Topic
Excitable medium
About: Excitable medium is a research topic. Over the lifetime, 586 publications have been published within this topic receiving 16034 citations.
Papers published on a yearly basis
Papers
TL;DR: In this paper, the effects of external noise on the dynamics of the excitable Fitz Hugh Nagumo system were investigated. And the authors showed that the coherence of these noise-induced oscillations is maximal for a certain noise amplitude.
Abstract: We study the dynamics of the excitable Fitz Hugh ‐ Nagumo system under external noisy driving. Noise activates the system producing a sequence of pulses. The coherence of these noise-induced oscillations is shown to be maximal for a certain noise amplitude. This new effect of coherence resonance is explained by different noise dependencies of the activation and the excursion times. A simple one-dimensional model based on the Langevin dynamics is proposed for the quantitative description of this phenomenon. [S0031-9007(97)02349-1] The response of dynamical systems to noise has attracted large attention recently. There are many examples demonstrating that noise can lead to more order in the dynamics. To be mentioned here are the effects of noiseinduced order in chaotic dynamics [1], synchronization by external noise [2], and stochastic resonance [3‐5]. Also, noise has been shown to play a stabilizing role in ensembles of coupled oscillators and maps [6]. Especially interesting is the phenomenon of stochastic resonance, which appears when a nonlinear system is simultaneously driven by noise and a periodic signal. At a certain noise amplitude the periodic response is maximal; this has been confirmed by numerous experimental studies (cf. [7,8]). In this paper we study the effect of noise on the autonomous excitable oscillator—the famous Fitz Hugh ‐ Nagumo system. We demonstrate that a characteristic correlation time of the noise-excited oscillations has a maximum for a certain noise amplitude, and present a theory of this effect. Contrary to the usual setup of stochastic resonance, no external periodic driving is assumed, so the coherence appears as a nonlinear response to purely noisy excitation. The phenomenon considered is also different from stochastic resonance without periodic force reported recently in Ref. [9], where the effect of noise on a limit cycle at a bifurcation point was studied. The Fitz Hugh‐Nagumo model is a simple but representative example of excitable systems that occur in different fields of application ranging from kinetics of chemical reactions and solid-state physics to biological processes [10]. Originally it was suggested for the description of nerve pulses [11]; it was also widely used for modeling of spiral waves in a two-dimensional excitable medium. Different aspects of the dynamics of this and similar excitable models in the presence of noise have been discussed in Refs. [12‐16]. The equations of motion are
1,765 citations
TL;DR: In this article, the authors compare and contrast the approaches taken by Greenberg, Zykov, Fife, Krinskii and others, with particular emphasis on the case of rotating spiral waves, and discuss some possible extensions of the singular perturbation approach to propagating wave surfaces in three-dimensional space.
802 citations
TL;DR: Regenerative spiral waves of release of free Ca2+ were observed by confocal microscopy in Xenopus laevis oocytes expressing muscarinic acetylcholine receptor subtypes and the absolute refractory period for Ca2- stores was determined.
Abstract: Intracellular calcium (Ca2+) is a ubiquitous second messenger. Information is encoded in the magnitude, frequency, and spatial organization of changes in the concentration of cytosolic free Ca2+. Regenerative spiral waves of release of free Ca2+ were observed by confocal microscopy in Xenopus laevis oocytes expressing muscarinic acetylcholine receptor subtypes. This pattern of Ca2+ activity is characteristic of an intracellular milieu that behaves as a regenerative excitable medium. The minimal critical radius for propagation of focal Ca2+ waves (10.4 micrometers) and the effective diffusion constant for the excitation signal (2.3 x 10(-6) square centimeters per second) were estimated from measurements of velocity and curvature of circular wavefronts expanding from foci. By modeling Ca2+ release with cellular automata, the absolute refractory period for Ca2+ stores (4.7 seconds) was determined. Other phenomena expected of an excitable medium, such as wave propagation of undiminished amplitude and annihilation of colliding wavefronts, were observed.
754 citations
TL;DR: It is shown that tissue mechanics significantly contributes to the dynamics of electrical propagation, and that a coupled electromechanical approach should be pursued in future electrophysiological modelling studies.
Abstract: We introduce the concept of a contracting excitable medium that is capable of conducting non-linear waves of excitation that in turn initiate contraction. Furthermore, these kinematic deformations have a feedback effect on the excitation properties of the medium. Electrical characteristics resemble basic models of cardiac excitation that have been used to successfully study mechanisms of reentrant cardiac arrhythmias in electrophysiology. We present a computational framework that employs electromechanical and mechanoelectric feedback to couple a three-variable FitzHugh-Nagumo-type excitation-tension model to the non-linear stress equilibrium equations, which govern large deformation hyperelasticity. Numerically, the coupled electromechanical model combines a finite difference method approach to integrate the excitation equations, with a Galerkin finite element method to solve the equations governing tissue mechanics. We present example computations demonstrating various effects of contraction on stationary rotating spiral waves and spiral wave break. We show that tissue mechanics significantly contributes to the dynamics of electrical propagation, and that a coupled electromechanical approach should be pursued in future electrophysiological modelling studies.
413 citations
Book•
1 Nov 1988
TL;DR: Investigating wave processes in one and two spatial dimensions by combining analytical studies on simplified systems with computer simulation surveys of more complicated models stresses dependence of wave characteristics on the properties of the excitable medium.
Abstract: From the Publisher:
Investigates wave processes in one and two spatial dimensions by combining analytical studies on simplified systems with computer simulation surveys of more complicated models. Stresses dependence of wave characteristics on the properties of the excitable medium. Includes an extensive appendix on super-computer techniques for simulating three-dimensional excitable media.
345 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 1 |
| 2024 | 1 |
| 2023 | 7 |
| 2022 | 16 |
| 2021 | 2 |
| 2020 | 8 |