Condition for alternans and stability of the 1:1 response pattern in a "memory" model of paced cardiac dynamics

Intracellular ion accumulation in the genesis of complex action potential dynamics under cardiac diseases

Intracellular ions, including sodium (Na^{+}), calcium (Ca^{2+}), and potassium (K^{+}), etc., accumulate slowly after a change of the state of the heart, such as a change of the heart rate. The goal of this study is to understand the roles of slow ion accumulation in the genesis of cardiac memory and complex action-potential duration (APD) dynamics that can lead to lethal cardiac arrhythmias. We carry out numerical simulations of a detailed action potential model of ventricular myocytes under normal and diseased conditions, which exhibit memory effects and complex APD dynamics. We develop a low-dimensional iterated map (IM) model to describe the dynamics of Na^{+}, Ca^{2+}, and APD and use it to uncover the underlying dynamical mechanisms. The development of the IM model is informed by simulation results under the normal condition. We then use the IM model to perform linear stability analyses and computer simulations to investigate the bifurcations and complex APD dynamics, which depend on the feedback loops between APD and intracellular Ca^{2+} and Na^{+} concentrations and the steepness of the APD response to the ion concentrations. When the feedback between APD and Ca^{2+} concentration is positive, a Hopf bifurcation leading to periodic oscillatory behavior occurs as the steepness of the APD response to the ion concentrations increases. The negative feedback loop between APD and Na^{+} concentration is required for the Hopf bifurcation. When the feedback between APD and Ca^{2+} concentration is negative, period-doubling bifurcations leading to high periodicity and chaos occurs. In this case, Na^{+} accumulation plays little role in the dynamics. Finally, we carry out simulations of the detailed action potential model under two diseased conditions, which exhibit steep APD responses to ion concentrations. Under both conditions, Hopf bifurcations leading to slow oscillations or period-doubling bifurcations leading to high periodicity and chaotic APD dynamics occur, depending on the strength of the ion pump-Na^{+}-Ca^{2+} exchanger. Using functions reconstructed from the simulation data, the IM model accurately captures the bifurcations and dynamics under the two diseased conditions. In conclusion, besides using computer simulations of a detailed high-dimensional action-potential model to investigate the effects of slow ion accumulation and short-term memory on bifurcations and genesis of complex APD dynamics in cardiac myocytes under diseased conditions, this study also provides a low-dimensional mathematical tool, i.e., the IM model, to allow stability analyses for uncovering the underlying mechanisms.

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.

Optimal entrainment for removal of pinned spiral waves

Cardiac fibrillation is caused by self-sustaining spiral waves that occur in the myocardium, some of which can be pinned to anatomical obstacles, making them more difficult to eliminate. A small electrical stimulation is often sufficient to unpin these spirals but only if it is applied during the vulnerable unpinning window. Even if these unpinning windows can be inferred from data, when multiple pinned spirals exist, their unpinning windows will not generally overlap. Using phase-based reduction techniques, we formulate and solve an optimal control problem to yield a time-varying external voltage gradient that can synchronize a collection of spiral waves that are pinned to a collection of heterogeneous obstacles. Upon synchronization, the unpinning windows overlap so that they can be simultaneously unpinned by applying an external voltage gradient pulse at an appropriate moment. Numerical validation is presented in bidomain model simulations. Results represent a proof-of-concept illustration of the proposed unpinning strategy which explicitly incorporates heterogeneity in the problem formulation and requires no real-time feedback about the system state.

The development of L-type Ca2+ current mediated alternans does not depend on the restitution slope in canine ventricular myocardium

Cardiac alternans have crucial importance in the onset of ventricular fibrillation. The early explanation for alternans development was the voltage-driven mechanism, where the action potential (AP) restitution steepness was considered as crucial determining factor. Recent results suggest that restitution slope is an inadequate predictor for alternans development, but several studies still claim the role of membrane potential as underlying mechanism of alternans. These controversial data indicate that the relationship of restitution and alternans development is not completely understood. APs were measured by conventional microelectrode technique from canine right ventricular papillary muscles. Ionic currents combined with fluorescent measurements were recorded by patch-clamp technique. APs combined with fluorescent measurements were monitored by sharp microelectrodes. Rapid pacing evoked restitution-independent AP duration (APD) alternans. When non-alternating AP voltage command was used, Ca²⁺_i-transient (CaT) alternans were not observed. When alternating rectangular voltage pulses were applied, CaT alternans were proportional to I_CaL amplitude alternans. Selective I_CaL inhibition did not influence the fast phase of APD restitution. In this study we found that I_CaL has minor contribution in shaping the fast phase of restitution curve suggesting that I_CaL—if it plays important role in the alternans mechanism—could be an additional factor that attenuates the reliability of APD restitution slope to predict alternans.

Universal mechanisms for self-termination of rapid cardiac rhythm

Excitable media sustain circulating waves. In the heart, sustained circulating waves can lead to serious impairment or even death. To investigate factors affecting the stability of such waves, we have used optogenetic techniques to stimulate a region at the apex of a mouse heart at a fixed delay after the detection of excitation at the base of the heart. For long delays, rapid circulating rhythms can be sustained, whereas for shorter delays, there are paroxysmal bursts of activity that start and stop spontaneously. By considering the dependence of the action potential and conduction velocity on the preceding recovery time using restitution curves, as well as the reduced excitability (fatigue) due to the rapid excitation, we model prominent features of the dynamics including alternation of the duration of the excited phases and conduction times, as well as termination of the bursts for short delays. We propose that this illustrates universal mechanisms that exist in biological systems for the self-termination of such activities.

Bifurcations Caused by Feedback between Voltage and Intracellular Ion Concentrations in Ventricular Myocytes

We develop an iterated map model to describe the bifurcations and complex dynamics caused by the feedback between voltage and intracellular Ca^{2+} and Na^{+} concentrations in paced ventricular myocytes. Voltage and Ca^{2+} can form either a positive or a negative feedback loop, while voltage and Na^{+} form a negative feedback loop. Under certain diseased conditions, when the feedback between voltage and Ca^{2+} is positive, Hopf bifurcations occur, leading to periodic oscillatory behaviors. When this feedback is negative, period-doubling bifurcation routes to alternans and chaos occur.

