Stimulus-induced critical point. Mechanism for electrical initiation of reentry in normal canine myocardium

A comprehensive framework for evaluation of high pacing frequency and arrhythmic optical mapping signals

Introduction: High pacing frequency or irregular activity due to arrhythmia produces complex optical mapping signals and challenges for processing. The objective is to establish an automated activation time-based analytical framework applicable to optical mapping images of complex electrical behavior. Methods: Optical mapping signals with varying complexity from sheep (N = 7) ventricular preparations were examined. Windows of activation centered on each action potential upstroke were derived using Hilbert transform phase. Upstroke morphology was evaluated for potential multiple activation components and peaks of upstroke signal derivatives defined activation time. Spatially and temporally clustered activation time points were grouped in to wave fronts for individual processing. Each activation time point was evaluated for corresponding repolarization times. Each wave front was subsequently classified based on repetitive or non-repetitive events. Wave fronts were evaluated for activation time minima defining sites of wave front origin. A visualization tool was further developed to probe dynamically the ensemble activation sequence. Results: Our framework facilitated activation time mapping during complex dynamic events including transitions to rotor-like reentry and ventricular fibrillation. We showed that using fixed AT windows to extract AT maps can impair interpretation of the activation sequence. However, the phase windowing of action potential upstrokes enabled accurate recapitulation of repetitive behavior, providing spatially coherent activation patterns. We further demonstrate that grouping the spatio-temporal distribution of AT points in to coherent wave fronts, facilitated interpretation of isolated conduction events, such as conduction slowing, and to derive dynamic changes in repolarization properties. Focal origins precisely detected sites of stimulation origin and breakthrough for individual wave fronts. Furthermore, a visualization tool to dynamically probe activation time windows during reentry revealed a critical single static line of conduction slowing associated with the rotation core. Conclusion: This comprehensive analytical framework enables detailed quantitative assessment and visualization of complex electrical behavior.

The physics of heart rhythm disorders

The global burden caused by cardiovascular disease is substantial, with heart disease representing the most common cause of death around the world. There remains a need to develop better mechanistic models of cardiac function in order to combat this health concern. Heart rhythm disorders, or arrhythmias, are one particular type of disease which has been amenable to quantitative investigation. Here we review the application of quantitative methodologies to explore dynamical questions pertaining to arrhythmias. We begin by describing single-cell models of cardiac myocytes, from which two and three dimensional models can be constructed. Special focus is placed on results relating to pattern formation across these spatially-distributed systems, especially the formation of spiral waves of activation. Next, we discuss mechanisms which can lead to the initiation of arrhythmias, focusing on the dynamical state of spatially discordant alternans, and outline proposed mechanisms perpetuating arrhythmias such as fibrillation. We then review experimental and clinical results related to the spatio-temporal mapping of heart rhythm disorders. Finally, we describe treatment options for heart rhythm disorders and demonstrate how statistical physics tools can provide insights into the dynamics of heart rhythm disorders.

R-on-T and the initiation of reentry revisited: Integrating old and new concepts

Initiation of reentry requires 2 factors: (1) a triggering event, most commonly focal excitations such as premature ventricular complexes (PVCs); and (2) a vulnerable substrate with regional dispersion of refractoriness and/or excitability, such as occurs during the T wave of the electrocardiogram when some areas of the ventricle have repolarized and recovered excitability but others have not. When the R wave of a PVC coincides in time with the T wave of the previous beat, this timing can lead to unidirectional block and initiation of reentry, known as the R-on-T phenomenon. Classically, the PVC triggering reentry has been viewed as arising focally from 1 region and propagating into another region whose recovery is delayed, resulting in unidirectional conduction block and reentry initiation. However, more recent evidence indicates that PVCs also can arise from the T wave itself. In the latter case, the PVC initiating reentry is not a separate event from the T wave but rather is causally generated from the repolarization gradient that manifests as the T wave. We call the former an "R-to-T" mechanism and the latter an "R-from-T" mechanism, which are initiation mechanisms distinct from each other. Both are important components of the R-on-T phenomenon and need to be taken into account when designing antiarrhythmic strategies. Strategies targeting suppression of triggers alone or vulnerable substrate alone may be appropriate in some instances but not in others. Preventing R-from-T arrhythmias requires suppressing the underlying dynamic tissue instabilities responsible for producing both triggers and substrate vulnerability simultaneously. The same principles are likely to apply to supraventricular arrhythmias.

Terminating spiral waves with a single designed stimulus: Teleportation as the mechanism for defibrillation

Many chemical and biological systems can sustain complex spiral wave dynamics. In the heart, spiral waves of electrical activity induce deadly arrhythmias and must be eliminated with a large, system-wide perturbation to restore a healthy rhythm. However, the high-energy shocks required for defibrillation therapies are very painful and can even damage heart tissue. In this study, we demonstrate a method for eliminating spiral waves with what should be the minimal possible stimulus required in space for termination. To do this, we show how a localized perturbation can be designed to annihilate simultaneously all spiral waves both free and bound. This identified mechanism is applicable to any excitable system and, for the heart, may lead to more efficient defibrillation strategies.

We identify and demonstrate a universal mechanism for terminating spiral waves in excitable media using an established topological framework. This mechanism dictates whether high- or low-energy defibrillation shocks succeed or fail. Furthermore, this mechanism allows for the design of a single minimal stimulus capable of defibrillating, at any time, turbulent states driven by multiple spiral waves. We demonstrate this method in a variety of computational models of cardiac tissue ranging from simple to detailed human models. The theory described here shows how this mechanism underlies all successful defibrillation and can be used to further develop existing and future low-energy defibrillation strategies.

Optogenetic Control of Human Induced Pluripotent Stem Cell-Derived Cardiac Tissue Models

Background

Optogenetics, using light‐sensitive proteins, emerged as a unique experimental paradigm to modulate cardiac excitability. We aimed to develop high‐resolution optogenetic approaches to modulate electrical activity in 2‐ and 3‐dimensional cardiac tissue models derived from human induced pluripotent stem cell (hiPSC)‐derived cardiomyocytes.

Methods and Results

To establish light‐controllable cardiac tissue models, opsin‐carrying HEK293 cells, expressing the light‐sensitive cationic‐channel CoChR, were mixed with hiPSC‐cardiomyocytes to generate 2‐dimensional hiPSC‐derived cardiac cell‐sheets or 3‐dimensional engineered heart tissues. Complex illumination patterns were designed with a high‐resolution digital micro‐mirror device. Optical mapping and force measurements were used to evaluate the tissues' electromechanical properties. The ability to optogenetically pace and shape the tissue's conduction properties was demonstrated by using single or multiple illumination stimulation sites, complex illumination patterns, or diffuse illumination. This allowed to establish in vitro models for optogenetic‐based cardiac resynchronization therapy, where the electrical activation could be synchronized (hiPSC‐derived cardiac cell‐sheets and engineered heart tissue models) and contractile properties improved (engineered heart tissues). Next, reentrant activity (rotors) was induced in the hiPSC‐derived cardiac cell‐sheets and engineered heart tissue models through optogenetics programmed‐ or cross‐field stimulations. Diffuse illumination protocols were then used to terminate arrhythmias, demonstrating the potential to study optogenetics cardioversion mechanisms and to identify optimal illumination parameters for arrhythmia termination.

