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建立了包含心房肌、心室肌、房室腔、室间隔并考虑心室肌分层结构的心电图元胞自动机模型.利用所建立的模型，仿真了电信号在心脏中的传导，计算了正常和缺血情况下的场点电势走势.数值结果表明：正常情况下，模拟所得的场点电势呈现与标准心电图一致的P波、QRS波群、T波和J波；在心内膜下肌细胞缺血情况下，出现T波倒置的现象；在心外膜下肌细胞缺血情况下，T波变得高耸；在透壁缺血情况下，T波提前形成，QT间期缩短.将正常和异常情况下的场点电势走势与临床结果进行了对比，并分析了其形成与持续机制.研究结果可为准确阐明心电图与心肌细胞电活动之间的关系、探讨心电图的产生与持续机制提供参考.The electrocardiogram (ECG) has broad applications in clinical diagnosis and prognosis of cardiovascular diseases. The accurate description for the question how the ECG come from the cardiac electrical activity is helpful for understanding the corresponding relation between the ECG waveform and cardiovascular disease. Experience is the primary method of studying the ECG, but the computer simulation method makes it more convenient to explore the effect of given factor for ECG waveform. Cellular automaton is a simple and effective computer simulation method. However, the cellular automaton model considering the main structure of the heart is not yet established. Therefore, we propose a cellular automaton model for the ECG considering the atria, the ventricle, and the ventricular septum. With this model, the conduction of the myocardial electrical activation is simulated by following the field potentials under healthy and diseased conditions, and the underlying mechanisms are analyzed. Through the computer simulations and analyses the results are obtained as follows. First, the conduction process of the electrical signal in this model is the same as that in the real heart. Second, under the healthy conditions, the behavior of the field potential appears as normal ECG, in which the P wave and the QRS wave group come from the depolarization of the atria and ventricle, respectively, on the other hand, the T wave and J wave come from the repolarization of the ventricle. The computer results support the conclusion that the J wave appears just because the existence of the notch in the epicardial transmembrane potential curve. Third, the endocardium ischemia conditions result in the T wave inversion. The mechanism is that the action potential duration of the ischemic endocardial cells is shorter than that under normal conditions, which makes larger the transmembrane potential gradient between the endocardium and the subepicardium, and then contributes a more negative value to the field potential. Fourth, the epicardium ischemia leads to the higher T wave, and this is because the shorter action potential duration of the ischemic epicardial cells brings in a larger transmembrane potential gradient between the epicardium and subepicardium, which makes the field voltage larger. Fifth, the T wave appears earlier under the through-wall ischemia. The action potential durations of cells of the endocardium, the epicardium, and the subepicardium all become shorter under the through-wall ischemia, then the repolarization processes of all of these three walls are ended earlier, which leads to the earlier T wave. The cellular automaton model proposed in this paper provides a reference for the further study of ECG.
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Keywords:
- cellular automaton /
- transmembrane potential /
- electrocardiogram /
- ischemia
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[17] Aslanidi O V, Clayton R H, Lambert J L, Holden A V 2005 J. Theor. Biol. 237 369
[18] Schenone E, Collin A, Gerbeau J F 2015 Chin. Phys. B 24 142
[19] Wolfram S 1984 Nature 311 419
[20] Moe G K, Rheinboldt W C, Abildskov J A 1964 Am. Heart J. 67 200
[21] Bollacker K D, Simpson E V, Johnson G A, Walcott G P 1991 13th Annual International Conference of the IEEE Engineering in Medicine and Biology Society Orlando, Florida, USA, October 31November 3, 1991 p627
[22] Makowiec D 2010 Int. J. Mod. Phys. C 21 107
[23] Deng M Y, Dai J Y, Zhang X L 2015 Chin. Phys. B 24 142
