Pro- and antiarrhythmic effects of ATP-sensitive potassium current activation on reentry during early afterdepolarization-mediated 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.

Calcium Handling Defects and Cardiac Arrhythmia Syndromes

Calcium ions (Ca²⁺) play a major role in the cardiac excitation-contraction coupling. Intracellular Ca²⁺ concentration increases during systole and falls in diastole thereby determining cardiac contraction and relaxation. Normal cardiac function also requires perfect organization of the ion currents at the cellular level to drive action potentials and to maintain action potential propagation and electrical homogeneity at the tissue level. Any imbalance in Ca²⁺ homeostasis of a cardiac myocyte can lead to electrical disturbances. This review aims to discuss cardiac physiology and pathophysiology from the elementary membrane processes that can cause the electrical instability of the ventricular myocytes through intracellular Ca²⁺ handling maladies to inherited and acquired arrhythmias. Finally, the paper will discuss the current therapeutic approaches targeting cardiac arrhythmias.

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.

Optimization of an In silico Cardiac Cell Model for Proarrhythmia Risk Assessment

Drug-induced Torsade-de-Pointes (TdP) has been responsible for the withdrawal of many drugs from the market and is therefore of major concern to global regulatory agencies and the pharmaceutical industry. The Comprehensive in vitro Proarrhythmia Assay (CiPA) was proposed to improve prediction of TdP risk, using in silico models and in vitro multi-channel pharmacology data as integral parts of this initiative. Previously, we reported that combining dynamic interactions between drugs and the rapid delayed rectifier potassium current (IKr) with multi-channel pharmacology is important for TdP risk classification, and we modified the original O'Hara Rudy ventricular cell mathematical model to include a Markov model of IKr to represent dynamic drug-IKr interactions (IKr-dynamic ORd model). We also developed a novel metric that could separate drugs with different TdP liabilities at high concentrations based on total electronic charge carried by the major inward ionic currents during the action potential. In this study, we further optimized the IKr-dynamic ORd model by refining model parameters using published human cardiomyocyte experimental data under control and drug block conditions. Using this optimized model and manual patch clamp data, we developed an updated version of the metric that quantifies the net electronic charge carried by major inward and outward ionic currents during the steady state action potential, which could classify the level of drug-induced TdP risk across a wide range of concentrations and pacing rates. We also established a framework to quantitatively evaluate a system's robustness against the induction of early afterdepolarizations (EADs), and demonstrated that the new metric is correlated with the cell's robustness to the pro-EAD perturbation of IKr conductance reduction. In summary, in this work we present an optimized model that is more consistent with experimental data, an improved metric that can classify drugs at concentrations both near and higher than clinical exposure, and a physiological framework to check the relationship between a metric and EAD. These findings provide a solid foundation for using in silico models for the regulatory assessment of TdP risk under the CiPA paradigm.

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.

Spontaneous initiation of premature ventricular complexes and arrhythmias in type 2 long QT syndrome

The occurrence of early afterdepolarizations (EADs) and increased dispersion of repolarization are two known factors for arrhythmogenesis in long QT syndrome. However, increased dispersion of repolarization tends to suppress EADs due to the source-sink effect, and thus how the two competing factors cause initiation of arrhythmias remains incompletely understood. Here we used optical mapping and computer simulation to investigate the mechanisms underlying spontaneous initiation of arrhythmias in type 2 long QT (LQT2) syndrome. In optical mapping experiments of transgenic LQT2 rabbit hearts under isoproterenol, premature ventricular complexes (PVCs) were observed to originate from the steep spatial repolarization gradient (RG) regions and propagated unidirectionally. The same PVC behaviors were demonstrated in computer simulations of tissue models of rabbits. Depending on the heterogeneities, these PVCs could lead to either repetitive focal excitations or reentry without requiring an additional vulnerable substrate. Systematic simulations showed that cellular phase 2 EADs were either suppressed or confined to the long action potential region due to the source-sink effect. Tissue-scale phase 3 EADs and PVCs occurred due to tissue-scale dynamical instabilities caused by RG and enhanced L-type calcium current (I_Ca,L), occurring under both large and small RG. Presence of cellular EADs was not required but potentiated PVCs when RG was small. We also investigated how other factors affect the dynamical instabilities causing PVCs. Our main conclusion is that tissue-scale dynamical instabilities caused by RG and enhanced I_Ca,L give rise to both the trigger and the vulnerable substrate simultaneously for spontaneous initiation of arrhythmias in LQT2 syndrome.

Perspective: a dynamics-based classification of ventricular arrhythmias

Despite key advances in the clinical management of life-threatening ventricular arrhythmias, culminating with the development of implantable cardioverter-defibrillators and catheter ablation techniques, pharmacologic/biologic therapeutics have lagged behind. The fundamental issue is that biological targets are molecular factors. Diseases, however, represent emergent properties at the scale of the organism that result from dynamic interactions between multiple constantly changing molecular factors. For a pharmacologic/biologic therapy to be effective, it must target the dynamic processes that underlie the disease. Here we propose a classification of ventricular arrhythmias that is based on our current understanding of the dynamics occurring at the subcellular, cellular, tissue and organism scales, which cause arrhythmias by simultaneously generating arrhythmia triggers and exacerbating tissue vulnerability. The goal is to create a framework that systematically links these key dynamic factors together with fixed factors (structural and electrophysiological heterogeneity) synergistically promoting electrical dispersion and increased arrhythmia risk to molecular factors that can serve as biological targets. We classify ventricular arrhythmias into three primary dynamic categories related generally to unstable Ca cycling, reduced repolarization, and excess repolarization, respectively. The clinical syndromes, arrhythmia mechanisms, dynamic factors and what is known about their molecular counterparts are discussed. Based on this framework, we propose a computational-experimental strategy for exploring the links between molecular factors, fixed factors and dynamic factors that underlie life-threatening ventricular arrhythmias. The ultimate objective is to facilitate drug development by creating an in silico platform to evaluate and predict comprehensively how molecular interventions affect not only a single targeted arrhythmia, but all primary arrhythmia dynamics categories as well as normal cardiac excitation-contraction coupling.

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.

Nonlinear and Stochastic Dynamics in the Heart

In a normal human life span, the heart beats about 2 to 3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems.