Biphasic restitution of action potential duration and complex dynamics in ventricular myocardium

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.

Biphasic action potential and chaos in a symmetrical Chua Corsage Memristor-based circuit

Neuromorphic computing provides unique computing and memory capabilities that could break the limitation of conventional von Neumann computing. Toward realizing neuromorphic computing, fabrication and synthetization of hardware elements and circuits to emulate biological neurons are crucial. Despite the striking progress in exploring neuron circuits, the existing circuits can only reproduce monophasic action potentials, and no studies report on circuits that could emulate biphasic action potentials, limiting the development of neuromorphic devices. Here, we present a simple third-order memristive circuit built with a classical symmetrical Chua Corsage Memristor (SCCM) to accurately emulate biological neurons and show that the circuit can reproduce monophasic action potentials, biphasic action potentials, and chaos. Applying the edge of chaos criterion, we calculate that the SCCM and the proposed circuit have the symmetrical edge of chaos domains with respect to the origin, which plays an important role in generating biphasic action potentials. Also, we draw a parameter classification map of the proposed circuit, showing the edge of chaos domain (EOCD), the locally active domain, and the locally passive domain. Near the calculated EOCD, the third-order circuit generates monophasic action potentials, biphasic action potentials, chaos, and ten types of symmetrical bi-directional neuromorphic phenomena by only tuning the input voltage, showing a resemblance to biological neurons. Finally, a physical SCCM circuit and some experimentally measured neuromorphic waveforms are exhibited. The experimental results agree with the numerical simulations, verifying that the proposed circuit is suitable as artificial neurons.

Thermal effects on cardiac alternans onset and development: A spatiotemporal correlation analysis

Alternans of cardiac action potential duration represent critical precursors for the development of life-threatening arrhythmias and sudden cardiac death. The system's thermal state affects these electrical disorders requiring additional theoretical and experimental efforts to improve a patient-specific clinical understanding. In such a scenario, we generalize a recent work from Loppini et al. [Phys. Rev. E 100, 020201(R) (2019)PREHBM2470-004510.1103/PhysRevE.100.020201] by performing an extended spatiotemporal correlation study. We consider high-resolution optical mapping recordings of canine ventricular wedges' electrical activity at different temperatures and pacing frequencies. We aim to recommend the extracted characteristic length as a potential predictive index of cardiac alternans onset and evolution within a wide range of system states. In particular, we show that a reduction of temperature results in a drop of the characteristic length, confirming the impact of thermal instabilities on cardiac dynamics. Moreover, we theoretically investigate the use of such an index to identify and predict different alternans regimes. Finally, we propose a constitutive phenomenological law linking conduction velocity, characteristic length, and temperature in view of future numerical investigations.

Global vs local control of cardiac alternans in a 1D numerical model of human ventricular tissue

Cardiac alternans is a proarrhythmic state in which the action potential duration (APD) of cardiac myocytes alternate between long and short values and often occurs under conditions of rapid pacing of cardiac tissue. In the ventricles, alternans is especially dangerous due to the life-threatening risk of developing arrhythmias, such as ventricular fibrillation. Alternans can be formed in periodically paced tissue as a result of pacing itself. Recently, it has been demonstrated that this pacing-induced alternans can be prevented by performing constant diastolic interval (DI) pacing, in which DI is independent of APD. However, constant DI pacing is difficult to implement in experimental settings since it requires the real-time measurement of APD. A more practical way was proposed based on electrocardiograms (ECGs), which give an indirect measure of the global DI relaxation period through the TR interval assessment. Previously, we demonstrated that constant TR pacing prevented alternans formation in isolated Langendorff-perfused rabbit hearts. However, the efficacy of "local" constant DI pacing vs "global" constant TR pacing in preventing alternans formation has never been investigated. Thus, the purpose of this study was to implement an ECG-based constant TR pacing in a 1D numerical model of human ventricular tissue and to compare the dynamical behavior of cardiac tissue with that resulted from a constant DI pacing. The results showed that both constant TR and constant DI pacing prevented the onset of alternans until lower basic cycle length when compared to periodic pacing. For longer cable lengths, constant TR pacing was shown to exhibit greater control on alternans than constant DI pacing.

Discordant Alternans as a Mechanism for Initiation of Ventricular Fibrillation In Vitro

Background Ventricular tachyarrhythmias are often preceded by short sequences of premature ventricular complexes. In a previous study, a restitution-based computational model predicted which sequences of stimulated premature complexes were most likely to induce ventricular fibrillation in canines in vivo. However, the underlying mechanism, based on discordant-alternans dynamics, could not be verified in that study. The current study seeks to elucidate the mechanism by determining whether the spatiotemporal evolution of action potentials and initiation of ventricular fibrillation in in vitro experiments are consistent with model predictions. Methods and Results Optical mapping voltage signals from canine right-ventricular tissue (n=9) were obtained simultaneously from the entire epicardium and endocardium during and after premature stimulus sequences. Model predictions of action potential propagation along a 1-dimensional cable were developed using action potential duration versus diastolic interval data. The model predicted sign-change patterns in action potential duration and diastolic interval spatial gradients with posterior probabilities of 91.1%, and 82.1%, respectively. The model predicted conduction block with 64% sensitivity and 100% specificity. A generalized estimating equation logistic-regression approach showed that model-prediction effects were significant for both conduction block ( P<1×10-15, coefficient 44.36) and sustained ventricular fibrillation ( P=0.0046, coefficient, 1.63) events. Conclusions The observed sign-change patterns favored discordant alternans, and the model successfully identified sequences of premature stimuli that induced conduction block. This suggests that the relatively simple discordant-alternans-based process that led to block in the model may often be responsible for ventricular fibrillation onset when preceded by premature beats. These observations may aid in developing improved methods for anticipating block and ventricular fibrillation.

