Control of electrical alternans in canine cardiac purkinje fibers

A translational approach to probe the proarrhythmic potential of cardiac alternans: a reversible overture to arrhythmogenesis?

Electrocardiographic alternans, a phenomenon of beat-to-beat alternation in cardiac electrical waveforms, has been implicated in the pathogenesis of ventricular arrhythmias and sudden cardiac death (SCD). In the clinical setting, a positive microvolt T-wave alternans test has been associated with a heightened risk of arrhythmic mortality and SCD during medium- and long-term follow-up. However, rather than merely being associated with an increased risk for SCD, several lines of preclinical and clinical evidence suggest that cardiac alternans may play a causative role in generating the acute electrophysiological substrate necessary for the onset of ventricular arrhythmias. Deficiencies in Ca(2+) transport processes have been implicated in the genesis of alternans at the subcellular and cellular level and are hypothesized to contribute to the conditions necessary for dispersion of refractoriness, wave break, reentry, and onset of arrhythmia. As such, detecting acute surges in alternans may provide a mechanism for predicting the impending onset of arrhythmia and opens the door to delivering upstream antiarrhythmic therapies. In this review, we discuss the preclinical and clinical evidence to support a causative association between alternans and acute arrhythmogenesis and outline the potential clinical implications of such an association.

Effects of pacing site and stimulation history on alternans dynamics and the development of complex spatiotemporal patterns in cardiac tissue

Alternans of action potential duration has been associated with T wave alternans and the development of arrhythmias because it produces large gradients of repolarization. However, little is known about alternans dynamics in large mammalian hearts. Using optical mapping to record electrical activations simultaneously from the epicardium and endocardium of 9 canine right ventricles, we demonstrate novel arrhythmogenic complex spatiotemporal dynamics. (i) Alternans predominantly develops first on the endocardium. (ii) The postulated simple progression from normal rhythm to concordant to discordant alternans is not always observed; concordant alternans can develop from discordant alternans as the pacing period is decreased. (iii) In contrast to smaller tissue preparations, multiple stationary nodal lines may exist and need not be perpendicular to the pacing site or to each other. (iv) Alternans has fully three-dimensional dynamics and the epicardium and endocardium can show significantly different dynamics: multiple nodal surfaces can be transmural or intramural and can form concave/convex surfaces resulting in islands of discordant alternans. (v) The complex spatiotemporal patterns observed during alternans are very sensitive to both the site of stimulation and the stimulation history. Alternans in canine ventricles not only exhibit larger amplitudes and persist for longer cycle length regimes compared to those found in smaller mammalian hearts, but also show novel dynamics not previously described that enhance dispersion and show high sensitivity to initial conditions. This indicates some underlying predisposition to chaos and can help to guide the design of new drugs and devices controlling and preventing arrhythmic events.

Suppression of cardiac alternans by alternating-period-feedback stimulations

Alternans response, comprising a sequence of alternating long and short action potential durations in heart tissue, seen during rapid periodic pacing can lead to conduction block resulting in potentially fatal cardiac failure. A method of pacing with feedback control is proposed to reduce the alternans and therefore the probability of subsequent cardiac failure. The reduction is achieved by feedback control using small perturbations of constant magnitude to the original, alternans-generating pacing period T, viz., using sequences of two alternating periods of T+ΔT and T-ΔT, with ΔT<<T. Such a control scheme for alternans suppression is demonstrated experimentally in isolated whole heart experiments. This alternans suppression scheme is further confirmed and investigated in detail by simulations of ion-channel-based cardiac models both for a single cell and in one-dimensional spatially extended systems. The mechanism of the success of our method can be understood in terms of dynamics in phase space, viz., as the state of activity of the cell being confined within a narrow volume of phase space for the duration of control, resulting in extremely diminished variation in successive action potential durations. Our method is much more robust to noise than previous alternans reduction techniques based on fixed point stabilization and should thus be more efficient in terms of experimental implementation, which has implications for clinical treatment for arrhythmia.

A novel pacing method to suppress repolarization alternans in vivo: implications for arrhythmia prevention

BACKGROUND

Repolarization alternans (RA), a pattern of ventricular repolarization that repeats on an every other beat basis, has been closely linked with the substrate associated with ventricular tachycardia/ventricular fibrillation.

OBJECTIVE

To evaluate a novel method to suppress RA.

