channels. We present a four-variable ordinary differential equation (ODE) system that caricatures the electrical and mechanical activity of a ventricular cell and their mutual interactions. A three-variable excitable system with restitution properties of the FitzHugh-Nagumo type is coupled to a fourth equation which describes changes in cell length during a lightly loaded contraction. The resulting four-variable system models MEF in a cell and can be incorporated into spatially distributed models for mechanoelectric behavior during wave propagation in the cardiac tissue.     

Spatially discordant alternans in cardiomyocyte monolayers

Repolarization alternans is a harbinger of sudden cardiac death, particularly when it becomes spatially discordant. Alternans, a beat-to-beat alternation in the action potential duration (APD) and intracellular Ca (Cai), can arise from either tissue heterogeneities or dynamic factors. Distinguishing between these mechanisms in normal cardiac tissue is difficult because of inherent complex three-dimensional tissue heterogeneities. To evaluate repolarization alternans in a simpler two-dimensional cardiac substrate, we optically recorded voltage and/or Cai in monolayers of cultured neonatal rat ventricular myocytes during rapid pacing, before and after exposure to BAY K 8644 to enhance dynamic factors promoting alternans. Under control conditions (n = 37), rapid pacing caused detectable APD alternans in 81% of monolayers, and Cai transient alternans in all monolayers, becoming spatially discordant in 62%. After BAY K 8644 (n = 28), conduction velocity restitution became more prominent, and APD and Cai alternans developed and became spatially discordant in all monolayers, with an increased number of nodal lines separating out-of-phase alternating regions. Nodal lines moved closer to the pacing site with faster pacing rates and changed orientation when the pacing site was moved, as predicted for the dynamically generated, but not heterogeneity-based, alternans. Spatial APD gradients during spatially discordant alternans were sufficiently steep to induce conduction block and reentry. These findings indicate that spatially discordant alternans severe enough to initiate reentry can be readily induced by pacing in two-dimensional cardiac tissue and behaves according to predictions for a predominantly dynamically generated mechanism.     

Oscillation in cycle length induces transient discordant and steady-state concordant alternans in the heart

Alternans is a beat-to-beat alternation of the cardiac action potential duration (APD) or intracellular calcium (Ca(i)) transient. In cardiac tissue, alternans can be spatially concordant or discordant, of which the latter has been shown to increase dispersion of repolarization and promote a substrate for initiation of ventricular fibrillation. Alternans has been studied almost exclusively under constant cycle length pacing conditions. However, heart rate varies greatly on a beat-by-beat basis in normal and pathological conditions. The purpose of this study was to determine if applying a repetitive but non-constant pacing pattern, specifically cycle length oscillation (CLO), promotes or suppresses a proarrhythmic substrate. We performed computational simulations and optical mapping experiments to investigate the potential consequences of CLO. In a single cell computational model, CLO induced APD and Ca(i) alternans, which became "phase-matched" with the applied oscillation. As a consequence of the phase-matching, in one-dimensional cable simulations, neonatal rat ventricular myocyte monolayers, and isolated adult guinea pig hearts CLO could transiently induce spatial and electromechanical discordant alternans followed by a steady-state of concordance. Our results demonstrated that under certain conditions, CLO can initiate ventricular fibrillation in the isolated hearts. On the other hand, CLO can also exert an antiarrhythmic effect by converting an existing state of discordant alternans to concordant alternans.     

