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.     

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.     

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.     

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.     

Nonlinear theory of the excitation of spin waves in ferrites by a longitudinal ultrahigh-frequency magnetic field

The problem of parametric excitation of spin waves in ferrites due to the action of a perturbing super high-frequency (SHF) magnetic field polarized along the direction of the constant magnetic field H₀ is considered in a nonlinear approximation. Such an examination enables one to determine the conditions for parametric excitation of spin waves and to find the amplitude and phase of the oscillations of the system's magnetization in the steady state. The frequency interval, within whose limits parametric excitation of spin waves is possible, is determined. Stability of the steady state under the conditions of parametric resonance is investigated. The results obtained are compared with existing experimental data.     

Scroll wave instability controlled by external fluctuations

Scroll waves, a characteristic dynamical pattern of three-dimensional excitable media, exhibit an instability under low excitability conditions. This unstable regime can be partially controlled by using random forcing in a clear manifestation of the ordering role of a stochastic external perturbation. Analytical and numerical results confirm this unexpected noise effect.     

轴对称非均匀弹性介质中引力波对声子的作用效应

采用Ｓｅｒｅｂｒｙａｎｙ的复空间中的复坐标法，讨论了轴对称非均匀弹性介质中引力波对声子的作用效应，并给出了由引力波产生的激发力的表达式和相应的声子解。解的形式表明，平行于对称轴方向传播的引力波只对声子场的径向分量、切向分量产生扰动，垂直于对称轴方向传播的引力波则对声子场的径向分量、切向分量和轴向分量均产生扰动，扰动强度取决于切变模量径向分布函数的具体形式和引力波的振幅。此外，本文还将所得结果与含有螺旋位错的拓扑声子空间中引力波的扰动效应作了比较。 关键词：     

Topological constraint on scroll wave pinning

Scroll waves in an excitable medium rotate about tubelike filaments, whose ends, when they exist, can lie on the external boundary of the medium or be pinned to an inclusion. We derive a topological rule that governs such pinning. It implies that some configurations cannot occur although they might otherwise have been expected. Heart tissue provides an application of these concepts. Computational illustrations based on a FitzHugh-Nagumo model are given.     

Bloch定理与散射平面波的干涉

从波动学的角度分析空晶格模型中的自由电子在周期性晶体势微扰作用下转变为晶体中Bloch电子的过程,揭示出了这一过程的物理实质,结果表明,在晶体势微扰作用下,代表空晶格模型中自由电子定态波函数的行进平面波在晶体内各点处产生了各种许可波矢的散射平面波,Bloch定理是晶体微观结构的平移对称性（即周期性）使得这些散射平面波产生干涉的结果。     

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.     

Topological Constraints on Scroll and Spiral Waves in Excitable Media

A conservation equation for topological charges of phase singularities （scroll and spiral waves） in excitable media is given. It provides some topological properties of scroll （spiral） waves： for example, the topological charge of the generated or annihilated spiral pair must be opposite. Additionally, we obtain another equation on scroll waves, which shows that singular filaments of scroll waves occur on a set of one-dimensional curves which may be either closed loops or infinite lines.     

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.     

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.     

Scroll-wave dynamics in the presence of ionic and conduction inhomogeneities in an anatomically realistic mathematical model for the pig heart

Nonlinear waves of the reaction–diffusion (RD) type occur in many biophysical systems, including the heart, where they initiate cardiac contraction. Such waves can form vortices called scroll waves, which result in the onset of life-threatening cardiac arrhythmias. The dynamics of scroll waves is affected by the presence of inhomogeneities, which, in a very general way, can be of (i) ionic type; i.e., they affect the reaction part, or (ii) conduction type, i.e., they affect the diffusion part of an RD-equation. We demonstrate, for the first time, by using a state-of-the-art, anatomically realistic model of the pig heart, how differences in the geometrical and biophysical nature of such inhomogeneities can influence scroll-wave dynamics in different ways. Our study reveals that conduction-type inhomogeneities become increasingly important at small length scales, i.e., in the case of multiple, randomly distributed, obstacles in space at the cellular scale (0.2–0.4 mm). Such configurations can lead to scroll-wave break up. In contrast, ionic inhomogeneities affect scroll-wave dynamics significantly at large length scales, when these inhomogeneities are localized in space at the tissue level (5–10 mm). In such configurations, these inhomogeneities can attract scroll waves, by pinning them to the heterogeneity, or lead to scroll-wave breakup.     

Anchoring of drifting spiral and scroll waves to impermeable inclusions in excitable media

Anchoring of spiral and scroll waves in excitable media has attracted considerable interest in the context of cardiac arrhythmias. Here, by bombarding inclusions with drifting spiral and scroll waves, we explore the forces exerted by inclusions onto an approaching spiral and derive the equations of motion governing spiral dynamics in the vicinity of inclusion. We demonstrate that these forces nonmonotonically depend on distance and can lead to complex behavior: (a)?anchoring to small but circumnavigating larger inclusions; (b)?chirality-dependent anchoring.     

Singular filaments organize chemical waves in three dimensions: III. Knotted waves

This is the third of a series of papers on the anatomy of three-dimensional organizing centers in excitable media. We here ask whether all self-consistent waves in excitable media are topologically equivalent to the experimentally-verified scroll ring, whose axis lies in a plane. As a test case we examine a scroll ring whose axis contains a knot. It proves to be incompatible with the requirements of physical chemistry unless simultaneously twisted by an amount equal to the “writhing number” of its axis (which is zero for planar closed curves). Appropriate initial conditions are suggested for experimentally creating a wave whose source is a scroll ring knotted and twisted in this way.     

MHD Wave Interaction within a Plasma Perturbed by Alfvén Waves

The interaction between fast magnetoacoustic waves within a plasma with periodical nonhomogeneities, perturbed by Alfvén waves has been studied. It has been ascertained the appearance of phenomena of a decay instability and an instability involving an increase of the amplitude oscillations. A study of the influence of perturbed plasma parameters on these instability phenomena has been made. It has been found that the optimal perturbing frequency for giving rise to the instability phenomenon is twice the frequency of fast magnetoacoustic waves.     

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.     

Interaction of shear waves and propagating cracks

Shear waves generated from an ultrasonic transducer are used to twist dynamically growing crack fronts; the response of crack front to such external perturbations is examined in order to investigate the primary cause of surface roughening in brittle materials. The response of the crack front is found to be linear in amplitude and frequency of the perturbing wave and without persistence. The response to random perturbations, e.g., by localized material inhomogeneities at the free surface, is also discussed.     

Spiral wave dynamics in excitable media with spherical geometries

We describe the spatial and temporal organization of spiral and scroll waves in spherical shells of different sizes and solid spheres. We present simulation results for the evolution of the dynamics and clustering of spiral waves as a function of the excitability of the medium. The excitability, topology, and size of the domain places restrictions on how single and multiarmed spiral waves are organized in space. The results in spherical geometries are compared with those in planar two-dimensional media. These studies are relevant to the dynamics of spiral waves in a variety of media including the heart, and chemical reactions on spherical surfaces.