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

In Vitro Safety "Clinical Trial" of the Cardiac Liability of Hydroxychloroquine and Azithromycin as COVID19 Polytherapy

Despite global efforts, there are no effective FDA-approved medicines for the treatment of SARS-CoV-2 infection. Potential therapeutics focus on repurposed drugs, some with cardiac liabilities. Here we report on a preclinical drug screening platform, a cardiac microphysiological system (MPS), to assess cardiotoxicity associated with hydroxychloroquine (HCQ) and azithromycin (AZM) polytherapy in a mock clinical trial. The MPS contained human heart muscle derived from patient-specific induced pluripotent stem cells. The effect of drug response was measured using outputs that correlate with clinical measurements such as QT interval (action potential duration) and drug-biomarker pairing. Chronic exposure to HCQ alone elicited early afterdepolarizations (EADs) and increased QT interval from day 6 onwards. AZM alone elicited an increase in QT interval from day 7 onwards and arrhythmias were observed at days 8 and 10. Monotherapy results closely mimicked clinical trial outcomes. Upon chronic exposure to HCQ and AZM polytherapy, we observed an increase in QT interval on days 4-8.. Interestingly, a decrease in arrhythmias and instabilities was observed in polytherapy relative to monotherapy, in concordance with published clinical trials. Furthermore, biomarkers, most of them measurable in patients' serum, were identified for negative effects of single drug or polytherapy on tissue contractile function, morphology, and antioxidant protection. The cardiac MPS can predict clinical arrhythmias associated with QT prolongation and rhythm instabilities. This high content system can help clinicians design their trials, rapidly project cardiac outcomes, and define new monitoring biomarkers to accelerate access of patients to safe COVID-19 therapeutics.

Why pacing frequency affects the production of early afterdepolarizations in cardiomyocytes: An explanation revealed by slow-fast analysis of a minimal model

Early afterdepolarizations (EADs) are pathological voltage oscillations in cardiomyocytes that have been observed in response to a number of pharmacological agents and disease conditions. Phase-2 EADs consist of small voltage fluctuations during the plateau of an action potential, typically under conditions in which the action potential is elongated. Although a single-cell behavior, EADs can lead to tissue-level arrhythmias. Much is currently known about the biophysical mechanisms (i.e., the roles of ion channels and intracellular Ca^{2+} stores) for the various forms of EADs, due partially to the development and analysis of mathematical models. This includes the application of slow-fast analysis, which takes advantage of timescale separation inherent in the system to simplify its analysis. We take this further, using a minimal three-dimensional model to demonstrate that phase-2 EADs are canards formed in the neighborhood of a folded node singularity. This allows us to predict the number of EADs that can be produced for a given parameter set, and provides guidance on parameter changes that facilitate or inhibit EAD production. With this approach, we demonstrate why periodic stimulation, as occurs in intact heart, preferentially facilitates EAD production when applied at low frequencies. We also explain the origin of complex alternan dynamics that can occur with intermediate-frequency stimulation, in which varying numbers of EADs are produced with each pulse. These revelations fall out naturally from an understanding of folded node singularities, but are difficult to glean from knowledge of the biophysical mechanism for EADs alone. Therefore, understanding the canard mechanism is a useful complement to understanding of the biophysical mechanism that has been developed over years of experimental and computational investigations.

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.

Global alternans instability and its effect on non-linear wave propagation: dynamical Wenckebach block and self terminating spiral waves

The main mechanism of formation of reentrant cardiac arrhythmias is via formation of waveblocks at heterogeneities of cardiac tissue. We report that heterogeneity and the area of waveblock can extend itself in space and can result formation of new additional sources, or termination of existing sources of arrhythmias. This effect is based on a new form of instability, which we coin as global alternans instability (GAI). GAI is closely related to the so-called (discordant) alternans instability, however its onset is determined by the global properties of the APD-restitution curve and not by its slope. The APD-restitution curve relates the duration of the cardiac pulse (APD) to the time interval between the pulses, and can easily be measured in an experimental or even clinical setting. We formulate the conditions for the onset of GAI, study its manifestation in various 1D and 2D situations and discuss its importance for the onset of cardiac arrhythmias.

