基于格子Boltzmann方法的钉扎螺旋波反馈控制  

Lattice Boltzmann method based feedback control approach for pinned spiral waves

作　　者：赖瑶瑶 陈鑫梦 柴振华[1,2,3] 施保昌[1,2,3] Lai Yao-Yao;Chen Xin-Meng;Chai Zhen-Hua;Shi Bao-Chang(School of Mathematics and Statistics,Huazhong University of Science and Technology,Wuhan 430074,China;Hubei Key Laboratory of Engineering Modeling and Scientific Computing,Huazhong University of Science and Technology,Wuhan 430074,China;Institute of Interdisciplinary Research for Mathematics and Applied Science,Huazhong University of Science and Technology,Wuhan 430074,China)

机构地区：[1]华中科技大学数学与统计学院,武汉430074 [2]华中科技大学,工程建模与科学计算湖北重点实验室,武汉430074 [3]华中科技大学,数学与应用学科交叉创新研究院,武汉430074

出　　处：《物理学报》2024年第4期78-87,共10页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:12072127,51836003)资助的课题.

摘　　要：螺旋波是心室跳动过速和纤维性颤动的根源,钉扎螺旋波相对于自由螺旋波来说更难消除.本文采用格子Boltzmann方法求解,以FitzHugh-Nagumo模型为对象,研究了使用反馈控制法消除钉扎螺旋波.数值结果表明,无论钉扎螺旋波钉在圆形障碍物还是矩形障碍物上,反馈控制法对其都具有很好的控制作用.此外,通过数值模拟系统研究了可激性系数、反馈控制信号幅度、记录反馈信号时间和障碍物的大小对钉扎螺旋波的控制情况.研究表明,钉扎螺旋波消除有三种情况.首先,反馈控制信号幅度和可激性系数与钉扎螺旋波消除所需的时间有关,反馈控制信号幅度越大或可激性系数越小,钉扎螺旋波消除越快.其次,障碍物大小和可激性系数影响着能成功消除钉扎螺旋波下记录反馈信号时间与加入反馈控制时间之间对应的时间间隔.最后,在保持加入反馈控制时间不变的情况下,记录反馈信号时间影响着能成功消除钉扎螺旋波所需的最小反馈控制信号幅度.Spiral waves are common in nature and have received a lot of attention.Spiral wave is the source of ventricular tachycardia and fibrillation,and pinned spiral wave is less likely to be eliminated than free spiral wave.Therefore,it is important to find an effective method to control the pinned spiral wave.In this work,we investigate the feedback control approach to eliminating pinned spiral wave based on the lattice Boltzmann method,by using the FitzHugh-Nagumo model as an object.The numerical results show that the feedback control method has a good control effect on the pinned spiral wave no matter whether it is pinned on a circular or rectangular obstacle.In addition,the excitability coefficient,amplitude of feedback control,recording feedback signal time and obstacle size are systematically investigated by numerical simulation.The study shows that there are three cases of pinned spiral wave cancellation.Firstly,the amplitude of feedback control and excitability coefficient are related to the time required to eliminate the pinned spiral wave,and the larger the amplitude of feedback control signal or the smaller the excitability coefficient,the faster the cancellation of the pinned spiral waveis.Secondly,the size of the obstacle and the excitability coefficient affect the time interval between the time of recording the feedback signal and the time of adding the feedback control that can successfully control the pinned spiral wave.Finally,the recorded feedback signal time affects the minimum amplitude of feedback control required to successfully eliminate the pinned spiral wave,while the added feedback control time is constant.According to the discussion in this paper,it can be seen that the feedback control method has a good control effect on the pinned spiral wave.

关 键 词：反馈控制法 钉扎螺旋波 FitzHugh-Nagumo模型 格子BOLTZMANN方法 

分 类 号：TN911.7[电子电信—通信与信息系统] R312[电子电信—信息与通信工程]