Phase reduction and phase-based optimal control for biological systems: a tutorial

A powerful technique for the analysis of nonlinear oscillators is the rigorous reduction to phase models, with a single variable describing the phase of the oscillation with respect to some reference state. An analog to phase reduction has recently been proposed for systems with a stable fixed point, and phase reduction for periodic orbits has recently been extended to take into account transverse directions and higher-order terms. This tutorial gives a unified treatment of such phase reduction techniques and illustrates their use through mathematical and biological examples. It also covers the use of phase reduction for designing control algorithms which optimally change properties of the system, such as the phase of the oscillation. The control techniques are illustrated for example neural and cardiac systems.

Isostable reduction of oscillators with piecewise smooth dynamics and complex Floquet multipliers

Phase-amplitude reduction is a widely applied technique in the study of limit cycle oscillators with the ability to represent a complicated and high-dimensional dynamical system in a more analytically tractable set of coordinates. Recent work has focused on the use of isostable coordinates, which characterize the transient decay of solutions toward a periodic orbit, and can ultimately be used to increase the accuracy of these reduced models. The breadth of systems to which this phase-amplitude reduction strategy can be applied, however, is still rather limited. In this work, the theory of phase-amplitude reduction using isostable coordinates is further developed to accommodate a broader set of dynamical systems. In the first part, limit cycles of piecewise smooth dynamical systems are considered and strategies are developed to compute the associated reduced equations. In the second part, the notion of isostable coordinates for complex-valued Floquet multipliers is introduced, resulting in one phaselike coordinate and one amplitudelike coordinate for each pair of complex conjugate Floquet multipliers. Examples are given with relevance to piecewise smooth representations of excitable cardiomyocytes and the relationship between the reduced coordinate system and the emergence of cardiac alternans is discussed. Also, phase-amplitude reduction is implemented for a chaotic, externally forced pendulum with complex Floquet multipliers and a resulting control strategy for the stabilization of its periodic solution is investigated.

Control of voltage-driven instabilities in cardiac myocytes with memory

Sudden cardiac death is known to be associated with dynamical instabilities in the heart, and thus control of dynamical instabilities is considered a potential therapeutic strategy. Different control methods were developed previously, including time-delayed feedback pacing control and constant diastolic interval pacing control. Experimental, theoretical, and simulation studies have examined the efficacy of these control methods in stabilizing action potential dynamics. In this study, we apply these control methods to control complex action potential (AP) dynamics under two diseased conditions: early repolarization syndrome and long QT syndrome, in which voltage-driven instabilities occur in the presence of short-term cardiac memory. In addition, we also develop a feedback pacing method to stabilize these instabilities. We perform theoretical analyses using iterated map models and carry out numerical simulations of AP models. We show that under the normal condition where the memory effect is minimal, all three methods can effectively control the action potential duration (APD) dynamics. Under the two diseased conditions where the memory effect is exacerbated, constant diastolic pacing control is least effective, while the feedback pacing control is most effective. Under a very strong memory effect, all three methods fail to stabilize the voltage-driven instabilities. The failure of effective control is due to memory and the all-or-none AP dynamics which results in very steep changes in APD.

Memory-induced nonlinear dynamics of excitation in cardiac diseases

Excitable cells, such as cardiac myocytes, exhibit short-term memory, i.e., the state of the cell depends on its history of excitation. Memory can originate from slow recovery of membrane ion channels or from accumulation of intracellular ion concentrations, such as calcium ion or sodium ion concentration accumulation. Here we examine the effects of memory on excitation dynamics in cardiac myocytes under two diseased conditions, early repolarization and reduced repolarization reserve, each with memory from two different sources: slow recovery of a potassium ion channel and slow accumulation of the intracellular calcium ion concentration. We first carry out computer simulations of action potential models described by differential equations to demonstrate complex excitation dynamics, such as chaos. We then develop iterated map models that incorporate memory, which accurately capture the complex excitation dynamics and bifurcations of the action potential models. Finally, we carry out theoretical analyses of the iterated map models to reveal the underlying mechanisms of memory-induced nonlinear dynamics. Our study demonstrates that the memory effect can be unmasked or greatly exacerbated under certain diseased conditions, which promotes complex excitation dynamics, such as chaos. The iterated map models reveal that memory converts a monotonic iterated map function into a nonmonotonic one to promote the bifurcations leading to high periodicity and chaos.

The influences of the M2R-GIRK4-RGS6 dependent parasympathetic pathway on electrophysiological properties of the mouse heart

A large body of work has established the prominent roles of the atrial M₂R-I_KACh signaling pathway, and the negative regulatory protein RGS6, in modulating critical aspects of parasympathetic influence on cardiac function, including pace-making, heart rate (HR) variability (HRV), and atrial arrhythmogenesis. Despite increasing evidence of its innervation of the ventricles, and the expression of M₂R, I_KACh channel subunits, and RGS6 in ventricle, the effects of parasympathetic modulation on ventricular electrophysiology are less clear. The main objective of our study was to investigate the contribution of M₂R-I_KACh signaling pathway elements in murine ventricular electrophysiology, using in-vivo ECG measurements, isolated whole-heart optical mapping and constitutive knockout mice lacking I_KACh (Girk4^–/–) or RGS6 (Rgs6^-/-). Consistent with previous findings, mice lacking GIRK4 exhibited diminished HR and HRV responses to the cholinergic agonist carbachol (CCh), and resistance to CCh-induced arrhythmic episodes. In line with its role as a negative regulator of atrial M₂R-I_KACh signaling, loss of RGS6 correlated with a mild resting bradycardia, enhanced HR and HRV responses to CCh, and increased propensity for arrhythmic episodes. Interestingly, ventricles from mice lacking GIRK4 or RGS6 both exhibited increased action potential duration (APD) at baseline, and APD was prolonged by CCh across all genotypes. Similarly, CCh significantly increased the slope of APD restitution in all genotypes. There was no impact of genotype or CCh on either conduction velocity or heterogeneity. Our data suggests that altered parasympathetic signaling through the M₂R-I_KACh pathway can affect ventricular electrophysiological properties distinct from its influence on atrial physiology.

