心肌细胞早后去极化节律产生的动力学机制研究
|
摘要
心脏的搏动作为动物生命的基础,长期以来备受人们关注。而早后去极化(earlyafter-depolarizations, EAD)作为一种心律失常现象,严重威胁着人们的身体健康和生活质量。目前对早后去极化(EAD)形成机制的研究并不明确,一方面是由于心肌细胞离子通道种类繁多,动作电位的形成过程复杂；另一方面,是由于目前的大多数研究更多关注对生物学现象的描述,较少关注其产生的深层次机理。
随着生命科学和非线性科学的进一步结合,非线性动力学的研究方法已经逐渐运用到了对心肌节律的研究中,并且成为了该领域的热点问题。新的研究视角为我们提供了一条进一步从理论层次认识心肌节律的途径。本研究利用非线性动力学方法对早后去极化(EAD)这一令人困扰的心律失常问题进行研究。在定性、定量刻画该现象的基础上,揭示了其产生的动力学机制。
在本研究中,以培养的心肌细胞作为实验模型,通过心肌细胞电生理的方法,记录到了稳定的EAD样搏动节律。同时,在随机性异质ML电耦合网络模型上对心肌细胞的EAD节律进行了仿真和理论分析。
主要结果有：
1.在培养的心肌细胞团上,通过Fura-2/AM染色的方法观察细胞内Ca2+离子振荡节律,发现位于培养心肌细胞团不同位点的细胞可以表现出同步的EAD样放电节律。用膜片钳技术检测了该细胞团上其中一个单细胞的膜电位振荡,发现该细胞的膜电位也表现出EAD样的节律。EAD节律表现为心肌细胞膜电位在复极化未完成时,又一次发生异常的去极化,并且形成一次不成熟的动作电位。
2.选用异质电耦合网络模拟心肌细胞团,网络的节点选用Morris-Lecar模型。在一定范围内随机选取单元振子参数,使得网络内的单元振子的参数配置不同,动力学行为也不同；参数选取在从周期1节律到去极化静息的Hopf分岔点附近,单元振子的行为要么为去极化静息,要么为周期1。在确定性网络,耦合强度增加会使得具有不同节律或电活动的细胞形成同步化周期1节律。考虑现实心肌细胞总是存在类似噪声的随机因素,选用引入了随机因素的网络进一步逼近实验中的心肌细胞团。在随机网络,耦合强度的增强可以提高心肌细胞网络节律的同步化水平,噪声的作用在很小程度上降低了节律的同步化程度,不会影响同步化现象,但是,噪声的作用使得同步化的周期1节律变为了同步化的EAD节律。
由于Hopf分岔是从去极化静息到周期1的临界点。在噪声作用下,心肌细胞团(网络)会在去极化静息和周期1之间随机跃迁,这就是EAD节律的特征和动力学机制。
上述结果表明,EAD节律是在Hopf分岔点附近的心肌细胞团或网络的同步化的随机振荡。而当振子的行为或参数远离Hopf分岔时,心肌细胞网络为同步化的周期1节律或静息。这说明异质的心肌细胞网络自身就具有产生多样同步节律的能力,包括所谓的“规则节律”(周期1节律)和“异常节律”(EAD节律)。各种不同节律的产生往往是系统参数的配置不同所引起的；而参数的变化可以引起各种节律之间的跃迁。这就为研究复杂的心肌节律的产生和跃迁提供了理论认识,并对由早后去极化(EAD)引起的心律失常的预防、诊断和治疗提供了新的思路。
As the basis of normal life, the beating of heart has been paid much attention for a long time. A kind of arrhythmia, early after-depolarization (EAD), has been the serious threat to the people's health and the quality of life. But the formation mechanism of EAD has not been clear. On the one hand, the cardiac ion channels, which participate in the cardiac action potential, are numerous and complex. On the other hand, most of the studies about currents are concentrated on the description of biological phenomena, while little studies on the deep formation mechanisms.
Following the further combination between life science and nonlinear dynamics, the method of the nonlinear dynamics has gradually used to reveal the mechanism of cardiac rhythm, and has been a hotspot. The novel angle provides a new pathway to learn more information about the cardiac rhythm in the theoretical level. In this paper, the method of the nonlinear dynamics is employed to study EAD being as a boring arrhythmia. On the basis of qualitative and quantitative description of EAD, the dynamics and formation mechanisms of EAD are identified.
In this study, the stable EAD rhythms are recorded in an experimental model--cultured cardiac myocytes by cardiac electrophysiology experiments. At the same time, the EAD rhythms are simulated and analyzed in the theoretical level by a mathematical network model, which is composed of heterogeneous units described by Morris-Lecar (ML) model with nearest-neighbor coupling method.
The main results were as follows:
1. Synchronized EAD rhythms of intracellular calcium concentration ([Ca2+]i) oscillation were discovered in different cells in cultured cardiac myocytes network, using Fura-2/AM staining method. EAD-like oscillation of membrane potential was recorded in a single cell located in the network, using patch clamp. The EAD was the abnormal depolarization generated during the repolarization, being as an immature action potential.