METHODS

We have developed a novel method to dynamically (on R-wave detection) trigger pacing pulses during the absolute refractory period. We have tested the ability of this method to control RA in a structurally normal swine heart in vivo.

RESULTS

RA induced by triggered pacing can be measured from both intracardiac and body surface leads and the amplitude of R-wave triggered pacing-induced alternans can be locally modulated by varying the amplitude and width of the pacing pulse. We have estimated that to induce a 1 μV change in alternans voltage on the body surface, coronary sinus, and left ventricle leads, a triggered pacing pulse delivered in the right ventricle of 0.04±0.02, 0.05±0.025, and 0.06±0.033 μC, respectively, is required. Similarly, to induce a 1 unit change in Kscore (ratio of alternans peak to noise), a pacing stimulus of 0.93±0.73, 0.32±0.29, and 0.33±0.37 μC, respectively, is required. We have been able to demonstrate that RA can be suppressed by R-wave triggered pacing from a site that is within or across ventricles. Lastly, we have demonstrated that the proposed method can be used to suppress spontaneously occurring alternans in the diseased heart.

CONCLUSION

We have developed a novel method to suppress RA in vivo.

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.

Cardiac alternans annihilation by distributed mechano-electric feedback (MEF)

The presence of the electrical alternans induces, through the mechanism of the excitation-contraction coupling, an alternation in the heart muscle contractile activity. In this work, we demonstrate the cardiac alternans annihilation by applied mechanical perturbation. In particular, we address annihilation of alternans in realistic heart size tissue by considering ionic currents suggested by Luo-Rudy-1 (LR1) model, in which the control algorithm involves a combined electrical boundary pacing control and a spatially distributed calcium based control which perturbs the calcium in the cells. Complimentary to this, we also address a novel mechanism of alternans annihilation which uses a Nash Panfilov model coupled with the stress equilibrium equations. The coupled model includes an additional variable to represent the active stress which defines the mechanical properties of the tissue.

Non-linear dynamics of cardiac alternans: subcellular to tissue-level mechanisms of arrhythmia

Cardiac repolarization alternans is a rhythm disturbance of the heart in which rapid stimulation elicits a beat-to-beat alternation in the duration of action potentials and magnitude of intracellular calcium transients in individual cardiac myocytes. Although this phenomenon has been identified as a potential precursor to dangerous reentrant arrhythmias and sudden cardiac death, significant uncertainty remains regarding its mechanism and no clinically practical means of halting its occurrence or progression currently exists. Cardiac alternans has well-characterized tissue, cellular, and subcellular manifestations, the mechanisms and interplay of which are an active area of research.

Nonlinear dynamics in cardiology

The dynamics of many cardiac arrhythmias, as well as the nature of transitions between different heart rhythms, have long been considered evidence of nonlinear phenomena playing a direct role in cardiac arrhythmogenesis. In most types of cardiac disease, the pathology develops slowly and gradually, often over many years. In contrast, arrhythmias often occur suddenly. In nonlinear systems, sudden changes in qualitative dynamics can, counterintuitively, result from a gradual change in a system parameter-this is known as a bifurcation. Here, we review how nonlinearities in cardiac electrophysiology influence normal and abnormal rhythms and how bifurcations change the dynamics. In particular, we focus on the many recent developments in computational modeling at the cellular level that are focused on intracellular calcium dynamics. We discuss two areas where recent experimental and modeling work has suggested the importance of nonlinearities in calcium dynamics: repolarization alternans and pacemaker cell automaticity.

A class of Monte-Carlo-based statistical algorithms for efficient detection of repolarization alternans

Cardiac repolarization alternans is an electrophysiologic condition identified by a beat-to-beat fluctuation in action potential waveform. It has been mechanistically linked to instances of T-wave alternans, a clinically defined ECG alternation in T-wave morphology, and associated with the onset of cardiac reentry and sudden cardiac death. Many alternans detection algorithms have been proposed in the past, but the majority have been designed specifically for use with T-wave alternans. Action potential duration (APD) signals obtained from experiments (especially those derived from optical mapping) possess unique characteristics, which requires the development and use of a more appropriate alternans detection method. In this paper, we present a new class of algorithms, based on the Monte Carlo method, for the detection and quantitative measurement of alternans. Specifically, we derive a set of algorithms (one an analytical and more efficient version of the other) and compare its performance with the standard spectral method and the generalized likelihood ratio test algorithm using synthetic APD sequences and optical mapping data obtained from an alternans control experiment. We demonstrate the benefits of the new algorithm in the presence of Gaussian and Laplacian noise and frame-shift errors. The proposed algorithms are well suited for experimental applications, and furthermore, have low complexity and are implementable using fixed-point arithmetic, enabling potential use with implantable cardiac devices.

