Dynamics and interaction of filaments in a computational model of re-entrant ventricular fibrillation

Markov modeling of phase singularity interaction effects in human atrial and ventricular fibrillation

Atrial and ventricular fibrillation (AF/VF) are characterized by the repetitive regeneration of topological defects known as phase singularities (PSs). The effect of PS interactions has not been previously studied in human AF and VF. We hypothesized that PS population size would influence the rate of PS formation and destruction in human AF and VF, due to increased inter-defect interaction. PS population statistics were studied in computational simulations (Aliev-Panfilov), human AF and human VF. The influence of inter-PS interactions was evaluated by comparison between directly modeled discrete-time Markov chain (DTMC) transition matrices of the PS population changes, and M/M/∞ birth-death transition matrices of PS dynamics, which assumes that PS formations and destructions are effectively statistically independent events. Across all systems examined, PS population changes differed from those expected with M/M/∞. In human AF and VF, the formation rates decreased slightly with PS population when modeled with the DTMC, compared with the static formation rate expected through M/M/∞, suggesting new formations were being inhibited. In human AF and VF, the destruction rates increased with PS population for both models, with the DTMC rate increase exceeding the M/M/∞ estimates, indicating that PS were being destroyed faster as the PS population grew. In human AF and VF, the change in PS formation and destruction rates as the population increased differed between the two models. This indicates that the presence of additional PS influenced the likelihood of new PS formation and destruction, consistent with the notion of self-inhibitory inter-PS interactions.

Prediction of Cardiac Mechanical Performance From Electrical Features During Ventricular Tachyarrhythmia Simulation Using Machine Learning Algorithms

In ventricular tachyarrhythmia, electrical instability features including action potential duration, dominant frequency, phase singularity, and filaments are associated with mechanical contractility. However, there are insufficient studies on estimated mechanical contractility based on electrical features during ventricular tachyarrhythmia using a stochastic model. In this study, we predicted cardiac mechanical performance from features of electrical instability during ventricular tachyarrhythmia simulation using machine learning algorithms, including support vector regression (SVR) and artificial neural network (ANN) models. We performed an electromechanical tachyarrhythmia simulation and extracted 12 electrical instability features and two mechanical properties, including stroke volume and the amplitude of myocardial tension (ampTens). We compared predictive performance according to kernel types of the SVR model and the number of hidden layers of the ANN model. In the SVR model, the prediction accuracies of stroke volume and ampTens were the highest when using the polynomial kernel and linear kernel, respectively. The predictive performance of the ANN model was better than that of the SVR model. The prediction accuracies were the highest when the ANN model consisted of three hidden layers. Accordingly, we propose the ANN model with three hidden layers as an optimal model for predicting cardiac mechanical contractility in ventricular tachyarrhythmia. The results of this study are expected to be used to indirectly estimate the hemodynamic response from the electrical cardiac map measured by the optical mapping system during cardiac surgery, as well as cardiac contractility under normal sinus rhythm conditions.

Relationship Between Electrical Instability and Pumping Performance During Ventricular Tachyarrhythmia: Computational Study

There are representative electrical parameters for understanding the mechanism of reentrant waves in studies on tachyarrhythmia, namely the action potential duration (APD), dominant frequency, phase singularity, and filament. However, there are no studies that have directly identified the correlation between these electrophysiological parameters and cardiac contractility. Therefore, we have identified individual and integrative correlations between these electrical phenomena and contractility during tachyarrhythmia by deriving regression equations and also investigated the electrophysiological parameters affecting cardiac contractility during tachyarrhythmia. We simulated ventricular tachyarrhythmia with 48 types of electrical patterns by applying four reentry generation methods and changing the electrical conductivity of the potassium channel, which has the greatest effect on ventricular tissue. The mechanical responses reflecting electrical complexity were obtained through deterministic simulations of excitation-contraction coupling. We used the stroke volume and amplitude of myocardial tension (ampTens) as the variables representing contractility. We derived stochastic models through single- and multivariable regression analyses to identify the electrical parameters affecting contractility during tachyarrhythmia. In single-variable regression analysis, the APD, dominant frequency, and filament, excluding phase singularity, have statistically significant correlations with the stroke volume and ampTens. Among them, the APD has the maximum influence on these two mechanical parameters (standard beta coefficient: 0.859 for stroke volume, 0.930 for ampTens). The stochastic model using all four electrical parameters fails to accurately predict contractility owing to the multicollinearity between the APD and dominant frequency. We have rederived the multi-variable stochastic model using three electrical parameters without the APD. The filament has the greatest effect on the stroke volume stochastically (standard beta coefficient: 0.853 and 0.752). The dominant frequency has the greatest effect on ampTens statistically (standard beta coefficient: -0.813). We conclude that among the electrical parameters, the APD has the highest individual influence on mechanical contraction, and the filament has the highest integrative influence in both statistical terms.

