Scroll waves in spherical shell geometries

The evolution of scroll waves in excitable media with spherical shell geometries is studied as a function of shell thickness and outer radius. The motion of scroll wave filaments that are the locii of phaseless points in the medium and organize the wave pattern is investigated. When the inner radius is sufficiently large the filaments remain attached to both the inner and outer surfaces. The minimum size of the sphere that supports spiral waves and the maximum number of spiral waves that can be sustained on a sphere of given size are determined for both regular and random initial distributions. When the inner radius is too small to support spiral waves the filaments detach from the inner surface and form a curved filament connecting the two spiral tips in the surface. In certain parameter domains the filament is an arc of a circle that shrinks with constant shape. For parameter values close to the meandering border, the filament grows and collisions with the sphere walls lead to turbulent filament dynamics. (c) 2001 American Institute of Physics.     

Eikonal formulation of the minimal principle for scroll wave filaments

Recently, Wellner et al. [Proc. Natl. Acad. Sci. U.S.A. 99, 8015 (2002)]] proposed a principle for predicting a stable scroll wave filament shape as a geodesic in a 3D space with a metric determined by the inverse diffusivity tensor of the medium. Using the Hamilton-Jacobi theory we show that this geodesic is the shortest path for a wave propagating through the medium. This allows the use of shortest path algorithms to predict filament shapes, which we confirm numerically for a medium with orthotropic anisotropy. Our method can be used in cardiac tissue experiments since it does not require knowledge of the tissue anisotropy.     

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.     

A geometric theory for scroll wave filaments in anisotropic excitable media

Scroll waves are an important example of self-organisation in excitable media. In cardiac tissue, scroll waves of electrical activity underlie lethal ventricular arrhythmias and fibrillation. They rotate around a topological line defect which has been termed the filament. Numerical investigation has shown that anisotropy can substantially affect the dynamics of scroll waves. It has recently been hypothesised that stationary scroll wave filaments in cardiac tissue describe geodesics in a space whose metric is the inverse diffusion tensor. Several computational studies have validated this hypothesis, but until now no quantitative theory has been provided to study the effects of anisotropy on scroll wave filaments. Here, we review in detail the recently developed covariant formalism for scroll wave dynamics in general anisotropy and derive the equations of motion of filaments. These equations are fully covariant under general spatial coordinate transformations and describe the motion of filaments in a curved space whose metric tensor is the inverse diffusion tensor. Our dynamic equations are valid for thin filaments and for general anisotropy and we show that stationary filaments obey the geodesic equation. We extend previous work by allowing spatial variations in the determinant of the diffusion tensor and the reaction parameters, leading to drift of the filament.     

Scroll wave dynamics in a model of the heterogeneous heart

Scroll waves are found in physical, chemical and biological systems and underlie many significant processes including life-threatening cardiac arrhythmias. The theory of scroll waves predicts scroll wave dynamics should be substantially affected by heterogeneity of cardiac tissue together with other factors including shape and anisotropy. In this study, we used our recently developed analytical model of the human ventricle to identify effects of shape, anisotropy, and regional heterogeneity of myocardium on scroll wave dynamics. We found that the main effects of apical-base heterogeneity were an increased scroll wave drift velocity and a shift towards the region of maximum action potential duration. We also found that transmural heterogeneity does not substantially affect scroll wave dynamics and only in extreme cases changes the attractor position.     

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.     

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.     

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.     

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 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.     

Covariant stringlike dynamics of scroll wave filaments in anisotropic cardiac tissue

It has been hypothesized that stationary scroll wave filaments in cardiac tissue describe a geodesic in a curved space whose metric is the inverse diffusion tensor. Several numerical studies support this hypothesis, but no analytical proof has been provided yet for general anisotropy. In this Letter, we derive dynamic equations for the filament in the case of general anisotropy. These equations are covariant under general spatial coordinate transformations and describe the motion of a stringlike object in a curved space whose metric tensor is the inverse diffusion tensor. Therefore the behavior of scroll wave filaments in excitable media with anisotropy is similar to the one of cosmic strings in a curved universe. Our dynamic equations are valid for thin filaments and for general anisotropy. We show that stationary filaments obey the geodesic equation.     

Alternative stable scroll waves and conversion of autowave turbulence

Rotating spiral and scroll waves (vortices) are investigated in the FitzHugh-Nagumo model of excitable media. The focus is on a parameter region in which there exists bistability between alternative stable vortices with distinct periods. Response functions are used to predict the filament tension of the alternative scrolls and it is shown that the slow-period scroll has negative filament tension, while the filament tension of the fast-period scroll changes sign within a hysteresis loop. The predictions are confirmed by direct simulations. Further investigations show that the slow-period scrolls display features similar to delayed after-depolarization and tend to develop into turbulence similar to ventricular fibrillation (VF). Scrolls with positive filament tension collapse or stabilize, similar to monomorphic ventricular tachycardia (VT). Perturbations, such as boundary interaction or shock stimulus, can convert the vortex with negative filament tension into the vortex with positive filament tension. This may correspond to transition from VF to VT unrelated to pinning.     

Interaction dynamics of a pair of vortex filament rings

Vortex filament-filament interactions are believed to underlie lethal arrhythmias in cardiac tissue but their dynamics remain poorly understood. We numerically replicate an experimentally postulated reentrant filament configuration as a pair of adjacent circular filaments (scroll rings) with common symmetry axes and varying initial radii and separation distances. The interaction properties are quantified in terms of the scroll-ring lifetime T(L) and direction of initial velocity V0. Two cases were examined, differing only in the direction of the wave around the filament, and observed drastic differences in T(L) between the cases as the separation distance between the rings was decreased. We conclude that ring interactions present unexpected behaviors associated with competing interaction and decay mechanisms.     

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.     

Organizing Filament of Small Amplitude Scroll Waves

We theoretically analyze the organizing filament of small amplitude scroll waves in general excitable media by perturbation method and explicitly give the expressions of coefficients in Keener theory.In particular for the excitable media with equal diffusion,we obtain a close system for the motion of the filament.With an example of the Oregonator Model,our results are in good agreement with those simulated by Windree.     

Periodic forcing of scroll rings and control of Winfree turbulence in excitable media

By simulations of the Barkley model, action of uniform periodic nonresonant forcing on scroll rings and wave turbulence in three-dimensional excitable media is investigated. Sufficiently strong rapid forcing converts expanding scroll rings into the collapsing ones and suppresses the Winfree turbulence caused by the negative tension of wave filaments. Slow strong forcing has an opposite effect, leading to expansion of scroll rings and induction of the turbulence. These effects are explained in the framework of the phenomenological kinematic theory of scroll waves.     

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.     

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.     

小型化行波管灯丝电源设计

综述了行波管灯丝基本工作过程及其对电源的特殊要求,分析了行波管灯丝负载基本特性,对灯丝电源设计的特殊性及问题进行了深入细致分析,通过对Topswitch系列控制芯片的性能特点分析,设计了以反激变换器为主电路的灯丝电源。根据灯丝启动特点及其对电源稳定性基本要求设计了高精度反馈电路与限流电路。通过Pspice仿真、样机实验及例行试验测试,验证了理论分析及设计的合理性与可行性,仿真与测试结果表明电源主电路、反馈电路及限流电路能够很好地满足行波管灯丝对电源的各项指标要求。     

飞秒光丝阵列对10 GHz电磁波的吸收特性

为了研究飞秒光丝阵列对10 GHz电磁波的吸收特性,建立了飞秒光丝阵列吸收电磁波的有限元模型,研究了光丝内电子温度、电子数密度、光丝直径和电磁波的极化等参数对吸收系数的影响。研究结果表明:当电磁波偏振方向与光丝轴向垂直时,阵列对电磁波是透明的;增加光丝内电子数密度或提高电子温度,吸收系数先增大后减小;当光丝直径与电磁波趋肤深度相等时,吸收系数达到最大值。对于S极化电磁波,当光丝直径为50 μm时,吸收系数随入射角的增大而变大;当光丝直径为100~200 μm时,在入射角较小时,吸收系数随入射角的增大而变大;在入射角较大时会出现吸收峰值,最高可达0.45,且光丝直径越大,吸收峰值对应的入射角就越小;对于P极化电磁波,吸收系数随入射角增大而降低。