Short-term action potential memory and electrical restitution: A cellular computational study on the stability of cardiac repolarization under dynamic pacing

Electrical restitution (ER) is a major determinant of repolarization stability and, under fast pacing rate, it reveals memory properties of the cardiac action potential (AP), whose dynamics have never been fully elucidated, nor their ionic mechanisms. Previous studies have looked at ER mainly in terms of changes in AP duration (APD) when the preceding diastolic interval (DI) changes and described dynamic conditions where this relationship shows hysteresis which, in turn, has been proposed as a marker of short-term AP memory and repolarization stability. By means of numerical simulations of a non-propagated human ventricular AP, we show here that measuring ER as APD versus the preceding cycle length (CL) provides additional information on repolarization dynamics which is not contained in the companion formulation. We focus particularly on fast pacing rate conditions with a beat-to-beat variable CL, where memory properties emerge from APD vs CL and not from APD vs DI and should thus be stored in APD and not in DI. We provide an ion-currents characterization of such conditions under periodic and random CL variability, and show that the memory stored in APD plays a stabilizing role on AP repolarization under pacing rate perturbations. The gating kinetics of L-type calcium current seems to be the main determinant of this safety mechanism. We also show that, at fast pacing rate and under otherwise identical pacing conditions, a periodically beat-to-beat changing CL is more effective than a random one in stabilizing repolarization. In summary, we propose a novel view of short-term AP memory, differentially stored between systole and diastole, which opens a number of methodological and theoretical implications for the understanding of arrhythmia development.

Stochastic Pacing Inhibits Spatially Discordant Cardiac Alternans

Depressed heart rate variability is a well-established risk factor for sudden cardiac death in survivors of acute myocardial infarction and for those with congestive heart failure. Although measurements of heart rate variability provide a valuable prognostic tool, it is unclear whether reduced heart rate variability itself is proarrhythmic or if it simply correlates with the severity of autonomic nervous system dysfunction. In this work, we investigate a possible mechanism by which heart rate variability could protect against cardiac arrhythmia. Specifically, in numerical simulations, we observe an inverse relationship between the variance of stochastic pacing and the occurrence of spatially discordant alternans, an arrhythmia that is widely believed to facilitate the development of cardiac fibrillation. By analyzing the effects of conduction velocity restitution, cellular dynamics, electrotonic coupling, and stochastic pacing on the nodal dynamics of spatially discordant alternans, we provide intuition for this observed behavior and propose control strategies to inhibit discordant alternans.

Alternans promotion in cardiac electrophysiology models by delay differential equations

Cardiac electrical alternans is a state of alternation between long and short action potentials and is frequently associated with harmful cardiac conditions. Different dynamic mechanisms can give rise to alternans; however, many cardiac models based on ordinary differential equations are not able to reproduce this phenomenon. A previous study showed that alternans can be induced by the introduction of delay differential equations (DDEs) in the formulations of the ion channel gating variables of a canine myocyte model. The present work demonstrates that this technique is not model-specific by successfully promoting alternans using DDEs for five cardiac electrophysiology models that describe different types of myocytes, with varying degrees of complexity. By analyzing results across the different models, we observe two potential requirements for alternans promotion via DDEs for ionic gates: (i) the gate must have a significant influence on the action potential duration and (ii) a delay must significantly impair the gate's recovery between consecutive action potentials.

Distinguishing mechanisms for alternans in cardiac cells using constant-diastolic-interval pacing

Alternans, a proarrhythmic dynamical state in which cardiac action potentials alternate between long and short durations despite a constant pacing period, traditionally has been explained at the cellular level using nonlinear dynamics principles under the assumption that the action potential duration (APD) is determined solely by the time elapsed since the end of the previous action potential, called the diastolic interval (DI). In this scenario, APDs at a steady state should be the same provided that the preceding DIs are the same. Nevertheless, experiments attempting to eliminate alternans by dynamically adjusting the timing of pacing stimuli to keep the DI constant showed that alternans persisted, contradicting the traditional theory. It is now widely known that alternans also can arise from a different mechanism associated with intracellular calcium cycling. Our goal is to determine whether intracellular calcium dynamics can explain the experimental findings regarding the persistence of alternans despite a constant DI. For this, we use mathematical models capable of producing alternans through both voltage- and calcium-mediated mechanisms. We show that for voltage-driven alternans, action potentials elicited from a constant-DI protocol are always the same. However, in the case of calcium-driven alternans, the constant-DI protocol can result in alternans. Reducing the strength of the calcium instability progressively reduces and finally eliminates constant-DI alternans. Our findings suggest that screening for the presence of alternans using a constant-DI protocol has the potential for differentiating between voltage-driven and calcium-driven alternans.

Theory of the development of alternans in the heart during controlled diastolic interval pacing

The beat-to-beat alternation in action potential durations (APDs) in the heart, called APD alternans, has been linked to the development of serious cardiac rhythm disorders, including ventricular tachycardia and fibrillation. The length of the period between action potentials, called the diastolic interval (DI), is a key dynamical variable in the standard theory of alternans development. Thus, methods that control the DI may be useful in preventing dangerous cardiac rhythms. In this study, we examine the dynamics of alternans during controlled-DI pacing using a series of single-cell and one-dimensional (1D) fiber models of alternans dynamics. We find that a model that combines a so-called memory model with a calcium cycling model can reasonably explain two key experimental results: the possibility of alternans during constant-DI pacing and the phase lag of APDs behind DIs during sinusoidal-DI pacing. We also find that these results can be replicated by incorporating the memory model into an amplitude equation description of a 1D fiber. The 1D fiber result is potentially concerning because it seems to suggest that constant-DI control of alternans can only be effective over only a limited region in space.