Conclusions

By combining optogenetics and hiPSC technologies, light‐controllable human cardiac tissue models could be established, in which tissue excitability can be modulated in a functional, reversible, and localized manner. This approach may bring a unique value for physiological/pathophysiological studies, for disease modeling, and for developing optogenetic‐based cardiac pacing, resynchronization, and defibrillation approaches.

Stop the beat to see the rhythm: excitation-contraction uncoupling in cardiac research

Optical mapping is an imaging technique that is extensively used in cardiovascular research, wherein parameter-sensitive fluorescent indicators are used to study the electrophysiology and excitation-contraction coupling of cardiac tissues. Despite many benefits of optical mapping, eliminating motion artifacts within the optical signals is a major challenge, as myocardial contraction interferes with the faithful acquisition of action potentials and intracellular calcium transients. As such, excitation-contraction uncoupling agents are frequently used to reduce signal distortion by suppressing contraction. When compared with other uncoupling agents, blebbistatin is the most frequently used, as it offers increased potency with minimal direct effects on cardiac electrophysiology. Nevertheless, blebbistatin may exert secondary effects on electrical activity, metabolism, and coronary flow, and the incorrect administration of blebbistatin to cardiac tissue can prove detrimental, resulting in erroneous interpretation of optical mapping results. In this "Getting It Right" perspective, we briefly review the literature regarding the use of blebbistatin in cardiac optical mapping experiments, highlight potential secondary effects of blebbistatin on cardiac electrical activity and metabolic demand, and conclude with the consensus of the authors on best practices for effectively using blebbistatin in optical mapping studies of cardiac tissue.

Bidomain modeling of electrical and mechanical properties of cardiac tissue

Throughout the history of cardiac research, there has been a clear need to establish mathematical models to complement experimental studies. In an effort to create a more complete picture of cardiac phenomena, the bidomain model was established in the late 1970s to better understand pacing and defibrillation in the heart. This mathematical model has seen ongoing use in cardiac research, offering mechanistic insight that could not be obtained from experimental pursuits. Introduced from a historical perspective, the origins of the bidomain model are reviewed to provide a foundation for researchers new to the field and those conducting interdisciplinary research. The interplay of theory and experiment with the bidomain model is explored, and the contributions of this model to cardiac biophysics are critically evaluated. Also discussed is the mechanical bidomain model, which is employed to describe mechanotransduction. Current challenges and outstanding questions in the use of the bidomain model are addressed to give a forward-facing perspective of the model in future studies.

Optogenetic modulation of cardiac action potential properties may prevent arrhythmogenesis in short and long QT syndromes

Abnormal action potential (AP) properties, as occurs in long or short QT syndromes (LQTS and SQTS, respectively), can cause life-threatening arrhythmias. Optogenetics strategies, utilizing light-sensitive proteins, have emerged as experimental platforms for cardiac pacing, resynchronization, and defibrillation. We tested the hypothesis that similar optogenetic tools can modulate the cardiomyocyte's AP properties, as a potentially novel antiarrhythmic strategy. Healthy control and LQTS/SQTS patient-specific human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) were transduced to express the light-sensitive cationic channel channelrhodopsin-2 (ChR2) or the anionic-selective opsin, ACR2. Detailed patch-clamp, confocal-microscopy, and optical mapping studies evaluated the ability of spatiotemporally defined optogenetic protocols to modulate AP properties and prevent arrhythmogenesis in the hiPSC-CMs cell/tissue models. Depending on illumination timing, light-induced ChR2 activation induced robust prolongation or mild shortening of AP duration (APD), while ACR2 activation allowed effective APD shortening. Fine-tuning these approaches allowed for the normalization of pathological AP properties and suppression of arrhythmogenicity in the LQTS/SQTS hiPSC-CM cellular models. We next established a SQTS-hiPSC-CMs-based tissue model of reentrant-arrhythmias using optogenetic cross-field stimulation. An APD-modulating optogenetic protocol was then designed to dynamically prolong APD of the propagating wavefront, completely preventing arrhythmogenesis in this model. This work highlights the potential of optogenetics in studying repolarization abnormalities and in developing novel antiarrhythmic therapies.

Increasing SERCA function promotes initiation of calcium sparks and breakup of calcium waves

KEY POINTS

Increasing sarcoplasmic/endoplasmic reticulum calcium ATPase (SERCA) pump activity enhances sarcoplasmic reticulum calcium (Ca) load, which increases both ryanodine receptor opening and driving force of Ca release flux. Both of these effects promote Ca spark formation and wave propagation. However, increasing SERCA activity also accelerates local cytosolic Ca decay as the wave front travels to the next cluster, which limits wave propagation. As a result, increasing SERCA pump activity has a biphasic effect on the propensity of arrhythmogenic Ca waves, but a monotonic effect to increase Ca spark frequency and amplitude.

ABSTRACT

Waves of sarcoplasmic reticulum (SR) calcium (Ca) release can cause arrhythmogenic afterdepolarizations in cardiac myocytes. Ca waves propagate when Ca sparks at one Ca release unit (CRU) recruit new Ca sparks in neighbouring CRUs. Under normal conditions, Ca sparks are too small to recruit neighbouring Ca sparks where Ca sensitivity is also low. However, under pathological conditions such as a Ca overload or ryanodine receptor (RyR) sensitization, Ca sparks can be larger and propagate more readily as macro-sparks or full Ca waves. Increasing SERCA pump activity promotes SR Ca load, which promotes RyR opening and increases driving force of the Ca release flux from SR to cytosol, promoting Ca waves. However, high sarcoplasmic/endoplasmic reticulum calcium ATPase (SERCA) activity can also decrease local cytosolic [Ca] as it approaches the next CRU, thereby reducing wave appearance and propagation. In this study, we use a physiologically detailed model of subcellular Ca cycling and experiments in phospholamban-knockout mice, to show how Ca waves are initiated and propagate and how different conditions contribute to the generation and propagation of Ca waves. We show that reducing diffusive coupling between Ca sparks by increasing SERCA activity prevents Ca waves by reducing [Ca] at the next CRU, as do Ca buffers, low intra-SR Ca diffusion and distance between CRUs. Increasing SR Ca uptake rate has a biphasic effect on Ca wave propagation; initially it enhances Ca spark probability and amplitude and CRU coupling, thereby promoting arrhythmogenic Ca wave propagation, but at higher levels SR Ca uptake can abort those arrhythmogenic Ca waves.

Wide-area low-energy surface stimulation of large mammalian ventricular tissue

The epicardial and endocardial surfaces of the heart are attractive targets to administer antiarrhythmic electrotherapies. Electrically stimulating wide areas of the surfaces of small mammalian ventricles is straightforward given the relatively small scale of their myocardial dimensions compared to the tissue space constant and electrical field. However, it has yet to be proven for larger mammalian hearts with tissue properties and ventricular dimensions closer to humans. Our goal was to address the feasibility and impact of wide-area electrical stimulation on the ventricular surfaces of large mammalian hearts at different stimulus strengths. This was accomplished by placing long line electrodes on the ventricular surfaces of pig hearts that span wide areas, and activating them individually. Stimulus efficacy was assessed and compared between surfaces, and tissue viability was evaluated. Activation time was dependent on stimulation strength and location, achieving uniform linear stimulation at 9x threshold strength. Endocardial stimulation activated more tissue transmurally than epicardial stimulation, which could be considered a potential target for future cardiac electrotherapies. Overall, our results indicate that electrically stimulating wide areas of the ventricular surfaces of large mammals is achievable with line electrodes, minimal tissue damage, and energies under the human pain threshold (100 mJ).

