Negative filament tension in the Luo-Rudy model of cardiac tissue

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, which lethality is widely known. One of the possible mechanisms of scroll wave instability is negative filament tension, which was studied theoretically using low-dimensional models of excitable medium. In this article we perform a numerical study of negative filament tension using the Luo-Rudy phase 1 model, which is widely used in cardiac electrophysiology. We show that this instability exists in this model, study its manifestation and discuss its relation to cardiac arrhythmogenesis.     

Three-dimensional spiral waves in an excitable reaction system: initiation and dynamics of scroll rings and scroll ring pairs

We report experimental results on spiral and scroll waves in the 1,4-cyclohexanedione Belousov-Zhabotinsky reaction. The propagating concentration waves are detected by two-dimensional photometry and optical tomography. Wave pulses can disappear in front-to-front and front-to-back collisions. This anomaly causes the nucleation of vortices from collisions of three nonrotating waves. In three-dimensional systems, these vortices are scroll rings that rotate around initially circular filaments. Depending on reactant concentrations, the filaments shrink or expand indicating positive and negative filament tensions, respectively. Shrinkage results in vortex annihilation. Expansion is accompanied by filament buckling and bending, which is interpreted as developing Winfree turbulence. We also describe the initiation of scroll ring pairs in four-wave collisions. The two filaments are stacked on top of each other and their motion suggests filament repulsion.     

Vortex Turbulence due to the Interplay of Filament Tension and Rotational Anisotropy

The mechanism of scroll wave turbulence is investigated in excitable media with rotational anisotropy. We adopt the Barkley model with heterogeneity in the diffusion constants. Through comparative numerical studies, we demonstrate the vortex turbulence results from the rotational anisotropy＇s cooperation with negative filament tension or competition with positive filament tension. The presence of rotational anisotropy can enlarge the parameter region leading to negative-tension induced wave turbulence in isotropic media.     

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.     

Negative filament tension at high excitability in a model of cardiac tissue

One of the fundamental mechanisms for the onset of turbulence in 3D excitable media is negative filament tension. Thus far, negative tension has always been obtained in media under low excitability. For this reason, its application to normal (nonischemic) cardiac tissue has been questionable, as such cardiac turbulence typically occurs at high excitability. Here, we report expansion of scroll rings (low curvature negative filament tension) in a medium with high excitability by numerical integration of the Luo-Rudy model of cardiac tissue. We discuss the relation between negative tension and the meandering of 2D spiral waves and the possible applications to cardiac modeling.     

异常心电节律VT和VF信号的复杂性分析

在替代随机数据假设检验的基础上,提出了针对确定性混沌信号的改进非线性算法,并应用于心脏中的异常节律心电信号分析.指出：室性心动过速(VT)和心室纤颤(VF)是不同于随机信号的,是具有复杂非线性特性的混沌信号.进而在信号定性分析的基础上,从非线性动力学的角度,提出新的复杂度和复杂率的定义和相关的检测方法,对VT和VF进行了定量分析.结果表明,异常心电节律VT和VF信号的定性和定量分析是客观的和准确可靠的. 关键词： 复杂离散度 Lempel-Ziv复杂度 复杂率 平均复杂度 复杂饱和度     

Scroll wave instabilities in an excitable chemical medium

Two kinds of scroll wave instabilities were studied experimentally in the excitable Belousov-Zhabotinsky reaction: three-dimensional meandering and negative line tension of the scroll wave filament. The filament displays a flat zigzag shape in the initial stages of the experiment. As the chemical medium ages, the filament assumes a wiggly shape while its length increases substantially. Numerical simulations underpin the experimental findings and their interpretation.     

Effects of reduced discrete coupling on filament tension in excitable media

Wave propagation in the heart has a discrete nature, because it is mediated by discrete intercellular connections via gap junctions. Although effects of discreteness on wave propagation have been studied for planar traveling waves and vortexes (spiral waves) in two dimensions, its possible effects on vortexes (scroll waves) in three dimensions are not yet explored. In this article, we study the effect of discrete cell coupling on the filament dynamics in a generic model of an excitable medium. We find that reduced cell coupling decreases the line tension of scroll wave filaments and may induce negative filament tension instability in three-dimensional excitable lattices.     