[24] Drouin E, Charpentier F, Gauthier C, Laurent K, Le M H 1995 J. Am. Coll. Cardiol. 26 185
[25] Antzelevitch C 2001 Cardiovasc. Res. 50 426
[26] Yu C G, Bai R, Chen D L, Huang Y 2008 Cardiac Electrophysiology Foundation and Clinic (Wuhan:Huazhong University of Science Technology Press) p168(in Chinese)[余承高, 白融, 陈栋梁, 黄勇2008心脏电生理学基础与临床(武汉:华中科技大学出版社)第168页]
[27] Zhu H, Sun Y, Rajagopal G, Mondry A, Dhar P Biomed. Eng. Online 3 29
[28] Tinniswood A D, Furse C M, Gandhi O P 1998 Phys. Med. Biol. 43 2361
[29] Hlaing T, DiMino T, Kowey P R, Yan G X Circulation 110 1036
[30] Yan G X, Joshi A, Guo D L, Hlaing T, Martin J, Xu X P, Kowey P R 2004 Circulation 110 1036
[31] Di Diego J M, Antzelevitch C 2014 J. Electrocardiol. 47 486
[32] Holland R P, Brooks H 1977 Am. J. Cardiol. 40 110
[33] Zhao S Y, Wang D W, Shen Y, Li L, Zhang H 2008 J. Clin. Exp. Med. 7 89 (in Chinese)[赵淑艳, 王道伟, 沈毅, 李莉, 张红2008临床和实验医学杂志7 89]
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[1] Yang X L, Liu G Z, Tong Y H, Yan H, Xu Z, Chen Q, Liu X, Zhang H H, Wang H B, Tan S H 2015 J. Geriatr. Cardiol. 12 448
[2] Singh R, Murphy J J 2015 Anaesthesia and Intensive Care Medicine 16 220
[3] Khalid U, Birnbaum Y 2016 Ann. Noninvas. Electr. 21 202
[4] Namana V, Patel J, Tripathi N, Mathur P 2016 QJM-Int. J. Med. 109 559
[5] Hwang C, Levis J T 2014 Perm. J. 18 e133
[6] Andersson H B, Hansen M B, Thorsberger M, Srensen T B, Nielsen J B, Graff C, Pehrson S, Svendsen J H 2015 J. Electrocardiol. 48 834
[7] Atienza F A, Carrin J R, Alberola A G, Alvarez J R, Muoz J J S, Snchez J M, Chvarri M V 2005 Rev. Esp. Cardiol. 58 41
[8] Yuan G Y, Zhang H, Wang G R 2013 Acta Phys. Sin. 62 160502 (in Chinese)[袁国勇, 张焕, 王光瑞2012 61 160502]
[9] Liu G Q, Ying H P 2014 Chin. Phys. B 23 050502
[10] He D H, Hu G, Zhan M, Ren W, Gao Z 2002 Phys. Rev. E 65 055204
[11] Zhang H, Chen J X, Li Y Q, Xu J R 2006 J. Chem. Phys. 125 204503
[12] Liu G Q, Ying H P, Luo H L, Liu X X, Yang J H 2016 Int. J. Bifurcat. Chaos 26 1650236
[13] Chen J X, Mao J W, Hu B B, Xu J R, He Y F, Li Y, Yuan X P 2009 Phys. Rev. E 79 066209
[14] Wang C N, Ma J 2013 Acta Phys. Sin. 62 084501 (in Chinese)[王春妮, 马军2013 62 084501]
[15] Chen J X, Peng L, Ma J, Ying H P 2014 Europhys. Lett. 107 38001
[16] Trudel M C, Dub B, Potse M, Gulrajani R M, Leon L J 2004 IEEE Trans. Bio-med. Eng. 51 1319
[17] Aslanidi O V, Clayton R H, Lambert J L, Holden A V 2005 J. Theor. Biol. 237 369
[18] Schenone E, Collin A, Gerbeau J F 2015 Chin. Phys. B 24 142
[19] Wolfram S 1984 Nature 311 419
[20] Moe G K, Rheinboldt W C, Abildskov J A 1964 Am. Heart J. 67 200
[21] Bollacker K D, Simpson E V, Johnson G A, Walcott G P 1991 13th Annual International Conference of the IEEE Engineering in Medicine and Biology Society Orlando, Florida, USA, October 31November 3, 1991 p627
[22] Makowiec D 2010 Int. J. Mod. Phys. C 21 107
[23] Deng M Y, Dai J Y, Zhang X L 2015 Chin. Phys. B 24 142
[24] Drouin E, Charpentier F, Gauthier C, Laurent K, Le M H 1995 J. Am. Coll. Cardiol. 26 185
[25] Antzelevitch C 2001 Cardiovasc. Res. 50 426
[26] Yu C G, Bai R, Chen D L, Huang Y 2008 Cardiac Electrophysiology Foundation and Clinic (Wuhan:Huazhong University of Science Technology Press) p168(in Chinese)[余承高, 白融, 陈栋梁, 黄勇2008心脏电生理学基础与临床(武汉:华中科技大学出版社)第168页]
[27] Zhu H, Sun Y, Rajagopal G, Mondry A, Dhar P Biomed. Eng. Online 3 29
[28] Tinniswood A D, Furse C M, Gandhi O P 1998 Phys. Med. Biol. 43 2361
[29] Hlaing T, DiMino T, Kowey P R, Yan G X Circulation 110 1036
[30] Yan G X, Joshi A, Guo D L, Hlaing T, Martin J, Xu X P, Kowey P R 2004 Circulation 110 1036
[31] Di Diego J M, Antzelevitch C 2014 J. Electrocardiol. 47 486
[32] Holland R P, Brooks H 1977 Am. J. Cardiol. 40 110
[33] Zhao S Y, Wang D W, Shen Y, Li L, Zhang H 2008 J. Clin. Exp. Med. 7 89 (in Chinese)[赵淑艳, 王道伟, 沈毅, 李莉, 张红2008临床和实验医学杂志7 89]
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