scholarly journals Parametric forcing of scroll-wave patterns in three-dimensional excitable media

2001 ◽  
Vol 149 (1-2) ◽  
pp. 107-122 ◽  
Author(s):  
Rolf-Martin Mantel ◽  
Dwight Barkley
Keyword(s):  
Three Dimensional ◽  
Excitable Media ◽  
Wave Patterns ◽  
Scroll Wave ◽  
Parametric Forcing

ON THE GENERATION OF SCROLL WAVES IN A THREE-DIMENSIONAL DISCRETE ACTIVE MEDIUM

1995 ◽  
Vol 05 (01) ◽  
pp. 313-320 ◽  
Author(s):  
LADISLAV PIVKA ◽  
ALEXANDER L. ZHELEZNYAK ◽  
CHAI WAH WU ◽  
LEON O. CHUA
Keyword(s):  
Neural Network ◽  
Active Medium ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Cellular Neural Network ◽  
Inhomogeneous Media ◽  
Wave Patterns ◽  
Scroll Wave ◽  
Scroll Waves

This paper reports on the simulation, in three-dimensional cellular-neural-network (CNN) arrays of Chua’s circuits, of basic three-dimensional scroll wave patterns observed previously from other media. Among the simulated patterns are the straight scroll wave, twisted scroll wave in both homogeneous and inhomogeneous media, as well as the scroll ring. These types of waves have been obtained for only one set of circuit parameters by varying the initial conditions.

scholarly journals Spiral waves within a bistability parameter region of an excitable medium

2022 ◽  
Author(s):  
Vladimir Zykov ◽  
Eberhard Bodenschatz
Keyword(s):  
Initial Conditions ◽  
Three Dimensional ◽  
Spiral Wave ◽  
Gradient Flow ◽  
Spiral Waves ◽  
Excitable Medium ◽  
Excitable Media ◽  
Circular Trajectory ◽  
Parameter Region ◽  
Scroll Wave

Abstract Spiral waves are a well-known and intensively studied dynamic phenomenon in excitable media of various types. Most studies have considered an excitable medium with a single stable resting state. However, spiral waves can be maintained in an excitable medium with bistability. Our calculations, performed using the widely used Barkley model, clearly show that spiral waves in the bistability region exhibit unique properties. For example, a spiral wave can either rotate around a core that is in an unexcited state, or the tip of the spiral wave describes a circular trajectory located inside an excited region. The boundaries of the parameter regions with positive and "negative" cores have been defined numerically and analytically evaluated. It is also shown that the creation of a positive or "negative" core may depend on the initial conditions, which leads to hysteresis of spiral waves. In addition, the influence of gradient flow on the dynamics of the spiral wave, which is related to the tension of the scroll wave filaments in a three-dimensional medium, is studied.

TWISTED SCROLL WAVES IN HETEROGENEOUS EXCITABLE MEDIA

1993 ◽  
Vol 03 (02) ◽  
pp. 445-450 ◽  
Author(s):  
ALEXANDER V. PANFILOV ◽  
JAMES P. KEENER
Keyword(s):  
Stationary Process ◽  
Three Dimensional ◽  
Excitable Medium ◽  
Excitable Media ◽  
Type Model ◽  
Refractory Periods ◽  
Scroll Wave ◽  
Scroll Waves

We study numerically the behavior of a scroll wave in a three-dimensional excitable medium with stepwise heterogeneity, using a FitzHugh Nagumo type model. We find that if the refractory periods in the two homogeneous subregions are sufficiently different, the scroll breaks into two scrolls rotating independently in each part of the medium. Eventually, the faster scroll eliminates the slower one leading to a stationary process, in which the scroll wave surviving in the region of faster recovery acts as a source for planar waves in the region of slower recovery.

scholarly journals Drift of Scroll Wave Filaments in an Anisotropic Model of the Left Ventricle of the Human Heart

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Sergei Pravdin ◽  
Hans Dierckx ◽  
Vladimir S. Markhasin ◽  
Alexander V. Panfilov
Keyword(s):  
Left Ventricle ◽  
Cardiac Arrhythmias ◽  
Human Heart ◽  
Cardiac Tissue ◽  
Three Dimensional ◽  
Excitable Media ◽  
Filament Dynamics ◽  
Myocardial Wall ◽  
Scroll Wave ◽  
Generic Description