Multi-scale approaches for the simulation of cardiac electrophysiology: II - Tissue-level structure and function

Computational models of the heart, from cell-level models, through one-, two- and three-dimensional tissue-level simplifications, to biophysically-detailed three-dimensional models of the ventricles, atria or whole heart, allow the simulation of excitation and propagation of this excitation, and have provided remarkable insight into the normal and pathological functioning of the heart. In this article we present equations for modelling cellular excitation (i.e. the cell action potential) from both a phenomenological and a biophysical perspective. Hodgkin-Huxley formalism is discussed, along with the current generation of biophysically-detailed cardiac cell models. Alternative Markovian formulations for modelling ionic currents are also presented. Equations describing propagation of this cellular excitation, through one-, two- and three-dimensional idealised or realistic tissues, are then presented. For all types of model, from cell to tissue, methods for discretisation and integration of the underlying equations are discussed. The article finishes with a discussion of two tissue-level experimental imaging techniques - diffusion tensor magnetic resonance imaging and optical imaging - that can be used to provide data for parameterisation and validation of cell- and tissue-level cardiac models.

Reconnection of multiple scroll rings in a three-dimensional reaction-diffusion system

Two scroll rings, placed in close proximity, can interact. When they come within one core length of each other, these waves can reconnect to form a single, large filament. In this article we show that three or more scroll rings can also reconnect when they come within the critical distance. Multiple scroll rings form larger vortices of varied filament geometry, depending on their initial sizes and placements. Different filaments, resulting from a reconnection of the same number of scroll rings placed in diverse ways, can have different lifetimes. In experiments with the Belousov-Zhabotinsky reaction and numerical simulations based on a corresponding reaction-diffusion model, we demonstrate the interaction and reconnection of multiple scroll waves and try to elucidate their lifetimes and dynamics.

Effect of Heart Structure on Ventricular Fibrillation in the Rabbit: A Simulation Study

Ventricular fibrillation (VF) is a lethal condition that affects millions worldwide. The mechanism underlying VF is unstable reentrant electrical waves rotating around lines called filaments. These complex spatio-temporal patterns can be studied using both experimental and numerical methods. Computer simulations provide unique insights including high resolution dynamics throughout the heart and systematic control of quantities such as fiber orientation and cellular kinetics that are not feasible experimentally. Here we study filament dynamics using two bi-ventricular 3-D high-resolution rabbit heart geometries, one with detailed fine structure and another without fine structure. We studied filament dynamics using anisotropic and isotropic conductivities, and with four cellular action potential models with different recovery kinetics. Spiral wave dynamics observed in isotropic two-dimensional sheets were not predictive of the behavior in the whole heart. In 2-D the four cell models exhibited stable reentry, meandering spiral waves, and spiral-wave breakup. In the whole heart with fine structure, all simulation results exhibited complex dynamics reminiscent of fibrillation observed experimentally. In the whole heart without fine structure, anisotropy acted to destabilize filament dynamics although the number of filaments was reduced compared to the heart with structure. In addition, in isotropic hearts without structure the two cell models that exhibited meandering spiral waves in 2-D, stabilized into figure-of-eight surface patterns. We also studied the sensitivity of filament dynamics to computer system configuration and initial conditions. After large simulation times, different macroscopic results sometimes occurred across different system configurations, likely due to a lack of bitwise reproducibility. The study conclusions were insensitive to initial condition perturbations, however, the exact number of filaments over time and their trends were altered by these changes. In summary, we present the following new results. First, we provide a new cell model that resembles the surface patterns of VF in the rabbit heart both qualitatively and quantitatively. Second, filament dynamics in the whole heart cannot be predicted from spiral wave dynamics in 2-D and we identified anisotropy as one destabilizing factor. Third, the exact dynamics of filaments are sensitive to a variety of factors, so we suggest caution in their interpretation and their quantitative analyses.

