Wave propagation in cardiac tissue and effects of intracellular calcium dynamics (computer simulation study)

Spatiotemporal evolution and prediction of [Ca(2+) ]i and APD alternans in isolated rabbit hearts

INTRODUCTION

Action potential duration (APD) alternans can be accompanied by alternans in intracellular calcium transients ([Ca(2+) ]i ), leading to electromechanical alternans. Electromechanical alternans is considered a substrate for ventricular fibrillation. Although some techniques have been developed to predict APD alternans, the onset of [Ca(2+) ]i alternans has never been predicted.

METHODS AND RESULTS

Simultaneous mapping of voltage and calcium was performed in 8 Langendorff-perfused rabbit hearts. APD, [Ca(2+) ]i amplitude (CaA) and duration (CaD) alternans were induced using a perturbed downsweep protocol. Local onset of alternans (B(onset) ) was defined as the cycle length (BCL) at which at least 10% of the RV exhibited alternans. We observed that the local onset of CaA alternans always occurred first, followed by APD and then CaD alternans. We constructed APD, CaD, and CaA restitution portraits for 2 regions of the heart defined at B(onset) : the 1:1alt region, which developed alternans, and the 1:1 region, which did not. Our results also show that the slopes S12 Max and SDyn were higher in 1:1alt region (SDyn  = 0.99 ± 0.04 vs 0.73 ± 0.06; S12 Max  = 0.95 ± 0.13 vs 0.65 ± 0.1, P < 0.05) prior to onset of CaD alternans, while S12 and S12 Max were significantly higher in the 1:1alt region (S12  = 0.59 ± 0.19 vs 0.19 ± 0.02; S12 Max  = 1.09 ± 0.1 vs 0.61 ± 0.08, P < 0.05) prior to onset of CaA alternans.

CONCLUSION

We successfully applied the restitution portrait technique to the prediction of [Ca(2+) ]i (both CaA and CaD) alternans. The slopes of the APD/CaD/CaA restitution portrait are definitive indicators of APD, CaD, and CaA alternans.

Epac activation, altered calcium homeostasis and ventricular arrhythmogenesis in the murine heart

The recently described exchange protein directly activated by cAMP (Epac) has been implicated in distinct protein kinase A-independent cellular signalling pathways. We investigated the role of Epac activation in adrenergically mediated ventricular arrhythmogenesis. In contrast to observations in control conditions (n = 20), monophasic action potentials recorded in 2 of 10 intrinsically beating and 5 of 20 extrinsically paced Langendorff-perfused wild-type murine hearts perfused with the Epac activator 8-pCPT-2'-O-Me-cAMP (8-CPT, 1 microM) showed spontaneous triggered activity. Three of 20 such extrinsically paced hearts showed spontaneous ventricular tachycardia (VT). Programmed electrical stimulation provoked VT in 10 of 20 similarly treated hearts (P < 0.001; n = 20). However, there were no statistically significant accompanying changes (P > 0.05) in left ventricular epicardial (40.7 +/- 1.2 versus 44.0 +/- 1.7 ms; n = 10) or endocardial action potential durations (APD(90); 51.8 +/- 2.3 versus 51.9 +/- 2.2 ms; n = 10), transmural (DeltaAPD(90)) (11.1 +/- 2.6 versus 7.9 +/- 2.8 ms; n = 10) or apico-basal repolarisation gradients, ventricular effective refractory periods (29.1 +/- 1.7 versus 31.2 +/- 2.4 ms in control and 8-CPT-treated hearts, respectively; n = 10) and APD(90) restitution characteristics. Nevertheless, fluorescence imaging of cytosolic Ca(2+) levels demonstrated abnormal Ca(2+) homeostasis in paced and resting isolated ventricular myocytes. Epac activation using isoproterenol in the presence of H-89 was also arrhythmogenic and similarly altered cellular Ca(2+) homeostasis. Epac-dependent effects were reduced by Ca(2+)/calmodulin-dependent protein kinase II (CaMKII) inhibition with 1 microM KN-93. These findings associate VT in an intact cardiac preparation with altered cellular Ca(2+) homeostasis and Epac activation for the first time, in the absence of altered repolarisation gradients previously implicated in reentrant arrhythmias through a mechanism dependent on CaMKII activity.

