Distributed predictive control of spiral wave in cardiac excitable media

doi:10.1088/1674-1056/19/5/050514

中国物理B ›› 2010, Vol. 19 ›› Issue (5): 50514-050514.doi: 10.1088/1674-1056/19/5/050514

Distributed predictive control of spiral wave in cardiac excitable media

甘正宁¹, 成新明²

(1)Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China;College of Electronic and Information Engineering, Changsha University of Science {& Technology, Changsha 410076, China; (2)School of Information Science and Engineering, Central South University, Changsha 410082, China

收稿日期:2009-07-10 修回日期:2009-12-18 出版日期:2010-05-15 发布日期:2010-05-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No.~10305005) and the Hunan Provincial Natural Science Foundation of China (Grant No.~07JJ6126).

Distributed predictive control of spiral wave in cardiac excitable media

Gan Zheng-Ning(甘正宁)^a)b)^† and Cheng Xin-Ming(成新明)^c)

^a Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China; ^b College of Electronic and Information Engineering, Changsha University of Science & Technology, Changsha 410076, China; ^c School of Information Science and Engineering, Central South University, Changsha 410082, China

Received:2009-07-10 Revised:2009-12-18 Online:2010-05-15 Published:2010-05-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No.~10305005) and the Hunan Provincial Natural Science Foundation of China (Grant No.~07JJ6126).

摘要/Abstract

摘要： In this paper, we propose the distributed predictive control strategies of spiral wave in cardiac excitable media. The modified FitzHugh--Nagumo model was used to express the cardiac excitable media approximately. Based on the control-Lyapunov theory, we obtained the distributed control equation, which consists of a positive control-Lyapunov function and a positive cost function. Using the equation, we investigate two kinds of robust control strategies: the time-dependent distributed control strategy and the space-time dependent distributed control strategy. The feasibility of the strategies was demonstrated via an illustrative example, in which the spiral wave was prevented to occur, and the possibility for inducing ventricular fibrillation was eliminated. The strategies are helpful in designing various cardiac devices. Since the second strategy is more efficient and robust than the first one, and the response time in the second strategy is far less than that in the first one, the former is suitable for the quick-response control systems. In addition, our spatiotemporal control strategies, especially the second strategy, can be applied to other cardiac models, even to other reaction-diffusion systems.

Abstract: In this paper, we propose the distributed predictive control strategies of spiral wave in cardiac excitable media. The modified FitzHugh--Nagumo model was used to express the cardiac excitable media approximately. Based on the control-Lyapunov theory, we obtained the distributed control equation, which consists of a positive control-Lyapunov function and a positive cost function. Using the equation, we investigate two kinds of robust control strategies: the time-dependent distributed control strategy and the space-time dependent distributed control strategy. The feasibility of the strategies was demonstrated via an illustrative example, in which the spiral wave was prevented to occur, and the possibility for inducing ventricular fibrillation was eliminated. The strategies are helpful in designing various cardiac devices. Since the second strategy is more efficient and robust than the first one, and the response time in the second strategy is far less than that in the first one, the former is suitable for the quick-response control systems. In addition, our spatiotemporal control strategies, especially the second strategy, can be applied to other cardiac models, even to other reaction-diffusion systems.

Key words: spiral wave, FitzHugh--Nagumo model, control-Lyapunov function

中图分类号: (Cardiac dynamics)

87.19.Hh

87.17.-d (Cell processes) 05.45.-a (Nonlinear dynamics and chaos) 02.30.Yy (Control theory)

甘正宁, 成新明. Distributed predictive control of spiral wave in cardiac excitable media[J]. 中国物理B, 2010, 19(5): 50514-050514.

Gan Zheng-Ning(甘正宁) and Cheng Xin-Ming(成新明). Distributed predictive control of spiral wave in cardiac excitable media[J]. Chin. Phys. B, 2010, 19(5): 50514-050514.

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Distributed predictive control of spiral wave in cardiac excitable media

Distributed predictive control of spiral wave in cardiac excitable media

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