Spontaneous Halt of Spiral Wave Drift in Homogeneous Excitable Media

2007 ◽  
Vol 2 (1) ◽  
pp. 73-81 ◽  
Author(s):  
Ю.Е. Елькин ◽  
Yu.E. Elkin
Keyword(s):  
Spiral Wave ◽  
Excitable Media ◽  
Wave Drift

scholarly journals A theory for spiral wave drift induced by ac and polarized electric fields in chemical excitable media

2017 ◽  
Vol 7 (1) ◽  
Author(s):  
Teng-Chao Li ◽  
Xiang Gao ◽  
Fei-Fei Zheng ◽  
De-Bei Pan ◽  
Bo Zheng ◽  
...  
Keyword(s):  
Electric Fields ◽  
Spiral Wave ◽  
Excitable Media ◽  
Wave Drift

Size matters: Effects of the size of heterogeneity on the wave re-entry and spiral wave formation in an excitable media

2021 ◽  
Vol 31 (5) ◽  
pp. 053131
Author(s):  
Karthikeyan Rajagopal ◽  
Shaobo He ◽  
Anitha Karthikeyan ◽  
Prakash Duraisamy
Keyword(s):  
Spiral Wave ◽  
Wave Formation ◽  
Excitable Media

scholarly journals LOCALIZATION OF RESPONSE FUNCTIONS OF SPIRAL WAVES IN THE FITZHUGH–NAGUMO SYSTEM

2006 ◽  
Vol 16 (05) ◽  
pp. 1547-1555 ◽  
Author(s):  
I. V. BIKTASHEVA ◽  
A. V. HOLDEN ◽  
V. N. BIKTASHEV
Keyword(s):  
External Force ◽  
Wave Solution ◽  
Spiral Wave ◽  
Spiral Waves ◽  
Two Dimensional ◽  
Response Functions ◽  
Space And Time ◽  
Wave Drift ◽  
Linearized Problem ◽  
Small Periodic

Dynamics of spiral waves in perturbed, e.g. slightly inhomogeneous or subject to a small periodic external force, two-dimensional autowave media can be described asymptotically in terms of Aristotelean dynamics, so that the velocities of the spiral wave drift in space and time are proportional to the forces caused by the perturbation. The forces are defined as a convolution of the perturbation with the spirals Response Functions, which are eigenfunctions of the adjoint linearized problem. In this paper we find numerically the Response Functions of a spiral wave solution in the classic excitable FitzHugh–Nagumo model, and show that they are effectively localized in the vicinity of the spiral core.

Publisher's Note: Interference patterns in spiral wave drift induced by a two-point feedback [Phys. Rev. E72, 065201 (2005)]

2005 ◽  
Vol 72 (6) ◽  
Author(s):  
V. S. Zykov ◽  
H. Brandtstädter ◽  
G. Bordiougov ◽  
H. Engel
Keyword(s):  
Spiral Wave ◽  
Wave Drift

scholarly journals Spiral Wave Formation in Three-Dimensional Excitable Media

1996 ◽  
Vol 77 (15) ◽  
pp. 3244-3247 ◽  
Author(s):  
Takashi Amemiya ◽  
Sándor Kádár ◽  
Petteri Kettunen ◽  
Kenneth Showalter
Keyword(s):  
Three Dimensional ◽  
Spiral Wave ◽  
Wave Formation ◽  
Excitable Media

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.

scholarly journals Optogenetics enables real-time spatiotemporal control over spiral wave dynamics in an excitable cardiac system

eLife ◽  
2018 ◽  
Vol 7 ◽  
Author(s):  
Rupamanjari Majumder ◽  
Iolanda Feola ◽  
Alexander S Teplenin ◽  
Antoine AF de Vries ◽  
Alexander V Panfilov ◽  
...  
Keyword(s):  
Real Time ◽  
Spiral Wave ◽  
Spiral Waves ◽  
Excitable Media ◽  
Wave Dynamics ◽  
Linear Waves ◽  
Cardiac System ◽  
Spatiotemporal Control ◽  
Forced Movement

Propagation of non-linear waves is key to the functioning of diverse biological systems. Such waves can organize into spirals, rotating around a core, whose properties determine the overall wave dynamics. Theoretically, manipulation of a spiral wave core should lead to full spatiotemporal control over its dynamics. However, this theory lacks supportive evidence (even at a conceptual level), making it thus a long-standing hypothesis. Here, we propose a new phenomenological concept that involves artificially dragging spiral waves by their cores, to prove the aforementioned hypothesis in silico, with subsequent in vitro validation in optogenetically modified monolayers of rat atrial cardiomyocytes. We thereby connect previously established, but unrelated concepts of spiral wave attraction, anchoring and unpinning to demonstrate that core manipulation, through controlled displacement of heterogeneities in excitable media, allows forced movement of spiral waves along pre-defined trajectories. Consequently, we impose real-time spatiotemporal control over spiral wave dynamics in a biological system.

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