Scroll wave dynamics in a three-dimensional cardiac tissue model: roles of restitution, thickness, and fiber rotation

Scroll wave (vortex) breakup is hypothesized to underlie ventricular fibrillation, the leading cause of sudden cardiac death. We simulated scroll wave behaviors in a three-dimensional cardiac tissue model, using phase I of the Luo-Rudy (LR1) action potential model. The effects of action potential duration (APD) restitution, tissue thickness, filament twist, and fiber rotation were studied. We found that APD restitution is the major determinant of scroll wave behavior and that instabilities arising from APD restitution are the main determinants of scroll wave breakup in this cardiac model. We did not see a "thickness-induced instability" in the LR1 model, but a minimum thickness is required for scroll breakup in the presence of fiber rotation. The major effect of fiber rotation is to maintain twist in a scroll wave, promoting filament bending and thus scroll breakup. In addition, fiber rotation induces curvature in the scroll wave, which weakens conduction and further facilitates wave break.     

Effects of Na(+) and K(+) channel blockade on vulnerability to and termination of fibrillation in simulated normal cardiac tissue

Na(+) and K(+) channel-blocking drugs have anti- and proarrhythmic effects. Their effects during fibrillation, however, remain poorly understood. We used computer simulation of a two-dimensional (2-D) structurally normal tissue model with phase I of the Luo-Rudy action potential model to study the effects of Na(+) and K(+) channel blockade on vulnerability to and termination of reentry in simulated multiple-wavelet and mother rotor fibrillation. Our main findings are as follows: 1) Na(+) channel blockade decreased, whereas K(+) channel blockade increased, the vulnerable window of reentry in heterogeneous 2-D tissue because of opposing effects on dynamical wave instability. 2) Na(+) channel blockade increased the cycle length of reentry more than it increased refractoriness. In multiple-wavelet fibrillation, Na(+) channel blockade first increased and then decreased the average duration or transient time () of fibrillation. In mother rotor fibrillation, Na(+) channel blockade caused peripheral fibrillatory conduction block to resolve and the mother rotor to drift, leading to self-termination or sustained tachycardia. 3) K(+) channel blockade increased dynamical instability by steepening action potential duration restitution. In multiple-wavelet fibrillation, this effect shortened because of enhanced wave instability. In mother rotor fibrillation, this effect converted mother rotor fibrillation to multiple-wavelet fibrillation, which then could self-terminate. Our findings help illuminate, from a theoretical perspective, the possible underlying mechanisms of termination of different types of fibrillation by antiarrhythmic drugs.     

Effects of simulated ischemia on spiral wave stability

Regional hyperkalemia during acute myocardial ischemia is a major factor promoting electrophysiological abnormalities leading to ventricular fibrillation (VF). However, steep action potential duration restitution, recently proposed to be a major determinant of VF, is typically decreased rather than increased by hyperkalemia and acute ischemia. To investigate this apparent contradiction, we simulated the effects of regional hyperkalemia and other ischemic components (anoxia and acidosis) on the stability of spiral wave reentry in simulated two-dimensional cardiac tissue by use of the Luo-Rudy ventricular action potential model. We found that the hyperkalemic "ischemic" area promotes wavebreak in the surrounding normal tissue by accelerating the rate of spiral wave reentry, even after the depolarized ischemic area itself has become unexcitable. Furthermore, wavebreak and fibrillation can be prevented if the dynamical instability of the normal tissue is reduced significantly by targeting electrical restitution properties, suggesting a novel therapeutic approach.     

Negative Tension of Scroll Wave Filaments and Turbulence in Three-Dimensional Excitable Media and Application in Cardiac Dynamics

Scroll waves are vortices that occur in three-dimensional excitable media. Scroll waves have been observed in a variety of systems including cardiac tissue, where they are associated with cardiac arrhythmias. The disorganization of scroll waves into chaotic behavior is thought to be the mechanism of ventricular fibrillation, whose lethality is widely known. One possible mechanism for this process of scroll wave instability is negative filament tension. It was discovered in 1987 in a simple two variables model of an excitable medium. Since that time, negative filament tension of scroll waves and the resulting complex, often turbulent dynamics was studied in many generic models of excitable media as well as in physiologically realistic models of cardiac tissue. In this article, we review the work in this area from the first simulations in FitzHugh–Nagumo type models to recent studies involving detailed ionic models of cardiac tissue. We discuss the relation of negative filament tension and tissue excitability and the effects of discreteness in the tissue on the filament tension. Finally, we consider the application of the negative tension mechanism to computational cardiology, where it may be regarded as a fundamental mechanism that explains differences in the onset of arrhythmias in thin and thick tissue.     