Optical Mapping

Optical mapping of electrical activity in the heart is based on voltage-sensitive and lipophilic fluorescence dyes. Optical signals recorded from cardiac cells correlate well with their transmembrane potentials. High spatiotemporal resolution, wide field mapping, and high sensitivity to transmembrane potential enable detailed characterization of action potential initiation and propagation. Optical mapping is used to study complex patterns of excitation propagation, including propagation across the sinoatrial and atrioventricular nodes and during atrial and ventricular arrhythmias.Optical mapping is used to study the role of reentrant activity in atrial and ventricular fibrillation.

Large-scale Interactive Numerical Experiments of Chaos, Solitons and Fractals in Real Time via GPU in a Web Browser

The study of complex systems has emerged as an important field with many discoveries still to be made. Computer simulation and visualization provide important tools for studying complex dynamics including chaos, solitons, and fractals, but available computing power has been a limiting factor. In this work, we describe a novel and highly efficient computing and visualization paradigm using a Web Graphics Library (WebGL 2.0) methodology along with our newly developed library (Abubu.js). Our approach harnesses the power of widely available and highly parallel graphics cards while maintaining ease of use by simplifying programming through hiding implementation details, running in a web browser without the need for compilation, and avoiding the use of plugins. At the same time, it allows for interactivity, such as changing parameter values on the fly, and its computing is so fast that zooming in on a region of a fractal like the Mandelbrot set can incur no delay despite having to recalculate values for the entire plane. We demonstrate our approach using a wide range of complex systems that display dynamics from fractals to standing and propagating waves in 1, 2 and 3 dimensions. We also include some models with instabilities that can lead to chaotic dynamics. For all the examples shown here we provide links to the codes for anyone to use, modify and further develop with other models. Overall, the enhanced visualization and computation capabilities provided by WebGL together with Abubu.js have great potential to facilitate new discoveries about complex systems.

Dynamics of sodium current mediated early afterdepolarizations

Early afterdepolarizations (EADs) have been attributed to two primary mechanisms: 1) recovery from inactivation of the L-type calcium (Ca) channel and/or 2) spontaneous Ca release, which depolarizes the membrane potential through the electrogenic sodium-calcium exchanger (NCX). The sodium (Na) current (I_Na), especially the late component of the Na current, has been recognized as an important player to set up the conditions for EADs by reducing repolarization reserve and increasing intracellular Na concentration, which leads to Ca overload. However, I_Na itself has not been considered as a direct initiator of EADs. A recent experimental study by Horvath et al. has shown that the amplitude of the late component of the Na current is as large as potassium (K) and Ca currents (∼1 pA/pF). This result suggests that I_Na by itself can exceeds the sum of outward currents and depolarize the membrane potential. In this study, we show that I_Na can also directly initiate EADs. Mathematical analysis reveals a fundamental dynamical origin of EADs arising directly from the Na channel reactivation. This system has three fixed points. The dynamics of the I_Na mediated EAD oscillation is different from that of the membrane voltage oscillation of the pacemaker cell, which has only one fixed point.

Role of abnormal repolarization in the mechanism of cardiac arrhythmia

In cardiac patients, life-threatening tachyarrhythmia is often precipitated by abnormal changes in ventricular repolarization and refractoriness. Repolarization abnormalities typically evolve as a consequence of impaired function of outward K⁺ currents in cardiac myocytes, which may be caused by genetic defects or result from various acquired pathophysiological conditions, including electrical remodelling in cardiac disease, ion channel modulation by clinically used pharmacological agents, and systemic electrolyte disorders seen in heart failure, such as hypokalaemia. Cardiac electrical instability attributed to abnormal repolarization relies on the complex interplay between a provocative arrhythmic trigger and vulnerable arrhythmic substrate, with a central role played by the excessive prolongation of ventricular action potential duration, impaired intracellular Ca²⁺ handling, and slowed impulse conduction. This review outlines the electrical activity of ventricular myocytes in normal conditions and cardiac disease, describes classical electrophysiological mechanisms of cardiac arrhythmia, and provides an update on repolarization-related surrogates currently used to assess arrhythmic propensity, including spatial dispersion of repolarization, activation-repolarization coupling, electrical restitution, TRIaD (triangulation, reverse use dependence, instability, and dispersion), and the electromechanical window. This is followed by a discussion of the mechanisms that account for the dependence of arrhythmic vulnerability on the location of the ventricular pacing site. Finally, the review clarifies the electrophysiological basis for cardiac arrhythmia produced by hypokalaemia, and gives insight into the clinical importance and pathophysiology of drug-induced arrhythmia, with particular focus on class Ia (quinidine, procainamide) and Ic (flecainide) Na⁺ channel blockers, and class III antiarrhythmic agents that block the delayed rectifier K⁺ channel (dofetilide).

Effect of anisotropy on ventricular vulnerability to unidirectional block and reentry by single premature stimulation during normal sinus rhythm in rat heart

Single high-intensity premature stimuli when applied to the ventricles during ventricular drive of an ectopic site, as in Winfree's "pinwheel experiment," usually induce reentry arrhythmias in the normal heart, while single low-intensity stimuli barely do. Yet ventricular arrhythmia vulnerability during normal sinus rhythm remains largely unexplored. With a view to define the role of anisotropy on ventricular vulnerability to unidirectional conduction block and reentry, we revisited the pinwheel experiment with reduced constraints in the in situ rat heart. New features included single premature stimulation during normal sinus rhythm, stimulation and unipolar potential mapping from the same high-resolution epicardial electrode array, and progressive increase in stimulation strength and prematurity from diastolic threshold until arrhythmia induction. Measurements were performed with 1-ms cathodal stimuli at multiple test sites (n = 26) in seven rats. Stimulus-induced virtual electrode polarization during sinus beat recovery phase influenced premature ventricular responses. Specifically, gradual increase in stimulus strength and prematurity progressively induced make, break, and graded-response stimulation mechanisms. Hence unidirectional conduction block occurred as follows: 1) along fiber direction, on right and left ventricular free walls (n = 23), initiating figure-eight reentry (n = 17) and tachycardia (n = 12), and 2) across fiber direction, on lower interventricular septum (n = 3), initiating spiral wave reentry (n = 2) and tachycardia (n = 1). Critical time window (55.1 ± 4.7 ms, 68.2 ± 6.0 ms) and stimulus strength lower limit (4.9 ± 0.6 mA) defined vulnerability to reentry. A novel finding of this study was that ventricular tachycardia evolves and is maintained by episodes of scroll-like wave and focal activation couplets. We also found that single low-intensity premature stimuli can induce repetitive ventricular response (n = 13) characterized by focal activations.NEW & NOTEWORTHY We performed ventricular cathodal point stimulation during sinus rhythm by progressively increasing stimulus strength and prematurity. Virtual electrode polarization and recovery gradient progressively induced make, break, and graded-response stimulation mechanisms. Unidirectional conduction block occurred along or across fiber direction, initiating figure-eight or spiral wave reentry, respectively, and tachycardia sustained by scroll wave and focal activations.