Stochastic Cardiac Pacing Increases Ventricular Electrical Stability—A Computational Study

The ventricular tissue is activated in a stochastic rather than in a deterministic rhythm due to the inherent heart rate variability (HRV). Low HRV is a known predictor for arrhythmia events and traditionally is attributed to autonomic nervous system tone damage. Yet, there is no model that directly assesses the antiarrhythmic effect of pacing stochasticity per se. One-dimensional (1D) and two-dimensional (2D) human ventricular tissues were modeled, and both deterministic and stochastic pacing protocols were applied. Action potential duration restitution (APDR) and conduction velocity restitution (CVR) curves were generated and analyzed, and the propensity and characteristics of action potential duration (APD) alternans were investigated. In the 1D model, pacing stochasticity was found to sustain a moderating effect on the APDR curve by reducing its slope, rendering the tissue less arrhythmogenic. Moreover, stochasticity was found to be a significant antagonist to the development of concordant APD alternans. These effects were generally amplified with increased variability in the pacing cycle intervals. In addition, in the 2D tissue configuration, stochastic pacing exerted a protective antiarrhythmic effect by reducing the spatial APD heterogeneity and converting discordant APD alternans to concordant ones. These results suggest that high cardiac pacing stochasticity is likely to reduce the risk of cardiac arrhythmias in patients.     

Inferring the cellular origin of voltage and calcium alternans from the spatial scales of phase reversal during discordant alternans

Beat-to-beat alternation of the action potential duration (APD) in paced cardiac cells has been linked to the onset of lethal arrhythmias. Both experimental and theoretical studies have shown that alternans at the single cell level can be caused by unstable membrane voltage (V(m)) dynamics linked to steep APD-restitution, or unstable intracellular calcium (Ca) cycling linked to high sensitivity of Ca release from the sarcoplasmic reticulum on sarcoplasmic reticulum Ca load. Identifying which of these two mechanisms is the primary cause of cellular alternans, however, has remained difficult since Ca and V(m) are bidirectionally coupled. Here, we use numerical simulations of a physiologically detailed ionic model to show that the origin of alternans can be inferred by measuring the length scales over which APD and Ca(i) alternans reverse phase during spatially discordant alternans. The main conclusion is that these scales are comparable to a few millimeters and equal when alternans is driven by APD restitution, but differ markedly when alternans is driven predominantly by unstable Ca cycling. In the latter case, APD alternans still reverses phase on a millimeter tissue scale due to electrotonic coupling, while Ca alternans reverses phase on a submillimeter cellular scale. These results show that experimentally accessible measurements of Ca(i) and V(m) in cardiac tissue can be used to shed light on the cellular origin of alternans.     

Formation of Spatially Discordant Alternans Due to Fluctuations and Diffusion of Calcium

Spatially discordant alternans (SDA) of action potential duration (APD) is a phenomenon where different regions of cardiac tissue exhibit an alternating sequence of APD that are out-of-phase. SDA is arrhythmogenic since it can induce spatial heterogeneity of refractoriness, which can cause wavebreak and reentry. However, the underlying mechanisms for the formation of SDA are not completely understood. In this paper, we present a novel mechanism for the formation of SDA in the case where the cellular instability leading to alternans is caused by intracellular calcium (Ca) cycling, and where Ca transient and APD alternans are electromechanically concordant. In particular, we show that SDA is formed when rapidly paced cardiac tissue develops alternans over many beats due to Ca accumulation in the sarcoplasmic reticulum (SR). The mechanism presented here relies on the observation that Ca cycling fluctuations dictate Ca alternans phase since the amplitude of Ca alternans is small during the early stages of pacing. Thus, different regions of a cardiac myocyte will typically develop Ca alternans which are opposite in phase at the early stages of pacing. These subcellular patterns then gradually coarsen due to interactions with membrane voltage to form steady state SDA of voltage and Ca on the tissue scale. This mechanism for SDA is distinct from well-known mechanisms that rely on conduction velocity restitution, and a Turing-like mechanism known to apply only in the case where APD and Ca alternans are electromechanically discordant. Furthermore, we argue that this mechanism is robust, and is likely to underlie a wide range of experimentally observed patterns of SDA.     