Model-based control of cardiac alternans in Purkinje fibers

This paper describes a systematic approach to suppressing cardiac alternans in simulated Purkinje fibers using localized current injections. We investigate the controllability and observability of the periodically paced Noble model for different locations of the recording and control electrodes. In particular, we show that the loss of controllability causes the failure of the control approach introduced by Echebarria and Karma [Chaos 12, 923 (2002)] for longer fiber lengths. Furthermore, we explain how the optimal locations for the recording and control electrodes and the timing of the feedback current can be selected, accounting for both linear and nonlinear effects, effectively doubling the length of fibers that can be controlled with previous methods.

Real-time experiment interface for biological control applications

The Real-time Experiment Interface (RTXI) is a fast and versatile real-time biological experimentation system based on Real-Time Linux. RTXI is open source and free, can be used with an extensive range of experimentation hardware, and can be run on Linux or Windows computers (when using the Live CD). RTXI is currently used extensively for two experiment types: dynamic patch clamp and closed-loop stimulation pattern control in neural and cardiac single cell electrophysiology. RTXI includes standard plug-ins for implementing commonly used electrophysiology protocols with synchronized stimulation, event detection, and online analysis. These and other user-contributed plug-ins can be found on the website (http://www.rtxi.org).

T-wave alternans and arrhythmogenesis in cardiac diseases

T-wave alternans, a manifestation of repolarization alternans at the cellular level, is associated with lethal cardiac arrhythmias and sudden cardiac death. At the cellular level, several mechanisms can produce repolarization alternans, including: (1) electrical restitution resulting from collective ion channel recovery, which usually occurs at fast heart rates but can also occur at normal heart rates when action potential is prolonged resulting in a short diastolic interval; (2) the transient outward current, which tends to occur at normal or slow heart rates; (3) the dynamics of early after depolarizations, which tends to occur during bradycardia; and (4) intracellular calcium cycling alternans through its interaction with membrane voltage. In this review, we summarize the cellular mechanisms of alternans arising from these different mechanisms, and discuss their roles in arrhythmogenesis in the setting of cardiac disease.

Control of action potential duration alternans in canine ventricular tissue

Cardiac action potential duration alternans is characterized by a beat-to-beat alternation in action potential waveform. Its presence has been putatively linked to the onset of lethal cardiac arrhythmias. Previous studies, which have been limited to cardiac Purkinje fibers, have shown that closed-loop alternans control techniques, which apply a succession of externally administered cycle perturbations, provide ineffectual spatial alternans elimination. A more complete understanding of alternans control in the more clinically relevant ventricular tissue is needed. Here, we study the spatial dynamics of alternans and alternans control in arterially perfused canine right ventricular preparations using optical mapping. We quantified the spatial efficacy of alternans control across 2.5 cm of tissue, focusing primarily on differences in spatial control within several sub-regions of tissue. Our results provide a basis for future investigations into multi-electrode-based control interventions of alternans in cardiac tissue.

Anomalous drift of spiral waves in heterogeneous excitable media

We study the drift of spiral waves in a simple model of heterogeneous excitable medium, having gradients in the distribution of ion-channel expression or cellular coupling. We report the anomalous drift of spiral waves toward regions having shorter period or stronger coupling, in reaction-diffusion models of excitable media. Such anomalous drift can promote the onset of complex spatiotemporal patterns, e.g., those responsible for life-threatening arrhythmias in the heart.

