Curvature mediated source and sink effects on the genesis of premature ventricular complexes in long QT syndrome.

Premature ventricular complexes (PVCs) are spontaneous excitations occurring in the ventricles of the heart, which are associated with ventricular arrhythmias and sudden cardiac death. Under long QT conditions, PVCs can be mediated by repolarization gradient (RG) and early afterdepolarizations (EADs), yet the effects of heterogeneities or geometry of the RG or EAD regions on PVC genesis remain incompletely understood. In this study, we use computer simulation to systematically investigate the effects of the curvature of the RG border region on PVC genesis under long QT conditions. We show that PVCs can be either promoted or suppressed by negative or positive RG border curvature depending on the source and sink conditions. When the origin of oscillation is in the source region and the source is too strong, a positive RG border curvature can promote PVCs by causing the source area to oscillate. When the origin of oscillation is in the sink region, a negative RG border curvature can promote PVCs by causing the sink area to oscillate. Furthermore, EAD-mediated PVCs are also promoted by negative border curvature. We also investigate the effects of wavefront curvature and show that PVCs are promoted by convex but suppressed by concave wavefronts, however, the effect of wavefront curvature is much smaller than that of RG border curvature. In conclusion, besides the increase of RG and occurrence of EADs caused by QT prolongation, the geometry of the RG border plays important roles in PVC genesis, which can greatly increase the risk of arrhythmias in cardiac diseases.

Intracellular ion accumulation in the genesis of complex action potential dynamics under cardiac diseases.

Intracellular ions, including sodium (Na^{+}), calcium (Ca^{2+}), and potassium (K^{+}), etc., accumulate slowly after a change of the state of the heart, such as a change of the heart rate. The goal of this study is to understand the roles of slow ion accumulation in the genesis of cardiac memory and complex action-potential duration (APD) dynamics that can lead to lethal cardiac arrhythmias. We carry out numerical simulations of a detailed action potential model of ventricular myocytes under normal and diseased conditions, which exhibit memory effects and complex APD dynamics. We develop a low-dimensional iterated map (IM) model to describe the dynamics of Na^{+}, Ca^{2+}, and APD and use it to uncover the underlying dynamical mechanisms. The development of the IM model is informed by simulation results under the normal condition. We then use the IM model to perform linear stability analyses and computer simulations to investigate the bifurcations and complex APD dynamics, which depend on the feedback loops between APD and intracellular Ca^{2+} and Na^{+} concentrations and the steepness of the APD response to the ion concentrations. When the feedback between APD and Ca^{2+} concentration is positive, a Hopf bifurcation leading to periodic oscillatory behavior occurs as the steepness of the APD response to the ion concentrations increases. The negative feedback loop between APD and Na^{+} concentration is required for the Hopf bifurcation. When the feedback between APD and Ca^{2+} concentration is negative, period-doubling bifurcations leading to high periodicity and chaos occurs. In this case, Na^{+} accumulation plays little role in the dynamics. Finally, we carry out simulations of the detailed action potential model under two diseased conditions, which exhibit steep APD responses to ion concentrations. Under both conditions, Hopf bifurcations leading to slow oscillations or period-doubling bifurcations leading to high periodicity and chaotic APD dynamics occur, depending on the strength of the ion pump-Na^{+}-Ca^{2+} exchanger. Using functions reconstructed from the simulation data, the IM model accurately captures the bifurcations and dynamics under the two diseased conditions. In conclusion, besides using computer simulations of a detailed high-dimensional action-potential model to investigate the effects of slow ion accumulation and short-term memory on bifurcations and genesis of complex APD dynamics in cardiac myocytes under diseased conditions, this study also provides a low-dimensional mathematical tool, i.e., the IM model, to allow stability analyses for uncovering the underlying mechanisms.

Dissecting the roles of calcium cycling and its coupling with voltage in the genesis of early afterdepolarizations in cardiac myocyte models.

Early afterdepolarizations (EADs) are abnormal depolarizations during the plateau phase of the action potential, which are known to be associated with lethal arrhythmias in the heart. There are two major hypotheses for EAD genesis based on experimental observations, i.e., the voltage (Vm)-driven and intracellular calcium (Ca)-driven mechanisms. In ventricular myocytes, Ca and Vm are bidirectionally coupled, which can affect each other's dynamics and result in new dynamics, however, the roles of Ca cycling and its coupling with Vm in the genesis of EADs have not been well understood. In this study, we use an action potential model that is capable of independent Vm and Ca oscillations to investigate the roles of Vm and Ca coupling in EAD genesis. Four different mechanisms of EADs are identified, which are either driven by Vm oscillations or Ca oscillations alone, or oscillations caused by their interactions. We also use 5 other ventricular action potential models to assess these EAD mechanisms and show that EADs in these models are mainly Vm-driven. These mechanistic insights from our simulations provide a theoretical base for understanding experimentally observed EADs and EAD-related arrhythmogenesis.