Greater accuracy and broadened applicability of phase reduction using isostable coordinates

The applicability of phase models is generally limited by the constraint that the dynamics of a perturbed oscillator must stay near its underlying periodic orbit. Consequently, external perturbations must be sufficiently weak so that these assumptions remain valid. Using the notion of isostables of periodic orbits to provide a simplified coordinate system from which to understand the dynamics transverse to a periodic orbit, we devise a strategy to correct for changing phase dynamics for locations away from the limit cycle. Consequently, these corrected phase dynamics allow for perturbations of larger magnitude without invalidating the underlying assumptions of the reduction. The proposed reduction strategy yields a closed set of equations and can be applied to periodic orbits embedded in arbitrarily high dimensional spaces. We illustrate the utility of this strategy in two models with biological relevance. In the first application, we find that an optimal control strategy for modifying the period of oscillation can be improved with the corrected phase reduction. In the second, the corrected phase reduced dynamics are used to understand adaptation and memory effects resulting from past perturbations.

Mechanism for Amplitude Alternans in Electrocardiograms and the Initiation of Spatiotemporal Chaos

It is widely believed that one major life-threatening transition to chaotic fibrillation occurs via spiral-wave breakup that is preceded by spatiotemporal dispersion of refractoriness due to alternations in the duration of the cardiac action potential (AP). However, recent clinical and experimental evidence suggests that other characteristics of the AP may contribute to, and perhaps drive, this dangerous dynamical instability. To identify the relative roles of AP characteristics, we performed experiments in rabbit hearts under conditions to minimize AP duration dynamics which unmasked pronounced AP amplitude alternans just before the onset of fibrillation. We used a simplified ionic cell model to derive a return map and a stability condition that elucidates a novel underlying mechanism for AP alternans and spiral breakup. We found that inactivation of the sodium current is key to developing amplitude alternans and is directly connected to conduction block and initiation of arrhythmias. Simulations in 2D where AP amplitude alternation led to turbulence confirm our hypothesis.

Memory-Induced Chaos in Cardiac Excitation

Excitable systems display memory, but how memory affects the excitation dynamics of such systems remains to be elucidated. Here we use computer simulation of cardiac action potential models to demonstrate that memory can cause dynamical instabilities that result in complex excitation dynamics and chaos. We develop an iterated map model that correctly describes these dynamics and show that memory converts a monotonic first return map of action potential duration into a nonmonotonic one, resulting in a period-doubling bifurcation route to chaos.

Cardiac dynamics: Alternans and arrhythmogenesis

Pre-existing heterogeneities present in cardiac tissue are essential for maintaining the normal electrical and mechanical functions of the heart. Exacerbation of such heterogeneities or the emergence of dynamic factors can produce repolarization alternans, which are beat-to-beat alternations in the action potential time course. Traditionally, this was explained by restitution, but additional factors, such as cardiac memory, calcium handling dynamics, refractory period restitution, and mechano-electric feedback, are increasingly recognized as the underlying causes. The aim of this article is to review the mechanisms that generate cardiac repolarization alternans and convert spatially concordant alternans to the more arrhythmogenic spatially discordant alternans. This is followed by a discussion on how alternans generate arrhythmias in a number of clinical scenarios, and concluded by an outline of future therapeutic targets for anti-arrhythmic therapy.

Nonlinear physics of electrical wave propagation in the heart: a review

The beating of the heart is a synchronized contraction of muscle cells (myocytes) that is triggered by a periodic sequence of electrical waves (action potentials) originating in the sino-atrial node and propagating over the atria and the ventricles. Cardiac arrhythmias like atrial and ventricular fibrillation (AF,VF) or ventricular tachycardia (VT) are caused by disruptions and instabilities of these electrical excitations, that lead to the emergence of rotating waves (VT) and turbulent wave patterns (AF,VF). Numerous simulation and experimental studies during the last 20 years have addressed these topics. In this review we focus on the nonlinear dynamics of wave propagation in the heart with an emphasis on the theory of pulses, spirals and scroll waves and their instabilities in excitable media with applications to cardiac modeling. After an introduction into electrophysiological models for action potential propagation, the modeling and analysis of spatiotemporal alternans, spiral and scroll meandering, spiral breakup and scroll wave instabilities like negative line tension and sproing are reviewed in depth and discussed with emphasis on their impact for cardiac arrhythmias.

Real-time feedback based control of cardiac restitution using optical mapping

Cardiac restitution is the shortening of the action potential duration with an increase in the heart rate. A shorter action potential duration enables a longer diastolic interval which ensures that the heart gets adequate time to refill with blood. At higher rates however, restitution becomes steep and thus, can lead to unstable electrical activity (alternans) in the heart, leading to fatal cardiac rhythms. It has been proposed that maintaining a shallow slope of cardiac restitution could have potentially anti-arrhythmic effects. Previous studies involved the control of action potential duration (APD) or diastolic interval (DI) in isolated tissue samples based on the feedback from single microelectrode recordings. This limited the spatial resolution of the feedback system. Here, we aimed to develop a real time feedback control system that enabled the detection of APDs from various single pixels based on optical mapping recordings. Stimuli were applied after a predefined fixed DI after detection of an APD. We validated our algorithm using optical mapping movies from an ex-vivo rabbit heart. Thus, we provide an optical mapping based approach for the control of cardiac restitution and a potential means to validate its anti-arrhythmic effects.

Impaired Sarcoplasmic Reticulum Calcium Uptake and Release Promote Electromechanically and Spatially Discordant Alternans: A Computational Study

Cardiac electrical dynamics are governed by cellular-level properties, such as action potential duration (APD) restitution and intracellular calcium (Ca) handling, and tissue-level properties, including conduction velocity restitution and cell-cell coupling. Irregular dynamics at the cellular level can lead to instabilities in cardiac tissue, including alternans, a beat-to-beat alternation in the action potential and/or the intracellular Ca transient. In this study, we incorporate a detailed single cell coupled map model of Ca cycling and bidirectional APD-Ca coupling into a spatially extended tissue model to investigate the influence of sarcoplasmic reticulum (SR) Ca uptake and release properties on alternans and conduction block. We find that an intermediate SR Ca uptake rate and larger SR Ca release resulted in the widest range of stimulus periods that promoted alternans. However, both reduced SR Ca uptake and release promote arrhythmogenic spatially and electromechanically discordant alternans, suggesting a complex interaction between SR Ca handling and alternans characteristics at the cellular and tissue level.