Electrophysiological heterogeneity and stability of reentry in simulated cardiac tissue

Generation of wave break is a characteristic feature of cardiac fibrillation. In this study, we investigated how dynamic factors and fixed electrophysiological heterogeneity interact to promote wave break in simulated two-dimensional cardiac tissue, by using the Luo-Rudy (LR1) ventricular action potential model. The degree of dynamic instability of the action potential model was controlled by varying the maximal amplitude of the slow inward Ca(2+) current to produce spiral waves in homogeneous tissue that were either nearly stable, meandering, hypermeandering, or in breakup regimes. Fixed electrophysiological heterogeneity was modeled by randomly varying action potential duration over different spatial scales to create dispersion of refractoriness. We found that the degree of dispersion of refractoriness required to induce wave break decreased markedly as dynamic instability of the cardiac model increased. These findings suggest that reducing the dynamic instability of cardiac cells by interventions, such as decreasing the steepness of action potential duration restitution, may still have merit as an antifibrillatory strategy.     

Pulsed low-energy stimulation initiates electric turbulence in cardiac tissue

Interruptions in nonlinear wave propagation, commonly referred to as wave breaks, are typical of many complex excitable systems. In the heart they lead to lethal rhythm disorders, the so-called arrhythmias, which are one of the main causes of sudden death in the industrialized world. Progress in the treatment and therapy of cardiac arrhythmias requires a detailed understanding of the triggers and dynamics of these wave breaks. In particular, two very important questions are: 1) What determines the potential of a wave break to initiate re-entry? and 2) How do these breaks evolve such that the system is able to maintain spatiotemporally chaotic electrical activity? Here we approach these questions numerically using optogenetics in an in silico model of human atrial tissue that has undergone chronic atrial fibrillation (cAF) remodelling. In the lesser studied sub-threshold illumination régime, we discover a new mechanism of wave break initiation in cardiac tissue that occurs for gentle slopes of the restitution characteristics. This mechanism involves the creation of conduction blocks through a combination of wavefront-waveback interaction, reshaping of the wave profile and heterogeneous recovery from the excitation of the spatially extended medium, leading to the creation of re-excitable windows for sustained re-entry. This finding is an important contribution to cardiac arrhythmia research as it identifies scenarios in which low-energy perturbations to cardiac rhythm can be potentially life-threatening.     

Effects of early afterdepolarizations on reentry in cardiac tissue: a simulation study

Early afterdepolarizations (EADs) are classically generated at slow heart rates when repolarization reserve is reduced by genetic diseases or drugs. However, EADs may also occur at rapid heart rates if repolarization reserve is sufficiently reduced. In this setting, spontaneous diastolic sarcoplasmic reticulum (SR) Ca release can facilitate cellular EAD formation by augmenting inward currents during the action potential plateau, allowing reactivation of the window L-type Ca current to reverse repolarization. Here, we investigated the effects of spontaneous SR Ca release-induced EADs on reentrant wave propagation in simulated one-, two-, and three-dimensional homogeneous cardiac tissue using a version of the Luo-Rudy dynamic ventricular action potential model modified to increase the likelihood of these EADs. We found: 1) during reentry, nonuniformity in spontaneous SR Ca release related to subtle differences in excitation history throughout the tissue created adjacent regions with and without EADs. This allowed EADs to initiate new wavefronts propagating into repolarized tissue; 2) EAD-generated wavefronts could propagate in either the original or opposite direction, as a single new wave or two new waves, depending on the refractoriness of tissue bordering the EAD region; 3) by suddenly prolonging local refractoriness, EADs caused rapid rotor displacement, shifting the electrical axis; and 4) rapid rotor displacement promoted self-termination by collision with tissue borders, but persistent EADs could regenerate single or multiple focal excitations that reinitiated reentry. These findings may explain many features of Torsades des pointes, such as perpetuation by focal excitations, rapidly changing electrical axis, frequent self-termination, and occasional degeneration to fibrillation.     