Scroll waves are three-dimensional vortices which occur in excitable media. Their formation in the heart results in the onset of cardiac arrhythmias, and the dynamics of their filaments determine the arrhythmia type. Most studies of filament dynamics were performed in domains with simple geometries and generic description of the anisotropy of cardiac tissue. Recently, we developed an analytical model of fibre structure and anatomy of the left ventricle (LV) of the human heart. Here, we perform a systematic study of the dynamics of scroll wave filaments for the cases of positive and negative tension in this anatomical model. We study the various possible shapes of LV and different degree of anisotropy of cardiac tissue. We show that, for positive filament tension, the final position of scroll wave filament is mainly determined by the thickness of the myocardial wall but, however, anisotropy attracts the filament to the LV apex. For negative filament tension, the filament buckles, and for most cases, tends to the apex of the heart with no or slight dependency on the thickness of the LV. We discuss the mechanisms of the observed phenomena and their implications for cardiac arrhythmias.

Twisted scroll wave dynamics: partially pinned waves in excitable chemical media

2019 ◽  
Vol 21 (5) ◽  
pp. 2419-2425 ◽  
Author(s):  
Porramain Porjai ◽  
Malee Sutthiopad ◽  
Kritsana Khaothong ◽  
Metinee Phantu ◽  
Nakorn Kumchaiseemak ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Excitable Media ◽  
Wave Dynamics ◽  
Scroll Wave ◽  
Scroll Waves

We present an investigation of the dynamics of scroll waves that are partially pinned to inert cylindrical obstacles of varying lengths and diameters in three-dimensional Belousov–Zhabotinsky excitable media.

A Simple Approach to the Study of Wave Patterns

2014 ◽  
Vol 156 (A3) ◽  
Keyword(s):  
Numerical Methods ◽  
Shallow Water ◽  
Froude Number ◽  
Critical Speed ◽  
Graphical Method ◽  
Three Dimensional ◽  
Simple Approach ◽  
Critical Depth ◽  
Simple Manner ◽  
Wave Patterns

The paper revisits some pioneering work of Sir Thomas Havelock on wave patterns with particular attention focused on his graphical method of analysis. Motivated by a desire to explore this method further using numerical methods, it is extended in a simple manner to give three-dimensional illustrations of the wave patterns of a point disturbance in deep and shallow water. All results are confined to the sub- and trans-critical regimes with some obtained very close to the critical Depth Froude Number. Some conclusions are drawn on the wave types produced when operating close to the critical speed and their decay with distance off.

THE DIFFERENTIAL GEOMETRY OF SCROLL WAVES

1991 ◽  
Vol 01 (04) ◽  
pp. 723-744 ◽  
Author(s):  
JOHN J. TYSON ◽  
STEVEN H. STROGATZ
Keyword(s):  
Traveling Waves ◽  
Three Dimensional ◽  
Spatial Arrangement ◽  
Topological Constraint ◽  
Linking Number ◽  
Physical Chemical ◽  
Statics And Dynamics ◽  
Scroll Wave ◽  
Chemical And Biological Systems ◽  
Belousov Zhabotinskii Reaction

Traveling waves of excitation organize physical, chemical, and biological systems in space and time. In the biological context they serve to communicate information rapidly over long distances and to coordinate the activity of tissues and organs. An example of particular beauty, complexity and importance is the three-dimensional rotating scroll wave observed in the Belousov–Zhabotinskii reaction and in the ventricle of the heart. A scroll wave rotates around a filamentous phase singularity that weaves through the three-dimensional medium. At any instant of time the geometry of the scroll wave can be reduced to the spatial arrangement of a ribbon whose edges are the singular filament and the tip of the scroll wave. This ribbon, when it closes on itself, must satisfy the topological constraint L = Tw + Wr, where L is the linking number of the two edges of the ribbon, Tw is the total twist of the ribbon, and Wr is the writhing number of the singular filament. We discuss the origin of this equation and its implications for scroll wave statics and dynamics.

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