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

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

Calcium transients modulate action potential repolarizations in ventricular fibrillation

Action potential alternans has been an indicator of ischemic disease and vulnerability to ventricular fibrillation (VF). The mechanisms of alternans are linked to the anomalies in intracellular Ca2+ (Cai) handling by either spontaneous Ca2+ release or modulation of action potential duration (APD), which may promote wave breaks in VF. We investigated possible role of Ca2+ in wave breaks by simultaneously measuring transmembrane potential (Vm) and intracellular Ca2+ concentration with voltage sensitive dye (RH237) and Ca2+ (Rhod-2) fluorescence probes. VF was induced by burst stimulation and the relationship between Vm and Ca2+ oscillations in VF were analyzed with cross-correlation analysis. The maximum correlation occurred at 12 ms delay between Vm and Cai, suggesting Vm still triggers Ca2+ release in VF as in normal excitation-contraction coupling. In addition, inverse correlation was found -20 ms between Vm and Cai, suggesting the amplitude of Cai can modulate action potential recovery in VF. In conclusion, Cai can influence action potential durations, which may promote wave breaks in VF.

Intracellular calcium cycling, early afterdepolarizations, and reentry in simulated long QT syndrome

OBJECTIVES

The purpose of this study was to investigate interactions between early afterdepolarizations (EADs) and reentry in long QT (LQT) syndromes.

BACKGROUND

EADs, a characteristic feature of congenital and acquired LQT syndromes, are classically bradycardia dependent. Mechanisms by which they promote tachyarrhythmias such as torsades de pointes and ventricular fibrillation are not fully understood. Recent evidence suggests that EADs also may occur at rapid heart rates as a sequela of spontaneous sarcoplasmic reticulum (SR) Ca(2+) release related to intracellular Ca(2+) overload. Here, we performed computer simulations to explore the arrhythmogenic consequences of this phenomenon.

METHODS

We used a modified version of the Luo-Rudy dynamic model in one-dimensional and two-dimensional cardiac tissue with the time-dependent K(+) currents I(Kr) or I(Ks) reduced by 50% to simulate acquired and congenital LQT syndromes.

RESULTS

(1) Spontaneous SR Ca(2+) release prolonged action potential duration but did not induce overt EADs unless K(+) current density was reduced to simulate acquired and congenital LQT syndromes. (2) In simulated LQT syndromes, EADs were capable of both terminating and reinitiating one-dimensional reentry. (3) A similar phenomenon in simulated 2D tissue led to reinitiation of spiral wave reentry that otherwise would have self-terminated. (4) Reentry reinitiation occurred only when the L-type Ca(2+) current and SR Ca(i) cycling were potentiated to simulate moderate sympathetic stimulation, consistent with the known arrhythmogenic effects of sympathetic activation (and protection by beta-blockers) in LQT syndromes.

CONCLUSIONS

These computer simulations suggest that EADs related to spontaneous SR Ca(2+) release can enhance arrhythmogenesis in LQT syndromes by reinitiating reentry.

Preventing alternans-induced spiral wave breakup in cardiac tissue: an ion-channel-based approach

The detailed processes involved in spiral wave breakup, believed to be one major mechanism by which tachycardia evolves into fibrillation, are still poorly understood. This has rendered difficult the proper design of an efficient and practical control stimulus protocol to eliminate such events. In order to gain new insights into the underlying electrophysiological and dynamical mechanisms of breakup, we applied linear perturbation theory to a steadily rotating spiral wave in two spatial dimensions. The tissue was composed of cells modeled using the Fenton-Karma equations whose parameters were chosen to emphasize alternans as a primary mechanism for breakup. Along with one meandering mode, not just one but several unstable alternans modes were found with differing growth rates, frequencies, and spatial structures. As the conductance of the fast inward current was increased, the instability of the modes increased, consistent with increased meandering and propensity for spiral breakup in simulations. We also explored a promising new approach, based on the theory, for the design of an energy efficient electrical stimulus protocol to control spiral wave breakup. The novelty lies in addressing the problem directly at the ion channel level and taking advantage of the inherent two dimensional nature of the rotating wave. With the help of the eigenmode method, we were able to calculate the exact timing and amplitude of the stimulus, and locate it optimally to maximize efficiency. The analysis led to a special-case example that demonstrated that a single, properly timed stimulus can have a global effect, suppressing all growing alternans modes over the entire tissue, thus inhibiting spiral wave breakup.