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.

Mechanisms linking T-wave alternans to spontaneous initiation of ventricular arrhythmias in rabbit models of long QT syndrome

KEY POINTS

T-wave alternans (TWA) and T-wave lability (TWL) are precursors of ventricular arrhythmias in long QT syndrome; however, the mechanistic link remains to be clarified. Computer simulations show that action potential duration (APD) prolongation and slowed heart rates promote APD alternans and chaos, manifesting as TWA and TWL, respectively. Regional APD alternans and chaos can exacerbate pre-existing or induce de novo APD dispersion, which combines with enhanced I_Ca,L to result in premature ventricular complexes (PVCs) originating from the APD gradient region. These PVCs can directly degenerate into re-entrant arrhythmias without the need for an additional tissue substrate or further exacerbate the APD dispersion to cause spontaneous initiation of ventricular arrhythmias. Experiments conducted in transgenic long QT rabbits show that PVC alternans occurs at slow heart rates, preceding spontaneous intuition of ventricular arrhythmias.

ABSTRACT

T-wave alternans (TWA) and irregular beat-to-beat T-wave variability or T-wave lability (TWL), the ECG manifestations of action potential duration (APD) alternans and variability, are precursors of ventricular arrhythmias in long QT syndromes. TWA and TWL in patients tend to occur at normal heart rates and are usually potentiated by bradycardia. Whether or how TWA and TWL at normal or slow heart rates are causally linked to arrhythmogenesis remains unknown. In the present study, we used computer simulations and experiments of a transgenic rabbit model of long QT syndrome to investigate the underlying mechanisms. Computer simulations showed that APD prolongation and slowed heart rates caused early afterdepolarization-mediated APD alternans and chaos, manifesting as TWA and TWL, respectively. Regional APD alternans and chaos exacerbated pre-existing APD dispersion and, in addition, APD chaos could also induce APD dispersion de novo via chaos desynchronization. Increased APD dispersion, combined with substantially enhanced I_Ca,L , resulted in a tissue-scale dynamical instability that gave rise to the spontaneous occurrence of unidirectionally propagating premature ventricular complexes (PVCs) originating from the APD gradient region. These PVCs could directly degenerate into re-entrant arrhythmias without the need for an additional tissue substrate or could block the following sinus beat to result in a longer RR interval, which further exacerbated the APD dispersion giving rise to the spontaneous occurrence of ventricular arrhythmias. Slow heart rate-induced PVC alternans was observed in experiments of transgenic LQT2 rabbits under isoproterenol, which was associated with increased APD dispersion and spontaneous occurrence of ventricular arrhythmias, in agreement with the theoretical predictions.

Real-Time Closed Loop Diastolic Interval Control Prevents Cardiac Alternans in Isolated Whole Rabbit Hearts

Cardiac alternans, a beat-to-beat alternation in action potential duration (APD), can lead to fatal arrhythmias. During periodic pacing, changes in diastolic interval (DI) depend on subsequent changes in APD, thus enhancing cardiac instabilities through a 'feedback' mechanism. Recently, an anti-arrhythmic Constant DI pacing protocol was proposed and shown to be effective in suppressing alternans in 0D and 1D in silico studies. However, previous experimental validation of Constant DI pacing in the heart has been unsuccessful due to the spatio-temporal complexity of 2D cardiac tissue and the technical challenges in its real-time implementation. Here, we developed a novel closed loop system to detect T-waves from real-time ECG data, enabling successful implementation of Constant DI pacing protocol, and performed high-resolution optical mapping experiments on isolated whole rabbit hearts to validate its anti-arrhythmic effects. The results were compared with: (1) Periodic pacing (feedback inherent) and (2) pacing with heart rate variability (HRV) (feedback modulation) introduced by using either Gaussian or Physiological patterns. We observed that Constant DI pacing significantly suppressed alternans in the heart, while maintaining APD spatial dispersion and flattening the slope of the APD restitution curve, compared to traditional Periodic pacing. In addition, introduction of HRV in Periodic pacing failed to prevent cardiac alternans, and was arrhythmogenic.

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.

Pro-arrhythmic effect of heart rate variability during periodic pacing

Clinically, healthy hearts have been associated with a high ventricular heart rate variability (HRV) while diseased hearts have been known to exhibit low ventricular HRV. Hence, low HRV is suggested to be a marker of cardiac ventricular arrhythmias. Over the past few years, there has been considerable amount of interest in incorporating HRV in pacing to emulate healthy heart conditions and re-stabilize the electrical activity in diseased hearts. Recently, we used single cell numerical simulations to demonstrate that HRV incorporated into periodic pacing promotes alternans formation and thus, can be pro-arrhythmic. Here, we performed high-resolution optical mapping experiments on Langendorff perfused, healthy whole mice hearts to validate our numerical findings. Our results indeed demonstrate that HRV promoted the onset of cardiac alternans, which is believed to be a precursor of fatal cardiac rhythms. Hence, our present study suggests that incorporating HRV into periodic pacing while addressing several clinical needs may not be safe. There is a pressing need to better understand paced cardiac dynamics and develop anti-arrhythmic pacing techniques that would prevent cardiac arrhythmias.