2. A network composed of heterogeneous units described by Morris-Lecar (ML) model with nearest-neighbor and electronic coupling method was employed to simulate the cultured cardiac myocytes. To insure the different parameter configuration of the unit oscillation, the parameters of unit oscillators was chosen randomly in a region. The dynamics of unit oscillator are different correspondingly. When the parameters of unit oscillator are chosen near Hopf bifurcation point from period 1 rhythm to depolarized rest, the behaviors are either depolarized rest or period 1 rhythm. Synchronized period 1 rhythms are simulated in the deterministic network whose cells exhibit different rhythms when the coupling strength is increased. Considering the fact that the stochastic factors similar to noise is inevitable in the real cardiac cells, the network containing stochastic component are chosen to further simulate the cardiac cells in the experiment. The synchronous degree of rhythms of the cardiac cells is enhanced by increase of the coupling strength in the stochastic network. Under the influence of noise, the synchronous degree of rhythms is slightly decreased, and the synchronized phenomenon did not change, but the synchronized period 1 rhythm is changed into synchronized EAD rhythm.
The Hopf bifurcation point is the critical point from depolarized rest to period 1 rhythm. Under the influence of noise, the behavior of the network is stochastic transition between the depolarized rest and period 1 rhythm. It is the characteristics and dynamics of the EAD rhythm.
The above results indicate that EAD rhythm is the synchronized stochastic oscillation of cardiac myocytes or the network near a Hopf bifurcation point. When the behavior or parameters of the oscillator is far from the Hopf bifurcation, the synchronized network of cardiac myocytes is period 1 rhythm or rest. It shows that the heterogeneous network of cardiac myocytes has the capability to produce various synchronous rhythms by itself, including the "regular rhythm" (period 1 rhythm) and "abnormal rhythm" (EAD rhythm). The difference of the various rhythms is the parameters configuration of system, which can lead the system to transit between the different rhythms. The results provide novel understanding for the formation and transition of cardiac myocytes rhythm, and new way to prevent, diagnose and treat the arrhythmia induced by EAD.
随着生命科学和非线性科学的进一步结合,非线性动力学的研究方法已经逐渐运用到了对心肌节律的研究中,并且成为了该领域的热点问题。新的研究视角为我们提供了一条进一步从理论层次认识心肌节律的途径。本研究利用非线性动力学方法对早后去极化(EAD)这一令人困扰的心律失常问题进行研究。在定性、定量刻画该现象的基础上,揭示了其产生的动力学机制。
在本研究中,以培养的心肌细胞作为实验模型,通过心肌细胞电生理的方法,记录到了稳定的EAD样搏动节律。同时,在随机性异质ML电耦合网络模型上对心肌细胞的EAD节律进行了仿真和理论分析。
主要结果有：
1.在培养的心肌细胞团上,通过Fura-2/AM染色的方法观察细胞内Ca2+离子振荡节律,发现位于培养心肌细胞团不同位点的细胞可以表现出同步的EAD样放电节律。用膜片钳技术检测了该细胞团上其中一个单细胞的膜电位振荡,发现该细胞的膜电位也表现出EAD样的节律。EAD节律表现为心肌细胞膜电位在复极化未完成时,又一次发生异常的去极化,并且形成一次不成熟的动作电位。
2.选用异质电耦合网络模拟心肌细胞团,网络的节点选用Morris-Lecar模型。在一定范围内随机选取单元振子参数,使得网络内的单元振子的参数配置不同,动力学行为也不同；参数选取在从周期1节律到去极化静息的Hopf分岔点附近,单元振子的行为要么为去极化静息,要么为周期1。在确定性网络,耦合强度增加会使得具有不同节律或电活动的细胞形成同步化周期1节律。考虑现实心肌细胞总是存在类似噪声的随机因素,选用引入了随机因素的网络进一步逼近实验中的心肌细胞团。在随机网络,耦合强度的增强可以提高心肌细胞网络节律的同步化水平,噪声的作用在很小程度上降低了节律的同步化程度,不会影响同步化现象,但是,噪声的作用使得同步化的周期1节律变为了同步化的EAD节律。
由于Hopf分岔是从去极化静息到周期1的临界点。在噪声作用下,心肌细胞团(网络)会在去极化静息和周期1之间随机跃迁,这就是EAD节律的特征和动力学机制。
上述结果表明,EAD节律是在Hopf分岔点附近的心肌细胞团或网络的同步化的随机振荡。而当振子的行为或参数远离Hopf分岔时,心肌细胞网络为同步化的周期1节律或静息。这说明异质的心肌细胞网络自身就具有产生多样同步节律的能力,包括所谓的“规则节律”(周期1节律)和“异常节律”(EAD节律)。各种不同节律的产生往往是系统参数的配置不同所引起的；而参数的变化可以引起各种节律之间的跃迁。这就为研究复杂的心肌节律的产生和跃迁提供了理论认识,并对由早后去极化(EAD)引起的心律失常的预防、诊断和治疗提供了新的思路。
As the basis of normal life, the beating of heart has been paid much attention for a long time. A kind of arrhythmia, early after-depolarization (EAD), has been the serious threat to the people's health and the quality of life. But the formation mechanism of EAD has not been clear. On the one hand, the cardiac ion channels, which participate in the cardiac action potential, are numerous and complex. On the other hand, most of the studies about currents are concentrated on the description of biological phenomena, while little studies on the deep formation mechanisms.