Tissue growth and remodeling

The growth and remodeling of a tissue depends on certain features in the history of its mechanical environment as well as its genetic makeup. The mechanical environment influences the tissue's developing morphology, the process of simply increasing the size of existing morphological structures, and the formation of the proteins of which the tissue is constructed. The relationships between genetic information, various epigenetic mechanisms and tissue development are discussed. The developmental growth and remodeling of most structural tissues are enhanced by the use of those tissues and retarded by their disuse. The mechanical or mathematical modeling of tissue growth and development using cellular automata models and continuum mechanical models is reviewed.

Afterdepolarizations promote the transition from ventricular tachycardia to fibrillation in a three-dimensional model of cardiac tissue

Recent experimental results regarding the action potential duration restitution curve have explained the transition from ventricular tachycardia (VT) to fibrillation (VF) in terms of spiral wave (SW) meandering and breakup. However, it remains unclear whether VF always has a steep restitution curve. The present study was designed to test the hypothesis that afterdepolarizations occur at excitable gaps during VF and affect the SW dynamics, even if the restitution curve is gentle. Homogeneous and isotropic 3-dimensional tissue was simulated with a LRd model. Because of the gentle restitution curve, it was not expected that SW instabilities would occur in this condition. In the tissue, a stationary SW reentry was initially observed; however, afterdepolarizations erupted from the excitable gap near the SW tip, and the SW then meandered widely. Following that, afterdepolarizations erupted far from the SW tip, resulting in SW breakup. In this manner, the wave dynamics degenerated into a chaotic state within a few seconds. Furthermore, not only triggered activity but also subthreshold afterdepolarizations were found to cause SW instabilities. These results suggest that afterdepolarizations may play an important role in the transition to VF and that the mechanism is independent of restitution properties.

Computational models of normal and abnormal action potential propagation in cardiac tissue: linking experimental and clinical cardiology

Computational models have the potential to make a huge impact on our understanding of normal and abnormal cardiac function. The aim of this article is to review tools that have been developed to simulate the electrophysiology of cardiac cells and tissue, and to show how computational models have been used to gain insight into normal and abnormal action potential propagation. Some of the practical problems experienced in the development and application of these models are described, and examples are given.

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.

Re-entrant cardiac arrhythmias in computational models of long QT myocardium

The long QT syndrome (LQTS) is an inherited disorder in which repolarization of cardiac ventricular cells is prolonged. Patients with the LQTS are at an increased risk of ventricular cardiac arrhythmias. Two phenotypes of the inherited LQTS are caused by defects in K(+)channels (LQT1 and LQT2) and one by defects in Na(+)channels (LQT3). Patients with LQT1 are more likely to have self-terminating arrhythmias than those with LQT3. The aim of this computational study was to propose an explanation for this finding by comparing the vulnerability of normal and LQT tissue to re-entry, and estimating the likelihood of self-termination by motion of re-entrant waves to an inexcitable boundary in simulated LQT1, LQT2 and LQT3 tissue. We modified a model of mammalian cardiac cells to simulate LQT1 by reducing maximal I(K(s))conductance, LQT2 by reducing maximal I(K(r))conductance, and LQT3 by preventing complete inactivation of I(Na)channels. Each simulated phenotype was incorporated into a computational model of action potential propagation in one- and two-dimensional homogeneous tissue. Simulated LQT tissue was no more vulnerable to re-entry than simulated normal tissue, but the motion of re-entrant waves in simulated LQT1 tissue was between 2 and 5 times greater than the motion of re-entrant waves in simulated LQT2 and LQT3 tissue. These findings suggest that LQT arrhythmias do not result from increased vulnerability to re-entry, and that re-entry once initiated is more likely to self-terminate by moving to an inexcitable tissue boundary in LQT1 than in LQT2 and LQT3. This finding is consistent with clinical observations.

Functional reentry's influence on intracellular calcium in the LRd membrane equations

