On the formation of circulating patterns of excitation in anisotropic excitable media

Mechanisms of ventricular arrhythmias: a dynamical systems-based perspective

Defining the cellular electrophysiological mechanisms for ventricular tachyarrhythmias is difficult, given the wide array of potential mechanisms, ranging from abnormal automaticity to various types of reentry and kk activity. The degree of difficulty is increased further by the fact that any particular mechanism may be influenced by the evolving ionic and anatomic environments associated with many forms of heart disease. Consequently, static measures of a single electrophysiological characteristic are unlikely to be useful in establishing mechanisms. Rather, the dynamics of the electrophysiological triggers and substrates that predispose to arrhythmia development need to be considered. Moreover, the dynamics need to be considered in the context of a system, one that displays certain predictable behaviors, but also one that may contain seemingly stochastic elements. It also is essential to recognize that even the predictable behaviors of this complex nonlinear system are subject to small changes in the state of the system at any given time. Here we briefly review some of the short-, medium-, and long-term alterations of the electrophysiological substrate that accompany myocardial disease and their potential impact on the initiation and maintenance of ventricular arrhythmias. We also provide examples of cases in which small changes in the electrophysiological substrate can result in rather large differences in arrhythmia outcome. These results suggest that an interrogation of cardiac electrical dynamics is required to provide a meaningful assessment of the immediate risk for arrhythmia development and for evaluating the effects of putative antiarrhythmic interventions.

The relative role of refractoriness and source-sink relationship in reentry generation during simulated acute ischemia

During acute myocardial ischemia, reentrant episodes may lead to ventricular fibrillation (VF), giving rise to potentially mortal arrhythmias. VF has been traditionally related to dispersion of refractoriness and more recently to the source-sink relationship. Our goal is to theoretically investigate the relative role of dispersion of refractoriness and source-sink mismatch in vulnerability to reentry in the specific situation of regional myocardial acute ischemia. The electrical activity of a regionally ischemic tissue was simulated using a modified version of the Luo-Rudy dynamic model. Ischemic conditions were varied to simulate the time-course of acute ischemia. Our results showed that dispersion of refractoriness increased with the severity of ischemia. However, no correlation between dispersion of refractoriness and the width of the vulnerable window was found. Additionally, in approximately 50% of the reentries, unidirectional block (UDB) took place in cells completely recovered from refractoriness. We examined patterns of activation after premature stimulation and they were intimately related to the source-sink relationship, quantified by the safety factor (SF). Moreover, the isoline where the SF dropped below unity matched the area where propagation failed. It was concluded that the mismatch of the source-sink relationship, rather than solely refractoriness, was the ultimate cause of the UDB leading to reentry. The SF represents a very powerful tool to study the mechanisms responsible for reentry.

Multiple mechanisms of spiral wave breakup in a model of cardiac electrical activity

It has become widely accepted that the most dangerous cardiac arrhythmias are due to reentrant waves, i.e., electrical wave(s) that recirculate repeatedly throughout the tissue at a higher frequency than the waves produced by the heart's natural pacemaker (sinoatrial node). However, the complicated structure of cardiac tissue, as well as the complex ionic currents in the cell, have made it extremely difficult to pinpoint the detailed dynamics of these life-threatening reentrant arrhythmias. A simplified ionic model of the cardiac action potential (AP), which can be fitted to a wide variety of experimentally and numerically obtained mesoscopic characteristics of cardiac tissue such as AP shape and restitution of AP duration and conduction velocity, is used to explain many different mechanisms of spiral wave breakup which in principle can occur in cardiac tissue. Some, but not all, of these mechanisms have been observed before using other models; therefore, the purpose of this paper is to demonstrate them using just one framework model and to explain the different parameter regimes or physiological properties necessary for each mechanism (such as high or low excitability, corresponding to normal or ischemic tissue, spiral tip trajectory types, and tissue structures such as rotational anisotropy and periodic boundary conditions). Each mechanism is compared with data from other ionic models or experiments to illustrate that they are not model-specific phenomena. Movies showing all the breakup mechanisms are available at http://arrhythmia.hofstra.edu/breakup and at ftp://ftp.aip.org/epaps/chaos/E-CHAOEH-12-039203/ INDEX.html. The fact that many different breakup mechanisms exist has important implications for antiarrhythmic drug design and for comparisons of fibrillation experiments using different species, electromechanical uncoupling drugs, and initiation protocols. (c) 2002 American Institute of Physics.