Restitution analysis of alternans using dynamic pacing and its comparison with S1S2 restitution in heptanol-treated, hypokalaemic Langendorff-perfused mouse hearts

Action potential duration (APD) and conduction velocity restitution explain the dependence of these parameters on the previous diastolic interval (DI). It is considered to be an adaptive mechanism for preserving diastole at fast heart rates. Hypokalaemia is known to induce ventricular arrhythmias that could be prevented by heptanol, the gap junction uncoupler, mediated through increases in ventricular refractory period (VERP) without alterations in APDs. The present study investigated alternans and restitution properties during normokalaemia, hypokalaemia alone or hypokalaemia with heptanol (0.1 mM) in Langendorff-perfused mouse hearts using a dynamic pacing protocol. APD90 alternans were elicited in the epicardium and endocardium during normokalaemia. Hypokalaemia increased the amplitudes of epicardial APD90 alternans when basic cycle lengths (BCLs) were ≤65 msec, which was associated with increases in maximum APD90 restitution gradients, critical DIs and APD90 heterogeneity. Heptanol (0.1 mM) did not exacerbate or reduce the APD90 alternans or alter these restitution parameters further. By contrast, endocardial APD90 alternans did not show increases in amplitudes during hypokalaemia at short BCLs studied, and restitution parameters were also unchanged. This was true whether in the presence or absence of 0.1 mM heptanol. The study demonstrates that anti-arrhythmic effects of heptanol exerted during hypokalaemia occurred despite exacerbation of APD90 alternans. This would suggest that even in the presence of arrhythmogenic APD90 alternans, arrhythmias could still be prevented by influencing VERP alone. Restitution data obtained here by dynamic pacing were compared to previous data from S1S2 pacing.

Characterizing Spatial Dynamics of Bifurcation to Alternans in Isolated Whole Rabbit Hearts Based on Alternate Pacing

Sudden cardiac death instigated by ventricular fibrillation (VF) is the largest cause of natural death in the USA. Alternans, a beat-to-beat alternation in the action potential duration, has been implicated as being proarrhythmic. The onset of alternans is mediated via a bifurcation, which may occur through either a smooth or a border-collision mechanism. The objective of this study was to characterize the mechanism of bifurcation to alternans based on experiments in isolated whole rabbit hearts. High resolution optical mapping was performed and the electrical activity was recorded from the left ventricle (LV) epicardial surface of the heart. Each heart was paced using an “alternate pacing protocol,” where the basic cycle length (BCL) was alternatively perturbed by ±δ. Local onset of alternans in the heart, BCL_start, was measured in the absence of perturbations (δ = 0) and was defined as the BCL at which 10% of LV exhibited alternans. The influences of perturbation size were investigated at two BCLs: one prior to BCL_start (BCL_prior = BCL_start + 20 ms) and one preceding BCL_prior (BCL_far = BCL_start + 40 ms). Our results demonstrate significant spatial correlation of the region exhibiting alternans with smooth bifurcation characteristics, indicating that transition to alternans in isolated rabbit hearts occurs predominantly through smooth bifurcation.

Spatial discordance and phase reversals during alternate pacing in discrete-time kinematic and cardiomyocyte ionic models

Alternans, a beat-to-beat alternation in the cardiac action potential duration (APD), is a dynamical instability linked with the initiation of arrhythmias and sudden cardiac death, and arises via a period-doubling bifurcation when myocytes are stimulated at fast rates. In this study, we analyze the stability of a propagating electrical wave in a one-dimensional cardiac myocyte model in response to an arrhythmogenic rhythm known as alternate pacing. Using a discrete-time kinematic model and complex frequency (Z) domain analysis, we derive analytical expressions to predict phase reversals and spatial discordance in the interbeat interval (IBI) and APD, which, importantly, cannot be predicted with a model that neglects the influence of cell coupling on repolarization. We identify key dimensionless parameters that determine the transition from spatial concordance to discordance. Finally, we show that the theoretical predictions agree closely with numerical simulations of an ionic myocyte model, over a wide range of parameters, including variable IBI, altered ionic current gating, and reduced cell coupling. We demonstrate a novel approach to predict instability in cardiac tissue during alternate pacing and further illustrate how this approach can be generalized to more detail models of myocyte dynamics.

Perspective: a dynamics-based classification of ventricular arrhythmias

Despite key advances in the clinical management of life-threatening ventricular arrhythmias, culminating with the development of implantable cardioverter-defibrillators and catheter ablation techniques, pharmacologic/biologic therapeutics have lagged behind. The fundamental issue is that biological targets are molecular factors. Diseases, however, represent emergent properties at the scale of the organism that result from dynamic interactions between multiple constantly changing molecular factors. For a pharmacologic/biologic therapy to be effective, it must target the dynamic processes that underlie the disease. Here we propose a classification of ventricular arrhythmias that is based on our current understanding of the dynamics occurring at the subcellular, cellular, tissue and organism scales, which cause arrhythmias by simultaneously generating arrhythmia triggers and exacerbating tissue vulnerability. The goal is to create a framework that systematically links these key dynamic factors together with fixed factors (structural and electrophysiological heterogeneity) synergistically promoting electrical dispersion and increased arrhythmia risk to molecular factors that can serve as biological targets. We classify ventricular arrhythmias into three primary dynamic categories related generally to unstable Ca cycling, reduced repolarization, and excess repolarization, respectively. The clinical syndromes, arrhythmia mechanisms, dynamic factors and what is known about their molecular counterparts are discussed. Based on this framework, we propose a computational-experimental strategy for exploring the links between molecular factors, fixed factors and dynamic factors that underlie life-threatening ventricular arrhythmias. The ultimate objective is to facilitate drug development by creating an in silico platform to evaluate and predict comprehensively how molecular interventions affect not only a single targeted arrhythmia, but all primary arrhythmia dynamics categories as well as normal cardiac excitation-contraction coupling.

