Spiral Wave Dynamics Research Articles

Electro-mechanical dynamics of spiral waves in a discrete 2D model of human atrial tissue.

We investigate the effect of mechano-electrical feedback and atrial fibrillation induced electrical remodelling (AFER) of cellular ion channel properties on the dynamics of spiral waves in a discrete 2D model of human atrial tissue. The tissue electro-mechanics are modelled using the discrete element method (DEM). Millions of bonded DEM particles form a network of coupled atrial cells representing 2D cardiac tissue, allowing simulations of the dynamic behaviour of electrical excitation waves and mechanical contraction in the tissue. In the tissue model, each cell is modelled by nine particles, accounting for the features of individual cellular geometry; and discrete inter-cellular spatial arrangement of cells is also considered. The electro-mechanical model of a human atrial single-cell was constructed by strongly coupling the electrophysiological model of Colman et al. to the mechanical myofilament model of Rice et al., with parameters modified based on experimental data. A stretch-activated channel was incorporated into the model to simulate the mechano-electrical feedback. In order to investigate the effect of mechano-electrical feedback on the dynamics of spiral waves, simulations of spiral waves were conducted in both the electromechanical model and the electrical-only model in normal and AFER conditions, to allow direct comparison of the results between the models. Dynamics of spiral waves were characterized by tracing their tip trajectories, stability, excitation frequencies and meandering range of tip trajectories. It was shown that the developed DEM method provides a stable and efficient model of human atrial tissue with considerations of the intrinsically discrete and anisotropic properties of the atrial tissue, which are challenges to handle in traditional continuum mechanics models. This study provides mechanistic insights into the complex behaviours of spiral waves and the genesis of atrial fibrillation by showing an important role of the mechano-electrical feedback in facilitating and promoting atrial fibrillation.

Effect of the form and anisotropy of the left ventricle on the drift of spiral waves

Three-dimensional spiral waves of electrical excitation in the myocardium are sources of dangerous cardiac arrhythmias. In this work, the dynamics of spiral waves of electrical excitation were studied in a symmetric anatomical model of the human heart left ventricle and a realistic ionic cell model of the human ventricular myocardium. Three factors that affect the drift waves in the heart were compared for the first time: the geometry of the heart wall, myocardial anisotropy, and wave chirality. Cardiac anisotropy was identified as a main factor in determining the drift of spiral waves. In the isotropic case, the dynamics were determined by the wall thickness, but did not depend on the wave chirality. In the anisotropic case, chirality was found to play a crucial role.

Spiral-wave dynamics in a mathematical model of human ventricular tissue with myocytes and Purkinje fibers.

We present systematic numerical studies of the possible effects of the coupling of human endocardial and Purkinje cells at cellular and two-dimensional tissue levels. We find that the autorhythmic-activity frequency of the Purkinje cell in a composite decreases with an increase in the coupling strength; this can even eliminate the autorhythmicity. We observe a delay between the beginning of the action potentials of endocardial and Purkinje cells in a composite; such a delay increases as we decrease the diffusive coupling, and eventually a failure of transmission occurs. An increase in the diffusive coupling decreases the slope of the action-potential-duration-restitution curve of an endocardial cell in a composite. By using a minimal model for the Purkinje network, in which we have a two-dimensional, bilayer tissue, with a layer of Purkinje cells on top of a layer of endocardial cells, we can stabilize spiral-wave turbulence; however, for a sparse distribution of Purkinje-ventricular junctions, at which these two layers are coupled, we can also obtain additional focal activity and many complex transient regimes. We also present additional effects resulting from the coupling of Purkinje and endocardial layers and discuss the relation of our results to the studies performed in anatomically accurate models of the Purkinje network.

Dynamics of a human spiral wave

With a few simple instructions, participants at the Atlanta Science Festival mimicked a phenomenon that can have fatal consequences in biological systems.

Hidden structures of information transport underlying spiral wave dynamics.

A spiral wave is a macroscopic dynamics of excitable media that plays an important role in several distinct systems, including the Belousov-Zhabotinsky reaction, seizures in the brain, and lethal arrhythmia in the heart. Because the spiral wave dynamics can exhibit a wide spectrum of behaviors, its precise quantification can be challenging. Here we present a hybrid geometric and information-theoretic approach to quantifying the spiral wave dynamics. We demonstrate the effectiveness of our approach by applying it to numerical simulations of a two-dimensional excitable medium with different numbers and spatial patterns of spiral waves. We show that, by defining the information flow over the excitable medium, hidden coherent structures emerge that effectively quantify the information transport underlying the spiral wave dynamics. Most importantly, we find that some coherent structures become more clearly defined over a longer observation period. These findings provide validity with our approach to quantitatively characterize the spiral wave dynamics by focusing on information transport. Our approach is computationally efficient and is applicable to many excitable media of interest in distinct physical, chemical, and biological systems. Our approach could ultimately contribute to an improved therapy of clinical conditions such as seizures and cardiac arrhythmia by identifying potential targets of interventional therapies.