Ventricular fibrillation: mechanisms of initiation and maintenance

Ventricular fibrillation (VF) is the major immediate cause of sudden cardiac death. Traditionally, VF has been defined as turbulent cardiac electrical activity, which implies a large amount of irregularity in the electrical waves that underlie ventricular excitation. During VF, the heart rate is too high (> 550 excitations/minute) to allow adequate pumping of blood. In the electrocardiogram (ECG), ventricular complexes that are ever-changing in frequency, contour, and amplitude characterize VF. This article reviews prevailing theories for the initiation and maintenance of VF, as well as its spatio-temporal organization. Particular attention is given to recent experiments and computer simulations suggesting that VF may be explained in terms of highly periodic three-dimensional rotors that activate the ventricles at exceedingly high frequency. Such rotors may show at least two different behaviors: (a) At one extreme, they may drift throughout the heart at high speeds producing beat-to-beat changes in the activation sequence. (b) At the other extreme, rotors may be relatively stationary, activating the ventricles at such high frequencies that the wave fronts emanating from them breakup at varying distances, resulting in complex spatio-temporal patterns of fibrillatory conduction. In either case, the recorded ECG patterns are indistinguishable from VF. The data discussed have paved the way for a better understanding of the mechanisms of VF in the normal, as well as the diseased, human heart.

The induction of reentry in cardiac tissue. The missing link: How electric fields alter transmembrane potential

This review examines the initiation of reentry in cardiac muscle by strong electric shocks. Specifically, it concentrates on the mechanisms by which electric shocks change the transmembrane potential of the cardiac membrane and create the physiological substrate required by the critical point theory for the initiation of rotors. The mechanisms examined include (1) direct polarization of the tissue by the stimulating current, as described by the one-dimensional cable model and its two- and three-dimensional extensions, (2) the presence of virtual anodes and cathodes, as described by the bidomain model with unequal anisotropy ratios of the intra- and extracellular spaces, (3) polarization of the tissue due to changing orientation of cardiac fibers, and (4) polarization of individual cells or groups of cells by the electric field ("sawtooth potential"). The importance of these mechanisms in the initiation of reentry is examined in two case studies: the induction of rotors using successive stimulation with a unipolar electrode, and the induction of rotors using cross-field stimulation. These cases reveal that the mechanism by which a unipolar stimulation induces arrhythmias can be explained in the framework of the bidomain model with unequal anisotropy ratios. In contrast, none of the examined mechanisms provide an adequate explanation for the induction of rotors by cross-field stimulation. Hence, this study emphasizes the need for further experimental and theoretical work directed toward explaining the mechanism of field stimulation. (c) 1998 American Institute of Physics.

Reentry: insights from theoretical simulations in a fixed pathway

This review article summarizes theoretical insights into the principles and mechanisms associated with reentrant activity in cardiac tissue. A mathematical ring model is used in computer simulations to investigate, at the cellular level, mechanistic aspects of initiation, perpetuation, and termination of reentry. Taking advantage of the ability to compute membrane processes in this model, we relate dynamic properties of the reentrant action potential (e.g., beat-to-beat alternans) to the underlying kinetics of membrane ionic channels. Effects on reentry of inhomogeneities in refractoriness, excitability, cellular coupling at gap junctions, and fiber cross-section are also studied.

Initiation and stability of reentry in two coupled excitable fibers

Reentry in the heart is the repeated excitation of the same tissue by a single excitation wave; it is responsible for several types of cardiac arrhythmia. The simplest model which permits the phenomenon of reentry is two laterally coupled excitable fibers; in this paper we examine such a model in order to establish a basis for the understanding of the fundamental physical processes underlying the process of reentry. Two versions of the FitzHugh-Nagumo equations are used to develop complementary numerical and analytical results for the coupled fiber model. On the basis of numerical studies, regions of qualitatively different behaviour are mapped in the parameter space of excitation threshold and coupling strength between the fibers, and the effect of the rate of recovery is explored. Some of these regions are also obtained analytically, in good agreement with the numerical results. Finally, the results are discussed in the light of recent work on the role of the anisotropy of cardiac tissue in the initiation of reentrant activity in the heart.

Intercellular conduction velocity variability as the basis for re-entrant arrhythmias in the ischemic myocardium

Re-entrant arrhythmias are the major cause of death from cardiovascular disease. A number of models or mechanisms have been proposed to explain the generation of re-entrant arrhythmias in the ischemic or damaged heart. However, none of these models can qualitatively predict the formation of re-entry movements with no modifications of the basic electrophysiologic characteristics of the myocardium. In this presentation we evaluate the concept that the generation of re-entrant arrhythmias is due to increased variance in the conduction characteristics of the cardiac tissue, rather than to modification of these properties. Using a model of a homogeneous two-dimensional matrix of excitable conducting cells, we derived the relationship between the relative standard deviation (RSD) and the probability of occurrence of a local ordered dispersion of velocities shown to have the potential to result in circular propagation. This probability was found to be insignificant when the RSD was lower than 10%, but increased dramatically for RSDs greater than 10%. On the basis of experimental RSD, the calculated probability for circus movement formation is one in 10,000 normal heart beats and one in two ischemic heart beats. The model provides new insight into the mechanism of re-entrant arrhythmias as well as new tools for diagnosis.