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采用人类心脏模型研究了用晚钠电流控制二维心脏组织中的螺旋波和时空混沌，我们提出这样的控制策略来产生晚钠电流：让慢失活门变量j始终等于0.7，同时实时调节钠电流的快失活门变量h的阈值电压VI ，即先让阈值电压VI经过T1时间从71.55 mV均匀减少到50.55 mV，然后经过T2时间再从50.55 mV均匀增加到71.55 mV，当阈值电压VI回到71.55 mV，钠电流的快、慢失活门变量恢复正常变化.数值模拟结果表明：只要适当选择控制时间，不论心肌细胞是否存在自发的晚钠电流，控制产生的晚钠电流都可以有效抑制螺旋波和时空混沌，而且需要的晚钠电流都很小，且控制时间都很短，因为螺旋波和时空混沌消失主要是通过传导障碍消失，少数情况下时空混沌是通过转变为靶波消失.我们希望这种控制方法能为室颤控制提供新的思路.Most Na+ channels open transiently upon depolarization of cardiac cell membrane and then are quickly inactivated. However, some Na+ channels remain active, which generate the late sodium current during the action potential plateau. So far, late sodium current has been regarded as a relevant contributor to arrhythmias and its inhibition can suppress re-entrant and multifocal ventricular fibrillation so that its inhibition may become a novel therapeutic strategy to treat cardiac arrhythmias in the future. Therefore, how to inhibit late sodium current has received special attention. Since both the late sodium current and defibrillation shocks can lead to the increase of action potential duration, the late sodium current can be used to terminate ventricular fibrillation. However, the suppression of spiral wave and spatiotemporal chaos in cardiac tissues via late sodium current has been neglected. In this paper, we use the model of human heart to study the suppression of spiral wave and spatiotemporal chaos in two-dimensional cardiac tissue by generating late sodium current. We suggest that such a control strategy to induce late sodium current. The slow inactivation gate of sodium channel is clamped to 0.7 while the threshold voltage of corresponding fast inactivation gate is real-timely modulated. We first reduce the threshold voltage from 71.55 mV to 50.55 mV within the time interval T1, and then increase it from 50.55 mV to 71.55 mV within the time interval T2. When the threshold voltage returns to 71.55 mV, the changes of the relevant inactivation gates of sodium channel go back to normal dynamic state. Numerical simulation results show that when the control parameters are properly chosen, the control-induced late sodium current can effectively suppress spiral wave and spatiotemporal chaos even if there are some cardiac cells with spontaneous late sodium current. The advantage of the control scheme is that the control-induced late sodium current is small. The control duration is short because the spiral wave and spatiotemporal chaos disappear mainly due to the conduction obstacle. In a few cases, the spatiotemporal chaos disappears through the transition from spiral wave to target wave. We hope that these results may provide a new strategy to treat heart disease.
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Keywords:
- spiral wave /
- spatiotemporal chaos /
- late sodium current /
- control
[1] Gray R A, Jalife J 1996 Int. J. Bifurcat. Chaos 6 415
[2] Navarrete E G, Liang P, Lan F, Sanchez-Freire V, Simmons C, Gong T, Sharma A, Burridge P W, Patlolla B, Lee A S, Wu H, Beygui R E, Wu S M, Robbins R C, Bers D M, Wu J C 2013 Circulation 128 S3
[3] Braunschweig F, Boriani G, Bauer A, Hatala R, Herrmann-Lingen C, Kautzner J, Pedersen S S, Pehrson S, Ricci R, Schalij M J 2010 Europace 12 1673
[4] Shajahan T K, Nayak A R, Pandit R 2009 PLoS One 4 e4738
[5] Wang C N, Ma J 2013 Acta Phys. Sin. 62 084501 (in Chinese)[王春妮, 马军 2013 62 084501]
[6] Tandri H, Weinberg S H, Chang K C, Zhu R, Trayanova N A, Tung L, Berger R D 2011 Sci. Tramsl. Med. 3 102ra96
[7] Lou Q, Chen J X, Zhao Y H, Shen F R, Fu Y, Wang L L, Liu Y 2012 Phys. Rev. E 85 026213
[8] Smagina Y, Sheintuch M 2014 arXiv preprint arXiv:arXiv:1410.0506
[9] Ji L, Zhou Y, Li Q, Qiao C, Ouyang Q 2013 Phys. Rev. E 88 042919