Interaction of a pair of parallel scroll waves

Interactions of pairs of scroll waves in three-dimensional excitable media were studied experimentally in the Belousov-Zhabotinsky reaction by optical tomography. The behavior of two scroll waves depended on the distance d between their filaments. When the interfilament distance was shorter than the wavelength λ of the scroll waves (but larger than the diameter of the spiral core), the filaments repelled each other. Once d ≈ λ, the two scroll waves synchronized, rotating around their filaments with both a common rotation frequency and a common pitch. The interfilament distance of synchronized scroll waves did not change. When fluctuations broke the symmetry of the rotation periods, the scroll with higher rotation frequency displaced the slower rotating one, until the latter was ousted or even annihilated. These behaviors were independent of the sense of rotation (co- or counter-rotating), the filament dynamics (rigidly rotating or meandering tip motion in two-dimensional media), and the presence or absence of a gradient of excitability parallel to the filaments.

Intermittent self-organization of scroll wave turbulence in three-dimensional excitable media

We study the asymptotic behavior of scroll wave turbulence in large three-dimensional excitable media modeled by FitzHugh-Nagumo equations. The focus is on the type of turbulence caused by negative tension of scroll wave filaments, which is considered to be one of the mechanisms of cardiac fibrillation. We discovered that the initial increase in turbulence complexity can be followed by intermittent self-organization, when complex filament tangles are replaced by a small number of relatively stable triple filament strands. The intermittency is the result of a competition between the destabilizing effect of negative tension and mutual attraction of filaments with similar orientation.

Filament behavior in a computational model of ventricular fibrillation in the canine heart

The aim of this paper was to quantify the behavior of filaments in a computational model of re-entrant ventricular fibrillation. We simulated cardiac activation in an anisotropic monodomain with excitation described by the Fenton-Karma model with Beeler-Reuter restitution, and geometry by the Auckland canine ventricle. We initiated re-entry in the left and right ventricular free walls, as well as the septum. The number of filaments increased during the first 1.5 s before reaching a plateau with a mean value of about 36 in each simulation. Most re-entrant filaments were between 10 and 20 mm long. The proportion of filaments touching the epicardial surface was 65%, but most of these were visible for much less than one period of re-entry. This paper shows that useful information about filament dynamics can be gleaned from models of fibrillation in complex geometries, and suggests that the interplay of filament creation and destruction may offer a target for antifibrillatory therapy.

Effect of regional differences in cardiac cellular electrophysiology on the stability of ventricular arrhythmias: a computational study

Re-entry is an important mechanism of cardiac arrhythmias. During re-entry a wave of electrical activation repeatedly propagates into recovered tissue, rotating around a rod-like filament. Breakdown of a single re-entrant wave into multiple waves is believed to underlie the transition from ventricular tachycardia to ventricular fibrillation. Several mechanisms of breakup have been identified including the effect of anisotropic conduction in the ventricular wall. Cells in the inner and outer layers of the ventricular wall have different action potential durations (APD), and support re-entrant waves with different periods. The aim of this study was to use a computational approach to study twisting and breakdown in a transmural re-entrant wave spanning these regions, and examine the relative role of this effect and anisotropic conduction. We used a simplified model of action potential conduction in the ventricular wall that we modified so that it supported stable re-entry in an anisotropic model with uniform APD. We first examined the effect of regional differences on breakdown in an isotropic model with transmural differences in APD, and found that twisting of the re-entrant filament resulted in buckling and breakdown during the second cycle of re-entry. We found that breakdown was amplified in the anisotropic model, resulting in complex activation in the region of longest APD. This study shows that regional differences in cardiac electrophysiology are a potentially important mechanism for destabilizing re-entry and may act synergistically with other mechanisms to mediate the transition from ventricular tachycardia to ventricular fibrillation.