Reconstructing three-dimensional reentrant cardiac electrical wave dynamics using data assimilation

For many years, reentrant scroll waves have been predicted and studied as an underlying mechanism for cardiac arrhythmias using numerical techniques, and high-resolution mapping studies using fluorescence recordings from the surfaces of cardiac tissue preparations have confirmed the presence of visible spiral waves. However, assessing the three-dimensional dynamics of these reentrant waves using experimental techniques has been limited to verifying stable scroll-wave dynamics in relatively thin preparations. We propose a different approach to recovering the three-dimensional dynamics of reentrant waves in the heart. By applying techniques commonly used in weather forecasting, we combine dual-surface observations from a particular experiment with predictions from a numerical model to reconstruct the full three-dimensional time series of the experiment. Here, we use model-generated surrogate observations from a numerical experiment to evaluate the performance of the ensemble Kalman filter in reconstructing such time series for a discordant alternans state in one spatial dimension and for scroll waves in three dimensions. We show that our approach is able to recover time series of both observed and unobserved variables matching the truth. Where nearby observations are available, the error is reduced below the synthetic observation error, with a smaller reduction with increased distance from observations. Our findings demonstrate that state reconstruction for spatiotemporally complex cardiac electrical dynamics is possible and will lead naturally to applications using real experimental data.

Constitutively Active Acetylcholine-Dependent Potassium Current Increases Atrial Defibrillation Threshold by Favoring Post-Shock Re-Initiation

Electrical cardioversion (ECV), a mainstay in atrial fibrillation (AF) treatment, is unsuccessful in up to 10–20% of patients. An important aspect of the remodeling process caused by AF is the constitutive activition of the atrium-specific acetylcholine-dependent potassium current (I_K,ACh → I_K,ACh-c), which is associated with ECV failure. This study investigated the role of I_K,ACh-c in ECV failure and setting the atrial defibrillation threshold (aDFT) in optically mapped neonatal rat cardiomyocyte monolayers. AF was induced by burst pacing followed by application of biphasic shocks of 25–100 V to determine aDFT. Blocking I_K,ACh-c by tertiapin significantly decreased DFT, which correlated with a significant increase in wavelength during reentry. Genetic knockdown experiments, using lentiviral vectors encoding a Kcnj5-specific shRNA to modulate I_K,ACh-c, yielded similar results. Mechanistically, failed ECV was attributed to incomplete phase singularity (PS) removal or reemergence of PSs (i.e. re-initiation) through unidirectional propagation of shock-induced action potentials. Re-initiation occurred at significantly higher voltages than incomplete PS-removal and was inhibited by I_K,ACh-c blockade. Whole-heart mapping confirmed our findings showing a 60% increase in ECV success rate after I_K,ACh-c blockade. This study provides new mechanistic insight into failing ECV of AF and identifies I_K,ACh-c as possible atrium-specific target to increase ECV effectiveness, while decreasing its harmfulness.

Temporal Stability of Rotors and Atrial Activation Patterns in Persistent Human Atrial Fibrillation: A High-Density Epicardial Mapping Study of Prolonged Recordings

OBJECTIVES

This study aimed to determine the spatiotemporal stability of rotors and other atrial activation patterns over 10 min in longstanding, persistent AF, along with the relationship of rotors to short cycle-length (CL) activity.

BACKGROUND

The prevalence, stability, and mechanistic importance of rotors in human atrial fibrillation (AF) remain unclear.

METHODS

Epicardial mapping was performed in 10 patients undergoing cardiac surgery, with bipolar electrograms recorded over 10 min using a triangular plaque (area: 6.75 cm²; 117 bipoles; spacing: 2.5 mm) applied to the left atrial posterior wall (n = 9) and the right atrial free wall (n = 4). Activations were identified throughout 6 discrete 10-s segments of AF spanning 10 min, and dynamic activation mapping was performed. The distributions of 4,557 generated activation patterns within each mapped region were compared between the 6 segments.

RESULTS

The dominant activation pattern was the simultaneous presence of multiple narrow wave fronts (26%). Twelve percent of activations represented transient rotors, seen in 85% of mapped regions with a median duration of 3 rotations. A total of 87% were centered on an area of short CL activity (<100 ms), although such activity had a positive predictive value for rotors of only 0.12. The distribution of activation patterns and wave-front directionality were highly stable over time, with a single dominant pattern within a 10-s AF segment recurring across all 6 segments in 62% of mapped regions.

CONCLUSIONS

In patients with longstanding, persistent AF, activation patterns are spatiotemporally stable over 10 min. Transient rotors can be demonstrated in the majority of mapped regions, are spatiotemporally associated with short CL activity, and, when recurrent, demonstrate anatomical determinism.

Dynamics of propagation of premature impulses in structurally remodeled infarcted myocardium: a computational analysis

Initiation of cardiac arrhythmias typically follows one or more premature impulses either occurring spontaneously or applied externally. In this study, we characterize the dynamics of propagation of single (S2) and double premature impulses (S3), and the mechanisms of block of premature impulses at structural heterogeneities caused by remodeling of gap junctional conductance (Gj) in infarcted myocardium. Using a sub-cellular computer model of infarcted tissue, we found that |I_Na,max|, prematurity (coupling interval with the previous impulse), and conduction velocity (CV) of premature impulses change dynamically as they propagate away from the site of initiation. There are fundamental differences between the dynamics of propagation of S2 and S3 premature impulses: for S2 impulses |I_Na,max| recovers fast, prematurity decreases and CV increases as propagation proceeds; for S3 impulses low values of |I_Na,max| persist, prematurity could increase, and CV could decrease as impulses propagate away from the site of initiation. As a consequence it is more likely that S3 impulses block at sites of structural heterogeneities causing source/sink mismatch than S2 impulses block. Whether premature impulses block at Gj heterogeneities or not is also determined by the values of Gj (and the space constant λ) in the regions proximal and distal to the heterogeneity: when λ in the direction of propagation increases >40%, premature impulses could block. The maximum slope of CV restitution curves for S2 impulses is larger than for S3 impulses. In conclusion: (1) The dynamics of propagation of premature impulses make more likely that S3 impulses block at sites of structural heterogeneities than S2 impulses block; (2) Structural heterogeneities causing an increase in λ (or CV) of >40% could result in block of premature impulses; (3) A decrease in the maximum slope of CV restitution curves of propagating premature impulses is indicative of an increased potential for block at structural heterogeneities.

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.

