Vulnerability to re-entry in simulated two-dimensional cardiac tissue: effects of electrical restitution and stimulation sequence

Electrical Restitution and Its Modifications by Antiarrhythmic Drugs in Undiseased Human Ventricular Muscle

Introduction

Re-entry is a basic mechanism of ventricular fibrillation, which can be elicited by extrasystolic activity, but the timing of an extrasystole can be critical. The action potential duration (APD) of an extrasystole depends on the proximity of the preceding beat, and the relation between its timing and its APD is called electrical restitution. The aim of the present work was to study and compare the effect of several antiarrhythmic drugs on restitution in preparations from undiseased human ventricular muscle, and other mammalian species.

Methods

Action potentials were recorded in preparations obtained from rat, guinea pig, rabbit, and dog hearts; and from undiseased human donor hearts using the conventional microelectrode technique. Preparations were stimulated with different basic cycle lengths (BCLs) ranging from 300 to 5,000 ms. To study restitution, single test pulses were applied at every 20th beat while the preparation was driven at 1,000 ms BCL.

Results

Marked differences were found between the animal and human preparations regarding restitution and steady-state frequency dependent curves. In human ventricular muscle, restitution kinetics were slower in preparations with large phase 1 repolarization with shorter APDs at 1000 ms BCL compared to preparations with small phase 1. Preparations having APD longer than 300 ms at 1000 ms BCL had slower restitution kinetics than those having APD shorter than 250 ms. The selective I_Kr inhibitors E-4031 and sotalol increased overall APD and slowed the restitution kinetics, while I_Ks inhibition did not influence APD and electrical restitution. Mexiletine and nisoldipine shortened APD, but only mexiletine slowed restitution kinetics.

Discussion

Frequency dependent APD changes, including electrical restitution, were partly determined by the APD at the BCL. Small phase 1 associated with slower restitution suggests a role of I_to in restitution. APD prolonging drugs slowed restitution, while mexiletine, a known inhibitor of I_Na, shortened basic APD but also slowed restitution. These results indicate that although basic APD has an important role in restitution, other transmembrane currents, such as I_Na or I_to, can also affect restitution kinetics. This raises the possibility that ion channel modifier drugs slowing restitution kinetics may have antiarrhythmic properties by altering restitution.

Discordant Alternans as a Mechanism for Initiation of Ventricular Fibrillation In Vitro

Background Ventricular tachyarrhythmias are often preceded by short sequences of premature ventricular complexes. In a previous study, a restitution-based computational model predicted which sequences of stimulated premature complexes were most likely to induce ventricular fibrillation in canines in vivo. However, the underlying mechanism, based on discordant-alternans dynamics, could not be verified in that study. The current study seeks to elucidate the mechanism by determining whether the spatiotemporal evolution of action potentials and initiation of ventricular fibrillation in in vitro experiments are consistent with model predictions. Methods and Results Optical mapping voltage signals from canine right-ventricular tissue (n=9) were obtained simultaneously from the entire epicardium and endocardium during and after premature stimulus sequences. Model predictions of action potential propagation along a 1-dimensional cable were developed using action potential duration versus diastolic interval data. The model predicted sign-change patterns in action potential duration and diastolic interval spatial gradients with posterior probabilities of 91.1%, and 82.1%, respectively. The model predicted conduction block with 64% sensitivity and 100% specificity. A generalized estimating equation logistic-regression approach showed that model-prediction effects were significant for both conduction block ( P<1×10-15, coefficient 44.36) and sustained ventricular fibrillation ( P=0.0046, coefficient, 1.63) events. Conclusions The observed sign-change patterns favored discordant alternans, and the model successfully identified sequences of premature stimuli that induced conduction block. This suggests that the relatively simple discordant-alternans-based process that led to block in the model may often be responsible for ventricular fibrillation onset when preceded by premature beats. These observations may aid in developing improved methods for anticipating block and ventricular fibrillation.

Effects of electrophysiological heterogeneity on vulnerability to re-entry in human ventricular tissue: A simulation study

In this study, we constructed a two-dimensional ventricular tissue sheet with cellular electrophysiology modified from the Ten Tusscher 2006 Model. Heterogeneity was created by dividing the tissue into endocardium, midmyocardium and epicardium, further enhanced by a central ischemic zone. Subsequently, we investigated how electrophysiological heterogeneity affects re-entry initiation and maintenance in this tissue. Furthermore, we analyzed the vulnerable window (VW) under several conditions and concluded that heterogeneity across various myocardia expands the VW further than the monolayer myocardium model does.

Global alternans instability and its effect on non-linear wave propagation: dynamical Wenckebach block and self terminating spiral waves

The main mechanism of formation of reentrant cardiac arrhythmias is via formation of waveblocks at heterogeneities of cardiac tissue. We report that heterogeneity and the area of waveblock can extend itself in space and can result formation of new additional sources, or termination of existing sources of arrhythmias. This effect is based on a new form of instability, which we coin as global alternans instability (GAI). GAI is closely related to the so-called (discordant) alternans instability, however its onset is determined by the global properties of the APD-restitution curve and not by its slope. The APD-restitution curve relates the duration of the cardiac pulse (APD) to the time interval between the pulses, and can easily be measured in an experimental or even clinical setting. We formulate the conditions for the onset of GAI, study its manifestation in various 1D and 2D situations and discuss its importance for the onset of cardiac arrhythmias.