Slow [Na]i Changes and Positive Feedback Between Membrane Potential and [Ca]i Underlie Intermittent Early Afterdepolarizations and Arrhythmias

BACKGROUND

Most cardiac arrhythmias occur intermittently. As a cellular precursor of lethal cardiac arrhythmias, early afterdepolarizations (EADs) during action potentials(APs) have been extensively investigated, and mechanisms for the occurrence of EADs on a beat-to-beat basis have been proposed. However, no previous study explains slow fluctuations in EADs, which may underlie intermittency of EAD trains and consequent arrhythmias. We hypothesize that the feedback of intracellular calcium and sodium concentrations ([Na](i) and [Ca](i)) that influence membrane voltage (V) can explain EAD intermittency.

METHODS AND RESULTS

AP recordings in rabbit ventricular myocytes revealed intermittent EADs, with slow fluctuations between runs of APs with EADs present or absent. We then used dynamical systems analysis and detailed mathematical models of rabbit ventricular myocytes that replicate the observed behavior and investigated the underlying mechanism. We found that a dominance of inward Na-Ca exchanger current (I(NCX)) over Ca-dependent inactivation of L-type Ca current (I(CaL)) forms a positive feedback between [Ca](i) and V, thus resulting in 2 stable AP states, with and without EADs (ie, bistability). Slow changes in [Na](i) determine the transition between these 2 states, forming a bistable on-off switch of EADs. Tissue simulations showed that this bistable switch of cellular EADs provided both a trigger and a functional substrate for intermittent arrhythmias in homogeneous tissues.

CONCLUSIONS

Our study demonstrates that the interaction among V, [Ca](i), and [Na](i) causes slow on-off switching (or bistability) of AP duration in cardiac myocytes and EAD-mediated arrhythmias and suggests a novel possible mechanism for intermittency of cardiac arrhythmias.

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.

Chaotic Synchronization and the Global Economy

A brief introductory article on the role of chaotic synchronization in the context of complex economic systems. The basic framework developed by the late Richard Goodwin in his book, Chaotic Economic Dynamics, of 1990 has been extended to massively complex dynamical systems of chaotic elements. Recent experimental results and speculative applications to global economic systems are presented.1

Effects of pacing magnitudes and forms on bistability width in a modeled ventricular tissue

Bistability in periodically paced cardiac tissue is relevant to cardiac arrhythmias and its control. In the present paper, one-dimensional tissue of the phase I Luo-Rudy model is numerically investigated. The effects of various parameters of pacing signals on bistability width are studied. The following conclusions are obtained: (i) Pacing can be classified into two types: pulsatile and sinusoidal types. Pulsatile pacing reduces bistability width as its magnitude is increased. Sinusoidal pacing increases the width as its amplitude is increased. (ii) In a pacing period the hyperpolarizing part plays a more important role than the depolarizing part. Variations of the hyperpolarizing ratio in a period evidently change the width of bistability and its variation tendency. (iii) A dynamical mechanism is proposed to qualitatively explain the phenomena, which reveals the reason for the different effects of pulsatile and sinusoidal pacing on bistability. The methods for changing bistability width by external pacing may help control arrhythmias in cardiology.

Oxidative stress, fibrosis, and early afterdepolarization-mediated cardiac arrhythmias

Animal and clinical studies have demonstrated that oxidative stress, a common pathophysiological factor in cardiac disease, reduces repolarization reserve by enhancing the L-type calcium current, the late Na, and the Na-Ca exchanger, promoting early afterdepolarizations (EADs) that can initiate ventricular tachycardia and ventricular fibrillation (VT/VF) in structurally remodeled hearts. Increased ventricular fibrosis plays a key facilitatory role in allowing oxidative-stress induced EADs to manifest as triggered activity and VT/VF, since normal non-fibrotic hearts are resistant to arrhythmias when challenged with similar or higher levels of oxidative stress. The findings imply that antifibrotic therapy, in addition to therapies designed to suppress EAD formation at the cellular level, may be synergistic in reducing the risk of sudden cardiac death.

Computational approaches to understand cardiac electrophysiology and arrhythmias

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

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.

Bifurcation and chaos in a model of cardiac early afterdepolarizations

Excitable cells can exhibit complex patterns of oscillations, such as spiking and bursting. In cardiac cells, pathological voltage oscillations, called early afterdepolarizations (EADs), have been widely observed under disease conditions, yet their dynamical mechanisms remain unknown. Here, we show that EADs are caused by Hopf and homoclinic bifurcations. During period pacing, chaos always occurs at the transition from no EAD to EADs as the stimulation frequency decreases, providing a distinct explanation for the irregular EAD behavior frequently observed in experiments.

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.