Phase 2 Re-Entry Without Ito: Role of Sodium Channel Kinetics in Brugada Syndrome Arrhythmias.

BACKGROUND: In Brugada syndrome (BrS), phase 2 re-excitation/re-entry (P2R) induced by the transient outward potassium current (Ito) is a proposed arrhythmia mechanism; yet, the most common genetic defects are loss-of-function sodium channel mutations. OBJECTIVES: The authors used computer simulations to investigate how sodium channel dysfunction affects P2R-mediated arrhythmogenesis in the presence and absence of Ito. METHODS: Computer simulations were carried out in 1-dimensional cables and 2-dimensional tissue using guinea pig and human ventricular action potential models. RESULTS: In the presence of Ito sufficient to generate robust P2R, reducing sodium current (INa) peak amplitude alone only slightly potentiated P2R. When INa inactivation kinetics were also altered to simulate reported effects of BrS mutations and sodium channel blockers, however, P2R occurred even in the absence of Ito. These effects could be potentiated by delaying L-type calcium channel activation or increasing ATP-sensitive potassium current, consistent with experimental and clinical findings. INa-mediated P2R also accounted for sex-related, day and night-related, and fever-related differences in arrhythmia risk in BrS patients. CONCLUSIONS: Altered INa kinetics synergize powerfully with reduced INa amplitude to promote P2R-induced arrhythmias in BrS in the absence of Ito, establishing a robust mechanistic link between altered INa kinetics and the P2R-mediated arrhythmia mechanism.

Heterogeneous cardiac sympathetic innervation gradients promote arrhythmogenesis in murine dilated cardiomyopathy.

Ventricular arrhythmias (VAs) in heart failure are enhanced by sympathoexcitation. However, radiotracer studies of catecholamine uptake in failing human hearts demonstrate a proclivity for VAs in patients with reduced cardiac sympathetic innervation. We hypothesized that this counterintuitive finding is explained by heterogeneous loss of sympathetic nerves in the failing heart. In a murine model of dilated cardiomyopathy (DCM), delayed PET imaging of sympathetic nerve density using the catecholamine analog [11C]meta-Hydroxyephedrine demonstrated global hypoinnervation in ventricular myocardium. Although reduced, sympathetic innervation in 2 distinct DCM models invariably exhibited transmural (epicardial to endocardial) gradients, with the endocardium being devoid of sympathetic nerve fibers versus controls. Further, the severity of transmural innervation gradients was correlated with VAs. Transmural innervation gradients were also identified in human left ventricular free wall samples from DCM versus controls. We investigated mechanisms underlying this relationship by in silico studies in 1D, 2D, and 3D models of failing and normal human hearts, finding that arrhythmogenesis increased as heterogeneity in sympathetic innervation worsened. Specifically, both DCM-induced myocyte electrical remodeling and spatially inhomogeneous innervation gradients synergistically worsened arrhythmogenesis. Thus, heterogeneous innervation gradients in DCM promoted arrhythmogenesis. Restoration of homogeneous sympathetic innervation in the failing heart may reduce VAs.

Fibroblasts in heart scar tissue directly regulate cardiac excitability and arrhythmogenesis.

After heart injury, dead heart muscle is replaced by scar tissue. Fibroblasts can electrically couple with myocytes, and changes in fibroblast membrane potential can lead to myocyte excitability, which suggests that fibroblast-myocyte coupling in scar tissue may be responsible for arrhythmogenesis. However, the physiologic relevance of electrical coupling of myocytes and fibroblasts and its impact on cardiac excitability in vivo have never been demonstrated. We genetically engineered a mouse that expresses the optogenetic cationic channel ChR2 (H134R) exclusively in cardiac fibroblasts. After myocardial infarction, optical stimulation of scar tissue elicited organ-wide cardiac excitation and induced arrhythmias in these animals. Complementing computational modeling with experimental approaches, we showed that gap junctional and ephaptic coupling, in a synergistic yet functionally redundant manner, excited myocytes coupled to fibroblasts.

Myofibroblast senescence promotes arrhythmogenic remodeling in the aged infarcted rabbit heart.