This paper examines relationships between transmembrane potential (Vm), [Ca2+]i dependent membrane ionic currents, and [Ca2+]i handling by the sarcoplasmic reticulum (SR) in a two-dimensional model of cardiac tissue. Luo-Rudy dynamic (LRd) membrane equations were used because they include detailed formulations for triggered SR Ca2+ release dependent on membrane Ca2+ influx (CICR) and for spontaneous SR Ca2+ release following calsequestrin buffer overload (SCR). Reentry's rapid rate (110-ms cycle length) elevated [Ca2+]i and limited CICR, which in turn promoted SCR that occurred at intervals of 320-350 ms, was preferential at sites located inside the functional center, and destabilized the reentrant activation sequence. Although adjustment of LRd parameters for SR Ca2+ modified SCR interval and peak [Ca2+]i in voltage clamp simulations with a command waveform representing Vm time course within the functional center, SCR persisted. Using the same command waveform, SCR also occurred with an alternate SR Ca2+ formulation that represented subcellular details underlying CICR. LRd parameter adjustments to promote CICR and limit SCR in subsequent reentry simulations failed to eliminate SCR completely, as they modulated SCR intervals in a manner consistent with the voltage clamp simulations. Taken together, our findings support a destabilizing influence of functional reentry on [Ca2+]i handling. However, [Ca2+]i instabilities did not always fractionate depolarization wavefronts during reentry. Fractionation depended, in part, upon CICR and SCR parameters in the LRd formulation for SR Ca2+ release.

Distributed computing for membrane-based modeling of action potential propagation

Action potential propagation simulations with physiologic membrane currents and macroscopic tissue dimensions are computationally expensive. We, therefore, analyzed distributed computing schemes to reduce execution time in workstation clusters by parallelizing solutions with message passing. Four schemes were considered in two-dimensional monodomain simulations with the Beeler-Reuter membrane equations. Parallel speedups measured with each scheme were compared to theoretical speedups, recognizing the relationship between speedup and code portions that executed serially. A data decomposition scheme based on total ionic current provided the best performance. Analysis of communication latencies in that scheme led to a load-balancing algorithm in which measured speedups at 89 +/- 2% and 75 +/- 8% of theoretical speedups were achieved in homogeneous and heterogeneous clusters of workstations. Speedups in this scheme with the Luo-Rudy dynamic membrane equations exceeded 3.0 with eight distributed workstations. Cluster speedups were comparable to those measured during parallel execution on a shared memory machine.

Intracellular Ca(2+) dynamics and the stability of ventricular tachycardia

Ventricular fibrillation (VF), the major cause of sudden cardiac death, is typically preceded by ventricular tachycardia (VT), but the mechanisms underlying the transition from VT to VF are poorly understood. Intracellular Ca(2+) overload occurs during rapid heart rates typical of VT and is also known to promote arrhythmias. We therefore studied the role of intracellular Ca(2+) dynamics in the transition from VT to VF, using a combined experimental and mathematical modeling approach. Our results show that 1) rapid pacing of rabbit ventricular myocytes at 35 degrees C led to increased intracellular Ca(2+) levels and complex patterns of action potential (AP) configuration and the intracellular Ca(2+) transients; 2) the complex patterns of the Ca(2+) transient arose directly from the dynamics of intracellular Ca(2+) cycling, and were not merely passive responses to beat-to-beat alterations in AP; 3) the complex Ca(2+) dynamics were simulated in a modified version of the Luo-Rudy (LR) ventricular action potential with improved intracellular Ca(2+) dynamics, and showed good agreement with the experimental findings in isolated myocytes; and 4) when incorporated into simulated two-dimensional cardiac tissue, this action potential model produced a form of spiral wave breakup from VT to a VF-like state in which intracellular Ca(2+) dynamics played a key role through its influence on Ca(2+)-sensitive membrane currents such as I(Ca), I(NaCa), and I(ns(Ca)). To the extent that spiral wave breakup is useful as a model for the transition from VT to VF, these findings suggest that intracellular Ca(2+) dynamics may play an important role in the destabilization of VT and its degeneration into VF.

Stretch-induced changes in heart rate and rhythm: clinical observations, experiments and mathematical models

Clinical and research data indicate that active and passive changes in the mechanical environment of the heart are capable of influencing both the initiation and the spread of cardiac excitation via pathways that are intrinsic to the heart. This direction of the cross-talk between cardiac electrical and mechanical activity is referred to as mechano-electric feedback (MEF). MEF is thought to be involved in the adjustment of heart rate to changes in mechanical load and would help to explain the precise beat-to-beat regulation of cardiac performance as it occurs even in the recently transplanted (and, thus, denervated) heart. Furthermore, there is clinical evidence that MEF may be involved in mechanical initiation of arrhythmias and fibrillation, as well as in the re-setting of disturbed heart rhythm by 'mechanical' first aid procedures. This review will outline the clinical relevance of cardiac MEF, describe cellular correlates to the responses observed in situ, and discuss the role that quantitative mathematical models may play in identifying the involvement of cardiac MEF in the regulation of heart rate and rhythm.