scholarly journals Negative Tension of Scroll Wave Filaments and Turbulence in Three-Dimensional Excitable Media and Application in Cardiac Dynamics

2012 ◽  
Vol 75 (8) ◽  
pp. 1351-1376 ◽  
Author(s):  
Sergio Alonso ◽  
Markus Bär ◽  
Alexander V. Panfilov
Keyword(s):  
Three Dimensional ◽  
Excitable Media ◽  
Cardiac Dynamics ◽  
Scroll Wave

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.

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.

THREE-DIMENSIONAL ASPECTS OF RE-ENTRY IN EXPERIMENTAL AND NUMERICAL MODELS OF VENTRICULAR FIBRILLATION

1999 ◽  
Vol 09 (04) ◽  
pp. 695-704 ◽  
Author(s):  
V. N. BIKTASHEV ◽  
A. V. HOLDEN ◽  
S. F. MIRONOV ◽  
A. M. PERTSOV ◽  
A. V. ZAITSEV
Keyword(s):  
Ventricular Fibrillation ◽  
Numerical Simulations ◽  
Numerical Models ◽  
Three Dimensional ◽  
Spiral Waves ◽  
Excitable Media ◽  
Ventricular Wall ◽  
Two Dimensional ◽  
Key Features ◽  
Scroll Waves

Ventricular fibrillation is believed to be produced by the breakdown of re-entrant propagation waves of excitation into multiple re-entrant sources. These re-entrant waves may be idealized as spiral waves in two-dimensional, and scroll waves in three-dimensional excitable media. Optically monitored, simultaneously recorded endocardial and epicardial patterns of activation on the ventricular wall do not always show spiral waves. We show that numerical simulations, even with a simple homogeneous excitable medium, can reproduce the key features of the simultaneous endo- and epicardial visualizations of propagating activity, and so these recordings may be interpreted in terms of scroll waves within the ventricular wall.

Complex patterns in three-dimensional excitable media with advection

2003 ◽  
Vol 18 (2) ◽  
pp. 375-384 ◽  
Author(s):  
E.M. Ortigosa ◽  
L.F. Romero ◽  
J.I. Ramos
Keyword(s):  
Three Dimensional ◽  
Excitable Media ◽  
Complex Patterns
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