Following the further combination between life science and nonlinear dynamics, the method of the nonlinear dynamics has gradually used to reveal the mechanism of cardiac rhythm, and has been a hotspot. The novel angle provides a new pathway to learn more information about the cardiac rhythm in the theoretical level. In this paper, the method of the nonlinear dynamics is employed to study EAD being as a boring arrhythmia. On the basis of qualitative and quantitative description of EAD, the dynamics and formation mechanisms of EAD are identified.
In this study, the stable EAD rhythms are recorded in an experimental model--cultured cardiac myocytes by cardiac electrophysiology experiments. At the same time, the EAD rhythms are simulated and analyzed in the theoretical level by a mathematical network model, which is composed of heterogeneous units described by Morris-Lecar (ML) model with nearest-neighbor coupling method.
The main results were as follows:
1. Synchronized EAD rhythms of intracellular calcium concentration ([Ca2+]i) oscillation were discovered in different cells in cultured cardiac myocytes network, using Fura-2/AM staining method. EAD-like oscillation of membrane potential was recorded in a single cell located in the network, using patch clamp. The EAD was the abnormal depolarization generated during the repolarization, being as an immature action potential.
2. A network composed of heterogeneous units described by Morris-Lecar (ML) model with nearest-neighbor and electronic coupling method was employed to simulate the cultured cardiac myocytes. To insure the different parameter configuration of the unit oscillation, the parameters of unit oscillators was chosen randomly in a region. The dynamics of unit oscillator are different correspondingly. When the parameters of unit oscillator are chosen near Hopf bifurcation point from period 1 rhythm to depolarized rest, the behaviors are either depolarized rest or period 1 rhythm. Synchronized period 1 rhythms are simulated in the deterministic network whose cells exhibit different rhythms when the coupling strength is increased. Considering the fact that the stochastic factors similar to noise is inevitable in the real cardiac cells, the network containing stochastic component are chosen to further simulate the cardiac cells in the experiment. The synchronous degree of rhythms of the cardiac cells is enhanced by increase of the coupling strength in the stochastic network. Under the influence of noise, the synchronous degree of rhythms is slightly decreased, and the synchronized phenomenon did not change, but the synchronized period 1 rhythm is changed into synchronized EAD rhythm.
The Hopf bifurcation point is the critical point from depolarized rest to period 1 rhythm. Under the influence of noise, the behavior of the network is stochastic transition between the depolarized rest and period 1 rhythm. It is the characteristics and dynamics of the EAD rhythm.
The above results indicate that EAD rhythm is the synchronized stochastic oscillation of cardiac myocytes or the network near a Hopf bifurcation point. When the behavior or parameters of the oscillator is far from the Hopf bifurcation, the synchronized network of cardiac myocytes is period 1 rhythm or rest. It shows that the heterogeneous network of cardiac myocytes has the capability to produce various synchronous rhythms by itself, including the "regular rhythm" (period 1 rhythm) and "abnormal rhythm" (EAD rhythm). The difference of the various rhythms is the parameters configuration of system, which can lead the system to transit between the different rhythms. The results provide novel understanding for the formation and transition of cardiac myocytes rhythm, and new way to prevent, diagnose and treat the arrhythmia induced by EAD.
引文
[1]Kowtha VC, Kunysz A, Clay JR, Glass L, Shrier A. Ionic mechanisms and nonlinear dynamics of embryonic chick heart cell aggregates[J]. Progress in Biophysics and Molecular Biology.1994,61(3):255-281.
[2]李澈.窦房结[M].北京：北京医科大学出版社,2001.
[3]姚泰.生理学[M].第五版.北京：人民卫生出版社,2002.
[4]Roden DM, Balser JR, George AL Jr, Anderson ME. Cardiac ion channels[J]. Annual Review of Physiology.2002(3),64:431-475.
[5]Chen PS, Joung B, Shinohara T, Das M, Chen Z, Lin SF. The initiation of the heart beat[J]. Circulation Journal.2010,74(2):221-225.
[6]Janse MJ. Electrophysiology of arrhythmias[J]. Archives des Maladies du Coeur et des Vaisseaux.1999,92(1):9-16.
[7]Verrier RL, Tan A. Heart rate, autonomic markers, and cardiac mortality[J], Heart Rhythm.2009,6(11):68-75.
[8]Burashnikov A, Antzelevitch C. Reinduction of atrial fibrillation immediately after termination of the arrhythmia is mediated by late phase 3 early afterdepolarization-induced triggered activity [J]. Circulation.2003, 107(18):2355-2360.