Analysis of Cardiac spiral wave dynamics at regional cooling using computer simulation model

Analysis of Cardiac spiral wave dynamics at regional cooling using computer simulation model

Dynamics of pulses and spiral waves in excitable media with an anomalous diffusion

Spiral waves and pulses in the excitable medium with an anomalous diffusion are studied. In the medium with an one-sided fractional diffusion in the [Formula: see text]-direction and a normal diffusion in the [Formula: see text]-direction, a pulse, traveling along the positive [Formula: see text]-direction, has a smaller velocity, which is different from the diffusion of a source in the other media. Its propagating velocity is a linear and increasing function of the square root of diffusion parameter, whose increasing rate depends on the fractional order. A minimal value of the diffusion parameter is needed for successfully propagating pulses, and the threshold becomes large with a decrease of the fractional order. For pulse trains, the frequency-locked bands are shifted along the increasing direction of the perturbation period when the fractional order is decreased. In the propagating process of a spiral wave, the tip drift is induced by the one-sided fractional diffusion, which may be explained by analyzing the SV area in front of the tip.

Comparison of Detailed and Simplified Models of Human Atrial Myocytes to Recapitulate Patient Specific Properties.

Computer studies are often used to study mechanisms of cardiac arrhythmias, including atrial fibrillation (AF). A crucial component in these studies is the electrophysiological model that describes the membrane potential of myocytes. The models vary from detailed, describing numerous ion channels, to simplified, grouping ionic channels into a minimal set of variables. The parameters of these models, however, are determined across different experiments in varied species. Furthermore, a single set of parameters may not describe variations across patients, and models have rarely been shown to recapitulate critical features of AF in a given patient. In this study we develop physiologically accurate computational human atrial models by fitting parameters of a detailed and of a simplified model to clinical data for five patients undergoing ablation therapy. Parameters were simultaneously fitted to action potential (AP) morphology, action potential duration (APD) restitution and conduction velocity (CV) restitution curves in these patients. For both models, our fitting procedure generated parameter sets that accurately reproduced clinical data, but differed markedly from published sets and between patients, emphasizing the need for patient-specific adjustment. Both models produced two-dimensional spiral wave dynamics for that were similar for each patient. These results show that simplified, computationally efficient models are an attractive choice for simulations of human atrial electrophysiology in spatially extended domains. This study motivates the development and validation of patient-specific model-based mechanistic studies to target therapy.

Spatiotemporal dynamics in a network composed of neurons with different excitabilities and excitatory coupling

Spiral waves have been observed in the biological experiments on rat cortex perfused with drugs which can block inhibitory synapse and switch neuron excitability from type II to type I. To simulate the spiral waves observed in the experiment, the spatiotemporal patterns are investigated in a network composed of neurons with type I and II excitabilities and excitatory coupling. Spiral waves emerge when the percentage (p) of neurons with type I excitability in the network is at middle levels, which is dependent on the coupling strength. Compared with other spatial patterns which appear at different p values, spiral waves exhibit optimal spatial correlation at a certain spatial frequency, implying the occurrence of spatial coherence resonance-like phenomenon. Some dynamical characteristics of the network such as mean firing frequency and synchronous degree can be well interpreted with distinct properties between type I excitability and type II excitability. The results not only identify dynamics of spiral waves in neuronal networks composed of neurons with different excitabilities, but also are helpful to understanding the emergence of spiral waves observed in the biological experiment.

Effects of abnormal excitation on the dynamics of spiral waves**Project supported by the National Natural Science Foundation of China (Grant Nos. 11365003 and 11165004).

The effect of physiological and pathological abnormal excitation of a myocyte on the spiral waves is investigated based on the cellular automaton model. When the excitability of the medium is high enough, the physiological abnormal excitation causes the spiral wave to meander irregularly and slowly. When the excitability of the medium is low enough, the physiological abnormal excitation leads to a new stable spiral wave. On the other hand, the pathological abnormal excitation destroys the spiral wave and results in the spatiotemporal chaos, which agrees with the clinical conclusion that the early after depolarization is the pro-arrhythmic mechanism of some anti-arrhythmic drugs. The mechanisms underlying these phenomena are analyzed.

Unstable spiral waves and local Euclidean symmetry in a model of cardiac tissue.