Progressive tissue remodeling after myocardial infarction (MI) promotes cardiac arrhythmias. This process is well studied in young animals, but little is known about pro-arrhythmic changes in aged animals. Senescent cells accumulate with age and accelerate age-associated diseases. Senescent cells interfere with cardiac function and outcome post-MI with age, but studies have not been performed in larger animals, and the mechanisms are unknown. Specifically, age-associated changes in timecourse of senescence and related changes in inflammation and fibrosis are not well understood. Additionally, the cellular and systemic role of senescence and its inflammatory milieu in influencing arrhythmogenesis with age is not clear, particularly in large animal models with cardiac electrophysiology more similar to humans than previously studied animal models. Here, we investigated the role of senescence in regulating inflammation, fibrosis, and arrhythmogenesis in young and aged infarcted rabbits. Aged rabbits exhibited increased peri-procedural mortality and arrhythmogenic electrophysiological remodeling at the infarct border zone (IBZ) compared to young rabbits. Studies of the aged infarct zone revealed persistent myofibroblast senescence and increased inflammatory signaling over a 12-week timecourse. Senescent IBZ myofibroblasts in aged rabbits appear to be coupled to myocytes, and our computational modeling showed that senescent myofibroblast-cardiomyocyte coupling prolongs action potential duration (APD) and facilitates conduction block permissive of arrhythmias. Aged infarcted human ventricles show levels of senescence consistent with aged rabbits, and senescent myofibroblasts also couple to IBZ myocytes. Our findings suggest that therapeutic interventions targeting senescent cells may mitigate arrhythmias post-MI with age.

Bifurcations to transient and oscillatory excitations in inhomogeneous excitable media: Insights into arrhythmogenesis in long QT syndrome.

Ventricular arrhythmias are the leading cause of sudden cardiac death. Understanding the mechanisms of arrhythmia initiation is important for developing effective therapeutics for prevention. Arrhythmias can be induced via premature external stimuli or occur spontaneously via dynamical instabilities. Computer simulations have shown that a large repolarization gradient due to regional prolongation of the action potential duration can result in instabilities leading to premature excitations and arrhythmias, but the bifurcation remains to be elucidated. In this study we carry out numerical simulations and linear stability analyses using a one-dimensional heterogeneous cable consisting of the FitzHugh-Nagumo model. We show that a Hopf bifurcation leads to local oscillations, which, once their amplitudes are large enough, lead to spontaneous propagating excitations. Depending on the degree of heterogeneities, these excitations can range from one to many and to be sustained oscillations, manifesting as premature ventricular contractions (PVCs) and sustained arrhythmias. The dynamics depends on the repolarization gradient and the length of the cable. Complex dynamics is also induced by the repolarization gradient. The mechanistic insights from the simple model may help in the understanding of the genesis of PVCs and arrhythmias in long QT syndrome.

Cardiac Alternans: From Bedside to Bench and Back.

Cardiac alternans arises from dynamical instabilities in the electrical and calcium cycling systems of the heart, and often precedes ventricular arrhythmias and sudden cardiac death. In this review, we integrate clinical observations with theory and experiment to paint a holistic portrait of cardiac alternans: the underlying mechanisms, arrhythmic manifestations and electrocardiographic signatures. We first summarize the cellular and tissue mechanisms of alternans that have been demonstrated both theoretically and experimentally, including 3 voltage-driven and 2 calcium-driven alternans mechanisms. Based on experimental and simulation results, we describe their relevance to mechanisms of arrhythmogenesis under different disease conditions, and their link to electrocardiographic characteristics of alternans observed in patients. Our major conclusion is that alternans is not only a predictor, but also a causal mechanism of potentially lethal ventricular and atrial arrhythmias across the full spectrum of arrhythmia mechanisms that culminate in functional reentry, although less important for anatomic reentry and focal arrhythmias.

Bistable spiral wave dynamics in electrically excitable media.

We show that a positive feedback loop between sodium current inactivation and wave-front ramp-up speed causes a saddle-node bifurcation to result in bistable planar and spiral waves in electrically excitable media, in which both slow and fast waves are triggered by different stimulation protocols. Moreover, the two types of spiral wave conduction may interact to give rise to more complex spiral wave dynamics. The transitions between different spiral wave behaviors via saddle-node bifurcation can be a candidate mechanism for transitions widely seen in cardiac arrhythmias and neural diseases.

Modeling Calcium Cycling in the Heart: Progress, Pitfalls, and Challenges.