Control of action potential duration alternans in canine cardiac ventricular tissue

Cardiac electrical alternans, characterized by a beat-to-beat alternation in action potential waveform, is a naturally occurring phenomenon, which can occur at sufficiently fast pacing rates. Its presence has been putatively linked to the onset of cardiac reentry, which is a precursor to ventricular fibrillation. Previous studies have shown that closed-loop alternans control techniques that apply a succession of externally administered cycle perturbations at a single site provide limited spatially-extended alternans elimination in sufficiently large cardiac substrates. However, detailed experimental investigations into the spatial dynamics of alternans control have been restricted to Purkinje fiber studies. A complete understanding of alternans control in the more clinically relevant ventricular tissue is needed. In this paper, we study the spatial dynamics of alternans and alternans control in arterially perfused canine right ventricular preparations using an optical mapping system capable of high-resolution fluorescence imaging. Specifically, we quantify the spatial efficacy of alternans control along 2.5 cm of tissue, focusing on differences in spatial control between different subregions of tissue. We demonstrate effective control of spatially-extended alternans up to 2.0 cm, with control efficacy attenuating as a function of distance. Our results provide a basis for future investigations into electrode-based control interventions of alternans in cardiac tissue.

Feedback-control induced pattern formation in cardiac myocytes: a mathematical modeling study

Cardiac alternans is a dangerous rhythm disturbance of the heart, in which rapid stimulation elicits a beat-to-beat alternation in the action potential duration (APD) and calcium (Ca) transient amplitude of individual myocytes. Recently, "subcellular alternans", in which the Ca transients of adjacent regions within individual myocytes alternate out-of-phase, has been observed. A previous theoretical study suggested that subcellular alternans may result during static pacing from a Turing-type symmetry breaking instability, but this was only predicted in a subset of cardiac myocytes (with negative Ca to voltage (Ca-->V(m)) coupling) and has never been directly verified experimentally. A recent experimental study, however, showed that subcellular alternans is dynamically induced in the remaining subset of myocytes during pacing with a simple feedback control algorithm ("alternans control"). Here we show that alternans control pacing changes the effective coupling between the APD and the Ca transient (V(m)-->Ca coupling), such that subcellular alternans is predicted to occur by a Turing instability in cells with positive Ca-->V(m) coupling. In addition to strengthening the understanding of the proposed mechanism for subcellular alternans formation, this work (in concert with previous theoretical and experimental results) illuminates subcellular alternans as a striking example of a biological Turing instability in which the diffusing morphogens can be clearly identified.

Applications of control theory to the dynamics and propagation of cardiac action potentials

Sudden cardiac arrest is a widespread cause of death in the industrialized world. Most cases of sudden cardiac arrest are due to ventricular fibrillation (VF), a lethal cardiac arrhythmia. Electrophysiological abnormalities such as alternans (a beat-to-beat alternation in action potential duration) and conduction block have been suspected to contribute to the onset of VF. This study focuses on the use of control-systems techniques to analyze and design methods for suppressing these precursor factors. Control-systems tools, specifically controllability analysis and Lyapunov stability methods, were applied to a two-variable Karma model of the action-potential (AP) dynamics of a single cell, to analyze the effectiveness of strategies for suppressing AP abnormalities. State-feedback-integral (SFI) control was then applied to a Purkinje fiber simulated with the Karma model, where only one stimulating electrode was used to affect the system. SFI control converted both discordant alternans and 2:1 conduction block back toward more normal patterns, over a wider range of fiber lengths and pacing intervals compared with a Pyragas-type chaos controller. The advantages conferred by using feedback from multiple locations in the fiber, and using integral (i.e., memory) terms in the controller, are discussed.

Off-site control of repolarization alternans in cardiac fibers

Repolarization alternans, a beat-to-beat alternation in action potential duration, has been putatively linked to the onset of cardiac reentry. Anti-alternans control strategies can eliminate alternans in individual cells by exploiting the rate dependence of action potential duration. The same approach, when applied to a common measuring/stimulating site at one end of a cardiac fiber, has been shown to have limited spatial efficacy. As a first step toward spatially distributed electrode control systems, we investigated "off-site" control in canine Purkinje fibers, in which the recording and control sites are different. We found experimentally that alternans can be eliminated at, or very near, the recording site, and that varying the location of the recording site along the fiber causes the node (the location with no alternans) to move along the fiber in close proximity to the recording site. Theoretical predictions based on an amplitude equation [B. Echebarria and A. Karma, Chaos 12, 923 (2002)] show that those findings follow directly from the wave nature of alternans: the most unstable mode of alternans along the fiber is a wave solution of a one-dimensional Helmholtz equation with a node position that only deviates slightly from the recording site by an amount dependent on electrotonic coupling. Computer simulations using a Purkinje fiber model confirm these theoretical and experimental results. Although off-site alternans control does not suppress alternans along the entire fiber, our results indicate that placing the node away from the stimulus site reduces alternans amplitude along the fiber, and may therefore have implications for antiarrhythmic strategies based on alternans termination.

