MATHEMATICAL MODEL OF SIGNAL PROPAGATION IN EXCITABLE MEDIA

JAKUB KANTNER; MICHAL BENES

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MATHEMATICAL MODEL OF SIGNAL PROPAGATION IN EXCITABLE MEDIA

机译：可激发介质中信号传播的数学模型

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This article deals with a model of signal propagation in excitablemedia based on a system of reaction-diffusion equations. Such media have theability to exhibit a large response in reaction to a small deviation from the reststate. An example of such media is the nerve tissue or the heart tissue. Thefirst part of the article briey describes the origin and the propagation of thecardiac action potential in the heart. In the second part, the mathematicalproperties of the model are discussed. Next, the numerical algorithm based onthe finite difference method is used to obtain computational studies in both ahomogeneous and heterogeneous medium with an emphasis on interactions ofthe propagating signals with obstacles in the medium.

机译：本文涉及易激发的信号传播模型基于反应扩散方程系统的媒体。这样的媒体有能够在反应中表现出大的反应与其余部分的小偏差状态。这种介质的一个例子是神经组织或心脏组织。这Brie的第一部分Y描述了原点和传播心脏的心脏动作潜力。在第二部分，数学讨论了模型的属性。接下来，基于的数值算法有限差分方法用于获得A中的计算研究均匀和异质介质强调相互作用介质中的障碍物传播信号。

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来源
《Discrete and Continuous Dynamical Systems,Series S》 |2021年第3期|935-951|共17页
作者
JAKUB KANTNER; MICHAL BENES;
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作者单位

Department of Mathematics Faculty of Nuclear Sciences and Physical EngineeringCzech Technical University in PragueTrojanova 13Prague 12000 Czech Republic;

Department of Mathematics Faculty of Nuclear Sciences and Physical EngineeringCzech Technical University in PragueTrojanova 13Prague 12000 Czech Republic;

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正文语种 eng
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Excitable media; reaction-diffusion equations; FitzHugh-Nagumo model; cardiac action potential; signal propagation; invariant regions;

机译：狂热的媒体;反应扩散方程;Fitzhugh-Nagumo模型;心脏动作潜力;信号传播;不变地区;

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专利

1. Models of unidirectional propagation in heterogeneous excitable media [J] . Alford JG Applied mathematics and computation . 2010,第4期

机译：异质可激发介质中的单向传播模型
2. Propagation through heterogeneous substrates in simple excitable media models [J] . Gil Bub, Alvin Shrier Chaos . 2002,第3期

机译：在简单的可激发介质模型中通过异质底物的传播
3. Computational biology of propagation in excitable media models of cardiac tissue [J] . Holden AV., Biktashev VN. Chaos, Solitons and Fractals: Applications in Science and Engineering: An Interdisciplinary Journal of Nonlinear Science . 2002,第8期

机译：心脏组织兴奋性介质模型中传播的计算生物学
4. Signal propagation in oscillatory media enabled by noise-induced excitability [C] . Ekkehard Ullner, Alexei Zaikin, Jordi Garcia-Ojalvo, Conference on Noise in Complex Systems and Stochastic Dynamics II; 20040526-20040528; Maspalomas; ES . 2004

机译：信号在振动介质中的传播受噪声诱发的兴奋性的影响
5. The effects of nonexcitable regions on signal propagation in excitable media: Propagation failure and reflection. [D] . Lewis, Timothy James. 1998

机译：不可激励区域对可激励介质中信号传播的影响：传播失败和反射。
6. A three-dimensional mathematical model for the signal propagation on a neurons membrane [O] . Konstantinos Xylouris, Gabriel Wittum 2015

机译：信号在神经元膜上传播的三维数学模型
7. Signal Separation Using a Mathematical Model of Physiological Signals for the Measurement of Heart Pulse Wave Propagation With Array Radar [O] . Takuya Sakamoto 2020

机译：信号分离使用生理信号的数学模型进行测量心脉冲波传播与阵列雷达

MATHEMATICAL MODEL OF SIGNAL PROPAGATION IN EXCITABLE MEDIA

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