Dynamics and Molecular Mechanisms of Ventricular Fibrillation in Structurally Normal Hearts

Ventricular fibrillation (VF) is the most severe cardiac rhythm disturbance and one of the most important immediate causes of sudden cardiac death. In the structurally normal heart, a small number of stable reentrant sources, perhaps 1 or 2, underlie the mechanism of VF, and the stabilization of the sources, their frequency, and the complexity of the turbulent waves they generate depend on the expression, spatial distribution, and intermolecular interactions of the 2 most important ion channels that control cardiac excitability: the inward rectifier potassium channel, Kir2.1, and the alpha subunit of the main cardiac sodium channel, NaV1.5.

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.

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.

How does β-adrenergic signalling affect the transitions from ventricular tachycardia to ventricular fibrillation?

AIMS

Ventricular tachycardia (VT) and fibrillation (VF) are the most lethal cardiac arrhythmias. The degeneration of VT into VF is associated with the breakup of a spiral wave of the action potential in cardiac tissue. β-Adrenergic (βAR) signalling potentiates the L-type Ca current (ICaL) faster than the slow delayed rectifier potassium current (IKs), which transiently prolongs the action potential duration (APD) and promotes early after depolarizations. In this study, we aimed at investigating how βAR signalling affects the transition from VT to VF.

METHODS AND RESULTS

We used a physiologically detailed computer model of the rabbit ventricular myocyte in a two-dimensional tissue to determine how spiral waves respond to βAR activation following administration of isoproterenol. A simplified mathematical model was also used to investigate the underlying dynamics. We found that the spatiotemporal behaviour of spiral waves strongly depends on the kinetics of βAR activation. When βAR activation is rapid, a stable spiral wave turns into small fragments and its electrocardiogram reveals the transition from VT to VF. This is due to the transiently steepened APD restitution induced by the faster activation of ICaL vs. IKs upon sudden βAR activation. The spiral wave may also disappear if its transient wavelength is too large to be supported by the tissue size upon sudden strong βAR activation that prolongs APD transiently. When βAR activation is gradual, a stable spiral wave remains such, because of more limited increase in both APD and slope of APD restitution due to more contemporaneous ICaL and IKs activation.

CONCLUSION

Changes in APD restitution during βAR activation revealed a novel transient spiral wave dynamics; this spatiotemporal characteristic strongly depends on the protocol of isoproterenol application.

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.

Stochastic cardiac pacing increases ventricular electrical stability--a computational study

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

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.

Role of temperature on nonlinear cardiac dynamics

Thermal effects affecting spatiotemporal behavior of cardiac tissue are discussed by relating temperature variations to proarrhythmic dynamics in the heart. By introducing a thermoelectric coupling in a minimal model of cardiac tissue, we are able to reproduce experimentally measured dynamics obtained simultaneously from epicardial and endocardial canine right ventricles at different temperatures. A quantitative description of emergent proarrhythmic properties of restitution, conduction velocity, and alternans regimes as a function of temperature is presented. Complex discordant alternans patterns that enhance tissue dispersion consisting of one wave front and three wave backs are described in both simulations and experiments. Possible implications for model generalization are finally discussed.

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.

Heart rate variability effect on the myocyte action potential duration restitution: insights from switched systems theory

The physiological heart rate presents a stochastic behavior known as heart rate variability (HRV). In this framework the influence of HRV on the action potential duration (APD) of the atrial myocyte is analyzed in a computer model. We have found that introducing HRV into the myocyte action potential model decreases the APD of the extra beat S2 in an S1-S2 protocol compared to constant heart rate. A possible theoretical explanation for this is also presented and is derived from switched systems theory. It is suggested to consider the myocyte action potential phase 4 and phase 2 as two operation modes of a switching system and analyze the stability of switching between them. Since random switching is known to have a stabilization effect on a switching system, this might explain why HRV has a stabilization effect on the myocyte APD restitution. Implications of this finding include reduced system stability for conditions with low HRV. A possible application for this phenomenon regards artificial pacemakers, where a preset added HRV is predicted to reduce susceptibility to arrhythmias.

MEMORY AND BISTABILITY IN A ONE-DIMENSIONAL LOOP OF MODEL CARDIAC CELLS

Unidirectional propagation has been studied in a one-dimensional loop of model cardiac cells represented as a homogeneous and isotropic cable. Membrane ionic currents were represented by a modified Beeler-Reuter model. The time constants of the gate variables of the slow inward current acting during the plateau of the action potential were divided by a parameter K ≥1. In the space-clamped model, increasing K shortens the action potential duration, changes the shape of the restitution curve and adds a slow memory component to the dynamics. In a paced regime, it promotes bistability in which period-1 and period-2 patterns coexist over an interval of pacing frequencies. In the loop, bistability is created between periodic and aperiodic modes of sustained reentry for an interval of loop length. The bistability of the space-clamped and loop model are both related to the form of the restitution curve.

