Zhilin Qu

From Pulsus to Pulseless The Saga of Cardiac Alternans

Computer simulations and nonlinear dynamics have provided invaluable tools for illuminating the underlying mechanisms of cardiac arrhythmias. Here, we review how this approach has led to major insights into the mechanisms of spatially discordant alternans, a key arrhythmogenic factor predisposing the heart to re-entry and lethal arrhythmias. During spatially discordant alternans, the action potential duration (APD) alternates out of phase in different regions of the heart, markedly enhancing dispersion of refractoriness so that ectopic beats have a high probability of inducing reentry. We show how, at the cellular level, instabilities in membrane voltage (ie, steep APD restitution slope) and intracellular Ca (Cai) cycling dynamics cause APD and the Cai transient to alternate and how the characteristics of alternans are affected by different “modes” of the bidirectional coupling between voltage and Cai. We illustrate how, at the tissue level, additional factors, such as conduction velocity restitution and ectopic beats, promote spatially discordant alternans. These insights have illuminated the mechanistic basis underlying the clinical association of cardiac alternans (eg, T wave alternans) with arrhythmia risk, which may lead to novel therapeutic approaches to avert sudden cardiac death.

Mechanisms of discordant alternans and induction of reentry in simulated cardiac tissue.

BackgroundT-wave alternans, which is associated with the genesis of cardiac fibrillation, has recently been related to discordant action potential duration (APD) alternans. However, the cellular electrophysiological mechanisms responsible for discordant alternans are poorly understood. Methods and ResultsWe simulated a 2D sheet of cardiac tissue using phase 1 of the Luo-Rudy cardiac action potential model. A steep (slope >1) APD restitution curve promoted concordant APD alternans and T-wave alternans without QRS alternans. When pacing was from a single site, discordant APD alternans occurred only when the pacing rate was fast enough to engage conduction velocity (CV) restitution, producing both QRS and T-wave alternans. Tissue heterogeneity was not required for this effect. Discordant alternans markedly increases dispersion of refractoriness and increases the ability of a premature stimulus to cause localized wavebreak and induce reentry. In the absence of steep APD restitution and of CV restitution, sustained discordant alternans did not occur, but reentry could be induced if there was marked electrophysiological heterogeneity. Both discordant APD alternans and preexisting APD heterogeneity facilitate reentry by causing the waveback to propagate slowly. ConclusionDiscordant alternans arises dynamically from APD and CV restitution properties and markedly increases dispersion of refractoriness. Preexisting and dynamically induced (via restitution) dispersion of refractoriness independently increase vulnerability to reentrant arrhythmias. Reduction of dynamically induced dispersion by appropriate alteration of electrical restitution has promise as an antiarrhythmic strategy.

Chaos and the Transition to Ventricular Fibrillation: A New Approach to Antiarrhythmic Drug Evaluation

Sudden cardiac death resulting from ventricular fibrillation can be separated into 2 components: initiation of tachycardia and degeneration of tachycardia to fibrillation. Clinical drug studies such as CAST and SWORD demonstrated that focusing exclusively on the first component is inadequate as a therapeutic modality. The hope for developing effective pharmacological therapy rests on a comprehensive understanding of the second component, the transition from tachycardia to fibrillation. We summarize evidence that the transition from tachycardia to fibrillation is a transition to spatiotemporal chaos, with similarities to the quasiperiodic transition to chaos seen in fluid turbulence. In this scenario, chaos results from the interaction of multiple causally independent oscillatory motions. Simulations in 2-dimensional cardiac tissue suggest that the destabilizing oscillatory motions during spiral-wave reentry arise from restitution properties of action potential duration and conduction velocity. The process of spiral-wave breakup in simulated cardiac tissue predicts remarkably well the sequence by which tachycardia degenerates to fibrillation in real cardiac tissue. Modifying action potential duration and conduction velocity restitution characteristics can prevent spiral-wave breakup in simulated cardiac tissue, suggesting that drugs with similar effects in real cardiac tissue may have antifibrillatory efficacy (the Restitution Hypothesis). If valid for the real heart, the Restitution Hypothesis will support a new paradigm for antiarrhythmic drug classification, incorporating an antifibrillatory profile based on effects on cardiac restitution and the traditional antitachycardia profile (classes 1 through 4).