Optimal velocity and safety of discontinuous conduction through the heterogeneous Purkinje-ventricular junction

Slow and discontinuous wave conduction through nonuniform junctions in cardiac tissues is generally considered unsafe and proarrythmogenic. However, the relationships between tissue structure, wave conduction velocity, and safety at such junctions are unknown. We have developed a structurally and electrophysiologically detailed model of the canine Purkinje-ventricular junction (PVJ) and varied its heterogeneity parameters to determine such relationships. We show that neither very fast nor very slow conduction is safe, and there exists an optimal velocity that provides the maximum safety factor for conduction through the junction. The resultant conduction time delay across the PVJ is a natural consequence of the electrophysiological and morphological differences between the Purkinje fiber and ventricular tissue. The delay allows the PVJ to accumulate and pass sufficient charge to excite the adjacent ventricular tissue, but is not long enough for the source-to-load mismatch at the junction to be enhanced over time. The observed relationships between the conduction velocity and safety factor can provide new insights into optimal conditions for wave propagation through nonuniform junctions between various cardiac tissues.

Model-based control of cardiac alternans on a ring

Cardiac alternans, a beat-to-beat alternation of cardiac electrical dynamics, and ventricular tachycardia, generally associated with a spiral wave of electrical activity, have been identified as frequent precursors of the life-threatening spatiotemporally chaotic electrical state of ventricular fibrillation (VF). Schemes for the elimination of alternans and the stabilization of spiral waves through the injection of weak external currents have been proposed as methods to prevent VF but have not performed at the level required for clinical implementation. In this paper we propose a control method based on linear-quadratic regulator (LQR) control. Unlike most previously proposed approaches, our method incorporates information from the underlying model to increase efficiency. We use a one-dimensional ringlike geometry, with a single control electrode, to compare the performance of our method with that of two other approaches, quasi-instantaneous suppression of unstable modes (QISUM) and time-delay autosynchronization (TDAS). We find that QISUM fails to suppress alternans due to conduction block. Although both TDAS and LQR succeed in suppressing alternans, LQR is able to suppress the alternans faster and using a much weaker control current. Our results highlight the benefits of a model-based control approach despite its inherent complexity compared with nonmodel-based control such as TDAS.

Dynamical mechanism for subcellular alternans in cardiac myocytes

RATIONALE

Cardiac repolarization alternans is an arrhythmogenic rhythm disturbance, manifested in individual myocytes as a beat-to-beat alternation of action potential durations and intracellular calcium transient magnitudes. Recent experimental studies have reported "subcellular alternans," in which distinct regions of an individual cell are seen to have counterphase calcium alternations, but the mechanism by which this occurs is not well understood. Although previous theoretical work has proposed a possible dynamical mechanism for subcellular alternans formation, no direct evidence for this mechanism has been reported in vitro. Rather, experimental studies have generally invoked fixed subcellular heterogeneities in calcium-cycling characteristics as the mechanism of subcellular alternans formation.

OBJECTIVE

In this study, we have generalized the previously proposed dynamical mechanism to predict a simple pacing algorithm by which subcellular alternans can be induced in isolated cardiac myocytes in the presence or absence of fixed subcellular heterogeneity. We aimed to verify this hypothesis using computational modeling and to confirm it experimentally in isolated cardiac myocytes. Furthermore, we hypothesized that this dynamical mechanism may account for previous reports of subcellular alternans seen in statically paced, intact tissue.

METHODS AND RESULTS

Using a physiologically realistic computational model of a cardiac myocyte, we show that our predicted pacing algorithm induces subcellular alternans in a manner consistent with theoretical predictions. We then use a combination of real-time electrophysiology and fluorescent calcium imaging to implement this protocol experimentally and show that it robustly induces subcellular alternans in isolated guinea pig ventricular myocytes. Finally, we use computational modeling to demonstrate that subcellular alternans can indeed be dynamically induced during static pacing of 1D fibers of myocytes during tissue-level spatially discordant alternans.

CONCLUSION

Here we provide the first direct experimental evidence that subcellular alternans can be dynamically induced in cardiac myocytes. This proposed mechanism may contribute to subcellular alternans formation in the intact heart.

