Synchronization of early afterdepolarizations and arrhythmogenesis in heterogeneous cardiac tissue models

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.

Directed graph mapping shows rotors maintain non-terminating and focal sources maintain self-terminating Torsade de Pointes in canine model

Torsade de Pointes is a polymorphic ventricular tachycardia which is as yet incompletely understood. While the onset of a TdP episode is generally accepted to be caused by triggered activity, the mechanisms for the perpetuation is still under debate. In this study, we analysed data from 54 TdP episodes divided over 5 dogs (4 female, 1 male) with chronic atrioventricular block. Previous research on this dataset showed both reentry and triggered activity to perpetuate the arrhythmia. 13 of those TdP episodes showed reentry as part of the driving mechanism of perpetuating the episode. The remaining 41 episodes were purely ectopic. Reentry was the main mechanism in long-lasting episodes (>14 beats), while focal sources were responsible for maintaining shorter episodes. Building on these results, we re-analysed the data using directed graph mapping This program uses principles from network theory and a combination of positional data and local activation times to identify reentry loops and focal sources within the data. The results of this study are twofold. First, concerning reentry loops, we found that on average non-terminating (NT) episodes (≥10 s) show significantly more simultaneous reentry loops than self-terminating (ST) TdP (<10 s). Non-terminating episodes have on average 2.72 ± 1.48 simultaneous loops, compared to an average of 1.33 ± 0.66 for self-terminating episodes. In addition, each NT episode showed a presence of (bi-)ventricular loops between 10.10% and 69.62% of their total reentry duration. Compared to the ST episodes, only 1 in 4 episodes (25%) showed (bi-)ventricular reentry, lasting only 7.12% of its total reentry duration. This suggests that while focal beats trigger TdP, macro-reentry and multiple simultaneous localized reentries are the major drivers of long-lasting episodes. Second, using heatmaps, we found focal sources to occur in preferred locations, instead of being distributed randomly. This may have implications on treatment if such focal origins can be disabled reliably.

Spatiotemporal patterns of early afterdepolarizations underlying abnormal T-wave morphologies in a tissue model of the Purkinje-ventricular system

Sudden cardiac death (SCD) is a leading cause of death worldwide, and the majority of SCDs are caused by acute ventricular arrhythmias (VAs). Early afterdepolarizations (EADs) are an important trigger of VA under pathological conditions, e.g., inherited or acquired long QT syndrome (LQTS). However, it remains unclear how EAD events at the cellular level are spatially organized at the tissue level to induce and maintain ventricular arrhythmias and whether the spatial-temporal patterns of EADs at the tissue level are associated with abnormal T-wave morphologies that are often observed in LQTS, such as broad-based, notched or bifid; late appearance; and pointed T-waves. Here, a tissue model of the Purkinje-ventricular system (PVS) was developed to quantitatively investigate the complex spatial-temporal dynamics of EADs during T-wave abnormalities. We found that (1) while major inhibition of ICaL can substantially reduce the excitability of the PVS leading to conduction failures, moderate ICaL inhibition can promote occurrences of AP alternans at short cycle lengths (CLs), and EAD events preferentially occur with a major reduction of IKr (>50%) at long CLs; (2) with a minor reduction of ICaL, spatially synchronized steady-state EAD events with inverted and biphasic T-waves can be "weakened" into beat-to-beat concurrences of spatially synchronized EADs and T-wave alternans, and as pacing CLs increase, beat-to-beat concurrences of localized EADs with late-appearing and pointed T-wave morphologies can be observed; (3) under certain conditions, localized EAD events in the midmyocardium may trigger slow uni-directional electric propagation with inverted (antegrade) or upright (retrograde) broad-based T-waves; (4) spatially discordant EADs were typically characterized by desynchronized spontaneous onsets of EAD events between two groups of PVS tissues with biphasic T-wave morphologies, and they can evolve into spatially discordant oscillating EAD patterns with sustained or self-terminated alternating EAD and electrocardiogram (ECG) patterns. Our results provide new insights into the spatiotemporal aspects of the onset and development of EADs and suggest possible mechanistic links between the complex spatial dynamics of EADs and T-wave morphologies.

Computational modeling of aberrant electrical activity following remuscularization with intramyocardially injected pluripotent stem cell-derived cardiomyocytes

Acute engraftment arrhythmias (EAs) remain a serious complication of remuscularization therapy. Preliminary evidence suggests that a focal source underlies these EAs stemming from the automaticity of immature pluripotent stem cell-derived cardiomyocytes (PSC-CMs) in nascent myocardial grafts. How these EAs arise though during early engraftment remains unclear. In a series of in silico experiments, we probed the origin of EAs-exploring aspects of altered impulse formation and altered impulse propagation within nascent PSC-CM grafts and at the host-graft interface. To account for poor gap junctional coupling during early PSC-CM engraftment, the voltage dependence of gap junctions and the possibility of ephaptic coupling were incorporated. Inspired by cardiac development, we also studied the contributions of another feature of immature PSC-CMs, circumferential sodium channel (NaCh) distribution in PSC-CMs. Ectopic propagations emerged from nascent grafts of immature PSC-CMs at a rate of <96 bpm. Source-sink effects dictated this rate and contributed to intermittent capture between host and graft. Moreover, ectopic beats emerged from dynamically changing sites along the host-graft interface. The latter arose in part because circumferential NaCh distribution in PSC-CMs contributed to preferential conduction slowing and block of electrical impulses from host to graft myocardium. We conclude that additional mechanisms, in addition to focal ones, contribute to EAs and recognize that their relative contributions are dynamic across the engraftment process.