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.

Isoprenaline increases the slopes of restitution trajectory in the conscious rabbit with ischemic heart failure

Roughly speaking, restitution is the dependence of recovery time of cardiac electrical activity on heart rate. Increased restitution slope is theorized to be predictive of sudden death after heart injury such as from coronary artery occlusion (ischemia). Adrenaline analogs are known to increase restitution slope in normal hearts, but their effects in failing hearts are unknown. Twenty-six rabbits underwent coronary ligation (n = 15) or sham surgery (n = 11) and implantation of a lead in the heart for recording electrocardiograms. Eight weeks later, unanesthetized rabbits were given 0.25-2.0 ml of 1 μmol/L isoprenaline intravenously, which increased heart rate. Heart rate was quantified by time between QRS peaks (RR) and heart activity duration by R to T peak time (QTp). Ligated rabbits (n = 6) had lower ejection fraction than sham rabbits (n = 7, p < 0.0001) indicative of heart failure, but similar baseline RR (269 ± 15 vs 292 ± 23 ms, p = 0.07), QTp (104 ± 17 vs 91 ± 9 ms, p = 0.1), and isoprenaline-induced minimum RR (204 ± 11 vs 208 ± 6 ms, p = 0.4). The trajectory of QTp vs TQ plots displayed hysteresis and regions of negative slope. The slope of the positive slope region was >1 in ligated rabbits (1.27 ± 0.66) and <1 in sham rabbits (0.35 ± 0.14, p = 0.004). The absolute value of the negative slope was greater in ligated rabbits (- 0.81 ± 0.52 vs - 0.35 ± 0.14, p = 0.04). Isoprenaline increased heart rate and slopes of restitution trajectory in failing hearts. The dynamics of restitution trajectory may hold clues for sudden death in heart failure patients.

Simulation of the undiseased human cardiac ventricular action potential: model formulation and experimental validation

Cellular electrophysiology experiments, important for understanding cardiac arrhythmia mechanisms, are usually performed with channels expressed in non myocytes, or with non-human myocytes. Differences between cell types and species affect results. Thus, an accurate model for the undiseased human ventricular action potential (AP) which reproduces a broad range of physiological behaviors is needed. Such a model requires extensive experimental data, but essential elements have been unavailable. Here, we develop a human ventricular AP model using new undiseased human ventricular data: Ca(2+) versus voltage dependent inactivation of L-type Ca(2+) current (I(CaL)); kinetics for the transient outward, rapid delayed rectifier (I(Kr)), Na(+)/Ca(2+) exchange (I(NaCa)), and inward rectifier currents; AP recordings at all physiological cycle lengths; and rate dependence and restitution of AP duration (APD) with and without a variety of specific channel blockers. Simulated APs reproduced the experimental AP morphology, APD rate dependence, and restitution. Using undiseased human mRNA and protein data, models for different transmural cell types were developed. Experiments for rate dependence of Ca(2+) (including peak and decay) and intracellular sodium ([Na(+)](i)) in undiseased human myocytes were quantitatively reproduced by the model. Early afterdepolarizations were induced by I(Kr) block during slow pacing, and AP and Ca(2+) alternans appeared at rates >200 bpm, as observed in the nonfailing human ventricle. Ca(2+)/calmodulin-dependent protein kinase II (CaMK) modulated rate dependence of Ca(2+) cycling. I(NaCa) linked Ca(2+) alternation to AP alternans. CaMK suppression or SERCA upregulation eliminated alternans. Steady state APD rate dependence was caused primarily by changes in [Na(+)](i), via its modulation of the electrogenic Na(+)/K(+) ATPase current. At fast pacing rates, late Na(+) current and I(CaL) were also contributors. APD shortening during restitution was primarily dependent on reduced late Na(+) and I(CaL) currents due to inactivation at short diastolic intervals, with additional contribution from elevated I(Kr) due to incomplete deactivation.

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.

Chaos in the genesis and maintenance of cardiac arrhythmias

Dynamical chaos, an irregular behavior of deterministic systems, has been widely shown in nature. It also has been demonstrated in cardiac myocytes in many studies, including rapid pacing-induced irregular beat-to-beat action potential alterations and slow pacing-induced irregular early afterdepolarizations, etc. Here we review the roles of chaos in the genesis of cardiac arrhythmias, the transition to ventricular fibrillation, and the spontaneous termination of fibrillation, based on evidence from computer simulation of mathematical models and experiments of animal models.

Irregularly appearing early afterdepolarizations in cardiac myocytes: random fluctuations or dynamical chaos?

Irregularly occurring early afterdepolarizations (EADs) in cardiac myocytes are traditionally hypothesized to be caused by random ion channel fluctuations. In this study, we combined 1), patch-clamp experiments in which action potentials were recorded at different pacing cycle lengths from isolated rabbit ventricular myocytes under several experimental conditions inducing EADs, including oxidative stress with hydrogen peroxide, calcium overload with BayK8644, and ionic stress with hypokalemia; 2), computer simulations using a physiologically detailed rabbit ventricular action potential model, in which repolarization reserve was reduced to generate EADs and random ion channel or path cycle length fluctuations were implemented; and 3), iterated maps with or without noise. By comparing experimental, modeling, and bifurcation analyses, we present evidence that noise-induced transitions between bistable states (i.e., between an action potential with and without an EAD) is not sufficient to account for the large variation in action potential duration fluctuations observed in experimental studies. We conclude that the irregular dynamics of EADs is intrinsically chaotic, with random fluctuations playing a nonessential, auxiliary role potentiating the complex dynamics.