[9]Volders PG, Vos MA, Szabo B, Sipido KR, de Groot SH, Gorgels AP, Wellens HJ, Lazzara R. Progress in the understanding of cardiac early afterdepolarizations and torsades de pointes:time to revise current concepts[J]. Cardiovascular Research. 2000,46(3):376-392.
[10]El-Sherif N, Caref EB, Yin H, Restivo M. The electrophysiological mechanism of ventricular arrhythmias in the long QT syndrome[J]. Circulation Research.1996, 79:474-492.
[11]Clusin WT. Calcium and cardiac arrhythmias:DADs, EADs, and alternans[J]. Critical Reviews in Clinical Laboratory Sciences.2003,40(3):337-375.
[12]Burashnikov A, Antzelevitch C. Late-phase 3 EAD. A unique mechanism contributing to initiation of atrial fibrillation[J]. Pacing and Clinical Electrophysiology.2006,29(3):290-295.
[13]Pogwizd SM, Bers DM. Cellular basis of triggered arrhythmias in heart failure[J]. Trends in Cardiovascular Medicine.2004,14(2):61-66.
[14]Verkerk AO, Veldkamp MW. Ionic mechanism of delayed afterdepolarizations in ventricular cells isolated from human end-stage failing hearts[J]. Circulation. 2001,104(22):2728-2733.
[15]Verkerk AO, Veldkamp MW. Calcium-activated Cl- current contributes to delayed afterdepolarizations in single Purkinje and ventricular myocytes[J]. Circulation. 2000,101(22):2639-2644.
[16]Wit AL, Rosen MR. The heart and cardiovascular system[M]. New York:Raven Press,1992.
[17]Burashnikov A, Antzelevitch C. Acceleration-induced action potential prolongation and early afterdepolarizations[J]. Journal of Cardiovascular Electrophysiology.1998,9:934-948.
[18]Burashnikov A, Antzelevitch C. Prominent IKs in epicardium and endocardium contributes to development of transmural dispersion of repolarization but protects against development of early after-depolarizations[J]. Journal of Cardiovascular Electrophysiology.2002,13:172-177.
[19]李澈.窦房结[M].北京：北京医科大学出版社,2001.
[20]Burashnikov A, Antzelevitch C. Block of IKs does not induce early afterdepolarization activity but promotes P-adrenergic agonist-induced delayed afterdepolarization activity[J]. Journal of Cardiovascular Electrophysiology.2000, 11:458-465.
[21]Zeng J, Rudy Y. Early afterdepolarizations in cardiac myocytes:mechanism and rate dependence [J]. Biophysical Journal.1995,68(3):949-964.
[22]Hiraoka M, Sunami A, Fan Z, Sawanobori T. Multiple ionic mechanisms of early afterdepolarizations in isolated ventricular myocytes from guinea pig hearts [J]. Annals of the New York Academy of Sciences.1991,644:33-47.
[23]Marban E, Robinson SW, Wier WG. Mechanisms of arrhythmogenic delayed and early afterdepolarizations in ferret ventricular muscle[J]. Journal of Clinical Investigation.1986,78:1185-1192.
[24]Volders PG, Kulcsar A, Vos MA, Sipido KR, Wellens HJ, Lazzara R, Szabo B. Similarities between early and delayed afterdepolarizations induced by isoproterenol in canine ventricular myocytes[J]. Cardiovascular Research.1997, 34:348-359.
[25]Glass L, Mackey MC. From clocks to chaos, the rhythm of life[M]. Princeton:Princeton University Press,1988.
[26]Chay TR. Ering rate theory in excitable membranes:application to neuronal oscillations[J]. Journal of Physical Chemistry.1983,87:2935-2940.
[27]刘秉正.非线性动力学与混沌基础[M].长春：东北师范大学出版社,1995.
[28]Kuznetsov YA, Elements of applied bifurcation theory [M]. New York:Springer-Verlag,1995.
[29]高普云.非线性动力学-分叉、混沌与孤立子[M].长沙：国防科技大学出版社,2005.
[30]Izhikevich EM, Dynamical systems in neuroscience:The geometry of excitability and bursting[M]. Cambridge:The MIT Press,2005.
[31]Izhikevich EM. Neural excitability, spiking and bursting[J]. International Journal of Bifurcation and Chaos.2000,10(6):1-96.
[32]Glass L. Synchronization and rhythmic processes in physiology[J]. Nature.2001, 410:277-284.
[33]Boccaletti S, Kurths J, Osipov G, Valladares DL, Zhou CS. The synchronization of chaotic systems[J]. Physics Reports.2002,366(1-2):1-101.
[34]Wang QY, Lu QS. Phase synchronization in small world chaotic neural networks[J]. Chinese Physics Letters.2005,22(6):1329-1332.
[35]Steinmetz PN, Roy A, Fitzgerald PJ, Hsian SS, Johnson KO, Neibur E. Attention modulates synchronized neuronal firing in primate somatosensory cortex[J]. Nature.2000,404:187-190.
[36]Gray CM, Konig P, Engel AK, Singer W. Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties[J]. Nature.1989,338(6213):334-337.
[37]王海霞.神经元放电模式和同步的动力学研究[D].北京：北京航空航天大学,2006.