Computerized mapping of fibrillation in normal ventricular myocardium

It is well known that the ability to fibrillate is intrinsic to a normal ventricle that exceeds a critical mass. The questions we address are how is ventricular fibrillation (VF) initiated and perpetuated in normal myocardium, and why is VF not seen more often in the general population if all ventricles have the ability to fibrillate. To study the mechanisms of VF, we used computerized mapping techniques with up to 512 channels of simultaneous multisite recordings for data acquisition. The data were then processed for dynamic display of the activation patterns and for mathematical analyses of the activation intervals. The results show that in normal ventricles, VF can be initiated by a single strong premature stimulus given during the vulnerable period of the cardiac cycle. The initial activations form a figure-eight pattern. Afterward, VF will perpetuate itself without any outside help. The self-perpetuation itself is due to at least two factors. One is that single wave fronts spontaneously break up into two or more wavelets. The second is that when two wavelets intersect perpendicular to each other, the second wavelet is broken by the residual refractoriness left over from the first wavelet. Mathematical analyses of the patterns of activation during VF revealed that VF is a form of chaos, and that transition from ventricular tachycardia (VT) to VF occurs via the quasiperiodic route. In separate experiments, we found that we can convert VF to VT by tissue size reduction. The physiological mechanism associated with the latter transition appears to be the reduction of the number of reentrant wave fronts and wandering wavelets. Based on these findings, we propose that the reentrant wave fronts and the wandering wavelets serve as the physiological equivalent of coupled oscillators. A minimal number of oscillators is needed for VF to perpetuate itself, and to generate chaotic dynamics; hence a critical mass is required to perpetuate VF. We conclude that VF in normal myocardium is a form of reentrant cardiac arrhythmia. A strong electrical stimulus initiates single or dual reentrant wave fronts that break up into multiple wavelets. Sometimes short-lived reentry is also generated during the course of VF. These organized reentrant and broken wavelets serve as coupled oscillators that perpetuate VF and maintain chaos. Although the ability to support these oscillators exists in a normal ventricle, the triggers required to generate them are nonexistent in the normal heart. Therefore, VF and sudden death do not happen to most people with normal ventricular myocardium. (c) 1998 American Institute of Physics.     

Visualization and characterization of small-scale spanwise vortices in turbulent channel flow

High-resolution particle-image velocimetry (PIV) measurements are made in the streamwise-wall-normal plane of turbulent channel flow at Re_τ=566, 1184 and 1759, facilitating documentation of the population trends and core diameters of small-scale spanwise vortices. Swirling strength, an unambiguous vortex-identification criterion and hence a local marker of rotation, is used to extract small-scale spanwise vortex cores from the instantaneous velocity fields. Once the small-scale vortices are properly extracted from the PIV realizations, their characteristics are studied in detail. The present results indicate that the very-near-wall region (y < 0.1h) is densely populated by spanwise vortices with clockwise (negative) rotation. This behavior supports the notion that hairpin-like vortices are generated very close to the wall and grow into the outer layer as they advect downstream. In contrast, counterclockwise (positive) spanwise vortices are scarce in the very-near-wall region, but their presence steadily increases within the logarithmic layer presumably due to a localized generation mechanism. The average core diameter of negative spanwise vortices is found to be larger than the average diameter of positive vortices, with few positive vortices having core diameters exceeding 80y.     

Arrhythmogenesis in the heart: Multiscale modeling of the effects of defibrillation shocks and the role of electrophysiological heterogeneity

The mechanisms of initiation of ventricular arrhythmias as well as those behind the complex spatiotemporal wave dynamics and its filament organization during ventricular fibrillation (VF) are the topic of intense research and debate. Mechanistic inquiry into the various mechanisms that lead to arrhythmia initiation and VF maintenance is hampered by the inability of current experimental techniques to resolve, with sufficient accuracy, electrical behavior confined to the depth of the ventricles. The objective of this article is to demonstrate that realistic 3D simulations of electrical activity in the heart are capable of bringing a new level of understanding of the mechanisms that underlie arrhythmia initiation and subsequent organization. The article does this by presenting the results of two multiscale simulation studies of ventricular electrical behavior. The first study aims to uncover the mechanisms responsible for rendering the ventricles vulnerable to electric shocks during a specific interval of time, the vulnerable window. The second study focuses on elucidating the role of electrophysiological heterogeneity, and specifically, differences in action potential duration in various ventricular structures, in VF organization. Both studies share common multiscale modeling approaches and analysis, including characterization of scroll-wave filament dynamics.     

Coherent structures and their stability in ion temperature gradient turbulence

Periodic arrays of large scale coherent vortices and their stability have been investigated, within the framework of /spl eta//sub i/ turbulence, using two-dimensional fluid simulation in slab geometry. These vortices, in combination with viscosity damping of small scales, contribute to the formation of a steady state in a system with linearly unstable modes. The steady state comprises of a few vortex convective turn over times and seems to be fairly robust. It has been recognized that a vortex chain, consisting of positive and negative vorticities, continues to move stably in the poloidal direction (along periodic direction). On the other hand, an initial isolated monopole vortex is unstable and leads to a long-lived stable dipolar structure after a few vortex turnover periods. A variety of simple collisional interaction processes among these coherent vortices have also been explored numerically.     

