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本文采用Luo-Rudy相I模型研究如何通过调控心肌细胞钠电流变化来控制心脏中的螺旋波和时空混沌，提出了这样的钠电流调控方案：当细胞将被激发时启动钠电流调节，若由模型方程得到的钠电流的绝对值小于钠电流控制阈值的绝对值，就让钠电流等于钠电流控制阈值，其他情况下则限制钠电流的绝对值不能高于一个给定的最大值；当膜电位上升超过-5 mV时，让钠电流自然演化.这种调节钠电流的方式保证了所有细胞几乎具有相同的钠电流幅值，从而使所有细胞具有相同的激发性，数值模拟结果表明，只要钠电流控制阈值达到一定临界值，就可以有效抑制螺旋波波头的旋转，导致螺旋波运动出系统边界而消失，以及时空混沌演化为螺旋波后消失，如果钠电流控制阈值足够大，螺旋波和时空混沌还可通过传导障碍而消失.这些结果能够为抗心律失常治疗提供新的思路.The variation of the function of sodium channel in cardiomyocyte is associated with multiple cardiac diseases. Increasing sodium channel availability can effectively increase sodium influx, leading to enhanced cardiomyocyte excitability, prolonged action potential duration and late sodium current activity, which may cause ventricular arrhythmia. On the other hand, enhancing cardiomyocyte excitability can effectively increase the conduction velocity of the medium in the rotation center of spiral wave, which can restrain the rotation of spiral wave, leading to the disappearance of spiral wave. However, how to increase the excitability of cardiomyocytes while avoiding arrhythmias has not yet been explored so far. In this paper, we study how to regulate the changes of sodium current in cardiac myocytes to control spiral wave and spatiotemporal chaos in a two-dimensional cardiac tissues by using the Luo-Rudy phase I model. We propose such a sodium current control scheme:when the cell is excited, the regulation of sodium current begins. If the absolute value of sodium current obtained from the model equation is less than the absolute value of sodium current control threshold, the sodium current is simply equal to the control threshold of sodium current. In other cases, the absolute value of sodium current cannot exceed the maximum value without control. When the membrane potential rises over-5 mV, the sodium current evolves naturally. This method of regulating sodium current ensures that all cells have almost the same amplitude of sodium current, while without obviously changing the excitation-time. All cells thus have the same excitability under the control of sodium current, so that the excitation of cell is less affected by spiral wave tip. The numerical simulation results show that as long as the control threshold of sodium current reaches a critical value, the rotation of spiral wave tip is effectively suppressed, causing spiral wave to move out of the system boundary and spatiotemporal chaos to disappear after it has evolved into a spiral wave. If the absolute value of sodium current control threshold is large enough, the spiral wave and spatiotemporal chaos would also disappear through conductive block. These results can provide a new idea for antiarrhythmic therapy.
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Keywords:
- spiral wave /
- spatiotemporal chaos /
- sodium current /
- control
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[2] Panfilov A V 1998 Chaos 8 57
[3] Panfilov A V, Holden A V 1990 Phys. Lett. A 151 23
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[17] Ji L, Zhou Y, Li Q, Qiao C, Ouyang Q 2013 Phys. Rev. E 88 042919
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[20] Chen J X, Zhang H, Qiao L Y, Liang H, Sun W G 2018 Commun. Nonlinear Sci. Numer. Simul. 54 202
[21] Chen J X, Guo M M, Ma J 2016 EPL 113 38004
[22] Ouyang Q, Swinney H L, Li G 2000 Phys. Rev. Lett. 84 1047
[23] Pei Z F, Xiao Y C, Meng J W, Hudmon A, Cummins T R 2016 Nat. Commun. 7 12035
[24] Müller-Ehmsen J, Brixius K, Schwinger R H 1998 J. Cardiovasc. Pharmacol. 31 684
[25] Luo C H, Rudy Y 1991 Circ. Res. 68 1501
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[1] Cherry E M, Fenton F H 2008 New J. Phys. 10 125016
[2] Panfilov A V 1998 Chaos 8 57
[3] Panfilov A V, Holden A V 1990 Phys. Lett. A 151 23
[4] Davidenko J M, Pertsov A V, Salomonsz R, Baxter W, Jalife J 1992 Nature 355 349
[5] Shajahan T K, Nayak A R, Pandit R 2009 PLoS One 4 e4738
[6] Burton R A B, Klimas A, Ambrosi C M, Tomek J, Corbett A, Entcheva E, Bub G 2015 Nat. Photon. 9 813
[7] Pan D B, Gao X, Feng X, Pan J T, Zhang H 2016 Sci. Rep. 6 21876
[8] Yamazaki M, Honjo H, Nakagawa H, Ishiguro Y S, OkunoY, Amino M, Sakuma I, Kamiya K, Kodama I 2007 Am. J. Physiol. Heart Circ. Physiol. 292 H539
[9] Hajjar K, Berbari I, Tawil C E, Chebl R B, Dagher G A 2018 Am. J. Emerg. Med. 36 1474
[10] Manzoni G M, Castelnuovo G, Compare A, Pagnini F, Essebag V, Proietti R 2015 Front. Psychol. 6 39
[11] Boink G J J, Christoffels V M, Robinson R B, Tan H L 2015 Trends Cardiovas. Med. 25 674
[12] Costabal F S, Yao J, Kuhl E 2018 Int. J. Numer. Methods Bio. 34 e2964
[13] Walcott G P, Killingsworth C R, Ideker R E 2003 Resuscitation 59 59
[14] Shajaha T K, Nayak A R, Pandit R 2009 PLoS One 4 e4738
[15] Yamazaki M, Honjo H, Ashihara T, Harada M, Sakuma I, Nakazawa K, Trayanova N, Hori M, Kalifa J, Jalife J, Kamiya K, Kodama I 2012 Heart Rhythm 9 107
[16] Stamp A T, Osipov G V, Collins J J 2002 Chaos 12 931
[17] Ji L, Zhou Y, Li Q, Qiao C, Ouyang Q 2013 Phys. Rev. E 88 042919
[18] Luther S, Fenton F H, Kornreich B G, Squires A, Bittihn P, Hornung D, Zabel M, Flanders J, Gladuli A, Campoy L, Cherry E M, Luther G, Hasenfuss G, Krinsky V I, Pumir A, Gilmour Jr R F, Bodenschatz E 2011 Nature 475 235
[19] Hörning M, Takagi S, Yoshikawa K 2012 Phys. Rev. E 85 061906
[20] Chen J X, Zhang H, Qiao L Y, Liang H, Sun W G 2018 Commun. Nonlinear Sci. Numer. Simul. 54 202
[21] Chen J X, Guo M M, Ma J 2016 EPL 113 38004
[22] Ouyang Q, Swinney H L, Li G 2000 Phys. Rev. Lett. 84 1047
[23] Pei Z F, Xiao Y C, Meng J W, Hudmon A, Cummins T R 2016 Nat. Commun. 7 12035
[24] Müller-Ehmsen J, Brixius K, Schwinger R H 1998 J. Cardiovasc. Pharmacol. 31 684
[25] Luo C H, Rudy Y 1991 Circ. Res. 68 1501
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