[38]Watts DJ, Strogatz SH. Collective dynamics of'small world' networks [J]. Nature. 1998,393:440-442.
[39]Anumonwo M, Wang HZ, Trabka-Janik E, Dunham B, Veenstra RD, Delmar M, Jalife J. Gap junctional channels in adult mammalian sinus nodal cells[J]. Circulation Research.1992,71:229-239.
[40]Panfilov AV. Spiral breakup in an array of coupled cells:the role of the intercellular conductance[J]. Physical Review Letters.2002,88:118101.
[41]Boyett MR, Honjo H, Kodam I.The sinoatrial node, a heterogeneous pacemaker structure[J]. Cardiovascular Research.2000,47(4):658-687.
[42]Boyett MR, Honjo H, Yamamoto M, Nikmaram MR, Niwa R, Kodama I. A downward gradient in action potential duration along the conduction path in and around the sinoatrial node[J]. American Journal of Physiology.1999, 276:686-698.
[43]Bub G, Shrier A, and Glass L. Global organization of dynamics in oscillatory heterogeneous excitable media[J]. Physical Review Letters.2005,94(2):028105.
[44]Bub G, Shrier A, Glass L. Spiral wave generation in heterogeneous excitable media [J]. Physical Review Letters.2002,88(5):058101.
[45]Kohl P. Heterogeneous cell coupling in the heart an electrophysiological role for fibroblasts[J]. Circulation Research.2003,93:381-383.
[46]Hodgkin AL, Huxley AF. A quantitative description of membrane current and its application to conduction and excitation in nerve[J]. The Journal of Physiology (London).1952,117:500-544.
[47]Morris C, Lecar H. Voltage oscillations in the barnacle giant muscle fiber[J]. Biophysical Journal.1981,35:193-213.
[48]Li YY, Zhang HM, Wei CL, Yang MH, Gu HG and Ren W. Stochastic signal induced multiple spatial coherence resonances and spiral waves in excitable media. Chinese Physics Letters.2009,26:030504.
[49]Tsumoto K, Kitajim H, Yoshinag T, Aihara K, Kawakami H. Bifurcations in Morris-Lecar neuron model[J]. Neurocomputing.2006,69:293-316.
[50]Tateno T, Pakdaman K. Random dynamics of the Morris-Lecar neural model[J]. Chaos.2004,14(3):511-530.
[51]Noble D. A modification of the Hodgkin-Huxley equations applicable to Purkinje fibre action and pacemaker potentials[J]. The Journal of Physiology (London). 1962,160:317-352.
[52]McAllister RE, Nobel D, Tsien RW. Reconstruction of the electrical activity of cardiac Purkinje fibres[J]. The Journal of Physiology (London).1975,251:1-59.
[53]Beeler G, Reuter H. Reconstruction of the action potential of ventricular myocardial fibres [J]. The Journal of Physiology (London).1977,268:177-210.
[54]DiFrancesco D, Noble D. A model of cardiac electrical activity incorporation ionic pumps and concentration changes[J]. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences.1985,307:353-398.
[55]Demir SS, Clark JW, Murphey CR. A mathematical model of a rabbit sinoatrial node cell[J]. American Journal of Physiology.1994,266(3):832-852.
[56]Zhang H, Holden AV, Kodama I, Honjo H, Lei M, Varghese T, Boyett MR. Mathematical models of action potentials in the periphery and center of the rabbit sinoatrial node[J]. American Journal of Physiology.2000,279:397-421.
[57]Luo CH, Rudy Y. A model of the ventricular cardiac action potential. depolarization, repolarization, and their interaction[J]. Circulation Research.1991, 68:1501-1526.
[58]Kanakov OI, Osipov GV, Chan CK, Kurths J. Cluster synchronization and spatio-temporal dynamics in networks of oscillatory and excitable Luo-Rudy cells[J]. Chaos.2007,17:015111-015119.
[59]Cai D, Lai YC, Winslow RL. Complex dynamics in coupled cardiac pacemaker cells[J]. Physical Review Letters.1993,71(15):2501-2504.
[60]刘志强,古华光,杨明浩,杨芬,范少光,任维.心肌细胞自发性搏动节律的分岔和混沌现[J].生物物理学报.2003,3：279-285.
[61]Ponard JG, Kondratyev AA, Kucera JP. Mechanisms of intrinsic beating variability in cardiac cell cultures and model pacemaker networks[J]. Biophysical Journal.2007,92:3734-3752.
[62]刘志强,古华光,杨明浩,李莉,刘红菊,范少光,任维.心肌细胞搏动的整数倍节律的实验观察[J].生物物理学报.2004,20(5)：355-362.
[63]刘红菊, 刘志强, 古华光, 杨明浩, 李莉, 任维.心肌单细胞兴奋模式转迁规律和转迁过程中延迟后去极化、早后去极化的生成[J].生物物理学报.2006,22(6)：441-448.
[64]刘红菊, 刘志强, 古华光, 杨明浩, 李莉, 任维.心肌单细胞兴奋模式转迁的非线性动力学机理[J].生物物理学报.2006,22(6)：489-454.