Light-induced termination of spiral wave arrhythmias by optogenetic engineering of atrial cardiomyocytes

AIMS

Atrial fibrillation (AF) is the most common cardiac arrhythmia and often involves reentrant electrical activation (e.g. spiral waves). Drug therapy for AF can have serious side effects including proarrhythmia, while electrical shock therapy is associated with discomfort and tissue damage. Hypothetically, forced expression and subsequent activation of light-gated cation channels in cardiomyocytes might deliver a depolarizing force sufficient for defibrillation, thereby circumventing the aforementioned drawbacks. We therefore investigated the feasibility of light-induced spiral wave termination through cardiac optogenetics.

METHODS AND RESULTS

Neonatal rat atrial cardiomyocyte monolayers were transduced with lentiviral vectors encoding light-activated Ca(2+)-translocating channelrhodopsin (CatCh; LV.CatCh∼eYFP↑) or eYFP (LV.eYFP↑) as control, and burst-paced to induce spiral waves rotating around functional cores. Effects of CatCh activation on reentry were investigated by optical and multi-electrode array (MEA) mapping. Western blot analyses and immunocytology confirmed transgene expression. Brief blue light pulses (10 ms/470 nm) triggered action potentials only in LV.CatCh∼eYFP↑-transduced cultures, confirming functional CatCh-mediated current. Prolonged light pulses (500 ms) resulted in reentry termination in 100% of LV.CatCh∼eYFP↑-transduced cultures (n = 31) vs. 0% of LV.eYFP↑-transduced cultures (n = 11). Here, CatCh activation caused uniform depolarization, thereby decreasing overall excitability (MEA peak-to-peak amplitude decreased 251.3 ± 217.1 vs. 9.2 ± 9.5 μV in controls). Consequently, functional coresize increased and phase singularities (PSs) drifted, leading to reentry termination by PS-PS or PS-boundary collisions.

CONCLUSION

This study shows that spiral waves in atrial cardiomyocyte monolayers can be terminated effectively by a light-induced depolarizing current, produced by the arrhythmogenic substrate itself, upon optogenetic engineering. These results provide proof-of-concept for shockless defibrillation.

A quantitative comparison of the behavior of human ventricular cardiac electrophysiology models in tissue

Numerical integration of mathematical models of heart cell electrophysiology provides an important computational tool for studying cardiac arrhythmias, but the abundance of available models complicates selecting an appropriate model. We study the behavior of two recently published models of human ventricular action potentials, the Grandi-Pasqualini-Bers (GPB) and the O'Hara-Virág-Varró-Rudy (OVVR) models, and compare the results with four previously published models and with available experimental and clinical data. We find the shapes and durations of action potentials and calcium transients differ between the GPB and OVVR models, as do the magnitudes and rate-dependent properties of transmembrane currents and the calcium transient. Differences also occur in the steady-state and S1–S2 action potential duration and conduction velocity restitution curves, including a maximum conduction velocity for the OVVR model roughly half that of the GPB model and well below clinical values. Between single cells and tissue, both models exhibit differences in properties, including maximum upstroke velocity, action potential amplitude, and minimum diastolic interval. Compared to experimental data, action potential durations for the GPB and OVVR models agree fairly well (although OVVR epicardial action potentials are shorter), but maximum slopes of steady-state restitution curves are smaller. Although studies show alternans in normal hearts, it occurs only in the OVVR model, and only for a narrow range of cycle lengths. We find initiated spiral waves do not progress to sustained breakup for either model. The dominant spiral wave period of the GPB model falls within clinically relevant values for ventricular tachycardia (VT), but for the OVVR model, the dominant period is longer than periods associated with VT. Our results should facilitate choosing a model to match properties of interest in human cardiac tissue and to replicate arrhythmia behavior more closely. Furthermore, by indicating areas where existing models disagree, our findings suggest avenues for further experimental work.

Quantification of transmembrane currents during action potential propagation in the heart

The measurement, quantitative analysis, theory, and mathematical modeling of transmembrane potential and currents have been an integral part of the field of electrophysiology since its inception. Biophysical modeling of action potential propagation begins with detailed ionic current models for a patch of membrane within a distributed cable model. Voltage-clamp techniques have revolutionized clinical electrophysiology via the characterization of the transmembrane current gating variables; however, this kinetic information alone is insufficient to accurately represent propagation. Other factors, including channel density, membrane area, surface/volume ratio, axial conductivities, etc., are also crucial determinants of transmembrane currents in multicellular tissue but are extremely difficult to measure. Here, we provide, to our knowledge, a novel analytical approach to compute transmembrane currents directly from experimental data, which involves high-temporal (200 kHz) recordings of intra- and extracellular potential with glass microelectrodes from the epicardial surface of isolated rabbit hearts during propagation. We show for the first time, to our knowledge, that during stable planar propagation the biphasic total transmembrane current (I(m)) dipole density during depolarization was ∼0.25 ms in duration and asymmetric in amplitude (peak outward current was ∼95 μA/cm(2) and peak inward current was ∼140 μA/cm(2)), and the peak inward ionic current (I(ion)) during depolarization was ∼260 μA/cm(2) with duration of ∼1.0 ms. Simulations of stable propagation using the ionic current versus transmembrane potential relationship fit from the experimental data reproduced these values better than traditional ionic models. During ventricular fibrillation, peak I(m) was decreased by 50% and peak I(ion) was decreased by 70%. Our results provide, to our knowledge, novel quantitative information that complements voltage- and patch-clamp data.

The effect of pinacidil on postshock activation and ventricular defibrillation threshold in canine hearts

AIM

To determine the postshock activation patterns with both successful and failed shocks in a canine model of ventricular fibrillation, and whether piniacidil, an early after-depolarization (EAD) inhibitor, altered the defibrillation threshold (DFT) and postshock activation patterns.

METHODS

In 6 beagles, a basket catheter with 64 unipolar electrodes was placed in the LV for global endocardial mapping, a monophasic action potential catheter was inserted into the LV apex, and a catheter with the negative electrode in the right ventricle and the positive electrode in the superior vena cava was inserted for defibrillation. The DFT, 90% action potential duration (APD(90)) and activation recovery interval (ARI) were evaluated before and after pinacidil administration (loading dosage 0.5 mg/kg and maintenance dosage 0.5 mg·kg(-1)·h(-1), iv). Electrical heterogeneities were defined with the dispersion of ARI. After successful and failed shocks with near-DFT strength, the earliest postshock activation patterns (focal or nonfocal endocardial activation), interval and location were detected.

RESULTS

Pinacidil significantly decreased APD(90) (from 178±16 ms to 168±18 ms) and ARI from (152±10 ms to 143±10 ms) at pacing cycle length of 300 ms. The drug significantly increased VF activation rate (from 10.0±1.9 Hz to 10.8±2.0 Hz). The drug did not affect the dispersion of ARI, neither it changed DFT (baseline: 480±110 V; pinacidil: 425±55 V, P>0.05). The earliest postshock activation arose locally on the LV apical endocardium before and after the drug treatment. Pinacidil significantly prolonged the postshock cycle length of cycles 2 to 5 for the successful episodes but not for the failed episodes.

CONCLUSION

Pinacidil increases the postshock cycle length suggesting that EAD may play a role in postshock activation, while it fails to alter DFT suggesting that EAD produced by shock does not determine a defibrillation success or failure.