Mechanisms of phase-3 early afterdepolarizations and triggered activities in ventricular myocyte models

Early afterdepolarizations (EADs) are abnormal depolarizations during the repolarizing phase of the action potential, which are associated with cardiac arrhythmogenesis. EADs are classified into phase-2 and phase-3 EADs. Phase-2 EADs occur during phase 2 of the action potential, with takeoff potentials typically above -40 mV. Phase-3 EADs occur during phase 3 of the action potential, with takeoff potential between -70 and -50 mV. Since the amplitude of phase-3 EADs can be as large as that of a regular action potential, they are also called triggered activities (TAs). This also makes phase-3 EADs and TAs much more arrhythmogenic than phase-2 EADs since they can propagate easily in tissue. Although phase-2 EADs have been widely observed, phase-3 EADs and TAs have been rarely demonstrated in isolated ventricular myocytes. Here we carry out computer simulations of three widely used ventricular action potential models to investigate the mechanisms of phase-3 EADs and TAs. We show that when the T-type Ca2+ current (ICa,T ) is absent (e.g., in normal ventricular myocytes), besides the requirement of increasing inward currents and reducing outward currents as for phase-2 EADs, the occurrence of phase-3 EADs and TAs requires a substantially large increase of the L-type Ca2+ current and the slow component of the delayed rectifier K+ current. The presence of ICa,T (e.g., in neonatal and failing ventricular myocytes) can greatly reduce the thresholds of these two currents for phase-3 EADs and TAs. This implies that ICa,T may play an important role in arrhythmogenesis in cardiac diseases.

Mechanisms underlying age-associated manifestation of cardiac sodium channel gain-of-function

Cardiac action potentials are initiated by sodium ion (Na+) influx through voltage-gated Na+ channels. Na+ channel gain-of-function (GOF) can arise in inherited conditions due to mutations in the gene encoding the cardiac Na+ channel, such as Long QT syndrome type 3 (LQT3). LQT3 can be a "concealed" disease, as patients with LQT3-associated mutations can remain asymptomatic until later in life; however, arrhythmias can also arise early in life in LQT3 patients, demonstrating a complex age-associated manifestation. We and others recently demonstrated that cardiac Na+ channels preferentially localize at the intercalated disc (ID) in adult cardiac tissue, which facilitates ephaptic coupling and formation of intercellular Na+ nanodomains that regulate pro-arrhythmic early afterdepolarization (EAD) formation in tissue with Na+ channel GOF. Several properties related to ephaptic coupling vary with age, such as cell size and Na+ channel and gap junction (GJ) expression and distribution: neonatal cells have immature IDs, with Na+ channels and GJs primarily diffusively distributed, while adult myocytes have mature IDs with preferentially localized Na+ channels and GJs. Here, we perform an in silico study varying critical age-dependent parameters to investigate mechanisms underlying age-associated manifestation of Na+ channel GOF in a model of guinea pig cardiac tissue. Simulations predict that total Na+ current conductance is a critical factor in action potential duration (APD) prolongation. We find a complex cell size/ Na+ channel expression relationship: increases in cell size (without concurrent increases in Na+ channel expression) suppress EAD formation, while increases in Na+ channel expression (without concurrent increases in cell size) promotes EAD formation. Finally, simulations with neonatal and early age-associated parameters predict normal APD with minimal dependence on intercellular cleft width; however, variability in cellular properties can lead to EADs presenting in early developmental stages. In contrast, for adult-associated parameters, EAD formation is highly dependent on cleft width, consistent with a mechanism underlying the age-associated manifestation of the Na+ channel GOF.

Evolution of mathematical models of cardiomyocyte electrophysiology

Advanced computational techniques and mathematical modeling have become more and more important to the study of cardiac electrophysiology. In this review, we provide a brief history of the evolution of cardiomyocyte electrophysiology models and highlight some of the most important ones that had a major impact on our understanding of the electrical activity of the myocardium and associated transmembrane ion fluxes in normal and pathological states. We also present the use of these models in the study of various arrhythmogenesis mechanisms, particularly the integration of experimental pharmacology data into advanced humanized models for in silico proarrhythmogenic risk prediction as an essential component of the Comprehensive in vitro Proarrhythmia Assay (CiPA) drug safety paradigm.