[65]刘志强,古华光,杨明浩,李莉,刘红菊,范少光,任维.心肌细胞团搏动整数倍节律的非线性动力学机制[J].生物物理学报.2004,20(5)：363-370.
[66]Kimura H, Oyamada Y, Ohshika H, Mori M, Oyamada M. Reversible inhibition of gap junctional intercellular communication, synchronous contraction, and synchronism of intracellular Ca2+fluctuation in cultured neonatal rat cardiac myocytes by heptanol[J]. Experimental Cell Research.1995,220(2):348-356.
[67]Anumonwo J, Tallini YN, Vetter FJ, Jalife J. Action potential characteristics and arrhythmogenic properties of the cardiac conduction system of the murine heart[J]. Circulation Research.2001,89:329-335.
[68]Cai D, Winslow RL, Noble D. Effects of gap junction conductance on dynamics of sinoatrial node cells two cell and large scale network models[J]. IEEE Transctions On Bio-Medical Engineering.1994,41:217-231.
[69]Boccaletti S, Kurths J, Osipov G. The synchronization of chaotic systems [J]. Physics Reports.2002,366:1-101.
[70]王青云.耦合神经元的同步和时滞影响的动力学研究[D].北京：北京航空航天大学,2006.
[71]Yamauchi Y, Harada A, Kawahara K. Changes in the fluctuation of interbeat intervals in spontaneously beating cultured cardiac myocytes:experimental and modeling studies[J]. Biological Cybernetics.2002,86(2):147-154.
[72]Winslow RL, Cai D, Varghese A, Lai Y. Generation and propagation of normal and abnormal pacemaker activity in network models of cardiac sinus node and atrium[J]. Chaos, Solitons and Fractals.1995,5(3-4):491-512.
[73]G.priori著,刘文玲译.心脏性猝死临床实践手册[M].北京：人民卫生出版社,2007.
[2]李澈.窦房结[M].北京：北京医科大学出版社,2001.
[3]姚泰.生理学[M].第五版.北京：人民卫生出版社,2002.
[4]Roden DM, Balser JR, George AL Jr, Anderson ME. Cardiac ion channels[J]. Annual Review of Physiology.2002(3),64:431-475.
[5]Chen PS, Joung B, Shinohara T, Das M, Chen Z, Lin SF. The initiation of the heart beat[J]. Circulation Journal.2010,74(2):221-225.
[6]Janse MJ. Electrophysiology of arrhythmias[J]. Archives des Maladies du Coeur et des Vaisseaux.1999,92(1):9-16.
[7]Verrier RL, Tan A. Heart rate, autonomic markers, and cardiac mortality[J], Heart Rhythm.2009,6(11):68-75.
[8]Burashnikov A, Antzelevitch C. Reinduction of atrial fibrillation immediately after termination of the arrhythmia is mediated by late phase 3 early afterdepolarization-induced triggered activity [J]. Circulation.2003, 107(18):2355-2360.
[9]Volders PG, Vos MA, Szabo B, Sipido KR, de Groot SH, Gorgels AP, Wellens HJ, Lazzara R. Progress in the understanding of cardiac early afterdepolarizations and torsades de pointes:time to revise current concepts[J]. Cardiovascular Research. 2000,46(3):376-392.
[10]El-Sherif N, Caref EB, Yin H, Restivo M. The electrophysiological mechanism of ventricular arrhythmias in the long QT syndrome[J]. Circulation Research.1996, 79:474-492.
[11]Clusin WT. Calcium and cardiac arrhythmias:DADs, EADs, and alternans[J]. Critical Reviews in Clinical Laboratory Sciences.2003,40(3):337-375.
[12]Burashnikov A, Antzelevitch C. Late-phase 3 EAD. A unique mechanism contributing to initiation of atrial fibrillation[J]. Pacing and Clinical Electrophysiology.2006,29(3):290-295.
[13]Pogwizd SM, Bers DM. Cellular basis of triggered arrhythmias in heart failure[J]. Trends in Cardiovascular Medicine.2004,14(2):61-66.
[14]Verkerk AO, Veldkamp MW. Ionic mechanism of delayed afterdepolarizations in ventricular cells isolated from human end-stage failing hearts[J]. Circulation. 2001,104(22):2728-2733.
[15]Verkerk AO, Veldkamp MW. Calcium-activated Cl- current contributes to delayed afterdepolarizations in single Purkinje and ventricular myocytes[J]. Circulation. 2000,101(22):2639-2644.
[16]Wit AL, Rosen MR. The heart and cardiovascular system[M]. New York:Raven Press,1992.
[17]Burashnikov A, Antzelevitch C. Acceleration-induced action potential prolongation and early afterdepolarizations[J]. Journal of Cardiovascular Electrophysiology.1998,9:934-948.
[18]Burashnikov A, Antzelevitch C. Prominent IKs in epicardium and endocardium contributes to development of transmural dispersion of repolarization but protects against development of early after-depolarizations[J]. Journal of Cardiovascular Electrophysiology.2002,13:172-177.