Effect of heterogeneities in the cellular microstructure on propagation of the cardiac action potential

Cardiac arrhythmias are initiated in regions that undergo cellular remodeling as a result of disease. Using a sub-cellular model of myocardium, we studied the mechanism of block caused by tissue microstructure remodeling: cell geometry [quantified as length/width (L/W) cell ratio] and cell-to-cell coupling (G(j)). Heterogeneities in cell L/W ratio and G ( j ) lead to block when excitability is reduced and the corresponding space constant λ (in the direction of propagation) increases by >40 %. Tissue architectures with elongated cells (i.e. large cell L/W ratios) that are better coupled (i.e. large G(j)) are less prone to block at sites of regional heterogeneities in cell geometry and/or cell coupling than tissue architectures consisting of cells with smaller L/W ratios and/or poorer coupling. Whether an increase in tissue anisotropic ratio (ANR) is arrhythmogenic or not depends on the cellular mechanism of the increase: ANR leads to an increased risk of block when G(j) decreases, but to a decreased risk of block when cell L/W ratio increases. Our findings are useful to understand the mechanisms of block in cardiac pathologies that result in tissue architecture remodeling.

The Na+/K+ pump is an important modulator of refractoriness and rotor dynamics in human atrial tissue

Pharmacological treatment of atrial fibrillation (AF) exhibits limited efficacy. Further developments require a comprehensive characterization of ionic modulators of electrophysiology in human atria. Our aim is to systematically investigate the relative importance of ionic properties in modulating excitability, refractoriness, and rotor dynamics in human atria before and after AF-related electrical remodeling (AFER). Computer simulations of single cell and tissue atrial electrophysiology were conducted using two human atrial action potential (AP) models. Changes in AP, refractory period (RP), conduction velocity (CV), and rotor dynamics caused by alterations in key properties of all atrial ionic currents were characterized before and after AFER. Results show that the investigated human atrial electrophysiological properties are primarily modulated by maximal value of Na(+)/K(+) pump current (G(NaK)) as well as conductances of inward rectifier potassium current (G(K1)) and fast inward sodium current (G(Na)). G(NaK) plays a fundamental role through both electrogenic and homeostatic modulation of AP duration (APD), APD restitution, RP, and reentrant dominant frequency (DF). G(K1) controls DF through modulation of AP, APD restitution, RP, and CV. G(Na) is key in determining DF through alteration of CV and RP, particularly in AFER. Changes in ionic currents have qualitatively similar effects in control and AFER, but effects are smaller in AFER. The systematic analysis conducted in this study unravels the important role of the Na(+)/K(+) pump current in determining human atrial electrophysiology.

Panoramic optical mapping shows wavebreak at a consistent anatomical site at the onset of ventricular fibrillation

AIMS

The first seconds of ventricular fibrillation (VF) are well organized and can consist of just one to two rotating waves (rotors). New rotors are spawned when local propagation block causes wave fragmentation. We hypothesized that this process, which leads to fully developed VF, begins at a consistent anatomic site.

METHODS AND RESULTS

We initiated VF with a stimulus timed to the local T-wave in 10 isolated pig hearts. Hearts were stained with a voltage-sensitive dye and four video cameras recorded electrical propagation panoramically across the epicardium. In each VF episode, we identified the position of the first wavebreak event that produced new rotor(s) that persisted for at least one cycle. The first such wavebreak occurred along the anterior right ventricular insertion (ARVI) in 26 of 32 VF episodes. In these episodes, wavebreak sites were 6 ± 4 mm from the midline of the ARVI. In the remaining 6 episodes, wavebreak sites were 24 ± 5 mm from the midline on either the LV or RV. During rapid pacing, conduction speed was locally depressed at the ARVI when waves crossed parallel to the midline. Action potential duration (APD) was slightly longer (2.2 ± 2.1 ms) at the ARVI compared with other sites (P< 0.01). Temporal APD alternans were small and not unique to the break site, suggesting that dynamic APD properties were not the cause of wavebreak.

CONCLUSION

The ARVI is the dominant site for wavebreak at the onset of VF in normal myocardium. This may be due to the anatomic complexity of the region.

Teaching cardiac electrophysiology modeling to undergraduate students: laboratory exercises and GPU programming for the study of arrhythmias and spiral wave dynamics

As part of a 3-wk intersession workshop funded by a National Science Foundation Expeditions in Computing award, 15 undergraduate students from the City University of New York(1) collaborated on a study aimed at characterizing the voltage dynamics and arrhythmogenic behavior of cardiac cells for a broad range of physiologically relevant conditions using an in silico model. The primary goal of the workshop was to cultivate student interest in computational modeling and analysis of complex systems by introducing them through lectures and laboratory activities to current research in cardiac modeling and by engaging them in a hands-on research experience. The success of the workshop lay in the exposure of the students to active researchers and experts in their fields, the use of hands-on activities to communicate important concepts, active engagement of the students in research, and explanations of the significance of results as the students generated them. The workshop content addressed how spiral waves of electrical activity are initiated in the heart and how different parameter values affect the dynamics of these reentrant waves. Spiral waves are clinically associated with tachycardia, when the waves remain stable, and with fibrillation, when the waves exhibit breakup. All in silico experiments were conducted by simulating a mathematical model of cardiac cells on graphics processing units instead of the standard central processing units of desktop computers. This approach decreased the run time for each simulation to almost real time, thereby allowing the students to quickly analyze and characterize the simulated arrhythmias. Results from these simulations, as well as some of the background and methodology taught during the workshop, is presented in this article along with the programming code and the explanations of simulation results in an effort to allow other teachers and students to perform their own demonstrations, simulations, and studies.

Role of KATP channels in the maintenance of ventricular fibrillation in cardiomyopathic human hearts

RATIONALE

Ventricular fibrillation (VF) leads to global ischemia. The modulation of ischemia-dependent pathways may alter the electrophysiological evolution of VF.

OBJECTIVE

We addressed the hypotheses that there is regional disease-related expression of K(ATP) channels in human cardiomyopathic hearts and that K(ATP) channel blockade promotes spontaneous VF termination by attenuating spatiotemporal dispersion of refractoriness.

METHODS AND RESULTS

In a human Langendorff model, electric mapping of 6 control and 9 treatment (10 μmol/L glibenclamide) isolated cardiomyopathic hearts was performed. Spontaneous defibrillation was studied and mean VF cycle length was compared regionally at VF onset and after 180 seconds between control and treatment groups. K(ATP) subunit gene expression was compared between LV endocardium versus epicardium in myopathic hearts. Spontaneous VF termination occurred in 1 of 6 control hearts and 7 of 8 glibenclamide-treated hearts (P=0.026). After 180 seconds of ischemia, a transmural dispersion in VF cycle length was observed between epicardium and endocardium (P=0.001), which was attenuated by glibenclamide. There was greater gene expression of all K(ATP) subunit on the endocardium compared with the epicardium (P<0.02). In an ischemic rat heart model, transmural dispersion of refractoriness (ΔERP(Transmural)=ERP(Epicardium)-ERP(Endocardium)) was verified with pacing protocols. ΔERP(Transmural) in control was 5 ± 2 ms and increased to 36 ± 5 ms with ischemia. This effect was greatly attenuated by glibenclamide (ΔERP(Transmural) for glibenclamide+ischemia=4.9 ± 4 ms, P=0.019 versus control ischemia).