Maintenance of intercellular coupling by the antiarrhythmic peptide rotigaptide suppresses arrhythmogenic discordant alternans

Discordant action potential alternans creates large gradients of refractoriness, which are thought to be the mechanisms linking T-wave alternans to cardiac arrhythmogenesis. Since intercellular coupling acts to maintain synchronization of repolarization between cells, we hypothesized that intercellular uncoupling, such as during ischemia, would initiate discordant alternans and that restoration of intercellular coupling by the gap junction opener rotigaptide may provide a novel approach for suppressing arrhythmogenic discordant alternans. Optical mapping was used to record action potentials from ventricular epicardium of Langendorff-perfused guinea pig hearts. Threshold for spatially synchronized (i.e., concordant) alternans and discordant alternans was determined by increasing heart rate step-wise during 1) baseline, 2) treatment with rotigaptide or vehicle, and 3) global low-flow ischemia + rotigaptide or vehicle. Ischemia reduced the threshold for concordant alternans in both groups from 362 +/- 8 to 305 +/- 9 beats/min (P < 0.01) and for discordant alternans from 423 +/- 6 to 381 +/- 7 beats/min (P < 0.01). Interestingly, rotigaptide also increased the threshold for discordant alternans relative to vehicle both before (438 +/- 7 vs. 407 +/- 8 beats/min, P < 0.05) and during (394 +/- 7 vs. 364 +/- 9 beats/min, P < 0.05) ischemia. Rotigaptide increased conduction velocity and prevented conduction slowing and dispersion of repolarization during ischemia. Confocal immunofluorescence revealed that total connexin43 quantity and cellular distribution were unchanged before or after low-flow ischemia, with and without rotigaptide. However, connexin43 dephosphorylation in response to low-flow ischemia was significantly prevented by rotigaptide (15.9 +/- 7.0 vs. 0.3 +/- 6.4%, P < 0.001). These data suggest that intercellular uncoupling plays an important role in the transition from concordant to discordant alternans. By suppressing discordant alternans, repolarization gradients, and connexinx43 dephosphorylation, rotigaptide may protect against ischemia-induced arrhythmias. Drugs that selectively open gap junctions offer a novel strategy for antiarrhythmic therapy.     

The Interrelations among Stochastic Pacing,Stability, and Memory in the Heart

Low pacing variabilty in the heart has been clinically reported as a risk factor for lethal cardiac arrhythmias and arrhythmic death. In a previous simulation study, we demonstrated that stochastic pacing sustains an antiarrhythmic effect by moderating the slope of the action potential duration (APD) restitution curve, by reducing the propensity of APD alternans, converting discordant to concordant alternans, and ultimately preventing wavebreaks. However, the dynamic mechanisms relating pacing stochasticity to tissue stability are not yet known. In this work, we develop a mathematical framework to describe the APD signal using an autoregressive stochastic model, and we establish the interrelations between stochastic pacing, cardiac memory, and cardiac stability, as manifested by the degree of APD alternans. Employing stability analysis tools, we show that increased stochasticity in the ventricular tissue activation sequence works to lower the maximal absolute eigenvalues of the stochastic model, thereby contributing to increased stability. We also show that the memory coefficients of the autoregressive model are modulated by pacing stochasticity in a nonlinear, biphasic way, so that for exceedingly high levels of pacing stochasticity, the antiarrhythmic effect is hampered by increasing APD variance. This work may contribute to establishment of an optimal antiarrhythmic pacing protocol in a future study.     

The Interrelations among Stochastic Pacing,Stability, and Memory in the Heart

Low pacing variabilty in the heart has been clinically reported as a risk factor for lethal cardiac arrhythmias and arrhythmic death. In a previous simulation study, we demonstrated that stochastic pacing sustains an antiarrhythmic effect by moderating the slope of the action potential duration (APD) restitution curve, by reducing the propensity of APD alternans, converting discordant to concordant alternans, and ultimately preventing wavebreaks. However, the dynamic mechanisms relating pacing stochasticity to tissue stability are not yet known. In this work, we develop a mathematical framework to describe the APD signal using an autoregressive stochastic model, and we establish the interrelations between stochastic pacing, cardiac memory, and cardiac stability, as manifested by the degree of APD alternans. Employing stability analysis tools, we show that increased stochasticity in the ventricular tissue activation sequence works to lower the maximal absolute eigenvalues of the stochastic model, thereby contributing to increased stability. We also show that the memory coefficients of the autoregressive model are modulated by pacing stochasticity in a nonlinear, biphasic way, so that for exceedingly high levels of pacing stochasticity, the antiarrhythmic effect is hampered by increasing APD variance. This work may contribute to establishment of an optimal antiarrhythmic pacing protocol in a future study.     