Cardiac contraction induces discordant alternans and localized block

In this paper we use a simplified model of cardiac excitation-contraction coupling to study the effect of tissue deformation on the dynamics of alternans, i.e., alternations in the duration of the cardiac action potential, that occur at fast pacing rates and are known to be proarrhythmic. We show that small stretch-activated currents can produce large effects and cause a transition from in-phase to off-phase alternations (i.e., from concordant to discordant alternans) and to conduction blocks. We demonstrate numerically and analytically that this effect is the result of a generic change in the slope of the conduction velocity restitution curve due to electromechanical coupling. Thus, excitation-contraction coupling can potentially play a relevant role in the transition to reentry and fibrillation.

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.

Nonlinear and Stochastic Dynamics in the Heart

In a normal human life span, the heart beats about 2 to 3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems.

Change of short-term memory effect in acute ischemic ventricular myocardium: a computational study

The ionic mechanism of change in short-term memory (STM) during acute myocardial ischemia has not been well understood. In this paper, an advanced guinea pig ventricular model developed by Luo and Rudy was used to investigate STM property of ischemic ventricular myocardium. STM response was calculated by testing the time to reach steady-state action potential duration (APD) after an abrupt shortening of basic cycling length (BCL) in the pacing protocol. Electrical restitution curves (RCs), which can simultaneously visualize multiple aspects of APD restitution and STM, were obtained from dynamic and local S1S2 restitution portrait (RP), which consist of a longer interval stimulus (S1) and a shorter interval stimulus (S2). The angle between dynamic RC and local S1S2 RC reflects the amount of STM. Our results indicated that compared with control (normal) condition, time constant of STM response in the ischemic condition decreased significantly. Meanwhile the angle which reflects STM amount is less in ischemic model than that in control model. By tracking the effect of ischemia on intracellular ion concentration and membrane currents, we declared that changes in membrane currents caused by ischemia exert subtle influences on STM; it is only the decline of intracellular calcium concentration that give rise to the most decrement of STM.

Using dominant eigenvalue analysis to predict formation of alternans in the heart

Ventricular fibrillation at the whole heart level is often preceded by the alternation of action potential duration (APD), i.e., alternans, at the cellular level. As proven in many experiments, traditional approaches based on the slope of the restitution curve have not been successful in predicting alternans formation. Recently, a technique has been theoretically developed based on dominant eigenvalue analysis to predict alternans formation in isolated cardiac myocytes. Here, we aimed to demonstrate that this technique can be applied to predict alternans formation at the whole heart level. Optical mapping was performed in Langendorff-perfused hearts from New Zealand white rabbits (n = 4), which were paced at decreasing basic cycle lengths to introduce APD alternans. In each heart, the basic cycle length corresponding to the local onset of alternans, B(onset), was determined and two regions of the heart were identified at B(onset): one region which exhibited alternans (1:1(alt)) and one which did not (1:1). Corresponding two-dimensional eigenvalue (λ) maps were generated using principal component analysis by analyzing action potentials after short perturbations from the steady state, and mean eigenvalues (λ[over ¯]) were calculated separately for the 1:1 and 1:1(alt) regions. We demonstrated that λ[over ¯] calculated at B(onset) was significantly different (p<0.05) between the two regions. Our results suggest that this dominant eigenvalue technique can be used to successfully predict the local alternans formation in the heart.

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.

Improving cardiac conduction with a skeletal muscle sodium channel by gene and cell therapy

The voltage-gated Na+ channel is a critical determinant of the action potential (AP) upstroke. Increasing Na+ conductance may speed AP propagation. In this study, we propose use of the skeletal muscle Na+ channel SkM1 as a more favorable gene than the cardiac isoform SCN5A to enhance conduction velocity in depolarized cardiac tissue. We used cells that electrically coupled with cardiac myocytes as a delivery platform to introduce the Na+ channels. Human embryonic kidney 293 cells were stably transfected with SkM1 or SCN5A. SkM1 had a more depolarized (18 mV shift) inactivation curve than SCN5A. We also found that SkM1 recovered faster from inactivation than SCN5A. When coupled with SkM1 expressing cells, cultured myocytes showed an increase in the dV/dtmax of the AP. Expression of SCN5A had no such effect. In an in vitro cardiac syncytium, coculture of neonatal cardiac myocytes with SkM1 expressing but not SCN5A expressing cells significantly increased the conduction velocity under both normal and depolarized conditions. In an in vitro reentry model induced by high-frequency stimulation, expression of SkM1 also enhanced angular velocity of the induced reentry. These results suggest that cells carrying a Na+ channel with a more depolarized inactivation curve can improve cardiac excitability and conduction in depolarized tissues.

Computational approaches to understand cardiac electrophysiology and arrhythmias

Cardiac rhythms arise from electrical activity generated by precisely timed opening and closing of ion channels in individual cardiac myocytes. These impulses spread throughout the cardiac muscle to manifest as electrical waves in the whole heart. Regularity of electrical waves is critically important since they signal the heart muscle to contract, driving the primary function of the heart to act as a pump and deliver blood to the brain and vital organs. When electrical activity goes awry during a cardiac arrhythmia, the pump does not function, the brain does not receive oxygenated blood, and death ensues. For more than 50 years, mathematically based models of cardiac electrical activity have been used to improve understanding of basic mechanisms of normal and abnormal cardiac electrical function. Computer-based modeling approaches to understand cardiac activity are uniquely helpful because they allow for distillation of complex emergent behaviors into the key contributing components underlying them. Here we review the latest advances and novel concepts in the field as they relate to understanding the complex interplay between electrical, mechanical, structural, and genetic mechanisms during arrhythmia development at the level of ion channels, cells, and tissues. We also discuss the latest computational approaches to guiding arrhythmia therapy.