[10] Li W, Janardhan A H, Fedorov V V, Sha Q, Schuessler R B, Efimov I R 2011 Circ. Arrhythm. Electrophysiol. 4 917
[11] 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]
[12] Burton R A B, Klimas A, Ambrosi C M, Tomek J, Corbett A, Entcheva E, Bub G 2015 Nat. Photon. 9 813
[13] Bingen B O, Engels M C, Schalij M J, Jangsangthong W, Neshati Z, Feola I, Ypey D L, Askar S F, Panfilov A V, Pijnappels D A, de Vries A A F 2014 Circ. Res. 102 176
[14] Nussinovitch U, Shinnawi R, Gepstein L 2014 Circ. Res.102 176
[15] Ambrosi C M, Entcheva E 2014 Methods Mol. Boil. 1181 215
[16] Shcherbakov D, Motovilov K, Erofeev I, Astafiev A 2012 Nat. Methods 9 396
[17] Mourot A, Fehrentz T, Le Feuvre Y, Smith C M, Herold C, Dalkara D, Nagy F, Trauner D, Kramer R H 2012 Nat. Methods 9 396
[18] Pourrier M, Williams S, Mcafee D, Belardinelli L, Fedida D 2014 J. Physiol. 592 411
[19] Belardinelli L, Liu G, Smith-Maxwell C, Wang W Q, El-Bizri N, Hirakawa R, Karpinski S, Li C H, Li X J, Crumb W, Wu L, Koltun D, Zablocki J, Yao L, Dhalla A K, Rajamani S, Shryock J C 2013 J. Pharmacol. Exp. Ther. 344 23
[20] Morita N, Lee J H, Xie Y, Sovari A, Qu Z, Weiss J N, Karagueuzian H S 2011 J. Am. Coll. Cardiol. 57 366
[21] Ten Tusscher K H W J, Noble D, Noble P J, Panfilov A V 2008 Am. J. Physiol. Heart Circ. Physiol. 294 H2031
[22] Song Y, Shryock J C, Belardinelli L 2008 Am. J. Physiol.Heart Circ. Physiol. 294 H2031
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[1] Gray R A, Jalife J 1996 Int. J. Bifurcat. Chaos 6 415
[2] Navarrete E G, Liang P, Lan F, Sanchez-Freire V, Simmons C, Gong T, Sharma A, Burridge P W, Patlolla B, Lee A S, Wu H, Beygui R E, Wu S M, Robbins R C, Bers D M, Wu J C 2013 Circulation 128 S3
[3] Braunschweig F, Boriani G, Bauer A, Hatala R, Herrmann-Lingen C, Kautzner J, Pedersen S S, Pehrson S, Ricci R, Schalij M J 2010 Europace 12 1673
[4] Shajahan T K, Nayak A R, Pandit R 2009 PLoS One 4 e4738
[5] Wang C N, Ma J 2013 Acta Phys. Sin. 62 084501 (in Chinese)[王春妮, 马军 2013 62 084501]
[6] Tandri H, Weinberg S H, Chang K C, Zhu R, Trayanova N A, Tung L, Berger R D 2011 Sci. Tramsl. Med. 3 102ra96
[7] Lou Q, Chen J X, Zhao Y H, Shen F R, Fu Y, Wang L L, Liu Y 2012 Phys. Rev. E 85 026213
[8] Smagina Y, Sheintuch M 2014 arXiv preprint arXiv:arXiv:1410.0506
[9] Ji L, Zhou Y, Li Q, Qiao C, Ouyang Q 2013 Phys. Rev. E 88 042919
[10] Li W, Janardhan A H, Fedorov V V, Sha Q, Schuessler R B, Efimov I R 2011 Circ. Arrhythm. Electrophysiol. 4 917
[11] 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]
[12] Burton R A B, Klimas A, Ambrosi C M, Tomek J, Corbett A, Entcheva E, Bub G 2015 Nat. Photon. 9 813
[13] Bingen B O, Engels M C, Schalij M J, Jangsangthong W, Neshati Z, Feola I, Ypey D L, Askar S F, Panfilov A V, Pijnappels D A, de Vries A A F 2014 Circ. Res. 102 176
[14] Nussinovitch U, Shinnawi R, Gepstein L 2014 Circ. Res.102 176
[15] Ambrosi C M, Entcheva E 2014 Methods Mol. Boil. 1181 215
[16] Shcherbakov D, Motovilov K, Erofeev I, Astafiev A 2012 Nat. Methods 9 396
[17] Mourot A, Fehrentz T, Le Feuvre Y, Smith C M, Herold C, Dalkara D, Nagy F, Trauner D, Kramer R H 2012 Nat. Methods 9 396
[18] Pourrier M, Williams S, Mcafee D, Belardinelli L, Fedida D 2014 J. Physiol. 592 411
[19] Belardinelli L, Liu G, Smith-Maxwell C, Wang W Q, El-Bizri N, Hirakawa R, Karpinski S, Li C H, Li X J, Crumb W, Wu L, Koltun D, Zablocki J, Yao L, Dhalla A K, Rajamani S, Shryock J C 2013 J. Pharmacol. Exp. Ther. 344 23
[20] Morita N, Lee J H, Xie Y, Sovari A, Qu Z, Weiss J N, Karagueuzian H S 2011 J. Am. Coll. Cardiol. 57 366
[21] Ten Tusscher K H W J, Noble D, Noble P J, Panfilov A V 2008 Am. J. Physiol. Heart Circ. Physiol. 294 H2031
[22] Song Y, Shryock J C, Belardinelli L 2008 Am. J. Physiol.Heart Circ. Physiol. 294 H2031
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