Dynamic origin of spatially discordant alternans in cardiac tissue

Alternans, a condition in which there is a beat-to-beat alternation in the electromechanical response of a periodically stimulated cardiac cell, has been linked to the genesis of life-threatening ventricular arrhythmias. Optical mapping of membrane voltage (V_m) and intracellular calcium (Ca_i) on the surface of animal hearts reveals complex spatial patterns of alternans. In particular, spatially discordant alternans has been observed in which regions with a large-small-large action potential duration (APD) alternate out-of-phase adjacent to regions of small-large-small APD. However, the underlying mechanisms that lead to the initiation of discordant alternans and govern its spatiotemporal properties are not well understood. Using mathematical modeling, we show that dynamic changes in the spatial distribution of discordant alternans can be used to pinpoint the underlying mechanisms. Optical mapping of V_m and Ca_i in paced rabbit hearts revealed that spatially discordant alternans induced by rapid pacing exhibits properties consistent with a purely dynamical mechanism as shown in theoretical studies. Our results support the viewpoint that spatially discordant alternans in the heart can be formed via a dynamical pattern formation process which does not require tissue heterogeneity.     

Voltage-mediated mechanism for calcium wave synchronization and arrhythmogenesis in atrial tissue

A wide range of atrial arrythmias are caused by molecular defects in proteins that regulate calcium (Ca) cycling. In many cases, these defects promote the propagation of subcellular Ca waves in the cell, which can perturb the voltage time course and induce dangerous perturbations of the action potential (AP). However, subcellular Ca waves occur randomly in cells and, therefore, electrical coupling between cells substantially decreases their effect on the AP. In this study, we present evidence that Ca waves in atrial tissue can synchronize in-phase owing to an order-disorder phase transition. In particular, we show that, below a critical pacing rate, Ca waves are desynchronized and therefore do not induce substantial AP fluctuations in tissue. However, above this critical pacing rate, Ca waves gradually synchronize over millions of cells, which leads to a dramatic amplification of AP fluctuations. We exploit an underlying Ising symmetry of paced cardiac tissue to show that this transition exhibits universal properties common to a wide range of physical systems in nature. Finally, we show that in the heart, phase synchronization induces spatially out-of-phase AP duration alternans which drives wave break and reentry. These results suggest that cardiac tissue exhibits a phase transition that is required for subcellular Ca cycling defects to induce a life-threatening arrhythmia.     

Arrhythmogenic Transient Dynamics in Cardiac Myocytes

Cardiac action potential alternans and early afterdepolarizations (EADs) are linked to cardiac arrhythmias. Periodic action potentials (period 1) in healthy conditions bifurcate to other states such as period 2 or chaos when alternans or EADs occur in pathological conditions. The mechanisms of alternans and EADs have been extensively studied under steady-state conditions, but lethal arrhythmias often occur during the transition between steady states. Why arrhythmias tend to develop during the transition is unclear. We used low-dimensional mathematical models to analyze dynamical mechanisms of transient alternans and EADs. We show that depending on the route from one state to another, action potential alternans and EADs may occur during the transition between two periodic steady states. The route taken depends on the time course of external perturbations or intrinsic signaling, such as β-adrenergic stimulation, which regulate cardiac calcium and potassium currents with differential kinetics.     