Circadian Rhythms of Early Afterdepolarizations and Ventricular Arrhythmias in a Cardiomyocyte Model

Sudden cardiac arrest is a malfunction of the heart's electrical system, typically caused by ventricular arrhythmias, that can lead to sudden cardiac death (SCD) within minutes. Epidemiological studies have shown that SCD and ventricular arrhythmias are more likely to occur in the morning than in the evening, and laboratory studies indicate that these daily rhythms in adverse cardiovascular events are at least partially under the control of the endogenous circadian timekeeping system. However, the biophysical mechanisms linking molecular circadian clocks to cardiac arrhythmogenesis are not fully understood. Recent experiments have shown that L-type calcium channels exhibit circadian rhythms in both expression and function in guinea pig ventricular cardiomyocytes. We developed an electrophysiological model of these cells to simulate the effect of circadian variation in L-type calcium conductance. In our simulations, we found that there is a circadian pattern in the occurrence of early afterdepolarizations (EADs), which are abnormal depolarizations during the repolarization phase of a cardiac action potential that can trigger fatal ventricular arrhythmias. Specifically, the model produces EADs in the morning, but not at other times of day. We show that the model exhibits a codimension-2 Takens-Bogdanov bifurcation that serves as an organizing center for different types of EAD dynamics. We also simulated a two-dimensional spatial version of this model across a circadian cycle. We found that there is a circadian pattern in the breakup of spiral waves, which represents ventricular fibrillation in cardiac tissue. Specifically, the model produces spiral wave breakup in the morning, but not in the evening. Our computational study is the first, to our knowledge, to propose a link between circadian rhythms and EAD formation and suggests that the efficacy of drugs targeting EAD-mediated arrhythmias may depend on the time of day that they are administered.

Intercellular Sodium Regulates Repolarization in Cardiac Tissue with Sodium Channel Gain of Function

In cardiac myocytes, action potentials are initiated by an influx of sodium (Na⁺) ions via voltage-gated Na⁺ channels. Na⁺ channel gain of function (GOF), arising in both inherited conditions associated with mutation in the gene encoding the Na⁺ channel and acquired conditions associated with heart failure, ischemia, and atrial fibrillation, enhance Na⁺ influx, generating a late Na⁺ current that prolongs action potential duration (APD) and triggering proarrhythmic early afterdepolarizations (EADs). Recent studies have shown that Na⁺ channels are highly clustered at the myocyte intercalated disk, facilitating formation of Na⁺ nanodomains in the intercellular cleft between cells. Simulations from our group have recently predicted that narrowing the width of the intercellular cleft can suppress APD prolongation and EADs in the presence of Na⁺ channel mutations because of increased intercellular cleft Na⁺ ion depletion. In this study, we investigate the effects of modulating multiple extracellular spaces, specifically the intercellular cleft and bulk interstitial space, in a novel computational model and experimentally via osmotic agents albumin, dextran 70, and mannitol. We perform optical mapping and transmission electron microscopy in a drug-induced (sea anemone toxin, ATXII) Na⁺ channel GOF isolated heart model and modulate extracellular spaces via osmotic agents. Single-cell patch-clamp experiments confirmed that the osmotic agents individually do not enhance late Na⁺ current. Both experiments and simulations are consistent with the conclusion that intercellular cleft narrowing or expansion regulates APD prolongation; in contrast, modulating the bulk interstitial space has negligible effects on repolarization. Thus, we predict that intercellular cleft Na⁺ nanodomain formation and collapse critically regulates cardiac repolarization in the setting of Na⁺ channel GOF.

In silico investigation of the mechanisms underlying atrial fibrillation due to impaired Pitx2

Atrial fibrillation (AF) is the most common sustained cardiac arrhythmia and is a major cause of stroke and morbidity. Recent genome-wide association studies have shown that paired-like homeodomain transcription factor 2 (Pitx2) to be strongly associated with AF. However, the mechanisms underlying Pitx2 modulated arrhythmogenesis and variable effectiveness of antiarrhythmic drugs (AADs) in patients in the presence or absence of impaired Pitx2 expression remain unclear. We have developed multi-scale computer models, ranging from a single cell to tissue level, to mimic control and Pitx2-knockout atria by incorporating recent experimental data on Pitx2-induced electrical and structural remodeling in humans, as well as the effects of AADs. The key findings of this study are twofold. We have demonstrated that shortened action potential duration, slow conduction and triggered activity occur due to electrical and structural remodelling under Pitx2 deficiency conditions. Notably, the elevated function of calcium transport ATPase increases sarcoplasmic reticulum Ca2+ concentration, thereby enhancing susceptibility to triggered activity. Furthermore, heterogeneity is further elevated due to Pitx2 deficiency: 1) Electrical heterogeneity between left and right atria increases; and 2) Increased fibrosis and decreased cell-cell coupling due to structural remodelling slow electrical propagation and provide obstacles to attract re-entry, facilitating the initiation of re-entrant circuits. Secondly, our study suggests that flecainide has antiarrhythmic effects on AF due to impaired Pitx2 by preventing spontaneous calcium release and increasing wavelength. Furthermore, our study suggests that Na+ channel effects alone are insufficient to explain the efficacy of flecainide. Our study may provide the mechanisms underlying Pitx2-induced AF and possible explanation behind the AAD effects of flecainide in patients with Pitx2 deficiency.