Intracellular calcium (Ca) cycling in the heart plays key roles in excitation-contraction coupling and arrhythmogenesis. In cardiac myocytes, the Ca release channels, i.e., the ryanodine receptors (RyRs), are clustered in the sarcoplasmic reticulum membrane, forming Ca release units (CRUs). The RyRs in a CRU act collectively to give rise to discrete Ca release events, called Ca sparks. A cell contains hundreds to thousands of CRUs, diffusively coupled via Ca to form a CRU network. A rich spectrum of spatiotemporal Ca dynamics is observed in cardiac myocytes, including Ca sparks, spark clusters, mini-waves, persistent whole-cell waves, and oscillations. Models of different temporal and spatial scales have been developed to investigate these dynamics. Due to the complexities of the CRU network and the spatiotemporal Ca dynamics, it is challenging to model the Ca cycling dynamics in the cardiac system, particularly at the tissue sales. In this article, we review the progress of modeling of Ca cycling in cardiac systems from single RyRs to the tissue scale, the pros and cons of the current models and different modeling approaches, and the challenges to be tackled in the future.

Synchronization of spatially discordant voltage and calcium alternans in cardiac tissue.

The heart is an excitable medium which is excited by membrane potential depolarization and propagation. Membrane potential depolarization brings in calcium (Ca) through the Ca channels to trigger intracellular Ca release for contraction of the heart. Ca also affects voltage via Ca-dependent ionic currents, and thus, voltage and Ca are bidirectionally coupled. It has been shown that the voltage subsystem or the Ca subsystem can generate its own dynamical instabilities which are affected by their bidirectional couplings, leading to complex dynamics of action potential and Ca cycling. Moreover, the dynamics become spatiotemporal in tissue in which cells are diffusively coupled through voltage. A widely investigated spatiotemporal dynamics is spatially discordant alternans (SDA) in which action potential duration (APD) or Ca amplitude exhibits temporally period-2 and spatially out-of-phase patterns, i.e., APD-SDA and Ca-SDA patterns, respectively. However, the mechanisms of formation, stability, and synchronization of APD-SDA and Ca-SDA patterns remain incompletely understood. In this paper, we use cardiac tissue models described by an amplitude equation, coupled iterated maps, and reaction-diffusion equations with detailed physiology (the ionic model) to perform analytical and computational investigations. We show that, when the Ca subsystem is stable, the Ca-SDA pattern always follows the APD-SDA pattern, and thus, they are always synchronized. When the Ca subsystem is unstable, synchronization of APD-SDA and Ca-SDA patterns depends on the stabilities of both subsystems, their coupling strengths, and the spatial scales of the initial Ca-SDA patterns. Spontaneous (initial condition-independent) synchronization is promoted by enhancing APD instability and reducing Ca instability as well as stronger Ca-to-APD and APD-to-Ca coupling, a pattern formation caused by dynamical instabilities. When Ca is more unstable and APD is less unstable or APD-to-Ca coupling is weak, synchronization of APD-SDA and Ca-SDA patterns is promoted by larger initially synchronized Ca-SDA clusters, i.e., initial condition-dependent synchronization. The synchronized APD-SDA and Ca-SDA patterns can be locked in-phase, antiphase, or quasiperiodic depending on the coupling relationship between APD and Ca. These theoretical and simulation results provide mechanistic insights into the APD-SDA and Ca-SDA dynamics observed in experimental studies.

Bistable nerve conduction.

It has been demonstrated experimentally that slow and fast conduction waves with distinct conduction velocities can occur in the same nerve system depending on the strength or the form of the stimulus, which give rise to two modes of nerve functions. However, the mechanisms remain to be elucidated. In this study, we use computer simulations of the cable equation with modified Hodgkin-Huxley kinetics and analytical solutions of a simplified model to show that stimulus-dependent slow and fast waves recapitulating the experimental observations can occur in the cable, which are the two stable conduction states of a bistable conduction behavior. The bistable conduction is caused by a positive feedback loop of the wavefront upstroke speed, mediated by the sodium channel inactivation properties. Although the occurrence of bistable conduction only requires the presence of the sodium current, adding a calcium current to the model further promotes bistable conduction by potentiating the slow wave. We also show that the bistable conduction is robust, occurring for sodium and calcium activation thresholds well within the experimentally determined ones of the known sodium and calcium channel families. Since bistable conduction can occur in the cable equation of Hodgkin-Huxley kinetics with a single inward current, i.e., the sodium current, it can be a generic mechanism applicable to stimulus-dependent fast and slow conduction not only in the nerve systems but also in other electrically excitable systems, such as cardiac muscles.

Kramers Rate Theory of Pacemaker Dynamics in Noisy Excitable Media.