Mechanisms of ventricular arrhythmias: a dynamical systems-based perspective

Defining the cellular electrophysiological mechanisms for ventricular tachyarrhythmias is difficult, given the wide array of potential mechanisms, ranging from abnormal automaticity to various types of reentry and kk activity. The degree of difficulty is increased further by the fact that any particular mechanism may be influenced by the evolving ionic and anatomic environments associated with many forms of heart disease. Consequently, static measures of a single electrophysiological characteristic are unlikely to be useful in establishing mechanisms. Rather, the dynamics of the electrophysiological triggers and substrates that predispose to arrhythmia development need to be considered. Moreover, the dynamics need to be considered in the context of a system, one that displays certain predictable behaviors, but also one that may contain seemingly stochastic elements. It also is essential to recognize that even the predictable behaviors of this complex nonlinear system are subject to small changes in the state of the system at any given time. Here we briefly review some of the short-, medium-, and long-term alterations of the electrophysiological substrate that accompany myocardial disease and their potential impact on the initiation and maintenance of ventricular arrhythmias. We also provide examples of cases in which small changes in the electrophysiological substrate can result in rather large differences in arrhythmia outcome. These results suggest that an interrogation of cardiac electrical dynamics is required to provide a meaningful assessment of the immediate risk for arrhythmia development and for evaluating the effects of putative antiarrhythmic interventions.

Using noise to determine cardiac restitution with memory

Variation in cardiac pacing cycles, as seen, for example, in heart rate variability, has been observed for decades. Contemporarily, various mathematical models have been constructed to investigate the electrical activity of paced cardiac cells. Yet there has not been a study of these cardiac models when there is variation in the pacing cycles such as noise. We present a method that uses the stochasticity of pacing cycles to determine approximate models of the dynamics of cardiac cells, and use these models to detect bifurcations to alternans.

Uncovering the dynamics of cardiac systems using stochastic pacing and frequency domain analyses

Alternans of cardiac action potential duration (APD) is a well-known arrhythmogenic mechanism which results from dynamical instabilities. The propensity to alternans is classically investigated by examining APD restitution and by deriving APD restitution slopes as predictive markers. However, experiments have shown that such markers are not always accurate for the prediction of alternans. Using a mathematical ventricular cell model known to exhibit unstable dynamics of both membrane potential and Ca²⁺ cycling, we demonstrate that an accurate marker can be obtained by pacing at cycle lengths (CLs) varying randomly around a basic CL (BCL) and by evaluating the transfer function between the time series of CLs and APDs using an autoregressive-moving-average (ARMA) model. The first pole of this transfer function corresponds to the eigenvalue (λ(alt)) of the dominant eigenmode of the cardiac system, which predicts that alternans occurs when λ(alt) ≤ -1. For different BCLs, control values of λ(alt) were obtained using eigenmode analysis and compared to the first pole of the transfer function estimated using ARMA model fitting in simulations of random pacing protocols. In all versions of the cell model, this pole provided an accurate estimation of λ(alt). Furthermore, during slow ramp decreases of BCL or simulated drug application, this approach predicted the onset of alternans by extrapolating the time course of the estimated λ(alt). In conclusion, stochastic pacing and ARMA model identification represents a novel approach to predict alternans without making any assumptions about its ionic mechanisms. It should therefore be applicable experimentally for any type of myocardial cell.

Ventricular fibrillation: dynamics and ion channel determinants

Ventricular fibrillation (VF) is the leading cause of sudden cardiac death. This brief review addresses issues relevant to the dynamics of the rotors responsible for functional reentry and VF. It also makes an attempt to summarize present-day knowledge of the manner in which the dynamic interplay between inward and outward transmembrane currents and the heterogeneous cardiac structure establish a substrate for the initiation and maintenance of rotors and VF. The fragmentary nature of our current understanding of ionic VF mechanisms does not even allow an approach toward a "Theory of VF". Yet some hope is provided by recently obtained insight into the roles played in VF by some of the sarcolemmal ion channels that control the excitation-recovery process. For example, strong evidence supports the idea that the interplay between the rapid-inward sodium current and the inward-rectifier potassium current controls rotor formation, as well as rotor stability and frequency. Solid evidence also exists for an involvement of L-type calcium current in the control of rotor frequency and in determining VF-to-ventricular tachycardia conversion. Less clear, however, is whether or not time dependent outward currents through voltage-gated potassium channels affect the fibrillatory process. Hopefully, taking advantage of currently available approaches of structural, molecular and cellular biology, together with computational and imaging techniques, will afford us the opportunity to further advance knowledge on VF mechanisms.

Toward prediction of the local onset of alternans in the heart

A beat-to-beat variation in the cardiac action potential duration is a phenomenon known as alternans. Alternans has been linked to ventricular fibrillation, and thus the ability to predict the onset of alternans could be clinically beneficial. Theoretically, it has been proposed that the slope of a restitution curve, which relates the duration of the action potential to the preceding diastolic interval, can predict the onset of alternans. Experimentally, however, this hypothesis has not been consistently proven, mainly because of the intrinsic complexity of the dynamics of cardiac tissue. It was recently shown that the restitution portrait, which combines several restitution curves simultaneously, is associated with the onset of alternans in isolated myocytes. Our main purpose in this study was to determine whether the restitution portrait is correlated with the onset of alternans in the heart, where the dynamics include a spatial complexity. We performed optical mapping experiments in isolated Langendorff-perfused rabbit hearts in which alternans was induced by periodic pacing at different frequencies, and identified the local onset of alternans, B(onset). We identified two regions of the heart: the area that exhibited alternans at B(onset) (1:1(alt)) and the area that did not (1:1). We constructed two-dimensional restitution portraits for the epicardial surface of the heart and measured the spatial distribution of three different slopes (the dynamic restitution slope, S(dyn)(RP), and two local S1-S2 slopes, S(12) and S(12)(max)) separately for these two regions. We found that the S(12) and S(12)(max) slopes differed significantly between the 1:1(alt) and 1:1 regions just before the onset of alternans, and S(dyn)(RP) slopes were statistically similar. In addition, we found that the slopes of the dynamic restitution curve S(dyn) were also statistically similar between these two regions. On the other hand, the quantitative values of all slopes were significantly different from the theoretically predicted value of one. These results demonstrate that the slopes measured in the restitution portrait correlate with the onset of alternans in the heart.