CONCLUSIONS

K(ATP) channel subunit gene expression is heterogeneously altered in the cardiomyopathic human heart. Blockade of K(ATP) channels promotes spontaneous defibrillation in cardiomyopathic human hearts by attenuating the ischemia-dependent spatiotemporal heterogeneity of refractoriness during early VF.

Na+ channel distribution and electrophysiological heterogeneities in guinea pig ventricular wall

We sought to explore the distribution pattern of Na+ channels across ventricular wall, and to determine its functional correlates, in the guinea pig heart. Voltage-dependent Na+ channel (Nav) protein expression levels were measured in transmural samples of ventricular tissue by Western blotting. Isolated, perfused heart preparations were used to record monophasic action potentials and volume-conducted ECG, and to measure effective refractory periods (ERPs) and pacing thresholds, in order to assess excitability, electrical restitution kinetics, and susceptibility to stimulation-evoked tachyarrhythmias at epicardial and endocardial stimulation sites. In both ventricular chambers, Nav protein expression was higher at endocardium than epicardium, with midmyocardial layers showing intermediate expression levels. Endocardial stimulation sites showed higher excitability, as evidenced by lower pacing thresholds during regular stimulation and downward displacement of the strength-interval curve reconstructed after extrasystolic stimulation compared with epicardium. ERP restitution assessed over a wide range of pacing rates showed greater maximal slope and faster kinetics at endocardial than epicardial stimulation sites. Flecainide, a Na+ channel blocker, reduced the maximal ERP restitution slope, slowed restitution kinetics, and eliminated epicardial-to-endocardial difference in dynamics of electrical restitution. Greater excitability and steeper electrical restitution have been associated with greater arrhythmic susceptibility of endocardium than epicardium, as assessed by measuring ventricular fibrillation threshold, inducibility of tachyarrhythmias by rapid cardiac pacing, and the magnitude of stimulation-evoked repolarization alternans. In conclusion, higher Na+ channel expression levels may contribute to greater excitability, steeper electrical restitution slopes and faster restitution kinetics, and greater susceptibility to stimulation-evoked tachyarrhythmias at endocardium than epicardium in the guinea pig heart.

Nicorandil normalizes prolonged repolarisation in the first transgenic rabbit model with Long-QT syndrome 1 both in vitro and in vivo

Transgenic rabbits expressing loss-of-function pore mutants of the human gene KCNQ1 (K(v)LQT1-Y315S) have a Long QT-Syndrome 1 (LQT1) phenotype. We evaluated for the first time the effect of nicorandil, an opener of ATP-sensitive potassium channels, and of isoproterenol on cardiac action potential duration and heart rate dependent dispersion of repolarisation in transgenic LQT1 rabbits. In vivo LQT1 and littermate control were subjected to transvenous electrophysiological studies; in vitro monophasic action potentials were recorded from explanted Langendorff-perfused hearts. In vivo ventricular effective refractory periods (VERP) at the right ventricular base were significantly prolonged in LQT1 as compared to littermate control, resulting in a more pronounced VERP dispersion in LQT1. This difference in VERP dispersion between LQT1 and littermate control disappeared after infusion of nicorandil. In vitro, mean action potential durations (APD(75) and APD(90)) of LQT1 were significantly prolonged compared to littermate control at baseline. Nicorandil decreased APD(75) and APD(90) in LQT1 and littermate control at all stimulated heart rates. After adding nicorandil, the APD(90) at all hearts rates and the APD(75) at high heart rates were no longer different. Dispersion of repolarisation (∆APD(75) and ∆APD(90)) was heart rate dependently decreased after nicorandil at all tested stimulation cycle lengths only in LQT1. We demonstrated phenotypic differences of LQT1 and littermate control in vivo and in vitro. Nicorandil 20μmol/l improved repolarisation abnormalities and heterogeneities in transgenic LQT1 rabbits.

Mechanisms of defibrillation

Electrical shock has been the one effective treatment for ventricular fibrillation for several decades. With the advancement of electrical and optical mapping techniques, histology, and computer modeling, the mechanisms responsible for defibrillation are now coming to light. In this review, we discuss recent work that demonstrates the various mechanisms responsible for defibrillation. On the cellular level, membrane depolarization and electroporation affect defibrillation outcome. Cell bundles and collagenous septae are secondary sources and cause virtual electrodes at sites far from shocking electrodes. On the whole-heart level, shock field gradient and critical points determine whether a shock is successful or whether reentry causes initiation and continuation of fibrillation.

Transmural ultrasound-based visualization of patterns of action potential wave propagation in cardiac tissue

The pattern of action potential propagation during various tachyarrhythmias is strongly suspected to be composed of multiple re-entrant waves, but has never been imaged in detail deep within myocardial tissue. An understanding of the nature and dynamics of these waves is important in the development of appropriate electrical or pharmacological treatments for these pathological conditions. We propose a new imaging modality that uses ultrasound to visualize the patterns of propagation of these waves through the mechanical deformations they induce. The new method would have the distinct advantage of being able to visualize these waves deep within cardiac tissue. In this article, we describe one step that would be necessary in this imaging process—the conversion of these deformations into the action potential induced active stresses that produced them. We demonstrate that, because the active stress induced by an action potential is, to a good approximation, only nonzero along the local fiber direction, the problem in our case is actually overdetermined, allowing us to obtain a complete solution. Use of two- rather than three-dimensional displacement data, noise in these displacements, and/or errors in the measurements of the fiber orientations all produce substantial but acceptable errors in the solution. We conclude that the reconstruction of action potential-induced active stress from the deformation it causes appears possible, and that, therefore, the path is open to the development of the new imaging modality.

Targeting device therapy: genomics of sudden death

This article discusses the development and use of genomic predictors to define the population at risk for sudden cardiac death, which is usually defined as death from cardiac causes within an hour of symptom onset. The identification of genetic predictors of sudden death in heart failure is in its earliest stages. Mutations in ion channels have been shown to cause inherited forms of sudden death; there is, however, little evidence that mutations or rare single nucleotide polymorphisms (SNPs) in those genes are important causes of the common forms of sudden death. Other common variants in ion channels and related genes are associated with sudden death in the setting of acute myocardial infarction or heart failure. Ultimately, we hope to identify a handful of SNPs that modulate the risk of sudden death in heart failure and to develop an algorithm to predict risk based on genotype.