The effect of spatial scale of resistive inhomogeneity on defibrillation of cardiac tissue

Defibrillation of cardiac tissue can be viewed in the context of dynamical systems theory as the attempt to move a dynamical system from the basin of attraction of one attractor (fibrillation) to another (the uniform rest state) by applying a stimulus whose form is physically constrained. Here we give an introduction to the physical mechanism of cardiac defibrillation from this dynamical perspective and examine the role of resistive inhomogeneity on defibrillation efficacy. Using numerical simulations with rotating waves on a one-dimensional periodic ring, we study the role of the spatial scale of resistive inhomogeneity on defibrillation. For a rotating wave on a periodic ring there are three stable attractors, namely the uniform rest state, a wave traveling clockwise and a wave traveling counterclockwise. As a result, the application of a stimulus has the potential for three different outcomes, namely elimination of the wave, phase resetting of the wave, and reversal of the wave. The results presented here show that with resistive inhomogeneities of large spatial scale, all three of these transitions are possible with large amplitude shocks, so that the probability of defibrillation is bounded well below one, independent of stimulus amplitude. On the other hand, resistive inhomogeneities of small spatial scale produce a defibrillation threshold that is qualitatively consistent with that found experimentally, namely the probability of defibrillation success is an increasing function that approaches one for large enough stimulus amplitude. Extending these results to higher dimensions, we describe conditions for successful defibrillation of functional reentry with large scale spatial inhomogeneity, but find that elimination of anatomical reentry is quite difficult. With small spatial scale inhomogeneity, there are no similar restrictions.     

Chaos in the genesis and maintenance of cardiac arrhythmias

Dynamical chaos, an irregular behavior of deterministic systems, has been widely shown in nature. It also has been demonstrated in cardiac myocytes in many studies, including rapid pacing-induced irregular beat-to-beat action potential alterations and slow pacing-induced irregular early afterdepolarizations, etc. Here we review the roles of chaos in the genesis of cardiac arrhythmias, the transition to ventricular fibrillation, and the spontaneous termination of fibrillation, based on evidence from computer simulation of mathematical models and experiments of animal models.     

Reentrant waves in a ring of embryonic chick ventricular cells imaged with a Ca2+ sensitive dye

According to the classic model initially formulated by Mines, reentrant cardiac arrhythmias may be associated with waves circulating in a ring geometry. This study was designed to study the dynamics of reentry in a ring geometry of cardiac tissue culture. Reentrant calcium waves in rings of cultured embryonic chick cardiac myocytes were imaged using a macroscope to monitor the fluorescence of intracellular Calcium Green-1 dye. The rings displayed a variety of stable rhythms including pacemaker activity and spontaneous reentry. Waves originating from a localized pacemaker could lead to reentry as a consequence of unidirectional block. In addition, more complex patterns were observed due to the interactions between reentrant and pacemaker rhythms. These rhythms included instances in which pacemakers accelerated the reentrant rhythm, and instances in which the excitation was blocked in the vicinity of pacemakers. During reentrant activity an appropriately timed electrical stimulus could induce resetting of activity or cause complete annihilation of the propagating waves. This experimental preparation reveals many spontaneously occuring complex rhythms. These complex rhythms are hypothesized to reflect interactions between spontaneous pacemakers, wave propagation, refractory period, and overdrive suppression. This preparation may serve as a useful model system to further investigate complex dynamics arising during reentrant rhythms in cardiac tissue.     

Effects of amiodarone on wave front dynamics during ventricular fibrillation in isolated swine right ventricle

The effects of acute amiodarone infusion on dynamics of ventricular fibrillation (VF) are unclear. Six isolated swine right ventricles (RVs) were studied in vitro. Activation patterns during VF were mapped optically, whereas action potentials were recorded with a glass microelectrode. At baseline, VF was associated with frequent spontaneous wave breaks. Amiodarone (2.5 microg/ml) reduced spontaneous wave breaks and increased the cycle length (CL) of VF from 83.3 +/- 17.8 ms at baseline to 118.4 +/- 25.8 ms during infusion (P < 0.05). Amiodarone increased the reentrant wave front CL (114.4 +/- 15.5 vs. 78.2 +/- 19.0 ms, P < 0.05) and central core area (4.1 +/- 3.8 vs. 0.9 +/- 0.3 mm2, P < 0.05). Within 30 min of infusion, VF terminated (n = 1), converted to ventricular tachycardia (VT) (n = 1) or continued at a slower rate (n = 4). Amiodarone flattened the APD restitution curves. We conclude that amiodarone reduced spontaneous wave breaks. It might terminate VF or convert VF to VT. These effects were associated with the flattening of APD restitution slope and increased core size of reentrant wave fronts.     