This paper investigates the properties of unstable single-spiral wave solutions arising in the Karma model of two-dimensional cardiac tissue. In particular, we discuss how such solutions can be computed numerically on domains of arbitrary shape and study how their stability, rotational frequency, and spatial drift depend on the size of the domain as well as the position of the spiral core with respect to the boundaries. We also discuss how the breaking of local Euclidean symmetry due to finite size effects as well as the spatial discretization of the model is reflected in the structure and dynamics of spiral waves. This analysis allows identification of a self-sustaining process responsible for maintaining the state of spiral chaos featuring multiple interacting spirals.

Unusual spiral wave dynamics in the Kessler-Levine model of an excitable medium.

The Kessler-Levine model is a two-component reaction-diffusion system that describes spatiotemporal dynamics of the messenger molecules in a cell-to-cell signaling process during the aggregation of social amoeba cells. An excitation wave arising in the model has a phase wave at the wave back, which simply follows the wave front after a fixed time interval with the same propagation velocity. Generally speaking, the medium excitability and the refractoriness are two important factors which determine the spiral wave dynamics in any excitable media. The model allows us to separate these two factors relatively easily since the medium refractoriness can be changed independently of the medium excitability. For rigidly rotating waves, the universal relationship has been established by using a modified free-boundary approach, which assumes that the front and the back of a propagating wave are thin in comparison to the wave plateau. By taking a finite thickness of the domain boundary into consideration, the validity of the proposed excitability measure has been essentially improved. A novel method of numerical simulation to suppress the spiral wave instabilities is introduced. The trajectories of the spiral tip observed for a long refractory period have been investigated under a systematic variation of the medium refractoriness.

Dynamics of spiral waves in an asymmetrically coupled two-layer excitable medium

The dynamics of spiral waves in the two-layer excitable media is studied by using the Br-Eiswirth model. The two media adopts the inhibitory and excitatory asymmetric couplings. Numerical results show that the excitatory asymmetric coupling can promote the frequency-locking of two spiral waves with different frequencies. The two spiral waves can achieve frequency-locking even if the frequency difference between them is large. The coupling causes the two spiral waves to have the strongest ability of frequency-locking; when the coupling between the two media is the inhibitory asymmetric coupling, the two spiral waves can achieve frequency-locking only when the frequency difference of the initial spiral waves is small. Furthermore, the range of frequency-locking is smaller than that of the general feedback coupling, and the frequency-locking ability of spiral waves reaches the minimum level. When the coupling strength and control parameters are chosen appropriately, the inhibitory and excitatory asymmetric coupling can keep the spiral wave unchanged in one medium and result in the transition from spiral wave to the resting state or target wave with low-frequency in the other. The coupling also induces the meandering of spiral waves or leads to the transition from two spiral waves to two target waves in the two-layer media. Finally the generated target waves either disappear or develop into the plane-wave-like oscillation patterns. Furthermore, the oscillation of the patterns is in antiphase. In addition, the locally intermittent frequency-locking of the two spiral waves is observed. These results can help understand the complicated phenomena occurring in the cardiac system.

The effect of cellular aging on the dynamics of spiral waves

Cellular aging can result in deterioration of electrical coupling, the extension of the action potential duration, and lower excitability of the cell. Those factors are introduced into the Greenberg—Hastings cellular automaton model and the effects of the cellular aging on the dynamics of spiral waves are studied. The numerical results show that a 50% reduction of the coupling strength of aging cells has a little influence on spiral waves. If the coupling strength of aging cells equals zero, the ability for the medium to maintain spiral waves will be reduced by approximately 50% when the aging cell ratio increases from 0 to 0.5, where the reduction of cell excitability plays a major role in inducing disappearance of spiral waves. When the relevant parameters are properly chosen, the cellular aging can lead to the meandering of spiral waves, the emergence of the binary spiral waves, and even the disappearance of spiral waves via the stopping rotation or shrinkage of wave. Physical mechanisms of the above phenomena are analyzed briefly.

Computational prediction of proarrhythmogenic effect of the V241F KCNQ1 mutation in human atrium

Genetic factors play an important role in the pathogenesis of atrial flutter (AF). Although mutation in KCNQ1 has been widely correlated with AF, the mechanism by which mutation promotes AF remains poorly understood. The purpose of this study was to investigate the proarrhythmic effect of V241F KCNQ1 mutation in human atrium using the electrophysiological model of human atrium. Using 2D and 3D cardiac electrophysiological models that incorporate the Courtemanche human atrial model, we simulated electrical conduction through atrial tissue and compared spiral wave dynamics under the wild-type and V241F KCNQ1 conditions. In 2D and 3D simulation, V241F KCNQ1 showed a stable and persistent wave without spiral break-up, whereas the wild-type wave was less stable, resulting in early self-termination. According to the results, we concluded that compared to the wild type, the electrical activity of the V241F KCNQ1 mutation is more likely to sustain spiral wave.