Arrhythmia phenotype in mouse models of human long QT

Enhanced dispersion of repolarization (DR) was proposed as a unifying mechanism, central to arrhythmia genesis in the long QT (LQT) syndrome. In mammalian hearts, K(+) channels are heterogeneously expressed across the ventricles resulting in 'intrinsic' DR that may worsen in long QT. DR was shown to be central to the arrhythmia phenotype of transgenic mice with LQT caused by loss of function of the dominant mouse K(+) currents. Here, we investigated the arrhythmia phenotype of mice with targeted deletions of KCNE1 and KCNH2 genes which encode for minK/IsK and Merg1 (mouse homolog of human ERG) proteins resulting in loss of function of I(Ks) and I(Kr), respectively. Both currents are important human K(+) currents associated with LQT5 and LQT2. Loss of minK, a protein subunit that interacts with KvLQT1, results in a marked reduction of I(Ks) giving rise to the Jervell and Lange-Nielsen syndrome and the reduced KCNH2 gene reduces MERG and I(Kr). Hearts were perfused, stained with di-4-ANEPPS and optically mapped to compare action potential durations (APDs) and arrhythmia phenotype in homozygous minK (minK(-/-)) and heterozygous Merg1 (Merg(+/-)) deletions and littermate control mice. MinK(-/-) mice has similar APDs and no arrhythmias (n = 4). Merg(+/-) mice had prolonged APDs (from 20 +/- 6 to 32 +/- 9 ms at the base, p < 0.01; from 18 +/- 5 to 25 +/- 9 ms at the apex, p < 0.01; n = 8), longer refractory periods (RP) (36 +/- 14 to 63 +/- 27 at the base, p < 0.01 and 34 +/- 5 to 53 +/- 21 ms at the apex, p < 0.03; n = 8), higher DR 10.4 +/- 4.1 vs. 14 +/- 2.3 ms, p < 0.02) and similar conduction velocities (n = 8). Programmed stimulation exposed a higher propensity to VT in Merg(+/-) mice (60% vs. 10%). A comparison of mouse models of LQT based on K(+) channel mutations important to human and mouse repolarization emphasizes DR as a major determinant of arrhythmia vulnerability.

Effects of hypocalcemia on electrical restitution and ventricular fibrillation

We have shown previously that verapamil reduces the slope of the action potential duration (APD) restitution relation, suppresses APD alternans and converts ventricular fibrillation (VF) into a periodic rhythm. To determine whether these effects result primarily from reduction of the APD restitution slope, as opposed to alteration of calcium dynamics unrelated to restitution, we tested the effects of hypocalcemia ([CaCl2]=31-125 microM) in canine ventricle. At normal [CaCl2] (2.0 mM), the slope of the APD restitution relation was >1, APD alternans occurred during rapid pacing and VF was inducible. During hypocalcemia the slope of the restitution relation remained >1 and the magnitude of APD alternans was unchanged. VF still was inducible and the mean cycle length and the variance of the FFT spectra during VF were not altered significantly. These results suggest that reduction of APD restitution slope, rather than blockade of ICa per se, is responsible for the antifibrillatory effects of verapamil in this model of pacing-induced VF, lending further support to the idea that APD restitution kinetics is a key determinant of VF.

Vortex filament dynamics in computational models of ventricular fibrillation in the heart

In three-dimensional cardiac tissue, the re-entrant waves that sustain ventricular fibrillation rotate around a line of phase singularity or vortex filament. The aim of this study was to investigate how the behavior of these vortex filaments is influenced by membrane kinetics, initial conditions, and tissue geometry in computational models of excitable tissue. A monodomain model of cardiac tissue was used, with kinetics described by a three-variable simplified ionic model (3V-SIM). Two versions of 3V-SIM were used, one with steep action potential duration restitution, and one with reduced excitability. Re-entrant fibrillation was then simulated in three tissue geometries: a cube, a slab, and an anatomically detailed model of rabbit ventricles. Filaments were identified using a phase-based method, and the number, size, origin, and orientation of filaments was tracked throughout each simulation. The main finding of this study is that kinetics, initial conditions, geometry, and anisotropy all affected the number, proliferation, and orientation of vortex filaments in re-entrant fibrillation. An important finding of this study was that the behavior of vortex filaments in simplified slab geometry representing part of the ventricular wall did not necessarily predict behavior in an anatomically detailed model of the rabbit ventricles.

Bradycardic onset of spiral wave re-entry: structural substrates

AIMS

The least understood aspect of re-entrant cardiac arrhythmias is how they start spontaneously. The known mechanisms for re-entry induction involve the application of premature electrical stimuli or rapid pacing, whereas in a clinical setting, re-entry often occurs at normal heart rates. Here, we propose a physiological mechanism of re-entry onset at normal and slow heart rates, which is based on structurally determined heterogeneities.

METHODS AND RESULTS

Using a two-dimensional tissue model with Luo-Rudy II kinetics, we study electrical propagation in the presence of macroscopic coupling heterogeneities. We find that spiral wave re-entry occurs if steep and smooth coupling gradients are situated side by side, with the critical steepness depending on the frequency of stimulation. We demonstrate how bradycardia can unmask a slow endogenous pacemaker in a poorly coupled region, subsequently leading to spiral wave re-entry.

CONCLUSION

In the presence of coupling heterogeneities, a single excitation coming from the less coupled region may induce spiral wave re-entry.

Tunnel propagation of postshock activations as a hypothesis for fibrillation induction and isoelectric window

Comprehensive understanding of the ventricular response to shocks is the approach most likely to succeed in reducing defibrillation threshold. We propose a new theory of shock-induced arrhythmogenesis that unifies all known aspects of the response of the heart to monophasic (MS) and biphasic (BS) shocks. The central hypothesis is that submerged "tunnel" propagation of postshock activations through shock-induced intramural excitable areas underlies fibrillation induction and the existence of isoelectric window. We conducted simulations of fibrillation induction using a realistic bidomain model of rabbit ventricles. Following pacing, MS and BS of various strengths/timings were delivered. The results demonstrated that, during the isoelectric window, an activation originated deep within the ventricular wall, arising from virtual electrodes; it then propagated fully intramurally through an excitable tunnel induced by the shock, until it emerged onto the epicardium, becoming the earliest-propagated postshock activation. Differences in shock outcomes for MS and BS were found to stem from the narrower BS intramural postshock excitable area, often resulting in conduction block, and the difference in the mechanisms of origin of the postshock activations, namely intramural virtual electrode-induced phase singularity for MS and virtual electrode-induced propagated graded response for BS. This study provides a novel analysis of the 3D mechanisms underlying the origin of postshock activations in the process of fibrillation induction by MS and BS and the existence of isoelectric window. The tunnel propagation hypothesis could open a new avenue for interventions exploration to achieve significantly lower defibrillation threshold.

The pinwheel experiment revisited: effects of cellular electrophysiological properties on vulnerability to cardiac reentry

In normal heart, ventricular fibrillation can be induced by a single properly timed strong electrical or mechanical stimulus. A mechanism first proposed by Winfree and coined the “pinwheel experiment” emphasizes the timing and strength of the stimulus in inducing figure-of-eight reentry. However, the effects of cellular electrophysiological properties on vulnerability to reentry in the pinwheel scenario have not been investigated. In this study, we extend Winfree's pinwheel experiment to show how the vulnerability to reentry is affected by the graded action potential responses induced by a strong premature stimulus, action potential duration (APD), and APD restitution in simulated monodomain homogeneous two-dimensional tissue. We find that a larger graded response, longer APD, or steeper APD restitution slope reduces the vulnerable window of reentry. Strong graded responses and long APD promote tip-tip interactions at long coupling intervals, causing the two initiated spiral wave tips to annihilate. Steep APD restitution promotes wave front-wave back interaction, causing conduction block in the central common pathway of figure-of-eight reentry. We derive an analytical treatment that shows good agreement with numerical simulation results.