[19]李澈.窦房结[M].北京：北京医科大学出版社,2001.
[20]Burashnikov A, Antzelevitch C. Block of IKs does not induce early afterdepolarization activity but promotes P-adrenergic agonist-induced delayed afterdepolarization activity[J]. Journal of Cardiovascular Electrophysiology.2000, 11:458-465.
[21]Zeng J, Rudy Y. Early afterdepolarizations in cardiac myocytes:mechanism and rate dependence [J]. Biophysical Journal.1995,68(3):949-964.
[22]Hiraoka M, Sunami A, Fan Z, Sawanobori T. Multiple ionic mechanisms of early afterdepolarizations in isolated ventricular myocytes from guinea pig hearts [J]. Annals of the New York Academy of Sciences.1991,644:33-47.
[23]Marban E, Robinson SW, Wier WG. Mechanisms of arrhythmogenic delayed and early afterdepolarizations in ferret ventricular muscle[J]. Journal of Clinical Investigation.1986,78:1185-1192.
[24]Volders PG, Kulcsar A, Vos MA, Sipido KR, Wellens HJ, Lazzara R, Szabo B. Similarities between early and delayed afterdepolarizations induced by isoproterenol in canine ventricular myocytes[J]. Cardiovascular Research.1997, 34:348-359.
[25]Glass L, Mackey MC. From clocks to chaos, the rhythm of life[M]. Princeton:Princeton University Press,1988.
[26]Chay TR. Ering rate theory in excitable membranes:application to neuronal oscillations[J]. Journal of Physical Chemistry.1983,87:2935-2940.
[27]刘秉正.非线性动力学与混沌基础[M].长春：东北师范大学出版社,1995.
[28]Kuznetsov YA, Elements of applied bifurcation theory [M]. New York:Springer-Verlag,1995.
[29]高普云.非线性动力学-分叉、混沌与孤立子[M].长沙：国防科技大学出版社,2005.
[30]Izhikevich EM, Dynamical systems in neuroscience:The geometry of excitability and bursting[M]. Cambridge:The MIT Press,2005.
[31]Izhikevich EM. Neural excitability, spiking and bursting[J]. International Journal of Bifurcation and Chaos.2000,10(6):1-96.
[32]Glass L. Synchronization and rhythmic processes in physiology[J]. Nature.2001, 410:277-284.
[33]Boccaletti S, Kurths J, Osipov G, Valladares DL, Zhou CS. The synchronization of chaotic systems[J]. Physics Reports.2002,366(1-2):1-101.
[34]Wang QY, Lu QS. Phase synchronization in small world chaotic neural networks[J]. Chinese Physics Letters.2005,22(6):1329-1332.
[35]Steinmetz PN, Roy A, Fitzgerald PJ, Hsian SS, Johnson KO, Neibur E. Attention modulates synchronized neuronal firing in primate somatosensory cortex[J]. Nature.2000,404:187-190.
[36]Gray CM, Konig P, Engel AK, Singer W. Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties[J]. Nature.1989,338(6213):334-337.
[37]王海霞.神经元放电模式和同步的动力学研究[D].北京：北京航空航天大学,2006.
[38]Watts DJ, Strogatz SH. Collective dynamics of'small world' networks [J]. Nature. 1998,393:440-442.
[39]Anumonwo M, Wang HZ, Trabka-Janik E, Dunham B, Veenstra RD, Delmar M, Jalife J. Gap junctional channels in adult mammalian sinus nodal cells[J]. Circulation Research.1992,71:229-239.
[40]Panfilov AV. Spiral breakup in an array of coupled cells:the role of the intercellular conductance[J]. Physical Review Letters.2002,88:118101.
[41]Boyett MR, Honjo H, Kodam I.The sinoatrial node, a heterogeneous pacemaker structure[J]. Cardiovascular Research.2000,47(4):658-687.
[42]Boyett MR, Honjo H, Yamamoto M, Nikmaram MR, Niwa R, Kodama I. A downward gradient in action potential duration along the conduction path in and around the sinoatrial node[J]. American Journal of Physiology.1999, 276:686-698.
[43]Bub G, Shrier A, and Glass L. Global organization of dynamics in oscillatory heterogeneous excitable media[J]. Physical Review Letters.2005,94(2):028105.
[44]Bub G, Shrier A, Glass L. Spiral wave generation in heterogeneous excitable media [J]. Physical Review Letters.2002,88(5):058101.
[45]Kohl P. Heterogeneous cell coupling in the heart an electrophysiological role for fibroblasts[J]. Circulation Research.2003,93:381-383.
[46]Hodgkin AL, Huxley AF. A quantitative description of membrane current and its application to conduction and excitation in nerve[J]. The Journal of Physiology (London).1952,117:500-544.
[47]Morris C, Lecar H. Voltage oscillations in the barnacle giant muscle fiber[J]. Biophysical Journal.1981,35:193-213.
[48]Li YY, Zhang HM, Wei CL, Yang MH, Gu HG and Ren W. Stochastic signal induced multiple spatial coherence resonances and spiral waves in excitable media. Chinese Physics Letters.2009,26:030504.