Spiral-wave dynamics in ionically realistic mathematical models for human ventricular tissue: the effects of periodic deformation.

We carry out an extensive numerical study of the dynamics of spiral waves of electrical activation, in the presence of periodic deformation (PD) in two-dimensional simulation domains, in the biophysically realistic mathematical models of human ventricular tissue due to (a) ten-Tusscher and Panfilov (the TP06 model) and (b) ten-Tusscher, Noble, Noble, and Panfilov (the TNNP04 model). We first consider simulations in cable-type domains, in which we calculate the conduction velocity θ and the wavelength λ of a plane wave; we show that PD leads to a periodic, spatial modulation of θ and a temporally periodic modulation of λ; both these modulations depend on the amplitude and frequency of the PD. We then examine three types of initial conditions for both TP06 and TNNP04 models and show that the imposition of PD leads to a rich variety of spatiotemporal patterns in the transmembrane potential including states with a single rotating spiral (RS) wave, a spiral-turbulence (ST) state with a single meandering spiral, an ST state with multiple broken spirals, and a state SA in which all spirals are absorbed at the boundaries of our simulation domain. We find, for both TP06 and TNNP04 models, that spiral-wave dynamics depends sensitively on the amplitude and frequency of PD and the initial condition. We examine how these different types of spiral-wave states can be eliminated in the presence of PD by the application of low-amplitude pulses by square- and rectangular-mesh suppression techniques. We suggest specific experiments that can test the results of our simulations.

Effect of Dichotomous Noise on Dynamics of Spiral Waves

This paper mainly researched the effect of dichotomous noise on the dynamics of spiral wave, provided a method to eliminate spiral waves by dichotomous noise. Spiral wave dynamics show regular changes under the action of dichotomous noise with noise strength, time correlation parameter, this rule change can be explained by spectral analysis.

How does β-adrenergic signalling affect the transitions from ventricular tachycardia to ventricular fibrillation?

Ventricular tachycardia (VT) and fibrillation (VF) are the most lethal cardiac arrhythmias. The degeneration of VT into VF is associated with the breakup of a spiral wave of the action potential in cardiac tissue. β-Adrenergic (βAR) signalling potentiates the L-type Ca current (ICaL) faster than the slow delayed rectifier potassium current (IKs), which transiently prolongs the action potential duration (APD) and promotes early after depolarizations. In this study, we aimed at investigating how βAR signalling affects the transition from VT to VF. We used a physiologically detailed computer model of the rabbit ventricular myocyte in a two-dimensional tissue to determine how spiral waves respond to βAR activation following administration of isoproterenol. A simplified mathematical model was also used to investigate the underlying dynamics. We found that the spatiotemporal behaviour of spiral waves strongly depends on the kinetics of βAR activation. When βAR activation is rapid, a stable spiral wave turns into small fragments and its electrocardiogram reveals the transition from VT to VF. This is due to the transiently steepened APD restitution induced by the faster activation of ICaL vs. IKs upon sudden βAR activation. The spiral wave may also disappear if its transient wavelength is too large to be supported by the tissue size upon sudden strong βAR activation that prolongs APD transiently. When βAR activation is gradual, a stable spiral wave remains such, because of more limited increase in both APD and slope of APD restitution due to more contemporaneous ICaL and IKs activation. Changes in APD restitution during βAR activation revealed a novel transient spiral wave dynamics; this spatiotemporal characteristic strongly depends on the protocol of isoproterenol application.

Core solutions of rigidly rotating spiral waves in highly excitable media.

Analytical spiral wave solutions for reaction-diffusion equations play an important role in studying spiral wave dynamics. In this paper, we focus on such analytical solutions in the case of highly excitable media. We present numerical evidence that, for rigidly rotating spiral waves in highly excitable media, the species values in the spiral core region do harmonic oscillations but not relaxation ones, and their amplitudes grow linearly with the distance from the rotation center. An analytical solution is proposed to describe such spiral wave dynamics, and the quantitative comparisons between the numerical results and the analytical solutions show that the proposed spiral core solution works well in highly excitable media.

Continuous Transition between Two Limits of Spiral Wave Dynamics in an Excitable Medium

By application of a free-boundary approach, we prove the existence of a continuous transition and a full spectrum of solutions between the two known limits of spiral wave dynamics. We identify a control parameter whose essential importance was not realized in earlier studies of spatiotemporal pattern selection in excitable media. The predictions of the free-boundary approach are in good quantitative agreement with results from numerical reaction-diffusion simulations performed on the modified Barkley model.