The Dynamics of Cardiac Fibrillation

Reentry occurs when the electrical wave propagating through the atria or ventricles breaks locally and forms a rotor (also called a scroll wave or functional reentry). If the waves propagating outward from a rotor develop additional wavebreaks (which may form new rotors), fibrillation results. Tissue heterogeneity, exacerbated by electrical and structural remodeling from cardiac disease, has traditionally been considered the major factor promoting wavebreak and its degeneration to fibrillation. Recently, however, dynamic factors have also been recognized to play a key role. Dynamic factors refer to cellular properties of the cardiac action potential and Ca(i) cycling, which dynamically generate wave instability and wavebreak, even in tissue that is initially completely homogeneous. Although the latter situation can only be created in computer simulations, its relevance to real (heterogeneous) cardiac tissue has been unequivocally demonstrated. Dynamic factors are related to membrane voltage (Vm) and Ca(i). Vm factors include electrical restitution of action potential duration and conduction velocity, short-term cardiac memory, and electrotonic currents. Ca(i) factors are related to dynamic Ca(i) cycling properties. They act synergistically, as well as with tissue heterogeneity, to promote wavebreak and fibrillation. As global properties, rather than local electrophysiological characteristics, dynamic factors represent an attractive target for novel therapies to prevent ventricular fibrillation.

Spatiotemporal Heterogeneity in the Induction of Ventricular Fibrillation by Rapid Pacing Importance of Cardiac Restitution Properties

The mechanism by which rapid pacing induces ventricular fibrillation (VF) is unclear. We performed computerized epicardial mapping studies in 10 dogs, using 19-beat pacing trains. The pacing interval (PI) of the first train was 300 ms and then was progressively shortened until VF was induced. For each PI, we constructed restitution curves for the effective refractory period (ERP). When the PI was long, the activation cycle length (CL) was constant throughout the mapped region. However, as the PI shortened, there was an increase in the spatiotemporal complexity of the CL variations and an increase in the slope of the ERP restitution curve. In 5 dogs, we documented the initiation of VF by wavebreak at the site of long-short CL variations. Computer simulation studies using the Luo-Rudy I ventricular action potential model in simulated 2-dimensional tissue reproduced the experimental results when normal ERP and conduction velocity (CV) restitution properties were intact. By altering CV and ERP restitutions in this model, we found that CV restitution creates spatial CL variations, whereas ERP restitution underlies temporal, beat-to-beat variations in refractoriness during rapid pacing. Together, the interaction of CV and ERP restitutions produces spatiotemporal oscillations in cardiac activation that increase in amplitude as the PI decreases, ultimately causing wavebreak at the site of intrinsic heterogeneity. This initial wavebreak then leads to the formation of spiral waves and VF. These findings support a key role for both CV and ERP restitutions in the initiation of VF by rapid pacing.

So Little Source, So Much Sink: Requirements for Afterdepolarizations to Propagate in Tissue

How early (EADs) and delayed afterdepolarizations (DADs) overcome electrotonic source-sink mismatches in tissue to trigger premature ventricular complexes remains incompletely understood. To study this question, we used a rabbit ventricular action potential model to simulate tissues in which a central area of contiguous myocytes susceptible to EADs or DADs was surrounded by unsusceptible tissue. In 1D tissue with normal longitudinal conduction velocity (0.55 m/s), the numbers of contiguous susceptible myocytes required for an EAD and a barely suprathreshold DAD to trigger a propagating action potential were 70 and 80, respectively. In 2D tissue, these numbers increased to 6940 and 7854, and in 3D tissue to 696,910 and 817,280. These numbers were significantly decreased by reduced gap junction conductance, simulated fibrosis, reduced repolarization reserve and heart failure electrical remodeling. In conclusion, the source-sink mismatch in well-coupled cardiac tissue powerfully protects the heart from arrhythmias due to sporadic afterdepolarizations. Structural and electrophysiological remodeling decrease these numbers significantly but still require synchronization mechanisms for EADs and DADs to overcome the robust protective effects of source-sink mismatch.

Ventricular Fibrillation How Do We Stop the Waves From Breaking

Abstract— Combined experimental and theoretical developments have demonstrated that in addition to preexisting electrophysiological heterogeneities, cardiac electrical restitution properties contribute to breakup of reentrant wavefronts during cardiac fibrillation. Developing therapies that favorably alter electrical restitution properties have promise as a new paradigm for preventing fibrillation.

An advanced algorithm for solving partial differential equation in cardiac conduction

An advanced integration method for solving reaction-diffusion-type equations for cardiac conduction is suggested. Operator splitting and adaptive time step methods were used in this method, which can significantly speed up integration while preserving accuracy.

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 hat propagate “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 (H2O2) 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.

Early Afterdepolarizations and Cardiac Arrhythmias

Early afterdepolarizations (EADs) are an important cause of lethal ventricular arrhythmias in long QT syndromes and heart failure, but the mechanisms by which EADs at the cellular scale cause arrhythmias such as polymorphic ventricular tachycardia (PVT) and torsades de pointes (TdP) at the tissue scale are not well understood. Here we summarize recent progress in this area, discussing (1) the ionic basis of EADs, (2) evidence that deterministic chaos underlies the irregular behavior of EADs, (3) mechanisms by which chaotic EADs synchronize in large numbers of coupled cells in tissue to overcome source-sink mismatches, (4) how this synchronization process allows EADs to initiate triggers and generate mixed focal reentrant ventricular arrhythmias underlying PVT and TdP, and (5) therapeutic implications.