Rhythmic activities, which are usually driven by pacemakers, are common in biological systems. In noisy excitable media, pacemakers are self-organized firing clusters, but the underlying dynamics remains to be elucidated. Here we develop a Kramers rate theory of coupled cells to describe the firing properties of pacemakers and their dependence on coupling strength and system size and dimension. The theory captures accurately the simulation results of tissue models with stochastic Hodgkin-Huxley equations except when transitions from pacemakers to spiral waves occur under weak coupling.

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.

Why Is Only Type 1 Electrocardiogram Diagnostic of Brugada Syndrome? Mechanistic Insights From Computer Modeling.

BACKGROUND: Three types of characteristic ST-segment elevation are associated with Brugada syndrome but only type 1 is diagnostic. Why only type 1 ECG is diagnostic remains unanswered. METHODS: Computer simulations were performed in single cells, 1-dimensional cables, and 2-dimensional tissues to investigate the effects of the peak and late components of the transient outward potassium current (Ito), sodium current, and L-type calcium current (ICa,L) as well as other potassium currents on the genesis of ECG morphologies and phase 2 reentry (P2R). RESULTS: Although a sufficiently large peak Ito was required to result in the type 1 ECG pattern and P2R, increasing the late component of Ito converted type 1 ECG to type 2 ECG and suppressed P2R. Increasing the peak Ito promoted spiral wave breakup, potentiating the transition from tachycardia to fibrillation, but increasing the late Ito prevented spiral wave breakup by flattening the action potential duration restitution and preventing P2R. A sufficiently large ICa,L conductance was needed for P2R to occur, but once above the critical conductance, blocking ICa,L promoted P2R. However, selectively blocking the window and late components of ICa,L suppressed P2R, countering the effect of the late Ito. Blocking either the peak or late components of sodium current promoted P2R, with the late sodium current blockade having the larger effect. As expected, increasing other potassium currents potentiated P2R, with ATP-sensitive potassium current exhibiting a larger effect than rapid and slow component of the delayed rectifier potassium current. CONCLUSIONS: The peak Ito promotes type 1 ECG and P2R, whereas the late Ito converts type 1 ECG to type 2 ECG and suppresses P2R. Blocking the peak ICa,L and either the peak or the late sodium current promotes P2R, whereas blocking the window and late ICa,L suppresses P2R. These results provide important insights into the mechanisms of arrhythmogenesis and potential therapeutic targets for treatment of Brugada syndrome. Graphic Abstract: A graphic abstract is available for this article.

Mitochondrial Contributions in the Genesis of Delayed Afterdepolarizations in Ventricular Myocytes.

Mitochondria fulfill the cell's energy demand and affect the intracellular calcium (Ca2+) dynamics via direct Ca2+ exchange, the redox effect of reactive oxygen species (ROS) on Ca2+ handling proteins, and other signaling pathways. Recent experimental evidence indicates that mitochondrial depolarization promotes arrhythmogenic delayed afterdepolarizations (DADs) in cardiac myocytes. However, the nonlinear interactions among the Ca2+ signaling pathways, ROS, and oxidized Ca2+/calmodulin-dependent protein kinase II (CaMKII) pathways make it difficult to reveal the mechanisms. Here, we use a recently developed spatiotemporal ventricular myocyte computer model, which consists of a 3-dimensional network of Ca2+ release units (CRUs) intertwined with mitochondria and integrates mitochondrial Ca2+ signaling and other complex signaling pathways, to study the mitochondrial regulation of DADs. With a systematic investigation of the synergistic or competing factors that affect the occurrence of Ca2+ waves and DADs during mitochondrial depolarization, we find that the direct redox effect of ROS on ryanodine receptors (RyRs) plays a critical role in promoting Ca2+ waves and DADs under the acute effect of mitochondrial depolarization. Furthermore, the upregulation of mitochondrial Ca2+ uniporter can promote DADs through Ca2+-dependent opening of mitochondrial permeability transition pores (mPTPs). Also, due to much slower dynamics than Ca2+ cycling and ROS, oxidized CaMKII activation and the cytosolic ATP do not appear to significantly impact the genesis of DADs during the acute phase of mitochondrial depolarization. However, under chronic conditions, ATP depletion suppresses and enhanced CaMKII activation promotes Ca2+ waves and DADs.

Life and death saddles in the heart.

Saddle points are responsible for threshold phenomena of many biological systems. In the heart, saddle points determine the normal excitability and conduction, but are also responsible for certain abnormal action potential behaviors associated with lethal arrhythmias. We investigate the dynamical mechanisms for the genesis of lethal extra heartbeats in heterogeneous cardiac tissue under two diseased conditions. For both conditions, the lethal events occur when the system is close to the saddle point, implying the pivotal role of the saddle point in cardiac arrhythmogenesis.