Dynamics of Vortex-Wave under a Travelling-Wave Modulation

The mechanism of destabilization is studied for the rotating vortices （scroll waves and spiral waves） in excitable media induced by a parameter modulation in the form of a travelling-wave. It is found that a rigid rotating spiral in the two-dimensional （2D） system undergoes a synchronized drift along a straight line, and a 3D scroll ring with its filament closed into a circle can be reoriented only if the direction of wave number of a travelling-wave perturbation is parallel to the ring plane. Then, in order to describe the behaviour of the synchronized drift of spiral wave and the reorientation of scroll ring, the approximate formulas are given to exhibit qualitative agreements with the observed results.     

Predicting filament drift in twisted anisotropy

Excitable media with twisted anisotropy have recently been attracting significant interest because of their applicability to wave propagation in heart tissue. Here we consider the dynamics of an intramural scroll wave whose filament lies initially within an arbitrary layer of mutually parallel cardiac fibers, and drifts parallel to itself from layer to layer. Earlier simulations have demonstrated that such a filament stabilizes in a layer whose fiber direction is the same as its own. In the present paper we analytically derive the trajectory of the filament, and obtain good agreement with earlier numerical data. For sufficiently sparse scrolls, our analysis predicts an equilibrium alignment perpendicular rather than parallel to the fibers.     

Distribution characteristics of intensity and phase vortices of speckle fields produced by N-pinhole random screens

We analyze the distribution properties of phase and phase vortices in a speckle field generated by N-pinhole random screens, and find that the phase vortex distributions show similarity and clustering in local regions. The phase patterns have a lot of sets composed of two phase vortices with opposite signs or four phase vortices which are positive and negative vortices alternately. Cases are also found where two adjacent phase vortices have the same topological charges. The density of phase vortices becomes larger with the increase of the radius of circumference and the number of pinholes on screen.Then, the relative positions of phase vortices can be adjusted by changing the radius of circumference and the number of pinholes.     

Symbolic dynamics of ventricular tachycardia and ventricular fibrillation

In this paper, the symbolic dynamics analysis was used to analyze the complexity of normal heartbeat signal (NSR), Ventricular tachycardia (VT) and ventricular fibrillation (VF) signals. By calculating the information entropy value of symbolic sequences, the complexities were quantified. Based on different information entropy values, NSR, VT and VF signals were distinguished with satisfactory results. The study showed that a sudden drop of symbolic sequence’s entropy value indicated that the patients most likely entered the episode of ventricular tachycardia and this was a crucial episode for the clinical treatment of patients. It had important clinical significance for the automatic diagnosis.     

Large scale dissipation and filament instability in two-dimensional turbulence

Coherent vortices in two-dimensional turbulence induce far-field effects that stabilize vorticity filaments and inhibit the generation of new vortices. We show that the large-scale energy sink often included in numerical simulations of statistically stationary two-dimensional turbulence reduces the stabilizing role of the vortices, leading to filament instability and to continuous formation of new coherent vortices. This counterintuitive effect sheds new light on the mechanisms responsible for vortex formation in forced-dissipated two-dimensional turbulence, and it has significant impact on the temporal evolution of the vortex population in freely decaying turbulence. The time dependence of vortex statistics in the presence of a large-scale energy sink can be approximately described by a modified version of the scaling theory developed for small-scale dissipation.     

Nucleation and collapse of scroll rings in excitable media

We describe a novel nucleation mechanism of scroll rings in three-dimensional reaction-diffusion systems with anomalous dispersion. The vortices form after the collision of two spherical wave fronts from a third, trailing wave that only partially annihilates in the wake of its predecessor. Depending on the relative positions of the three relevant wave sources, one obtains untwisted or twisted scroll rings. The formation of both vortex structures is demonstrated for a modified Belousov-Zhabotinsky reaction.     

对偶超导模型n=90—110的近似解析解

研究了对偶超导模型的大n涡旋。 基于变分原理得出了Abelian Higgs模型在n=90—110的近似涡旋解析解, 并计算了涡旋张力对n的依赖性。 发现, 每根涡旋的张力大致随n线性增长。 期望该解对理解Abelian Higgs模型中的大量子数涡旋的墙行为具有一定价值。 The large n vortices in the dual superconductor model was investigated. An approximate analytical solution was obtained for n fold quantized vortices with n=90—110 by variationally solving the AbelianHiggs model, and the vortex tension was calculated as a function of n. It was found that the vortex tension rises linearly as n grows. It is hoped that our solution shines light on the understanding of the wall behavior of the large n vortices in Abelian Higgs model.