Phase singularities and filaments: simplifying complexity in computational models of ventricular fibrillation

In the whole heart, millions of cardiac cells are involved in ventricular fibrillation (VF). Experimental studies indicate that VF is sustained by re-entrant activity, and that each re-entrant wave rotates around a filament of phase singularity. Filaments act as organising centres, and offer a way to simplify and quantify the complex spatio-temporal behaviour observed in VF. Where a filament touches the surface of fibrillating myocardium re-entrant activity can be observed, however the behaviour of filaments within bulk ventricular myocardium is difficult to observe directly using present experimental techniques. Large scale computational simulations of VF in three-dimensional (3D) tissue offer a tool to investigate the properties and behaviour of filaments, and the aim of this paper is to review recent advances in this area as well as to compare recent computational studies of fibrillation in whole ventricle geometries.     

Predicting initiation and termination of atrial fibrillation from the ECG.

Atrial fibrillation is the most common cardiac arrhythmia, affecting more than two million people in the US. Several therapies for patients with atrial fibrillation are available, but methods to help physicians select the optimal therapy for an individual patient are still required. Knowledge of whether a patient with a normal ECG will exhibit atrial fibrillation in the future, as well as whether atrial fibrillation will terminate spontaneously, would be very useful in clinical routine. The paper presents a software system for predicting the initiation and termination of atrial fibrillation from the ECG. The algorithms have been validated on ECGs from several signal databases. Prediction of the initiation of atrial fibrillation was achieved by detecting premature heart beats and analyzing the morphology of their P waves. Prediction of the termination of atrial fibrillation was based on calculation of the major atrial frequency. This frequency has been shown to decrease significantly prior to the termination of atrial fibrillation. Nevertheless, the effect is much less distinct in the large data set used for this study compared to previous studies. The initiation of atrial fibrillation, however, could be correctly predicted in approximately 75% of the data analyzed.     

Surfactant effects in model airway closure experiments.

The capillary instability that occurs on an annular film lining a tube is studied as a model of airway closure. Small waves in the film can amplify and form a plug across the tube. This dynamical behavior is studied using theoretical models and bench-top experiments. Our model predicts the initial growth rate of the instability and its dependence on surfactant effects. In experiments, an annular film is formed by infusion of water into an initially oil-filled glass capillary tube. The thickness of the oil film varies with the infusion flow rate. The instability growth rate and closure time are measured for a range of film thicknesses. Our theory predicts that a thinner film and higher surfactant activity enhance stability; surfactant can decrease the growth rate to 25% of its surfactant-free value. In experiments, we find that surfactant can decrease the growth rate to 20% and increase the closure time by a factor of 3.8. Functional values of a critical film thickness for closure support the theory that it increases in the presence of surfactant.     

Scroll-wave dynamics in human cardiac tissue: lessons from a mathematical model with inhomogeneities and fiber architecture

Cardiac arrhythmias, such as ventricular tachycardia (VT) and ventricular fibrillation (VF), are among the leading causes of death in the industrialized world. These are associated with the formation of spiral and scroll waves of electrical activation in cardiac tissue; single spiral and scroll waves are believed to be associated with VT whereas their turbulent analogs are associated with VF. Thus, the study of these waves is an important biophysical problem. We present a systematic study of the combined effects of muscle-fiber rotation and inhomogeneities on scroll-wave dynamics in the TNNP (ten Tusscher Noble Noble Panfilov) model for human cardiac tissue. In particular, we use the three-dimensional TNNP model with fiber rotation and consider both conduction and ionic inhomogeneities. We find that, in addition to displaying a sensitive dependence on the positions, sizes, and types of inhomogeneities, scroll-wave dynamics also depends delicately upon the degree of fiber rotation. We find that the tendency of scroll waves to anchor to cylindrical conduction inhomogeneities increases with the radius of the inhomogeneity. Furthermore, the filament of the scroll wave can exhibit drift or meandering, transmural bending, twisting, and break-up. If the scroll-wave filament exhibits weak meandering, then there is a fine balance between the anchoring of this wave at the inhomogeneity and a disruption of wave-pinning by fiber rotation. If this filament displays strong meandering, then again the anchoring is suppressed by fiber rotation; also, the scroll wave can be eliminated from most of the layers only to be regenerated by a seed wave. Ionic inhomogeneities can also lead to an anchoring of the scroll wave; scroll waves can now enter the region inside an ionic inhomogeneity and can display a coexistence of spatiotemporal chaos and quasi-periodic behavior in different parts of the simulation domain. We discuss the experimental implications of our study.     

