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

Optogenetic Modulation of Arrhythmia Triggers: Proof-of-Concept from Computational Modeling

Introduction

Early afterdepolarizations (EADs) are secondary voltage depolarizations associated with reduced repolarization reserve (RRR) that can trigger lethal arrhythmias. Relating EADs to triggered activity is difficult to study, so the ability to suppress or provoke EADs would be experimentally useful. Here, we use computational simulations to assess the feasibility of subthreshold optogenetic stimulation modulating the propensity for EADs (cell-scale) and EAD-associated ectopic beats (organ-scale).

Methods

We modified a ventricular ionic model by reducing rapid delayed rectifier potassium (0.25-0.1 × baseline) and increasing L-type calcium (1.0-3.5 × baseline) currents to create RRR conditions with varying severity. We ran simulations in models of single cardiomyocytes and left ventricles from post-myocardial infarction patient MRI scans. Optogenetic stimulation was simulated using either ChR2 (depolarizing) or GtACR1 (repolarizing) opsins.

Results

In cell-scale simulations without illumination, EADs were seen for 164 of 416 RRR conditions. Subthreshold stimulation of GtACR1 reduced EAD incidence by up to 84.8% (25/416 RRR conditions; 0.1 μW/mm2); in contrast, subthreshold ChR2 excitation increased EAD incidence by up to 136.6% (388/416 RRR conditions; 50 μW/mm2). At the organ scale, we assumed simultaneous, uniform illumination of the epicardial and endocardial surfaces. GtACR1-mediated suppression (10-50 μW/mm2) and ChR2-mediated unmasking (50-100 μW/mm2) of EAD-associated ectopic beats were feasible in three distinct ventricular models.

Conclusions

Our findings suggest that optogenetics could be used to silence or provoke both EADs and EAD-associated ectopic beats. Validation in animal models could lead to exciting new experimental regimes and potentially to novel anti-arrhythmia treatments.

Supplementary Information

The online version contains supplementary material available at 10.1007/s12195-023-00781-z.

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.

Early Afterdepolarisations Induced by an Enhancement in the Calcium Current

Excitable biological cells, such as cardiac muscle cells, can exhibit complex patterns of oscillations such as spiking and bursting. Moreover, it is well known that an enhancement in calcium currents may yield certain kind of cardiac arrhythmia, so-called early afterdepolarisations (EADs). The presence of EADs strongly correlates with the onset of dangerous cardiac arrhythmia. In this paper we study mathematically and numerically the dynamics of a cardiac muscle cell with respect to the calcium current by investigating a simplistic system of differential equations. For the study of this phenomena, we use bifurcation theory, numerical bifurcation analysis, geometric singular perturbation theory and computational methods to investigate a nonlinear multiple time scales system. It will turn out that EADs related to an enhanced calcium current are canard–induced and that we have to combine these theories to derive a better understanding of the dynamics behind EADs. Moreover, a suitable time scale separation argument determines the important and sensitive system parameters which are related to the occurrence of EADs.

Early afterdepolarizations in cardiac action potentials as mixed mode oscillations due to a folded node singularity

Early afterdepolarizations (EADs) are pathological voltage oscillations during the repolarization phase of cardiac action potentials. They are considered as potential precursors to cardiac arrhythmias and have recently gained much attention in the context of preclinical drug safety testing under the Comprehensive in vitro Proarrhythmia Assay (CiPA) paradigm. From the viewpoint of multiple time scales theory, the onset of EADs has previously been studied by means of mathematical action potential models with one slow ion channel gating variable. In this article, we for the first time associate EADs with mixed mode oscillations in dynamical systems with two slow gating variables and present a folded node singularity of the slow flow as a novel mechanism for EADs genesis. We derive regions of the pharmacology parameter space in which EADs occur using both the folded node analysis and a full system bifurcation analysis, and we suggest the normal distance to the boundary of the EADs region as a mechanism-based risk metric to computationally estimate a drug’s proarrhythmic liability.

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.

Myofilament protein dynamics modulate EAD formation in human hypertrophic cardiomyopathy

Patients with hypertrophic cardiomyopathy (HCM), a disease associated with sarcomeric protein mutations, often suffer from sudden cardiac death (SCD) resulting from arrhythmia. In order to advance SCD prevention strategies, our understanding of how sarcomeric mutations in HCM patients contribute to enhanced arrhythmogenesis needs to be improved. Early afterdepolarizations (EADs) are an important mechanism underlying arrhythmias associated with HCM-SCD. Although the ionic mechanisms underlying EADs have been studied in general, whether myofilament protein dynamics mechanisms also underlie EADs remains unknown. Thus, our goals were to investigate if myofilament protein dynamics mechanisms underlie EADs and to uncover how those mechanisms are affected by pacing rate, sarcomere length (SL), and different levels of HCM-induced myofilament remodeling. To achieve this, a mechanistically-based bidirectionally coupled human electrophysiology-force myocyte model under the conditions of HCM was constructed. HCM ionic remodeling included a reduced repolarization reserve, while HCM myofilament modeling involved altered thin filament activation. We found that the mechanoelectric feedback (MEF) on calcium dynamics in the bidirectionally coupled model, via Troponin C buffering of cytoplasmic Ca²⁺, was the myofilament mechanism underlying EADs. Incorporating MEF diminished the degree of repolarization reserve reduction necessary for EADs to emerge and increased the frequency of EAD occurrence, especially at faster pacing rates. Longer SLs and enhanced thin filament activation diminished the effects of MEF on EADs. Together these findings demonstrate that myofilament protein dynamics mechanisms play an important role in EAD formation.