Induction of ventricular arrhythmias following mechanical impact: A simulation study in 3D

Commotio cordis, mechanical induction of heart rhythm disturbances, including sudden cardiac death, in the absence of corresponding structural damage, has been reported with increasing frequency in young individuals participating in sporting activities. Recently, the electrophysiological changes during c. cordis have been attributed to mechano-electric feedback, and particularly, to the recruitment of stretch-activated ion channels. The underlying mechanisms, however, by which a mechanical impact results in ventricular fibrillation, remain unknown. This study employs a 3D realistic model of rabbit ventricular geometry and fiber orientation to elucidate the electrophysiological mechanisms involved in arrhythmia induction following acute mechanical stimulation of the heart. Impact effects are modeled through stretch-activated ion channel activation in a 3D region of the ventricles representing the impact profile. Both cation-nonselective and potassium-selective stretch-activated ion channels are recruited upon mechanical impact. The impact is administered at various coupling intervals following pacing at the apex. To aid in the interpretation of results, the effect of mechanical stimulation on single cell action potentials is also examined. The results demonstrate that the region of impact is characterized by different types of cellular responses, including generation of a new action potential, shortening, or lengthening of action potential duration. The impact induces sustained reentry only when (1) a new activation is elicited by mechanical stimulation (caused by activation of cation-nonselective stretch-activated ion channels), and (2) upon return to the original region of impact, this activation does not encounter an extension of action potential duration (prevented by activation of potassium-selective stretch-activated ion channels).     

Simulations of propagated mouse ventricular action potentials: effects of molecular heterogeneity

The molecular heterogeneity of repolarizing currents produces significant spatial heterogeneity and/or dispersion of repolarization in many mammalian cardiac tissues. Transgenic mice are prominent experimental models for the study of the molecular basis of repolarization and arrhythmias. However, it is debated whether the small mouse heart can sustain physiologically relevant heterogeneity of repolarization. We used a comprehensive model of the mouse action potential (AP) to predict how small a region of the cardiac tissue can maintain spatial gradients of repolarization due to differential expression of channels. Our simulations of a one-dimensional multicellular ring or cable predict that substantial gradients in repolarization and intracellular Ca(2+) concentration transients can be maintained through heterogeneity of expression of K(+) channels in distances of approximately 10 cells that are sufficient to block propagation. The abruptness of expression gradients and the site of stimulation can cause Ca(2+) transient oscillations and affect the stability of Ca(2+) dynamics and AP propagation. Two different mechanisms of instability of AP propagation in one-dimensional cable occur at fast pacing rates. Transitions from periodic activity to alternans or to irregular behavior were observed. Abrupt gradients of channel expression can cause alternans at slower pacing rates than gradual changes. Our simulations demonstrate the importance of incorporating realistic Ca(2+) dynamics and current densities into models of propagated AP. They also emphasize that microscopic aspects of tissue organization are important for predicting large-scale propagation phenomena. Finally, our results predict that the mouse heart should be able to sustain substantial molecularly based heterogeneity of repolarization.     

Disrupted Calcium Release as a Mechanism for Atrial Alternans Associated with Human Atrial Fibrillation