Generation of auroral kilometric radiation by a finite-size source in a dipole magnetic field

Generation, amplification, and propagation of auroral kilometric radiation in a narrow three-dimensional plasma cavity in which a weakly relativistic electron beam propagates is studied in the geometrical optics approximation. It is shown that the waves that start with a group velocity directed earthward and have optimal relation between the wave vector components determining the linear growth rate and the wave residence time inside the amplification region undergo the largest amplification. Taking into account the longitudinal velocity of fast electrons results in the shift of the instability domain toward wave vectors directed to the Earth and leads to a change in the dispersion relation, due to which favorable conditions are created for the generation of waves with frequencies above the cutoff frequency for the cold background plasma at the wave generation altitude. The amplification factor for these waves is lower than for waves that have the same wave vectors but are excited by the electron beams with lower velocities along the magnetic field. For waves excited at frequencies below the cutoff frequency of the background plasma at the generation altitude, the amplification factor increases with increasing longitudinal electron velocity, because these waves reside for a longer time in the amplification region.     

Theoretical analysis of the magnetocardiographic pattern for reentry wave propagation in a three-dimensional human heart model

We present a computational study of reentry wave propagation using electrophysiological models of human cardiac cells and the associated magnetic field map of a human heart. We examined the details of magnetic field variation and related physiological parameters for reentry waves in two-dimensional (2-D) human atrial tissue and a three-dimensional (3-D) human ventricle model. A 3-D mesh system representing the human ventricle was reconstructed from the surface geometry of a human heart. We used existing human cardiac cell models to simulate action potential (AP) propagation in atrial tissue and 3-D ventricular geometry, and a finite element method and the Galerkin approximation to discretize the 3-D domain spatially. The reentry wave was generated using an S1-S2 protocol. The calculations of the magnetic field pattern assumed a horizontally layered conductor for reentry wave propagation in the 3-D ventricle. We also compared the AP and magnetocardiograph (MCG) magnitudes during reentry wave propagation to those during normal wave propagation. The temporal changes in the reentry wave motion and magnetic field map patterns were also analyzed using two well-known MCG parameters: the current dipole direction and strength. The current vector in a reentry wave forms a rotating spiral. We delineated the magnetic field using the changes in the vector angle during a reentry wave, demonstrating that the MCG pattern can be helpful for theoretical analysis of reentry waves.     

Arrhythmogenic effects of ultra-long and bistable cardiac action potentials

Contemporary accounts of the initiation of cardiac arrhythmias typically rely on after-depolarizations as the trigger for reentrant activity. The after-depolarizations are usually triggered by calcium entry or spontaneous release within the cells of the myocardium or the conduction system. Here we propose an alternative mechanism whereby arrhythmias are triggered autonomously by cardiac cells that fail to repolarize after a normal heartbeat. We investigated the proposal by representing the heart as an excitable medium of FitzHugh-Nagumo cells where a proportion of cells were capable of remaining depolarized indefinitely. As such, those cells exhibit bistable membrane dynamics. We found that heterogeneous media can tolerate a surprisingly large number of bistable cells and still support normal rhythmic activity. Yet there is a critical limit beyond which the medium is persistently arrhythmogenic. Numerical analysis revealed that the critical threshold for arrhythmogenesis depends on both the strength of the coupling between cells and the extent to which the abnormal cells resist repolarization. Moreover, arrhythmogenesis was found to emerge preferentially at tissue boundaries where cells naturally have fewer neighbors to influence their behavior. These findings may explain why atrial fibrillation typically originates from tissue boundaries such as the cuff of the pulmonary vein.     

Atrial fibrillation as the nonstationary process: analysis of chaotic dynamics

A method for the mathematical analysis of recordings of the myocardium electrical activity during ventricular fibrillation is proposed. The method is based on evaluating the indices of the orderliness of the process. The entropy was one of the indices used. The analysis of EGG during ventricular fibrillation (an acute experiment on rats) revealed certain regularities in the apparently chaotic process of fibrillar oscillations. The entropy increased at the first stages of the fibrillation and then reached its maximal level. A gradual decrease in the entropy level preceded the spontaneous termination of fibrillation. This indicates that different stages of the process the degree of its disorganization changes. Upon spontaneous termination of fibrillation, quantitative changes transfer to qualitative changes. This reflects the transition of the myocardial system to another level of structural and functional organization.