Asymptotic Behavior of Fronts and Pulses of the Bidomain Model
Asymptotic Behavior of Fronts and Pulses of the Bidomain Model
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双域模型的前沿和脉冲的渐近行为
DOI：
10.1137/21m1416904
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发表时间：
2022
影响因子：
2.1
通讯作者：
Sakakibara Koya
中科院分区：
文献类型：
--
作者：
Matano Hiroshi;Mori Yoichiro;Nara Mitsunori;Sakakibara Koya
bidomain模型是心脏电生理学的标准模型。本文研究了二维Bidomain艾伦-Cahn方程和Bidomain FitzHugh-Nagumo方程的平面波前和平面脉冲的不稳定性和渐近行为。以前的工作表明，bidomain艾伦-Cahn方程的平面前沿可能变得不稳定，与经典的艾伦-Cahn方程。在平面锋面失稳后，发展出一个旋转的锯齿形锋面，其形状可以用简单的几何参数用一个合适的弗兰克图来解释。我们还表明，通过该前线变得不稳定的Hopf分岔可以是超临界或亚临界的参数制度，其中一个稳定的平面前和曲折的前可以共存。我们的计算研究bidomain FitzHugh-Nagumo脉冲解决方案表明，脉冲也可以变得不稳定，像bidomain艾伦-卡恩前线。然而，不像比多曼艾伦-卡恩的情况下，不稳定的脉冲不一定发展成锯齿形脉冲。对于某些参数的选择，不稳定的脉冲可以完全分解。这些研究是可能的，通过开发一个数值方案，允许在一个无限的程度的二维带状域的bidomain方程的精确计算。
The bidomain model is the standard model for cardiac electrophysiology. This paper investigates the instability and asymptotic behavior of planar fronts and planar pulses of the bidomain Allen--Cahn equation and the bidomain FitzHugh--Nagumo equation in two spatial dimensions. Previous work showed that planar fronts of the bidomain Allen--Cahn equation could become unstable in contrast to the classical Allen--Cahn equation. After the planar front is destabilized, a rotating zigzag front develops whose shape can be explained by simple geometric arguments using a suitable Frank diagram. We also show that the Hopf bifurcation through which the front becomes unstable can be either supercritical or subcritical by demonstrating a parameter regime in which a stable planar front and zigzag front can coexist. Our computational studies of the bidomain FitzHugh--Nagumo pulse solution show that the pulses can also become unstable, like the bidomain Allen--Cahn fronts. However, unlike the bidomain Allen--Cahn case, the destabilized pulse does not necessarily develop into a zigzag pulse. For certain choices of parameters, the destabilized pulse can disintegrate entirely. These studies are made possible by developing a numerical scheme that allows for the accurate computation of the bidomain equation in a two-dimensional strip domain of an infinite extent.