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.

Period doubling cascades of limit cycles in cardiac action potential models as precursors to chaotic early Afterdepolarizations

Background

Early afterdepolarizations (EADs) are pathological voltage oscillations during the repolarization phase of cardiac action potentials (APs). EADs are caused by drugs, oxidative stress or ion channel disease, and they are considered as potential precursors to cardiac arrhythmias in recent attempts to redefine the cardiac drug safety paradigm. The irregular behaviour of EADs observed in experiments has been previously attributed to chaotic EAD dynamics under periodic pacing, made possible by a homoclinic bifurcation in the fast subsystem of the deterministic AP system of differential equations.

Results

In this article we demonstrate that a homoclinic bifurcation in the fast subsystem of the action potential model is neither a necessary nor a sufficient condition for the genesis of chaotic EADs. We rather argue that a cascade of period doubling (PD) bifurcations of limit cycles in the full AP system paves the way to chaotic EAD dynamics across a variety of models including a) periodically paced and spontaneously active cardiomyocytes, b) periodically paced and non-active cardiomyocytes as well as c) unpaced and spontaneously active cardiomyocytes. Furthermore, our bifurcation analysis reveals that chaotic EAD dynamics may coexist in a stable manner with fully regular AP dynamics, where only the initial conditions decide which type of dynamics is displayed.

Conclusions

EADs are a potential source of cardiac arrhythmias and hence are of relevance both from the viewpoint of drug cardiotoxicity testing and the treatment of cardiomyopathies. The model-independent association of chaotic EADs with period doubling cascades of limit cycles introduced in this article opens novel opportunities to study chaotic EADs by means of bifurcation control theory and inverse bifurcation analysis. Furthermore, our results may shed new light on the synchronization and propagation of chaotic EADs in homogeneous and heterogeneous multicellular and cardiac tissue preparations.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-017-0422-4) contains supplementary material, which is available to authorized users.

Transgenic rabbit models to investigate the cardiac ion channel disease long QT syndrome

Long QT syndrome (LQTS) is a rare inherited channelopathy caused mainly by different mutations in genes encoding for cardiac K(+) or Na(+) channels, but can also be caused by commonly used ion-channel-blocking and QT-prolonging drugs, thus affecting a much larger population. To develop novel diagnostic and therapeutic strategies to improve the clinical management of these patients, a thorough understanding of the pathophysiological mechanisms of arrhythmogenesis and potential pharmacological targets is needed. Drug-induced and genetic animal models of various species have been generated and have been instrumental for identifying pro-arrhythmic triggers and important characteristics of the arrhythmogenic substrate in LQTS. However, due to species differences in features of cardiac electrical function, these different models do not entirely recapitulate all aspects of the human disease. In this review, we summarize advantages and shortcomings of different drug-induced and genetically mediated LQTS animal models - focusing on mouse and rabbit models since these represent the most commonly used small animal models for LQTS that can be subjected to genetic manipulation. In particular, we highlight the different aspects of arrhythmogenic mechanisms, pro-arrhythmic triggering factors, anti-arrhythmic agents, and electro-mechanical dysfunction investigated in transgenic LQTS rabbit models and their translational application for the clinical management of LQTS patients in detail. Transgenic LQTS rabbits have been instrumental to increase our understanding of the role of spatial and temporal dispersion of repolarization to provide an arrhythmogenic substrate, genotype-differences in the mechanisms for early afterdepolarization formation and arrhythmia maintenance, mechanisms of hormonal modification of arrhythmogenesis and regional heterogeneities in electro-mechanical dysfunction in LQTS.

Perpetuation of torsade de pointes in heterogeneous hearts: competing foci or re-entry?

KEY POINTS

The underlying mechanism of torsade de pointes (TdP) remains of debate: perpetuation may be due to (1) focal activity or (2) re-entrant activity. The onset of TdP correlates with action potential heterogeneities in different regions of the heart. We studied the mechanism of perpetuation of TdP in silico using a 2D model of human cardiac tissue and an anatomically accurate model of the ventricles of the human heart. We found that the mechanism of perpetuation TdP depends on the degree of heterogeneity. If the degree of heterogeneity is large, focal activity alone can sustain a TdP, otherwise re-entrant activity emerges. This result can help to understand the relationship between the mechanisms of TdP and tissue properties and may help in developing new drugs against it.

ABSTRACT

Torsade de pointes (TdP) can be the consequence of cardiac remodelling, drug effects or a combination of both. The mechanism underlying TdP is unclear, and may involve triggered focal activity or re-entry. Recent work by our group has indicated that both cases may exist, i.e. TdPs induced in the chronic atrioventricular block (CAVB) dog model may have a focal origin or are due to re-entry. Also it was found that heterogeneities might play an important role. In the current study we have used computational modelling to further investigate the mechanisms involved in TdP initiation and perpetuation, especially in the CAVB dog model, by the addition of heterogeneities with reduced repolarization reserve in comparison with the surrounding tissue. For this, the TNNP computer model was used for computations. We demonstrated in 2D and 3D simulations that ECGs with the typical TdP morphology can be caused by both multiple competing foci and re-entry circuits as a result of introduction of heterogeneities, depending on whether the heterogeneities have a large or a smaller reduced repolarization reserve in comparison with the surrounding tissue. Large heterogeneities can produce ectopic TdP, while smaller heterogeneities will produce re-entry-type TdP.

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.