Abnormal restitution property of action potential duration and conduction delay in Brugada syndrome: both repolarization and depolarization abnormalities

AIMS

This study sought to examine the action potential duration restitution (APDR) property and conduction delay in Brugada syndrome (BrS) patients. A steeply sloped APDR curve and conduction delay are known to be important determinants for the occurrence of ventricular fibrillation (VF).

METHODS AND RESULTS

Endocardial monophasic action potential was obtained from 39 BrS patients and 9 control subjects using the contact electrode method. Maximum slopes of the APDR curve were obtained at both the right ventricular outflow tract (RVOT) and the right ventricular apex (RVA). The onset of activation delay (OAD) after premature stimulation was examined as a marker of conduction delay. Maximum slope of the APDR curve in BrS patients was significantly steeper than that in control subjects at both the RVOT and the RVA (0.77 +/- 0.21 vs. 058 +/- 0.14 at RVOT, P = 0.009; 0.98 +/- 0.23 vs. 0.62 +/- 0.16 at RVA, P = 0.001). The dispersion of maximum slope of the APDR curve between the RVOT and the RVA was also larger in BrS patients than in control subjects. The OAD was significantly longer in BrS patients than in control subjects from the RVOT to RVA and from the RVA to RVOT (from RVOT to RVA: 256 +/- 12 vs. 243 +/- 7 ms, P = 0.003; from RVA to RVOT: 252 +/- 11 vs. 241 +/- 9 ms, P = 0.01).

CONCLUSIONS

Abnormal APDR properties and conduction delay were observed in BrS patients. Both repolarization and depolarization abnormalities are thought to be related to the development of VF in BrS patients.

Synchronization of chaotic early afterdepolarizations in the genesis of cardiac arrhythmias

The synchronization of coupled oscillators plays an important role in many biological systems, including the heart. In heart diseases, cardiac myocytes can exhibit abnormal electrical oscillations, such as early afterdepolarizations (EADs), which are associated with lethal arrhythmias. A key unanswered question is how cellular EADs partially synchronize in tissue, as is required for them to propagate. Here, we present evidence, from computational simulations and experiments in isolated myocytes, that irregular EAD behavior is dynamical chaos. We then show in electrically homogeneous tissue models that chaotic EADs synchronize globally when the tissue is smaller than a critical size. However, when the tissue exceeds the critical size, electrotonic coupling can no longer globally synchronize EADs, resulting in regions of partial synchronization that shift in time and space. These regional partially synchronized EADs then form premature ventricular complexes that propagate into recovered tissue without EADs. This process creates multiple premature ventricular complexes that propagate as [corrected] "shifting" foci resembling polymorphic ventricular tachycardia. Shifting foci encountering shifting repolarization gradients can also develop localized wave breaks leading to reentry and fibrillation. As predicted by the theory, rabbit hearts exposed to oxidative stress (H(2)O(2)) exhibited multiple shifting foci causing polymorphic tachycardia and fibrillation. This mechanism explains how collective cellular behavior integrates at the tissue scale to generate lethal cardiac arrhythmias over a wide range of heart rates.

Coupled Iterated Map Models of Action Potential Dynamics in a One-dimensional Cable of Cardiac Cells

Low-dimensional iterated map models have been widely used to study action potential dynamics in isolated cardiac cells. Coupled iterated map models have also been widely used to investigate action potential propagation dynamics in one-dimensional (1D) coupled cardiac cells, however, these models are usually empirical and not carefully validated. In this study, we first developed two coupled iterated map models which are the standard forms of diffusively coupled maps and overcome the limitations of the previous models. We then determined the coupling strength and space constant by quantitatively comparing the 1D action potential duration profile from the coupled cardiac cell model described by differential equations with that of the coupled iterated map models. To further validate the coupled iterated map models, we compared the stability conditions of the spatially uniform state of the coupled iterated maps and those of the 1D ionic model and showed that the coupled iterated map model could well recapitulate the stability conditions, i.e., the spatially uniform state is stable unless the state is chaotic. Finally, we combined conduction into the developed coupled iterated map model to study the effects of coupling strength on wave stabilities and showed that the diffusive coupling between cardiac cells tends to suppress instabilities during reentry in a 1D ring and the onset of discordant alternans in a periodically paced 1D cable.

The link between repolarisation alternans and ventricular arrhythmia: does the cellular phenomenon extend to the clinical problem?