Multiple Dynamical Mechanisms of Phase-2 Early Afterdepolarizations in a Human Ventricular Myocyte Model: Involvement of Spontaneous SR Ca 2+ Release

Early afterdepolarization (EAD) is known to cause lethal ventricular arrhythmias in long QT syndrome (LQTS). In this study, dynamical mechanisms of EAD formation in human ventricular myocytes (HVMs) were investigated using the mathematical model developed by ten Tusscher and Panfilov (Am J Physiol Heart Circ Physiol 291, 2006). We explored how the rapid (IKr) and slow (IKs) components of delayed-rectifier K+ channel currents, L-type Ca2+ channel current (ICa L), Na+/Ca2+ exchanger current (INCX), and intracellular Ca2+ handling via the sarcoplasmic reticulum (SR) contribute to initiation, termination and modulation of phase-2 EADs during pacing in relation to bifurcation phenomena in non-paced model cells. Parameter-dependent dynamical behaviors of the non-paced model cell were determined by calculating stabilities of equilibrium points (EPs) and limit cycles, and bifurcation points to construct bifurcation diagrams. Action potentials (APs) and EADs during pacing were reproduced by numerical simulations for constructing phase diagrams of the paced model cell dynamics. Results are summarized as follows: (1) A modified version of the ten Tusscher-Panfilov model with accelerated ICaL inactivation could reproduce bradycardia-related EADs in LQTS type 2 and β-adrenergic stimulation-induced EADs in LQTS type 1. (2) Two types of EADs with different initiation mechanisms, ICaL reactivation-dependent and spontaneous SR Ca2+ release-mediated EADs, were detected. (3) Termination of EADs (AP repolarization) during pacing depended on the slow activation of IKs. (4) Spontaneous SR Ca2+ releases occurred at higher Ca2+ uptake rates, attributable to the instability of steady-state intracellular Ca2+ concentrations. Dynamical mechanisms of EAD formation and termination in the paced model cell are closely related to stability changes (bifurcations) in dynamical behaviors of the non-paced model cell, but they are model-dependent. Nevertheless, the modified ten Tusscher-Panfilov model would be useful for systematically investigating possible dynamical mechanisms of EAD-related arrhythmias in LQTS.

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

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

Determinants of early afterdepolarization properties in ventricular myocyte models

Early afterdepolarizations (EADs) are spontaneous depolarizations during the repolarization phase of an action potential in cardiac myocytes. It is widely known that EADs are promoted by increasing inward currents and/or decreasing outward currents, a condition called reduced repolarization reserve. Recent studies based on bifurcation theories show that EADs are caused by a dual Hopf-homoclinic bifurcation, bringing in further mechanistic insights into the genesis and dynamics of EADs. In this study, we investigated the EAD properties, such as the EAD amplitude, the inter-EAD interval, and the latency of the first EAD, and their major determinants. We first made predictions based on the bifurcation theory and then validated them in physiologically more detailed action potential models. These properties were investigated by varying one parameter at a time or using parameter sets randomly drawn from assigned intervals. The theoretical and simulation results were compared with experimental data from the literature. Our major findings are that the EAD amplitude and takeoff potential exhibit a negative linear correlation; the inter-EAD interval is insensitive to the maximum ionic current conductance but mainly determined by the kinetics of I_Ca,L and the dual Hopf-homoclinic bifurcation; and both inter-EAD interval and latency vary largely from model to model. Most of the model results generally agree with experimental observations in isolated ventricular myocytes. However, a major discrepancy between modeling results and experimental observations is that the inter-EAD intervals observed in experiments are mainly between 200 and 500 ms, irrespective of species, while those of the mathematical models exhibit a much wider range with some models exhibiting inter-EAD intervals less than 100 ms. Our simulations show that the cause of this discrepancy is likely due to the difference in I_Ca,L recovery properties in different mathematical models, which needs to be addressed in future action potential model development.

Early afterdepolarizations (EADs) are abnormal depolarizations during the plateau phase of action potential in cardiac myocytes, arising from a dual Hopf-homoclinic bifurcation. The same bifurcations are also responsible for certain types of bursting behaviors in other cell types, such as beta cells and neuronal cells. EADs are known to play important role in the genesis of lethal arrhythmias and have been widely studied in both experiments and computer models. However, a detailed comparison between the properties of EADs observed in experiments and those from mathematical models have not been carried out. In this study, we performed theoretical analyses and computer simulations of different ventricular action potential models as well as different species to investigate the properties of EADs and compared these properties to those observed in experiments. While the EAD properties in the action potential models capture many of the EAD properties seen in experiments, the inter-EAD intervals in the computer models differ a lot from model to model, and some of them show very large discrepancy with those observed in experiments. This discrepancy needs to be addressed in future cardiac action potential model development.

Effects of early afterdepolarizations on excitation patterns in an accurate model of the human ventricles

Early Afterdepolarizations, EADs, are defined as the reversal of the action potential before completion of the repolarization phase, which can result in ectopic beats. However, the series of mechanisms of EADs leading to these ectopic beats and related cardiac arrhythmias are not well understood. Therefore, we aimed to investigate the influence of this single cell behavior on the whole heart level. For this study we used a modified version of the Ten Tusscher-Panfilov model of human ventricular cells (TP06) which we implemented in a 3D ventricle model including realistic fiber orientations. To increase the likelihood of EAD formation at the single cell level, we reduced the repolarization reserve (RR) by reducing the rapid delayed rectifier Potassium current and raising the L-type Calcium current. Varying these parameters defined a 2D parametric space where different excitation patterns could be classified. Depending on the initial conditions, by either exciting the ventricles with a spiral formation or burst pacing protocol, we found multiple different spatio-temporal excitation patterns. The spiral formation protocol resulted in the categorization of a stable spiral (S), a meandering spiral (MS), a spiral break-up regime (SB), spiral fibrillation type B (B), spiral fibrillation type A (A) and an oscillatory excitation type (O). The last three patterns are a 3D generalization of previously found patterns in 2D. First, the spiral fibrillation type B showed waves determined by a chaotic bi-excitable regime, i.e. mediated by both Sodium and Calcium waves at the same time and in same tissue settings. In the parameter region governed by the B pattern, single cells were able to repolarize completely and different (spiral) waves chaotically burst into each other without finishing a 360 degree rotation. Second, spiral fibrillation type A patterns consisted of multiple small rotating spirals. Single cells failed to repolarize to the resting membrane potential hence prohibiting the Sodium channel gates to recover. Accordingly, we found that Calcium waves mediated these patterns. Third, a further reduction of the RR resulted in a more exotic parameter regime whereby the individual cells behaved independently as oscillators. The patterns arose due to a phase-shift of different oscillators as disconnection of the cells resulted in continuation of the patterns. For all patterns, we computed realistic 9 lead ECGs by including a torso model. The B and A type pattern exposed the behavior of Ventricular Tachycardia (VT). We conclude that EADs at the single cell level can result in different types of cardiac fibrillation at the tissue and 3D ventricle level.

Computational Cardiac Modeling Reveals Mechanisms of Ventricular Arrhythmogenesis in Long QT Syndrome Type 8: CACNA1C R858H Mutation Linked to Ventricular Fibrillation

Functional analysis of the L-type calcium channel has shown that the CACNA1C R858H mutation associated with severe QT interval prolongation may lead to ventricular fibrillation (VF). This study investigated multiple potential mechanisms by which the CACNA1C R858H mutation facilitates and perpetuates VF. The Ten Tusscher-Panfilov (TP06) human ventricular cell models incorporating the experimental data on the kinetic properties of L-type calcium channels were integrated into one-dimensional (1D) fiber, 2D sheet, and 3D ventricular models to investigate the pro-arrhythmic effects of CACNA1C mutations by quantifying changes in intracellular calcium handling, action potential profiles, action potential duration restitution (APDR) curves, dispersion of repolarization (DOR), QT interval and spiral wave dynamics. R858H “mutant” L-type calcium current (I_CaL) augmented sarcoplasmic reticulum calcium content, leading to the development of afterdepolarizations at the single cell level and focal activities at the tissue level. It also produced inhomogeneous APD prolongation, causing QT prolongation and repolarization dispersion amplification, rendering R858H “mutant” tissue more vulnerable to the induction of reentry compared with other conditions. In conclusion, altered I_CaL due to the CACNA1C R858H mutation increases arrhythmia risk due to afterdepolarizations and increased tissue vulnerability to unidirectional conduction block. However, the observed reentry is not due to afterdepolarizations (not present in our model), but rather to a novel blocking mechanism.

Spatial Patterns of Excitation at Tissue and Whole Organ Level Due to Early Afterdepolarizations

Early after depolarizations (EAD) occur in many pathological conditions, such as congenital or acquired channelopathies, drug induced arrhythmias, and several other situations that are associated with increased arrhythmogenicity. In this paper we present an overview of the relevant computational studies on spatial EAD dynamics in 1D, 2D, and in 3D anatomical models and discuss the relation of EADs to cardiac arrhythmias. We also discuss unsolved problems and highlight new lines of research in this area.

Revealing the Concealed Nature of Long-QT Type 3 Syndrome

BACKGROUND

Gain-of-function mutations in the voltage-gated sodium channel (Nav1.5) are associated with the long-QT-3 (LQT3) syndrome. Nav1.5 is densely expressed at the intercalated disk, and narrow intercellular separation can modulate cell-to-cell coupling via extracellular electric fields and depletion of local sodium ion nanodomains. Models predict that significantly decreasing intercellular cleft widths slows conduction because of reduced sodium current driving force, termed "self-attenuation." We tested the novel hypothesis that self-attenuation can "mask" the LQT3 phenotype by reducing the driving force and late sodium current that produces early afterdepolarizations (EADs).