A theoretical study of the initiation, maintenance and termination of gastric slow wave re-entry

Gastric slow wave dysrhythmias are associated with motility disorders. Periods of tachygastria associated with slow wave re-entry were recently recognized as one important dysrhythmia mechanism, but factors promoting and sustaining gastric re-entry are currently unknown. This study reports two experimental forms of gastric re-entry and presents a series of multi-scale models that define criteria for slow wave re-entry initiation, maintenance and termination. High-resolution electrical mapping was conducted in porcine and canine models and two spatiotemporal patterns of re-entrant activities were captured: single-loop rotor and double-loop figure-of-eight. Two separate multi-scale mathematical models were developed to reproduce the velocity and entrainment frequency of these experimental recordings. A single-pulse stimulus was used to invoke a rotor re-entry in the porcine model and a figure-of-eight re-entry in the canine model. In both cases, the simulated re-entrant activities were found to be perpetuated by tachygastria that was accompanied by a reduction in the propagation velocity in the re-entrant pathways. The simulated re-entrant activities were terminated by a single-pulse stimulus targeted at the tip of re-entrant wave, after which normal antegrade propagation was restored by the underlying intrinsic frequency gradient.

MAIN FINDINGS

(i) the stability of re-entry is regulated by stimulus timing, intrinsic frequency gradient and conductivity; (ii) tachygastria due to re-entry increases the frequency gradient while showing decreased propagation velocity; (iii) re-entry may be effectively terminated by a targeted stimulus at the core, allowing the intrinsic slow wave conduction system to re-establish itself.

Stem cells can form gap junctions with cardiac myocytes and exert pro-arrhythmic effects

Stem cell therapy has been suggested to be a promising option for regeneration of injured myocardium, for example following a myocardial infarction. For clinical use cell-based therapies have to be safe and applicable and are aimed to renovate the architecture of the heart. Yet for functional and coordinated activity synchronized with the host myocardium stem cells have to be capable of forming electrical connections with resident cardiomyocytes. In this paper we discuss whether stem cells are capable of establishing functional electrotonic connections with cardiomyocytes and whether these may generate a risk for arrhythmias. Application of stem cells in the clinical setting with outcomes concerning arrhythmogenic safety and future perspectives will also briefly be touched upon.

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.

Computing the stability of steady-state solutions of mathematical models of the electrical activity in the heart

Instabilities in the electro-chemical resting state of the heart can generate ectopic waves that in turn can initiate arrhythmias. We derive methods for computing the resting state for mathematical models of the electro-chemical process underpinning a heartbeat, and we estimate the stability of the resting state by invoking the largest real part of the eigenvalues of a linearized model. The implementation of the methods is described and a number of numerical experiments illustrate the feasibility of the methods. In particular, we test the methods for problems where we can compare the solutions with analytical results, and problems where we have solutions computed by independent software. The software is also tested for a fairly realistic 3D model.

Unstable eigenmodes are possible drivers for cardiac arrhythmias

The well-organized contraction of each heartbeat is enabled by an electrical wave traversing and exciting the myocardium in a regular manner. Perturbations to this wave, referred to as arrhythmias, can lead to lethal fibrillation if not treated within minutes. One manner in which arrhythmias originate is an ill-fated interaction of the regular electrical signal controlling the heartbeat, the sinus wave, with an ectopic stimulus. It is not fully understood how and when ectopic waves are generated. Based on mathematical models, we show that ectopic beats can be characterized in terms of unstable eigenmodes of the resting state.

Influences of sites and protocols on inducing ventricular fibrillation: A computer simulation study

In cardiac electrophysiological study, several electrical stimulation protocols have been employed to induce ventricular fibrillations (VF). In addition, sites of inducing may have different impacts on inducing results as well as different inducing protocols. To study whether VF inducing method is determinant of induced outcome, we simulated VFs induced with different protocols at different sites based on the Wei-Harumi whole heart model. Simulations showed that only certain combinations of pacing protocols and sites could induce sustainable VFs, which had similar frequency distributions. This result suggested that the interactions between protocols and sites determine the odds of successful inducing but once the VF was induced, the pattern was solely determined by inner cardiac properties.

Liberation of a pinned spiral wave by a single stimulus in excitable media

The unpinning of a spiral wave from an anatomic obstacle by the application of a single stimulus near the core of the rotating wave was studied experimentally in a cell culture of cardiomyocyte monolayers as well as by computer simulations. It is shown that, with suitable positioning and timing, a single stimulus is sufficient for the successful unpinning of a pinned spiral wave. Successful unpinning is achieved when two conditions are fulfilled: (1) The stimulus is delivered in the vulnerable window of the rotating wave, and (2) the stimulus is delivered in a spatial zone in proximity to the obstacle, where the shape of the zone is defined by the phase of the anchored spiral wave. Two different scenarios for successful unpinning are discussed, which are distinguished by the distance to the stimuli applied to the obstacle.