T-wave alternans is considered a potentially useful clinical marker for the risk of ventricular arrhythmia in patients with heart disease. Cellular repolarisation alternans is thought to underlie T-wave alternans, and moreover, to cause re-entrant ventricular arrhythmia. This review examines the experimental and clinical evidence linking repolarisation alternans and T-wave alternans with the occurrence of ventricular arrhythmia. Repolarisation alternans, manifest as alternating changes in action potential duration, is observed in isolated ventricular cardiomyocytes and in multicellular preparations. Its underlying causes are discussed particularly with respect to the role of intracellular Ca(2+). The repolarisation alternans observed at the single cell level is compared to the alternating behaviour observed in isolated multicellular preparations including the perfused ventricular wedge and Langendorff perfused heart. The evidence concerning spatial differences in repolarisation alternans is considered, particularly the situation where adjacent regions of myocardium exhibit repolarisation alternans of different phases. This extreme behaviour, known as discordant alternans, is thought to produce marked gradients of repolarisation that can precipitate unidirectional block and re-entrant ventricular arrhythmias. Finally, the difficulties in extrapolating between experimental models of alternans and arrhythmias and the clinical manifestation are discussed. The areas where experimental evidence is weak are highlighted, and areas for future research are outlined.

Rhythms of high-grade block in an ionic model of a strand of regionally ischemic ventricular muscle

Electrical alternans, a beat-to-beat alternation in the electrocardiogram or electrogram, is frequently seen during the first few minutes of acute myocardial ischemia, and is often immediately followed by malignant cardiac arrhythmias such as ventricular tachycardia and ventricular fibrillation. As ischemia progresses, higher-order periodic rhythms (e.g., period-4) can replace the period-2 alternans rhythm. This is also seen in modelling work on a two-dimensional (2-D) sheet of regionally ischemic ventricular muscle. In addition, in the experimental work, ventricular arrhythmias are overwhelmingly seen only after the higher-order rhythms arise. We investigate an ionic model of a strand of ischemic ventricular muscle, constructed as a 3-cm-long 1-D cable with a centrally located 1-cm-long segment exposed to an elevated extracellular potassium concentration ([K(+)](o)). As [K(+)](o) is raised in this "ischemic segment" to represent one major effect of ongoing ischemia, the sequence of rhythms {1:1-->2:2 (alternans)-->2:1} is seen. With further increase in [K(+)](o), one sees higher-order periodic 2N:M rhythms {2:1-->4:2-->4:1-->6:2-->6:1-->8:2-->8:1}. In a 2N:M cycle, only M of the 2N action potentials generated at the proximal end of the cable successfully traverse the ischemic segment, with the remaining ones being blocked within the ischemic segment. Finally, there is a transition to complete block {8:1-->2:0-->1:0} (in an n:0 rhythm, all action potentials die out within the ischemic segment). Changing the length of the ischemic segment results in different rhythms and transitions being seen: e.g., when the ischemic segment is 2 cm long, the period-6 rhythms are not seen; when it is 0.5 cm long, there is a 3:1 rhythm interposed between the 2:1 and 1:0 rhythms. We discuss the relevance of our results to the experimental observations on the higher-order rhythms that presage reentrant ischemic ventricular arrhythmias.

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.

Dispersion of refractoriness and induction of reentry due to chaos synchronization in a model of cardiac tissue

Ventricular fibrillation is a lethal condition caused by multiple chaotically wandering electrical wavelets in the heart, reentering their own and each other's territories. The development of effective therapies requires a detailed understanding of how these reentrant waves are initiated. In this Letter, we demonstrate a novel mechanism for inducing reentry, in which chaos synchronization causes large-scale heterogeneities of refractoriness transverse to the direction of propagation. These regions of increased refractoriness create localized conduction block, which induces spiral wave reentry.

Cellular alternans: a mechanism linking calcium cycling proteins to cardiac arrhythmogenesis

Essentially all previous research on alternans has been restricted to normal myocardium, whereas sudden cardiac death (SCD) occurs most commonly in patients with ventricular dysfunction (i.e., heart failure), which is associated with marked disruption of proteins responsible for normal calcium cycling in myocytes. Several lines of evidence from studies in normal hearts suggest a link between impaired calcium cycling which characterizes ventricular mechanical dysfunction and impaired calcium cycling that is responsible for alternans. In normal myocardium, cells which exhibit the slowest calcium cycling, and not the slowest repolarization, are most susceptible to alternans. Decreased expression of key calcium cycling proteins is observed in alternans-prone cells. Sarcoplasmic reticulum ATPase (SERCA2a) expression is decreased, suggesting a mechanism for the slower sarcoplasmic reticulum (SR) calcium reuptake observed in alternans-prone cells. In addition, diminished ryanodine receptor (RyR) function leading to abnormal calcium release from the SR is also linked to cellular alternans. Although impaired contractile function clearly predisposes to SCD, the mechanisms linking mechanical to electrophysiological dysfunction in the heart are unclear. We propose that cellular calcium alternans may be an important mechanism linking mechanical dysfunction to cardiac arrhythmogenesis.