[49]Tsumoto K, Kitajim H, Yoshinag T, Aihara K, Kawakami H. Bifurcations in Morris-Lecar neuron model[J]. Neurocomputing.2006,69:293-316.
[50]Tateno T, Pakdaman K. Random dynamics of the Morris-Lecar neural model[J]. Chaos.2004,14(3):511-530.
[51]Noble D. A modification of the Hodgkin-Huxley equations applicable to Purkinje fibre action and pacemaker potentials[J]. The Journal of Physiology (London). 1962,160:317-352.
[52]McAllister RE, Nobel D, Tsien RW. Reconstruction of the electrical activity of cardiac Purkinje fibres[J]. The Journal of Physiology (London).1975,251:1-59.
[53]Beeler G, Reuter H. Reconstruction of the action potential of ventricular myocardial fibres [J]. The Journal of Physiology (London).1977,268:177-210.
[54]DiFrancesco D, Noble D. A model of cardiac electrical activity incorporation ionic pumps and concentration changes[J]. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences.1985,307:353-398.
[55]Demir SS, Clark JW, Murphey CR. A mathematical model of a rabbit sinoatrial node cell[J]. American Journal of Physiology.1994,266(3):832-852.
[56]Zhang H, Holden AV, Kodama I, Honjo H, Lei M, Varghese T, Boyett MR. Mathematical models of action potentials in the periphery and center of the rabbit sinoatrial node[J]. American Journal of Physiology.2000,279:397-421.
[57]Luo CH, Rudy Y. A model of the ventricular cardiac action potential. depolarization, repolarization, and their interaction[J]. Circulation Research.1991, 68:1501-1526.
[58]Kanakov OI, Osipov GV, Chan CK, Kurths J. Cluster synchronization and spatio-temporal dynamics in networks of oscillatory and excitable Luo-Rudy cells[J]. Chaos.2007,17:015111-015119.
[59]Cai D, Lai YC, Winslow RL. Complex dynamics in coupled cardiac pacemaker cells[J]. Physical Review Letters.1993,71(15):2501-2504.
[60]刘志强,古华光,杨明浩,杨芬,范少光,任维.心肌细胞自发性搏动节律的分岔和混沌现[J].生物物理学报.2003,3：279-285.
[61]Ponard JG, Kondratyev AA, Kucera JP. Mechanisms of intrinsic beating variability in cardiac cell cultures and model pacemaker networks[J]. Biophysical Journal.2007,92:3734-3752.
[62]刘志强,古华光,杨明浩,李莉,刘红菊,范少光,任维.心肌细胞搏动的整数倍节律的实验观察[J].生物物理学报.2004,20(5)：355-362.
[63]刘红菊, 刘志强, 古华光, 杨明浩, 李莉, 任维.心肌单细胞兴奋模式转迁规律和转迁过程中延迟后去极化、早后去极化的生成[J].生物物理学报.2006,22(6)：441-448.
[64]刘红菊, 刘志强, 古华光, 杨明浩, 李莉, 任维.心肌单细胞兴奋模式转迁的非线性动力学机理[J].生物物理学报.2006,22(6)：489-454.
[65]刘志强,古华光,杨明浩,李莉,刘红菊,范少光,任维.心肌细胞团搏动整数倍节律的非线性动力学机制[J].生物物理学报.2004,20(5)：363-370.
[66]Kimura H, Oyamada Y, Ohshika H, Mori M, Oyamada M. Reversible inhibition of gap junctional intercellular communication, synchronous contraction, and synchronism of intracellular Ca2+fluctuation in cultured neonatal rat cardiac myocytes by heptanol[J]. Experimental Cell Research.1995,220(2):348-356.
[67]Anumonwo J, Tallini YN, Vetter FJ, Jalife J. Action potential characteristics and arrhythmogenic properties of the cardiac conduction system of the murine heart[J]. Circulation Research.2001,89:329-335.
[68]Cai D, Winslow RL, Noble D. Effects of gap junction conductance on dynamics of sinoatrial node cells two cell and large scale network models[J]. IEEE Transctions On Bio-Medical Engineering.1994,41:217-231.
[69]Boccaletti S, Kurths J, Osipov G. The synchronization of chaotic systems [J]. Physics Reports.2002,366:1-101.
[70]王青云.耦合神经元的同步和时滞影响的动力学研究[D].北京：北京航空航天大学,2006.
[71]Yamauchi Y, Harada A, Kawahara K. Changes in the fluctuation of interbeat intervals in spontaneously beating cultured cardiac myocytes:experimental and modeling studies[J]. Biological Cybernetics.2002,86(2):147-154.
[72]Winslow RL, Cai D, Varghese A, Lai Y. Generation and propagation of normal and abnormal pacemaker activity in network models of cardiac sinus node and atrium[J]. Chaos, Solitons and Fractals.1995,5(3-4):491-512.
[73]G.priori著,刘文玲译.心脏性猝死临床实践手册[M].北京：人民卫生出版社,2007.