Studies on Feedback Control of Cardiac Alternans

A beat-to-beat variation in the electric wave propagation morphology in myocardium is referred to as cardiac alternans and it has been linked to the onset of life threatening arrhythmias and sudden cardiac death. Experimental studies have demonstrated that alternans can be annihilated by the feedback modulation of the basic pacing interval in a small piece of cardiac tissue. In this work, we study the capability of feedback control to suppress alternans both spatially and temporally in an extracted rabbit heart and in a cable of cardiac cells. This work demonstrates real-time control of cardiac alternans in an extracted rabbit heart and provides an analysis of the control methodology applied in the case of a one-dimensional (1D) cable of cardiac cells. The real-time system control is realized through feedback by proportional perturbation of the basic pacing cycle length (PCL). The measurements of the electric wave propagation are obtained by optical mapping of fluorescent dye from the surface of the heart and are fed into a custom-designed software that provides the control action signal that perturbs the basic pacing cycle length. In addition, a novel pacing protocol that avoids conduction block is applied. A numerical analysis, complementary to the experimental study is also carried out, by the ionic model of a 1D cable of cardiac cells under a self-referencing feedback protocol, which is identical to the one applied in the experimental study. Further, the amplitude of alternans linear parabolic PDE that is associated with the 1D ionic cardiac cell cable model under full state feedback control is analyzed. We provide an analysis of the amplitude of alternans parabolic PDE which admits a standard evolutionary form in a well defined functional space. Standard modal decomposition techniques are used in the analysis and the controller synthesis is carried out through pole-placement. State and output feedback controller realizations are developed and the important issue of measurement noise in the controller implementation is addressed. The analysis of stabilization of the amplitude of alternans PDE is in agreement with the experimental results and numerical results produced by the ionic 1D cable of cardiac cells model. Finally, a discussion is provided in light of these results in order to use control to suppress alternans in the human myocardium.

Amplitude equation approach to spatiotemporal dynamics of cardiac alternans

Amplitude equations are derived that describe the spatiotemporal dynamics of cardiac alternans during periodic pacing of one- [B. Echebarria and A. Karma, Phys. Rev. Lett. 88, 208101 (2002)] and two-dimensional homogeneous tissue and one-dimensional anatomical reentry in a ring of homogeneous tissue. These equations provide a simple physical understanding of arrhythmogenic patterns of period-doubling oscillations of action potential duration with a spatially varying phase and amplitude, as well as explicit quantitative predictions that can be compared to ionic model simulations or experiments. The form of the equations is expected to be valid for a large class of ionic models but the coefficients are derived analytically only for a two-variable ionic model and calculated numerically for the original Noble model of Purkinje fiber action potential. In paced tissue, this theory explains the formation of "spatially discordant alternans" by a linear instability mechanism that produces a periodic pattern of out-of-phase domains of alternans. The wavelength of this pattern, equal to twice the spacing between nodes separating out-of-phase domains, is shown to depend on three fundamental length scales that are determined by the strength of cell-to-cell coupling and conduction velocity (CV) restitution. Moreover, the patterns of alternans can be either stationary, with fixed nodes, or traveling, with moving nodes and hence quasiperiodic oscillations of action potential duration, depending on the relative strength of the destabilizing effect of CV restitution and the stabilizing effect of diffusive coupling. For the ring geometry, we recover the results of Courtemanche, Glass, and Keener [Phys. Rev. Lett. 70, 2182 (1993)] with two important modifications due to cell-to-cell diffusive coupling. First, this coupling breaks the degeneracy of an infinite-dimensional Hopf bifurcation such that the most unstable mode of alternans corresponds to the longest quantized wavelength of the ring. Second, the Hopf frequency, which determines the velocity of the node along the ring, depends both on the steepness of CV restitution and the strength of this coupling, with the net result that quasiperiodic behavior can arise with a constant conduction velocity. In both the paced geometries and the ring, the onset of alternans is different in tissue than for a paced isolated cell. The implications of these results for alternans dynamics during two-dimensional reentry are briefly discussed.

