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现代生物技术已经能够通过让钠离子通道的基因突变来改变其弛豫时间常数.本文采用Luo-Rudy相I模型研究了如何调控钠通道门的弛豫时间常数来控制心脏中的螺旋波和时空混沌.我们提出这样的控制策略：通过让钠电流触发门的弛豫时间常数增大倍，同时让其快失活门始终不关闭，来降低钠电流激活和失活的速率.数值模拟结果表明：逐渐增加将导致钠电流的触发门变量更慢，达到最大值，并且其振幅也逐渐减少，从而使心肌细胞动作电位的幅度和持续时间都逐渐减少.在足够大的情况下，螺旋波和时空混沌不能在介质中传播，但是低频平面波可以在介质中传播，原因是介质激发性和波传播速度大幅度降低了.因此在适当选取控制时间和足够大的情况下，可以有效消除心脏中的螺旋波和时空混沌.螺旋波和时空混沌主要通过传导障碍消失，也观察到螺旋波转变为靶波、螺旋波波头回缩、时空混沌转变为螺旋波消失的现象.当相关参数适当选择时，还观察到螺旋波转变为自维持靶波现象，相应的靶波源是旋转方向相反的螺旋波对.这些结果为心脏病的基因治疗提供了有用信息.Much evidence shows that the appearance and instability of the spiral wave in cardiac tissue can be linked to a kind of heart disease. Therefore there needs a method of controlling spiral wave more safely and effectively. The intelligent modification of specific ion channel to achieve desired control is the future direction of gene therapy in heart disease. The key question that has to be answered is which ion channel is the best candidate for controlling spiral wave. Modern biological technology has been able to make the mutation of sodium channel gene to change its relaxation time constant. In this paper, we adopt the Luo-Rudy phase I model to investigate how to regulate the relaxation time constant of sodium channel gate to control spiral wave and spatiotemporal chaos in cardiac tissues. We suggest a control strategy which slows down the rate of sodium current activation and inactivation by increasing the relaxation time constant of the sodium activation gate by up to times while its fast inactivation gate is clamped to 0.77. Numerical simulation results show that a gradual increase of will cause the activation gate of sodium current to reach maximum more slowly, and its amplitude is gradually reduced, so that the amplitude and duration of the action potential of cardiomyocyte are gradually reduced. When the factor is large enough, the spiral wave and spatiotemporal chaos cannot propagate in the medium except planar wave with low frequency. The reason is that the excitabilities of medium and wave speed significantly decrease. Therefore, the spiral waves and spatiotemporal chaos can be effectively eliminated when the control time is properly selected and the factor is large enough. Spiral wave and spatiotemporal chaos disappear mainly due to conduction obstacle. In some cases, spiral wave can disappear through the transition from spiral wave to target wave or tip retraction. Spatiotemporal chaos disappears after spatiotemporal chaos has evolved into meandering spiral wave. When the parameters are chosen properly, the phenomenon that spiral wave evolves into a self-sustained target wave is also observed. The corresponding target wave source is the pair of spiral waves with opposite rotation directions. These results can provide useful information for gene therapy in heart disease.
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Keywords:
- relaxation time constant /
- activation gate /
- spiral wave /
- spatiotemporal chaos
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[1] Gurevich E L, Moskalenko A S, Zanin A L, Astrov Y A, Purwins H G 2003 Phys. Rev. A 307 299
[2] Ecke R E, Hu Y, Mainieri R, Ahlers G 1995 Science 269 1704
[3] Winfree A T 1972 Science 175 634
[4] Belmonte A, Ouyang Q, Flesselles J M 1997 J. Phys. Ⅱ France 7 1425
[5] Davidenko J M, Pertsov A V, Salomonsz R, Baxter W, Jalife J 1992 Nature 355 349
[6] Huang X Y, Xu W F, Liang J M, Takagaki K, Gao X, Wu J Y 2010 Neuron 68 978
[7] Pertsov A M, Davidenko J M, Salomonsz R, Baxter W T, Jalife J 1993 Circ. Res. 72 631
[8] Lechleiter J, Girard S, Peralta E, Clapham D 1991 Science 252 123
[9] Witkowski F X, Leon L J, Penkoske P A, Giles W R, Spano M L, Ditto W L, Winfree A T 1998 Nature 392 78
[10] Yang H J, Yang J Z 2007 Phys. Rev. E 76 016206
[11] Liu F C, Wang X F, Li X C, Dong L F 2007 Chin. Phys. 16 2640
[12] Liu Y, Li S R, Ma J, Ying H P 2009 Chin. Phys. B 18 98
[13] Deng M Y, Tang G N, Kong L J, Liu M R 2010 Acta Phys. Sin. 59 2339 (in Chinese) [邓敏艺, 唐国宁, 孔令江, 刘慕仁2010 59 2339]
[14] Pan F, Li W X, Wang X Y, Tang G N 2015 Acta Phys. Sin. 64 218202 (in Chinese) [潘飞, 黎维新, 王小艳, 唐国宁2015 64 218202]
[15] Pan D B, Gao X, Feng X, Pan J T, Zhang H 2016 Sci. Rep. 6 21876
[16] Yuan G Y, Xu A G, Wang G R, Chen S G 2010 Europhys. Lett. 90 10013
[17] Wang P Y, Xie P, Yin H W 2003 Chin. Phys. 12 674
[18] Gray R A 2002 Chaos 12 941
[19] Li W W, Janardhan A H, Fedorov V V, Sha Q, Schuessler R B, Efimov I R 2011 Circ. Arrhythm. Electrophysiol. 4 917
[20] Zhang H, Cao Z J, Wu N J, Ying H P, Hu G 2005 Phys. Rev. Lett. 94 188301
[21] Magome N, Kanaporis G, Moisan N, Tanaka K, Agladze K 2011 Tissue Eng.: Part A 17 21
[22] Nattel S, Carlsson L 2006 Nat. Rev. Drug Discov. 5 1034
[23] Antzelevitch C, Brugada P, Brugada J, Brugada R, Shimizu W, Gussak I, Riera A R P 2002 Circ. Res. 91 1114
[24] ten-Tusscher K H W J, Panfilov A V 2006 Phys. Med. Biol. 51 6141
[25] Tran D X, Sato D, Yochelis A, Weiss J N, Garfinkel A, Qu Z 2009 Phys. Rev. Lett. 102 258103
[26] ten-Tusscher K H W J, Hren R, Panfilov A V 2007 Circ. Res. 100 e87
[27] ten-Tusscher K H W J, Panfilov A V 2006 Am. J. Physiol. Heart Circ. Physiol. 291 H1088
[28] Zhang Z S, Tranquillo J, Neplioueva V, Bursac N, Grant A O 2007 Am. J. Physiol. Heart Circ. Physiol. 292 H399
[29] Osterrieder W, Noma A, Trautwein W 1980 Pflgers Arch. 386 101
[30] Qu Z, Garfinkel A, Chen P S, Weiss J N 2000 Circulation 102 1664
[31] ten-Tusscher K H W J 2005 Ph. D. Dissertation (Netherlands: Utrecht University)
[32] Luo C H, Rudy Y 1991 Circ. Res. 68 1501
[33] Hsiao P Y, Tien H C, Lo C P, Juang J M J, Wang Y H, Sung R J 2013 Appl. Clin. Genet. 6 1
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