Atrial fibrillation (AF) is the most common cardiac arrhythmia, but our knowledge of the arrhythmogenic substrate is incomplete. Alternans, the beat-to-beat alternation in the shape of cardiac electrical signals, typically occurs at fast heart rates and leads to arrhythmia. However, atrial alternans have been observed at slower pacing rates in AF patients than in controls, suggesting that increased vulnerability to arrhythmia in AF patients may be due to the proarrythmic influence of alternans at these slower rates. As such, alternans may present a useful therapeutic target for the treatment and prevention of AF, but the mechanism underlying alternans occurrence in AF patients at heart rates near rest is unknown. The goal of this study was to determine how cellular changes that occur in human AF affect the appearance of alternans at heart rates near rest. To achieve this, we developed a computational model of human atrial tissue incorporating electrophysiological remodeling associated with chronic AF (cAF) and performed parameter sensitivity analysis of ionic model parameters to determine which cellular changes led to alternans. Of the 20 parameters tested, only decreasing the ryanodine receptor (RyR) inactivation rate constant (ki_Ca) produced action potential duration (APD) alternans seen clinically at slower pacing rates. Using single-cell clamps of voltage, fluxes, and state variables, we determined that alternans onset was Ca²⁺-driven rather than voltage-driven and occurred as a result of decreased RyR inactivation which led to increased steepness of the sarcoplasmic reticulum (SR) Ca²⁺ release slope. Iterated map analysis revealed that because SR Ca²⁺ uptake efficiency was much higher in control atrial cells than in cAF cells, drastic reductions in ki_Ca were required to produce alternans at comparable pacing rates in control atrial cells. These findings suggest that RyR kinetics may play a critical role in altered Ca²⁺ homeostasis which drives proarrhythmic APD alternans in patients with AF.     

Mechanisms and determinants of ultralong action potential duration and slow rate-dependence in cardiac myocytes

In normal cardiac myocytes, the action potential duration (APD) is several hundred milliseconds. However, experimental studies showed that under certain conditions, APD could be excessively long (or ultralong), up to several seconds. Unlike the normal APD, the ultralong APD increases sensitively with pacing cycle length even when the pacing rate is very slow, exhibiting a sensitive slow rate-dependence. In addition, these long action potentials may or may not exhibit early afterdepolarizations (EADs). Although these phenomena are well known, the underlying mechanisms and ionic determinants remain incompletely understood. In this study, computer simulations were performed with a simplified action potential model. Modifications to the L-type calcium current (I(Ca,L)) kinetics and the activation time constant of the delayed rectifier K current were used to investigate their effects on APD. We show that: 1) the ultralong APD and its sensitive slow rate-dependence are determined by the steady-state window and pedestal I(Ca,L) currents and the activation speed and the recovery of the delayed rectifier K current; 2) whether an ultralong action potential exhibits EADs or not depends on the kinetics of I(Ca,L); 3) increasing inward currents elevates the plateau voltage, which in general prolongs APD, however, this can also shorten APD when the APD is already ultralong under certain conditions; and 4) APD alternans occurs at slow pacing rates due to the sensitive slow rate-dependence and the ionic determinants are different from the ones causing APD alternans at fast heart rates.     

Vulnerable window for conduction block in a one-dimensional cable of cardiac cells, 2: multiple extrasystoles

Unidirectional conduction block of premature extrasystoles can lead to initiation of cardiac reentry, causing lethal arrhythmias including ventricular fibrillation. Multiple extrasystoles are often more effective at inducing unidirectional conduction block and reentry than a single extrasystole. Since the substrate for conduction block is spatial dispersion of refractoriness, in this study we investigate how the first extrasystole modulates this dispersion to influence the "vulnerable window" for conduction block by subsequent extrasystoles, particularly in relation to action potential duration restitution and conduction velocity restitution properties. Using a kinematic model to represent wavefront-waveback interactions and simulations with the Luo-Rudy model in a one-dimensional cable of cardiac cells, we show that in homogeneous tissue, a premature extrasystole can create a large dispersion of refractoriness leading to conduction block of a subsequent extrasystole. In heterogeneous tissue, however, a premature extrasystole can either reduce or enhance the dispersion of refractoriness depending on its propagation direction with respect to the previous beat. With multiple extrasystoles at random coupling intervals, vulnerability to conduction block is proportional to their number. In general, steep action potential duration restitution and broad conduction velocity restitution promote dispersion of refractoriness in response to multiple extrasystoles, and thus enhance vulnerability to conduction block. These restitution properties also promote spatially discordant alternans, a setting which is particularly prone to conduction block. The equivalent dispersion of refractoriness created dynamically in homogeneous tissue by spatially discordant alternans is more likely to cause conduction block than a comparable degree of preexisting dispersion in heterogeneous tissue.