Nonlinear dynamics of cardiac excitation-contraction coupling: an iterated map study

Cardiac myocytes are excitable cells in which an external current stimulus depolarizes the membrane potential to elicit an action potential. This action potential then triggers calcium release from intracellular stores, which mediates contraction. Conversely, intracellular calcium also modulates membrane currents, affecting action potential morphology and action potential duration (APD). The interactions between action potential and calcium, termed excitation-contraction coupling, give rise to a rich spectrum of nonlinear dynamics, especially at rapid heart rates, which are important for cardiac contraction and the development of lethal arrhythmias. In this study, we developed a nonlinear iterated map model to investigate the dynamics of cardiac excitation-contraction coupling in a periodically stimulated cell. We first studied the nonlinear dynamics due to APD restitution, a functional relation between APD and its preceding diastolic interval. We then studied the nonlinear dynamics due to intracellular calcium cycling when total cell calcium is constant or varies at a beat-to-beat basis. Finally, we studied the nonlinear dynamics due to the bidirectional coupling of the two dynamical systems. Saddle-node bifurcations leading to bistability, period-doubling bifurcations leading to alternans, and period-doubling routes to chaos can independently occur in both action potential or intracellular calcium cycling subsystems as heart rate increases. A Hopf bifurcation leading to quasiperiodicity occurs when the two dynamical systems are coupled. Although these dynamics are predicted from low-dimensional iterated maps, the approach here provides valuable information which can be used as a basis to explore dynamical features of physiologically detailed ionic models, to illuminate experimental findings, and to design experimentally testable predictions for new biological experiments.

Dynamics and Cardiac Arrhythmias

Cardiac arrhythmias, characterized by single or multiple reentrant circuits, represent a dynamic phenomenon in an excitable medium. In this review, we provide a brief overview of how cardiac action potential duration restitution, conduction velocity restitution, and intracellular calcium cycling regulate the dynamics of action potential excitation and wave propagation in relation to the genesis and maintenance of cardiac arrhythmias.

Action potential duration restitution portraits of mammalian ventricular myocytes: role of calcium current

Construction of the action potential duration (APD) restitution portrait allows visualization of multiple aspects of the dynamics of periodically paced myocytes at various basic cycle lengths (BCLs). For the first time, we obtained the restitution portrait of isolated rabbit and guinea pig cardiac ventricular myocytes and analyzed the time constant, tau, of APD accommodation and the slopes of different types of restitution curves, Sdyn and S12, measured at varying BCLs. Our results indicate that both tau and the individual slopes are species and pacing dependent. In contrast, the mutual relationship between slopes Sdyn and S12 does not depend on pacing history, being a generic feature of the species. In addition, the maximum slope S12, measured in the restitution portrait at the lowest BCL, predicts the onset of alternans. Further, we investigated the role of the L-type calcium current, ICa-L, in the restitution portrait. We found that ICa-L dramatically affects APD accommodation, as well as the individual slopes Sdyn and S12 measured in the restitution portrait. However, peak calcium current plays a role only at small values of BCL. In conclusion, the results demonstrate that the restitution portrait is a powerful technique to investigate restitution properties of periodically paced cardiac myocytes and the onset of alternans, in particular. Moreover, the data also show that ICa-L plays a crucial role in multiple aspects of cardiac dynamics measured through the restitution portrait.

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

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

Importance of spatiotemporal heterogeneity of cellular restitution in mechanism of arrhythmogenic discordant alternans

BACKGROUND

Spatially discordant cellular alternans form a substrate for development of unidirectional block and ventricular fibrillation. However, the mechanisms responsible for discordant alternans remain poorly understood. Previous work suggests electrical restitution is critical to the development of alternans in single cells.

OBJECTIVES

The purpose of this study was to investigate the hypothesis that spatial and temporal heterogeneities of restitution underlie the mechanism eliciting discordant alternans.

METHODS

Steady-state pacing was used to elicit concordant cellular alternans in nine Langendorff-perfused guinea pig hearts. A single extrastimulus (S2) was applied every 51st beat following either the even or the odd beat of alternans. The cellular response to S2 was determined using optical mapping to generate action potential duration (APD) restitution curves from 256 ventricular sites for both the even and the odd beats.

RESULTS

Restitution kinetics were temporally heterogeneous during alternans, as restitution curves between the even and the odd beats differed significantly. Temporal heterogeneity was quantified by the average separation of restitution between the two curves, or Delta-restitution. Delta-Restitution was spatially heterogeneous and proportional to the amount of alternans at a given ventricular site. A computer simulation based on the experimental results showed the mechanism of discordant alternans was dependent on both spatial and temporal heterogeneities of restitution.

CONCLUSION

Both temporal and spatial heterogeneities of restitution exist during cellular alternans in the intact heart. Temporal heterogeneities of restitution, quantified by Delta-restitution, are proportional to the magnitude of cellular alternans. The combination of spatial and temporal heterogeneities of restitution may underlie the genesis of discordant alternans.

Two-Term Asymptotic Approximation of a Cardiac Restitution Curve

If spatial extent is neglected, ionic models of cardiac cells consist of systems of ordinary differential equations (ODEs) which have the property of excitability, i.e., a brief stimulus produces a prolonged evolution (called an action potential in the cardiac context) before the eventual return to equilibrium. Under repeated stimulation, or pacing, cardiac tissue exhibits electrical restitution: the steady-state action potential duration (APD) at a given pacing period B shortens as B is decreased. Independent of ionic models, restitution is often modeled phenomenologically by a one-dimensional mapping of the form APD(next) = f(B - APD(previous)). Under some circumstances, a restitution function f can be derived as an asymptotic approximation to the behavior of an ionic model.In this paper, extending previous work, we derive the next term in such an asymptotic approximation for a particular ionic model consisting of two ODEs. The two-term approximation exhibits excellent quantitative agreement with the actual restitution curve, whereas the leading-order approximation significantly underestimates actual APD values.