Control of electrical alternans in simulations of paced myocardium using extended time-delay autosynchronization

Experimental studies have linked alternans, an abnormal beat-to-beat alternation of cardiac action potential duration, to the genesis of lethal arrhythmias such as ventricular fibrillation. Prior studies have considered various closed-loop feedback control algorithms for perturbing interstimulus intervals in such a way that alternans is suppressed. However, some experimental cases are restricted in that the controller's stimuli must preempt those of the existing waves that are propagating in the tissue, and therefore only shortening perturbations to the underlying pacing are allowed. We present results demonstrating that a technique known as extended time-delay autosynchronization (ETDAS) can effectively control alternans locally while operating within the above constraints. We show that ETDAS, which has already been used to control chaos in physical systems, has numerous advantages over previously proposed alternans control schemes.

Optical mapping system with real-time control capability

Real-time, closed-loop intervention is an emerging experiment-control method that promises to provide invaluable new insight into cardiac electrophysiology. One example is the investigation of closed-loop feedback control of cardiac activity (e.g., alternans) as a possible method of preventing arrhythmia onset. To date, such methods have been investigated only in vitro using microelectrode systems, which are hindered by poor spatial resolution and are not well suited for atrial or ventricular tissue preparations. We have developed a system that uses optical mapping techniques and an electrical stimulator as the sensory and effector arms, respectively, of a closed-loop, real-time control system. The system consists of a 2,048 x 1 pixel line-scan charge-coupled device camera that records optical signals from the tissue. Custom-image processing and control software, which is implemented on top of a hard real-time operation system (RTAI Linux), process the data and make control decisions with a deterministic delay of <1 ms. The system is tested in two ways: 1) it is used to control, in real time, simulated optical signals of electrical alternans; and 2) it uses precisely timed, feedback-controlled initiation of antitachycardia pacing to terminate reentrant arrhythmias in an arterially perfused swine right ventricle stained with voltage-sensitive fluorescent dye 4{beta-[2-(di-n-butylamino)-6-napathy]vinyl}pyridinium (di-4-ANEPPS). Thus real-time control of cardiac activity using optical mapping techniques is feasible. Such a system is attractive because it offers greater measurement resolution than the electrode-based systems with which real-time control has been used previously.

Characterizing the contribution of voltage- and calcium-dependent coupling to action potential stability: implications for repolarization alternans

Experiments have provided suggestive but inconclusive insights into the relative contributions of transmembrane voltage and intracellular calcium handling to the development of cardiac electrical instabilities such as repolarization alternans. In this study, we applied a novel combination of techniques (action potential voltage clamping, calcium-transient clamping, and stability analysis) to cardiac cell models to more clearly determine the roles that voltage- and calcium-dependent coupling play in regulating action potential stability and the development of alternans subsequent to the loss of stability. Using these techniques, we are able to demonstrate that voltage- and calcium-dependent coupling exhibit varying degrees of influence on action potential stability across models. Our results indicate that cellular dynamic instabilities such as alternans may be initiated by either voltage- or calcium-dependent mechanisms or by some combination of the two. Based on these modeling results, we propose novel single-cell experiments that incorporate action-potential voltage clamping, calcium imaging, and real-time measurement of action potential stability. These experiments will make it possible to experimentally determine the relative contribution of voltage coupling to the regulation of action potential stability in real cardiac myocytes, thereby providing further insights into the mechanism of alternans.

A model for multi-site pacing of fibrillation using nonlinear dynamics feedback

Traditionally, cardiac defibrillation requires a strong electric shock. Many unwanted side effects of this shock could be eliminated if defibrillation were performed using weak stimuli applied to several locations throughout the heart. Such multi-site pacing algorithms have been shown to defibrillate both experimentally (Pak et al., Am J Physiol 285:H2704-H2711, 2003) and theoretically (Puwal and Roth, J Biol Systems 14:101-112, 2006). Gauthier et al. (Chaos, 12:952-961, 2002) proposed a method to pace the heart using an algorithm based on nonlinear dynamics feedback applied through a single electrode. Our study applies a related but simpler algorithm, which essentially configures each electrode as a demand pacemaker, to simulate the multi-site pacing of fibrillating cardiac tissue. We use the numerical model developed by Fenton et al. (Chaos, 12:852-892, 2002) as the reaction term in a reaction-diffusion equation that we solve over a two-dimensional sheet of tissue. The defibrillation rate after pacing for 3 s is about 30%, which is significantly higher than the spontaneous defibrillation rate and is higher than observed in previous experimental and theoretical studies. Tuning the algorithm period can increase this rate to 45%.