The transfer functions of cardiac tissue during stochastic pacing

The restitution properties of cardiac action potential duration (APD) and conduction velocity (CV) are important factors in arrhythmogenesis. They determine alternans, wavebreak, and the patterns of reentrant arrhythmias. We developed a novel approach to characterize restitution using transfer functions. Transfer functions relate an input and an output quantity in terms of gain and phase shift in the complex frequency domain. We derived an analytical expression for the transfer function of interbeat intervals (IBIs) during conduction from one site (input) to another site downstream (output). Transfer functions can be efficiently obtained using a stochastic pacing protocol. Using simulations of conduction and extracellular mapping of strands of neonatal rat ventricular myocytes, we show that transfer functions permit the quantification of APD and CV restitution slopes when it is difficult to measure APD directly. We find that the normally positive CV restitution slope attenuates IBI variations. In contrast, a negative CV restitution slope (induced by decreasing extracellular [K(+)]) amplifies IBI variations with a maximum at the frequency of alternans. Hence, it potentiates alternans and renders conduction unstable, even in the absence of APD restitution. Thus, stochastic pacing and transfer function analysis represent a powerful strategy to evaluate restitution and the stability of conduction.

Using computational modeling to predict arrhythmogenesis and antiarrhythmic therapy

The use of computational modeling to predict arrhythmia and arrhythmogensis is a relatively new field, but has nonetheless dramatically enhanced our understanding of the physiological and pathophysiological mechanisms that lead to arrhythmia. This review summarizes recent advances in the field of computational modeling approaches with a brief review of the evolution of cellular action potential models, and the incorporation of genetic mutations to understand fundamental arrhythmia mechanisms, including how simulations have revealed situation specific mechanisms leading to multiple phenotypes for the same genotype. The review then focuses on modeling drug blockade to understand how the less-than-intuitive effects some drugs have to either ameliorate or paradoxically exacerbate arrhythmia. Quantification of specific arrhythmia indicies are discussed at each spatial scale, from channel to tissue. The utility of hERG modeling to assess altered repolarization in response to drug blockade is also briefly discussed. Finally, insights gained from Ca(2+) dynamical modeling and EC coupling, neurohumoral regulation of cardiac dynamics, and cell signaling pathways are also reviewed.

Critical scale of propagation influences dynamics of waves in a model of excitable medium

BACKGROUND

Duration and speed of propagation of the pulse are essential factors for stability of excitation waves. We explore the propagation of excitation waves resulting from periodic stimulation of an excitable cable to determine the minimal stable pulse duration in a rate-dependent modification of a Chernyak-Starobin-Cohen reaction-diffusion model.

RESULTS

Various pacing rate dependent features of wave propagation were studied computationally and analytically. We demonstrated that the complexity of responses to stimulation and evolution of these responses from stable propagation to propagation block and alternans was determined by the proximity between the minimal level of the recovery variable and the critical excitation threshold for a stable solitary pulse.

CONCLUSION

These results suggest that critical propagation of excitation waves determines conditions for transition to unstable rhythms in a way similar to unstable cardiac rhythms. Established conditions were suitably accurate regardless of rate dependent features and the magnitude of the slopes of restitution curves.

Termination of equine atrial fibrillation by quinidine: an optical mapping study

OBJECTIVE

To perform the first optical mapping studies of equine atrium to assess the spatiotemporal dynamics of atrial fibrillation (AF) and of its termination by quinidine.

ANIMALS

Intact, perfused atrial preparations obtained from four horses with normal cardiovascular examinations.

MATERIALS AND METHODS

AF was induced by a rapid pacing protocol with or without acetylcholine perfusion, and optical mapping was used to determine spatial dominant frequency distributions, electrical activity maps, and single-pixel optical signals. Following induction of AF, quinidine gluconate was perfused into the preparation and these parameters were monitored during quinidine-induced termination of AF.

RESULTS

Equine AF develops in the context of spatial gradients in action potential duration (APD) and diastolic interval (DI) that produce alternans, conduction block, and Wenckebach conduction in different regions at fast pacing rates. Quinidine terminates AF and prevents subsequent reinduction by reducing the maximal frequency and increasing frequency homogeneity.

CONCLUSIONS

Heterogeneity of APD and DI promote alternans and conduction block at fast pacing rates in the equine atrium, predisposing to the development of AF. Quinidine terminates AF by reducing maximum frequency and increasing frequency homogeneity. Our results are consistent with the hypothesis that quinidine increases effective refractory period, thereby decreasing frequency.

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.

Cardiac electrical dynamics: maximizing dynamical heterogeneity

The relationships between key features of the cardiac electrical activity, such as electrical restitution, discordant alternans, wavebreak, and reentry, and the onset of ventricular tachyarrhythmias have been characterized extensively under the condition of constant rapid pacing. However, it is unlikely that this scenario applies directly to the clinical situation, where the induction of ventricular tachycardia (VT) typically is associated with the interruption of normal cardiac rhythm by several premature beats. To address this issue, we have developed a general theory to explain why specific patterns of premature stimuli increase dynamic heterogeneity of repolarization and precipitate conduction block. The theory predicts that conduction block is caused by (1) creation of a spatial gradient in diastolic interval (DI) by waves traveling at slightly different velocities (ie, conduction velocity dispersion) and (2) amplification of the spatial gradient in DI over subsequent action potentials, secondary to a strong dependence of action potential duration on the preceding DI (ie, a steep action potential duration restitution function). Tests of this theory have been conducted in computer models of homogeneous tissue, where increased spatial dispersion of repolarization during premature stimulation can be attributed solely to the development of dynamical heterogeneity, and in a canine model exhibiting spontaneously occurring VT and sudden death. Our results thus far indicate that the probability of inducing ventricular fibrillation (VF) in the animal model is highest for those sequences predicted to cause conduction block in the computer model. An understanding of the mechanisms underlying these observations will help to identify key electrical phenomena in the onset of VT and fibrillation. Drug and electrical therapies can then be improved by targeting these specific phenomena.