Global Endocardial Electrical Restitution in Human Right and Left Ventricles Determined by Noncontact Mapping

OBJECTIVES

This study was aimed at evaluating global characteristics of electrical restitution in the human ventricle using noncontact mapping.

BACKGROUND

Steep action potential restitution (slope >1) and conduction velocity (CV) restitution have been linked with propensity to ventricular fibrillation, but clinical measurement of global electrical restitution had not been feasible.

METHODS

Activation-recovery interval (ARI) and CV restitution curves were simultaneously constructed from 16 regional segments of the left and right ventricles in 8 patients (6 male, 2 female, age 42 +/- 17 years) following successful ablation of idiopathic ventricular tachycardia in the absence of structural disease guided by the Ensite 3000 system (Endocardial Solutions Inc., St. Paul, Minnesota). The ARIs were determined from reconstructed unipolar electrograms as validated with monophasic action potential recordings. The ARI restitution slopes were determined using the overlapping least-squares linear segments.

RESULTS

Global electrical restitution curves were heterogeneous in shape and distribution. ARI restitution slope was >1 at 25% of 128 sites. The overall mean slope was 0.79 and was greater in the left than the right ventricle (0.93 +/- 0.49 vs. 0.65 +/- 0.26, p < 0.001). Dispersion of ARI restitution slopes increased with decreasing diastolic intervals. The CV restitution operated over a narrower range of diastolic intervals compared with ARI restitution, reaching a plateau (10 +/- 6 ms vs. 38 +/- 13 ms, p < 0.001) after refractoriness. The magnitude of CV restitution was also greater (steeper) than ARI restitution (25 +/- 10% vs. 18 +/- 9%, p < 0.001).

CONCLUSIONS

Noncontact mapping can be used to examine global electrical restitution in the human ventricle. The ARI restitution is heterogeneous, with a slope >1 at 25% of all sites. The heterogeneity of ARI and CV restitution may be important in determining myocardial electrical stability.

Rate-dependent propagation of cardiac action potentials in a one-dimensional fiber

Action potential duration (APD) restitution, which relates APD to the preceding diastolic interval (DI), is a useful tool for predicting the onset of abnormal cardiac rhythms. However, it is known that different pacing protocols lead to different APD restitution curves (RCs). This phenomenon, known as APD rate dependence, is a consequence of memory in the tissue. In addition to APD restitution, conduction velocity restitution also plays an important role in the spatiotemporal dynamics of cardiac tissue. We present results concerning rate-dependent restitution in the velocity of propagating action potentials in a one-dimensional fiber. Our numerical simulations show that, independent of the amount of memory in the tissue, the wave-back velocity exhibits pronounced rate dependence and the wave-front velocity does not. Moreover, the discrepancy between wave-back velocity RCs is most significant for a small DI. We provide an analytical explanation of these results, using a system of coupled maps to relate the wave-front and wave-back velocities. Our calculations show that rate-dependent wave-back velocity can be present even if neither APD nor wave-front velocity exhibits rate dependence.

Molecular mechanisms and global dynamics of fibrillation: an integrative approach to the underlying basis of vortex-like reentry

Art Winfree's scientific legacy has been particularly important to our laboratory whose major goal is to understand the mechanisms of ventricular fibrillation (VF). Here, we take an integrative approach to review recent studies on the manner in which nonlinear electrical waves organize to result in VF. We describe the contribution of specific potassium channel proteins and of the myocardial fiber structure to such organization. The discussion centers on data derived from a model of stable VF in the Langendorff-perfused guinea pig heart that demonstrates distinct patterns of organization in the left (LV) and right (RV) ventricles. Analysis of optical mapping data reveals that VF excitation frequencies are distributed throughout the ventricles in clearly demarcated domains. The highest frequency domains are found on the anterior wall of the LV at a location where sustained reentrant activity is present. The optical data suggest that a high frequency rotor that remains stationary in the LV is the mechanism that sustains VF in this model. Computer simulations predict that the inward rectifying potassium current (IK1) is an essential determinant of rotor stability and frequency, and patch-clamp results strongly suggest that the outward component of IK1 of cells in the LV is significantly larger than in the RV. Additional computer simulations and analytical procedures predict that the filaments of the reentrant activity (scroll waves) adopt a non-random configuration depending on fiber organization within the ventricular wall. Using the minimal principle we have concluded that filaments align with the trajectory of least resistance (i.e. the geodesic) between their endpoints. Overall, the data discussed have opened new and potentially exciting avenues of research on the possible role played by inward rectifier channels in the mechanism of VF, as well as the organization of its reentrant sources in three-dimensional cardiac muscle. Such an integrative approach may lead us toward an understanding of the molecular and structural basis of VF and hopefully to new preventative approaches.

Ventricular fibrillation: new insights into mechanisms

Device therapy with implantable cardioverter-defibrillators is currently the only proven effective therapy against sudden cardiac death due to ventricular fibrillation. However, the expanded clinical indications for device therapy come at a staggering cost to an already overburdened health care system. Given these statistics, it is both highly desirable and economically imperative to develop alternative therapies. New insights into the mechanisms of ventricular fibrillation, particularly the role of dynamic factors causing wave instability, are providing a promising avenue for developing novel therapies to prevent sudden cardiac death.