Transition from ventricular fibrillation to ventricular tachycardia: a simulation study on the role of Ca(2+)-channel blockers in human ventricular tissue

We study the effect of blocking the L-type Ca(2+)-channel on fibrillation in simulations in two-dimensional (2D) isotropic sheets of ventricular tissue and in a three-dimensional anisotropic anatomical model of human ventricles, using a previously developed model of human ventricular cells. Ventricular fibrillation (VF) was obtained as a result of spiral wave breakup and consisted of a varying number of chaotically wandering wavelets activating tissue at a frequency of about 6.0 Hz. We show that blocking the Ca(2+)-current by 75% can convert ventricular fibrillation into a periodic regime with a small number of stable spiral waves, ranging from six in 2D sheets of 25 x 25 cm to a single spiral in the anatomical model of human ventricles. The dominant frequency during this process changed to about 10.0 Hz in the 2D simulations, but to only 5.0 Hz in the whole heart simulations where a single spiral wave anchored around an anatomical obstacle. We show that the observed effects were due to a flattening of the electrical restitution curve, which prevented the generation of wave breaks and stabilized the activation patterns.

Computational framework for simulating the mechanisms and ECG of re-entrant ventricular fibrillation

Ventricular arrhythmias remain an important cause of morbidity and mortality in the Western world. Although the underlying mechanisms of these arrhythmias can be studied experimentally, these investigations are in general limited to mapping electrical activity on the heart surface. Computational models of action potential propagation offer a potentially powerful way to study electrical activation and arrhythmias, but current models are not easy to link to the clinical environment. In this paper, we describe a framework for computing action potential propagation in which the geometry, electrophysiology and regional properties of ventricular myocardium can be specified so that, for example, different models for cardiac cellular electrophysiology can be used. We have computed action potential propagation during both normal beats and re-entry in an anatomically accurate model of ventricular geometry. By computing the resultant electric current flow in the torso we have also generated simulated ECG signals that result from specific activation patterns in the ventricular model. Models can be powerful tools for explaining observations, and this approach is able to provide a direct link between the different configurations of re-entry observed in computational and experimental studies, and the ECG signals observed in patients.

Enhanced self-termination of re-entrant arrhythmias as a pharmacological strategy for antiarrhythmic action

Ventricular tachycardia and fibrillation are potentially lethal cardiac arrhythmias generated by high frequency, irregular spatio-temporal electrical activity. Re-entrant propagation has been demonstrated as a mechanism generating these arrhythmias in computational and in vitro animal models of these arrhythmias. Re-entry can be idealised in homogenous isotropic virtual cardiac tissues as spiral and scroll wave solutions of reaction-diffusion equations. A spiral wave in a bounded medium can be terminated if its core reaches a boundary. Ventricular tachyarrhythmias in patients are sometimes observed to spontaneously self-terminate. One possible mechanism for self-termination of a spiral wave is meander of its core to an inexcitable boundary. We have previously proposed the hypothesis that the spatial extent of meander of a re-entrant wave in the heart can be directly related to its probability of self-termination, and so inversely related to its lethality. Meander in two-dimensional virtual ventricular tissues based on the Oxsoft family of cell models, with membrane excitation parameters simulating the inherited long Q-T syndromes has been shown to be consistent with this hypothesis: the largest meander is seen in the syndrome with the lowest probability of death per arrhythmic episode. Here we extend our previous results to virtual tissues based on the Luo-Rudy family of models. Consistent with our hypothesis, for both families of models, whose different ionic mechanisms produce different patterns of meander, the LQT virtual tissue with the larger meander simulates the syndrome with the lower probability of death per episode. Further, we search the parameter space of the repolarizing currents to find their conductance parameter values that give increased meander of spiral waves. These parameters may provide targets for antiarrhythmic drugs designed to act by increasing the likelihood of self-termination of re-entrant arrhythmias. (c) 2002 American Institute of Physics.