METHODS AND RESULTS

Acute interstitial edema was used to increase intercellular cleft width in isolated guinea pig heart experiments. In a drug-induced LQT3 model, acute interstitial edema exacerbated action potential duration prolongation and produced EADs, in particular, at slow pacing rates. In a computational cardiac tissue model incorporating extracellular electric field coupling, intercellular cleft sodium nanodomains, and LQT3-associated mutant channels, myocytes produced EADs for wide intercellular clefts, whereas for narrow clefts, EADs were suppressed. For both wide and narrow clefts, mutant channels were incompletely inactivated. However, for narrow clefts, late sodium current was reduced via self-attenuation, a protective negative feedback mechanism, masking EADs.

CONCLUSIONS

We demonstrated a novel mechanism leading to the concealing and revealing of EADs in LQT3 models. Simulations predict that this mechanism may operate independent of the specific mutation, suggesting that future therapies could target intercellular cleft separation as a compliment or alternative to sodium channels.

Dynamical mechanisms of phase-2 early afterdepolarizations in human ventricular myocytes: insights from bifurcation analyses of two mathematical models

Early afterdepolarization (EAD) is known as a cause of ventricular arrhythmias in long QT syndromes. We theoretically investigated how the rapid (I_Kr) and slow (I_Ks) components of delayed-rectifier K⁺ channel currents, L-type Ca²⁺ channel current (I_CaL), Na⁺/Ca²⁺ exchanger current (I_NCX), Na⁺-K⁺ pump current (I_NaK), intracellular Ca²⁺ (Ca_i) handling via sarcoplasmic reticulum (SR), and intracellular Na⁺ concentration (Na_i) contribute to initiation, termination, and modulation of phase-2 EADs, using two human ventricular myocyte models. Bifurcation structures of dynamical behaviors in model cells were explored by calculating equilibrium points, limit cycles (LCs), and bifurcation points as functions of parameters. EADs were reproduced by numerical simulations. The results are summarized as follows: 1) decreasing I_Ks and/or I_Kr or increasing I_CaL led to EAD generation, to which mid-myocardial cell models were especially susceptible; the parameter regions of EADs overlapped the regions of stable LCs. 2) Two types of EADs (termination mechanisms), I_Ks activation-dependent and I_CaL inactivation-dependent EADs, were detected; I_Ks was not necessarily required for EAD formation. 3) Inhibiting I_NCX suppressed EADs via facilitating Ca²⁺-dependent I_CaL inactivation. 4) Ca_i dynamics (SR Ca²⁺ handling) and Na_i strongly affected bifurcations and EAD generation in model cells via modulating I_CaL, I_NCX, and I_NaK Parameter regions of EADs, often overlapping those of stable LCs, shifted depending on Ca_i and Na_i in stationary and dynamic states. 5) Bradycardia-related induction of EADs was mainly due to decreases in Na_i at lower pacing rates. This study demonstrates that bifurcation analysis allows us to understand the dynamical mechanisms of EAD formation more profoundly.

NEW & NOTEWORTHY

We investigated mechanisms of phase-2 early afterdepolarization (EAD) by bifurcation analyses of human ventricular myocyte (HVM) models. EAD formation in paced HVMs basically depended on bifurcation phenomena in non-paced HVMs, but was strongly affected by intracellular ion concentrations in stationary and dynamic states. EAD generation did not necessarily require I_Ks.

A Computational Study of the Factors Influencing the PVC-Triggering Ability of a Cluster of Early Afterdepolarization-Capable Myocytes

Premature ventricular complexes (PVCs), which are abnormal impulse propagations in cardiac tissue, can develop because of various reasons including early afterdepolarizations (EADs). We show how a cluster of EAD-generating cells (EAD clump) can lead to PVCs in a model of cardiac tissue, and also investigate the factors that assist such clumps in triggering PVCs. In particular, we study, through computer simulations, the effects of the following factors on the PVC-triggering ability of an EAD clump: (1) the repolarization reserve (RR) of the EAD cells; (2) the size of the EAD clump; (3) the coupling strength between the EAD cells in the clump; and (4) the presence of fibroblasts in the EAD clump. We find that, although a low value of RR is necessary to generate EADs and hence PVCs, a very low value of RR leads to low-amplitude EAD oscillations that decay with time and do not lead to PVCs. We demonstrate that a certain threshold size of the EAD clump, or a reduction in the coupling strength between the EAD cells, in the clump, is required to trigger PVCs. We illustrate how randomly distributed inexcitable obstacles, which we use to model collagen deposits, affect PVC-triggering by an EAD clump. We show that the gap-junctional coupling of fibroblasts with myocytes can either assist or impede the PVC-triggering ability of an EAD clump, depending on the resting membrane potential of the fibroblasts and the coupling strength between the myocyte and fibroblasts. We also find that the triggering of PVCs by an EAD clump depends sensitively on factors like the pacing cycle length and the distribution pattern of the fibroblasts.

