一种体现心肌细胞传导记忆的元胞自动机模型

doi:10.16088/j.issn.1001-6600.2017.04.001

摘要/Abstract

摘要： 元胞自动机是研究心肌电信号动力学行为的重要辅助工具,但经典Greenberg-Hastings元胞自动机具有恒常的速度分布,不能反映心肌细胞电信号传导速度对历史状态的记忆。本文在Greenberg-Hastings元胞自动机基础上考虑心肌细胞上一个状态周期对心肌组织电信号传导速度的影响,建立了一种体现心肌细胞传导记忆的元胞自动机模型。利用所建立的模型,本文不仅能模拟心肌组织中稳定螺旋波的产生与维持,还再现了螺旋波的多普勒失稳、爱克豪斯失稳以及这2种失稳同时产生的现象,这些螺旋波失稳现象是经典Greenberg-Hastings元胞自动机模型所无法产生的,并对以上现象的产生原因进行了分析。本文的结果为进一步利用元胞自动机方法探讨心肌细胞传导记忆性对螺旋波动力学规律的影响提供了参考。

关键词: 元胞自动机, 传导恢复, 螺旋波, 多普勒失稳, 爱克豪斯失稳

Abstract: Cellular automaton is an important method for studying cardiac signal dynamics, but the cells in traditional Greenberg-Hastings cellular automaton have the constant conduction velocity distribution, which cannot reflect the relation between the cardiac signal conduction velocity and the preceding state period. In this paper, a cellular automaton model connected to the conduction restitution of cardiac cells is established. In this model, the conduction velocity of the electrical cardiac signal depends on the preceding state period of the myocardial cells. With this model, the production and maintenance of stable spiral waves in myocardial tissue are simulated, and the phenomena of the Doppler and Eckhaus instability of spiral waves are exhibited, which can not be produced by the traditional Greenberg-Hastings cellular automaton. The causes of the above phenomena are analyzed in this paper. This work provides an useful guidence for further study of the electrical cardiac signal in the future.

Key words: cellular automaton, conduction restitution, spiral wave, Doppler instability, Eckhaus instability

中图分类号:

O411.3

张学良,谭惠丽,白克钊,唐国宁,邓敏艺. 一种体现心肌细胞传导记忆的元胞自动机模型[J]. 广西师范大学学报（自然科学版）, 2017, 35(4): 1-9.

ZHANG Xueliang,TAN Huili, BAI Kezhao, TANG Guoning,DENG Minyi. A Cellular Automaton Model Connected to the ConductionRestitution Property of Cardiac Cells[J]. Journal of Guangxi Normal University(Natural Science Edition), 2017, 35(4): 1-9.

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