Turbulent states and their transitions in mathematical models for ventricular tissue: the effects of random interstitial fibroblasts

We study the dynamical behaviors of two types of spiral- and scroll-wave turbulence states, respectively, in two-dimensional (2D) and three-dimensional (3D) mathematical models, of human, ventricular, myocyte cells that are attached to randomly distributed interstitial fibroblasts; these turbulence states are promoted by (a) the steep slope of the action-potential-duration-restitution (APDR) plot or (b) early afterdepolarizations (EADs). Our single-cell study shows that (1) the myocyte-fibroblast (MF) coupling G_{j} and (2) the number N_{f} of fibroblasts in an MF unit lower the steepness of the APDR slope and eliminate the EAD behaviors of myocytes; we explore the pacing dependence of such EAD suppression. In our 2D simulations, we observe that a spiral-turbulence (ST) state evolves into a state with a single, rotating spiral (RS) if either (a) G_{j} is large or (b) the maximum possible number of fibroblasts per myocyte N_{f}^{max} is large. We also observe that the minimum value of G_{j}, for the transition from the ST to the RS state, decreases as N_{f}^{max} increases. We find that, for the steep-APDR-induced ST state, once the MF coupling suppresses ST, the rotation period of a spiral in the RS state increases as (1) G_{j} increases, with fixed N_{f}^{max}, and (2) N_{f}^{max} increases, with fixed G_{j}. We obtain the boundary between ST and RS stability regions in the N_{f}^{max}-G_{j} plane. In particular, for low values of N_{f}^{max}, the value of G_{j}, at the ST-RS boundary, depends on the realization of the randomly distributed fibroblasts; this dependence decreases as N_{f}^{max} increases. Our 3D studies show a similar transition from scroll-wave turbulence to a single, rotating, scroll-wave state because of the MF coupling. We examine the experimental implications of our study and propose that the suppression (a) of the steep slope of the APDR or (b) EADs can eliminate spiral- and scroll-wave turbulence in heterogeneous cardiac tissue, which has randomly distributed fibroblasts.

A Comparative Study of Early Afterdepolarization-Mediated Fibrillation in Two Mathematical Models for Human Ventricular Cells

Early afterdepolarizations (EADs), which are abnormal oscillations of the membrane potential at the plateau phase of an action potential, are implicated in the development of cardiac arrhythmias like Torsade de Pointes. We carry out extensive numerical simulations of the TP06 and ORd mathematical models for human ventricular cells with EADs. We investigate the different regimes in both these models, namely, the parameter regimes where they exhibit (1) a normal action potential (AP) with no EADs, (2) an AP with EADs, and (3) an AP with EADs that does not go back to the resting potential. We also study the dependence of EADs on the rate of at which we pace a cell, with the specific goal of elucidating EADs that are induced by slow or fast rate pacing. In our simulations in two- and three-dimensional domains, in the presence of EADs, we find the following wave types: (A) waves driven by the fast sodium current and the L-type calcium current (Na-Ca-mediated waves); (B) waves driven only by the L-type calcium current (Ca-mediated waves); (C) phase waves, which are pseudo-travelling waves. Furthermore, we compare the wave patterns of the various wave-types (Na-Ca-mediated, Ca-mediated, and phase waves) in both these models. We find that the two models produce qualitatively similar results in terms of exhibiting Na-Ca-mediated wave patterns that are more chaotic than those for the Ca-mediated and phase waves. However, there are quantitative differences in the wave patterns of each wave type. The Na-Ca-mediated waves in the ORd model show short-lived spirals but the TP06 model does not. The TP06 model supports more Ca-mediated spirals than those in the ORd model, and the TP06 model exhibits more phase-wave patterns than does the ORd model.

Mechanisms of ventricular arrhythmias: from molecular fluctuations to electrical turbulence

Ventricular arrhythmias have complex causes and mechanisms. Despite extensive investigation involving many clinical, experimental, and computational studies, effective biological therapeutics are still very limited. In this article, we review our current understanding of the mechanisms of ventricular arrhythmias by summarizing the state of knowledge spanning from the molecular scale to electrical wave behavior at the tissue and organ scales and how the complex nonlinear interactions integrate into the dynamics of arrhythmias in the heart. We discuss the challenges that we face in synthesizing these dynamics to develop safe and effective novel therapeutic approaches.

A study of early afterdepolarizations in a model for human ventricular tissue

Sudden cardiac death is often caused by cardiac arrhythmias. Recently, special attention has been given to a certain arrhythmogenic condition, the long-QT syndrome, which occurs as a result of genetic mutations or drug toxicity. The underlying mechanisms of arrhythmias, caused by the long-QT syndrome, are not fully understood. However, arrhythmias are often connected to special excitations of cardiac cells, called early afterdepolarizations (EADs), which are depolarizations during the repolarizing phase of the action potential. So far, EADs have been studied mainly in isolated cardiac cells. However, the question on how EADs at the single-cell level can result in fibrillation at the tissue level, especially in human cell models, has not been widely studied yet. In this paper, we study wave patterns that result from single-cell EAD dynamics in a mathematical model for human ventricular cardiac tissue. We induce EADs by modeling experimental conditions which have been shown to evoke EADs at a single-cell level: by an increase of L-type Ca currents and a decrease of the delayed rectifier potassium currents. We show that, at the tissue level and depending on these parameters, three types of abnormal wave patterns emerge. We classify them into two types of spiral fibrillation and one type of oscillatory dynamics. Moreover, we find that the emergent wave patterns can be driven by calcium or sodium currents and we find phase waves in the oscillatory excitation regime. From our simulations we predict that arrhythmias caused by EADs can occur during normal wave propagation and do not require tissue heterogeneities. Experimental verification of our results is possible for experiments at the cell-culture level, where EADs can be induced by an increase of the L-type calcium conductance and by the application of I blockers, and the properties of the emergent patterns can be studied by optical mapping of the voltage and calcium.

Early afterdepolarizations in cardiac myocytes: beyond reduced repolarization reserve

Early afterdepolarizations (EADs) are secondary voltage depolarizations during the repolarizing phase of the action potential, which can cause lethal cardiac arrhythmias. The occurrence of EADs requires a reduction in outward current and/or an increase in inward current, a condition called reduced repolarization reserve. However, this generalized condition is not sufficient for EAD genesis and does not explain the voltage oscillations manifesting as EADs. Here, we summarize recent progress that uses dynamical theory to build on and advance our understanding of EADs beyond the concept of repolarization reserve, towards the goal of developing a holistic and integrative view of EADs and their role in arrhythmogenesis. We first introduce concepts from nonlinear dynamics that are relevant to EADs, namely, Hopf bifurcation leading to oscillations and basin of attraction of an equilibrium or oscillatory state. We then present a theory of phase-2 EADs in nonlinear dynamics, which includes the formation of quasi-equilibrium states at the plateau voltage, their stabilities, and the bifurcations leading to and terminating the oscillations. This theory shows that the L-type calcium channel plays a unique role in causing the nonlinear dynamical behaviours necessary for EADs. We also summarize different mechanisms of phase-3 EADs. Based on the dynamical theory, we discuss the roles of each of the major ionic currents in the genesis of EADs, and potential therapeutic targets.

β-adrenergic stimulation activates early afterdepolarizations transiently via kinetic mismatch of PKA targets

Sympathetic stimulation regulates cardiac excitation-contraction coupling in hearts but can also trigger ventricular arrhythmias caused by early afterdepolarizations (EADs) in pathological conditions. Isoproterenol (ISO) stimulation can transiently cause EADs which could result from differential kinetics of L-type Ca current (ICaL) vs. delayed rectifier potassium current (IKs) effects, but multiple PKA targets complicate mechanistic analysis. Utilizing a biophysically detailed model integrating Ca and β-adrenergic signaling, we investigate how different phosphorylation kinetics and targets influence β-adrenergic-induced transient EADs. We found that: 1) The faster time course of ICaL vs. IKs increases recapitulates experimentally observed ISO-induced transient EADs (which are due to ICaL reactivation). These EADs disappear at steady state ISO and do not occur during more gradual ISO application. 2) This ICaL vs. IKs kinetic mismatch with ISO can also induce transient EADs due to spontaneous sarcoplasmic reticulum (SR) Ca release and Na/Ca exchange current. The increased ICaL, SR Ca uptake and action potential duration (APD) raise SR Ca to cause spontaneous SR Ca release, but eventual IKs activation and APD shortening abolish these EADs. 3) Phospholemman (PLM) phosphorylation decreases both types of EADs by increasing outward Na/K-ATPase current (INaK) for ICaL-mediated EADs, and reducing intracellular Na and Ca loading for SR Ca-release-mediated EADs. Slowing PLM phosphorylation kinetics abolishes this protective effect. 4) Blocking phospholamban (PLB) phosphorylation has little effect on ICaL-mediated transient EADs, but abolishes SR Ca-release-mediated transient EADs by limiting SR Ca loading. 5) RyR phosphorylation has little effect on either transient EAD type. Our study emphasizes the importance of understanding non-steady state kinetics of several systems in mediating β-adrenergic-induced EADs and arrhythmias.

Mechanisms and determinants of ultralong action potential duration and slow rate-dependence in cardiac myocytes

In normal cardiac myocytes, the action potential duration (APD) is several hundred milliseconds. However, experimental studies showed that under certain conditions, APD could be excessively long (or ultralong), up to several seconds. Unlike the normal APD, the ultralong APD increases sensitively with pacing cycle length even when the pacing rate is very slow, exhibiting a sensitive slow rate-dependence. In addition, these long action potentials may or may not exhibit early afterdepolarizations (EADs). Although these phenomena are well known, the underlying mechanisms and ionic determinants remain incompletely understood. In this study, computer simulations were performed with a simplified action potential model. Modifications to the L-type calcium current (I_Ca,L) kinetics and the activation time constant of the delayed rectifier K current were used to investigate their effects on APD. We show that: 1) the ultralong APD and its sensitive slow rate-dependence are determined by the steady-state window and pedestal I_Ca,L currents and the activation speed and the recovery of the delayed rectifier K current; 2) whether an ultralong action potential exhibits EADs or not depends on the kinetics of I_Ca,L; 3) increasing inward currents elevates the plateau voltage, which in general prolongs APD, however, this can also shorten APD when the APD is already ultralong under certain conditions; and 4) APD alternans occurs at slow pacing rates due to the sensitive slow rate-dependence and the ionic determinants are different from the ones causing APD alternans at fast heart rates.