心肌缺血和心衰机制的建模仿真研究
|
摘要
心血管疾病已经成为威胁人类健康和生命的一大杀手。常见的心脏疾病如心肌缺血(Myocardial Ischemia)、心衰(Heart Failure)会导致心脏的收缩和舒张功能受损,无法保证心脏活动的正常运行,进而影响身体的新陈代谢。相对收缩舒张带来的损害,心律失常带来的损害更加突然、不可预料和致命。心脏是一个局部异质的组织,不同的地方其电生理特性并不相同,但是发生病变之后这些固有的透壁异质特性会改变并常常使差异加大,从而诱发折返等心律失常。因此,找出支撑透壁异质特性的离子电流基础对治疗心脏疾病更加重要。
心肌系统是一个很多成分相互作用的生理系统,由于实验技术发展水平的限制,目前实验方法对一些现象的背后机制都缺乏有效地研究。相对于实验方法,计算机模型由于可以独立控制各个成分,成为了辅助实验研究疾病机制的一种重要工具。
本论文立足于根据实验数据建立的能重现心脏活动特征的计算机模型,利用模型发现疾病机制,尝试更有效直接的治疗方案。内容有以下几个方面。
1)心肌缺血机制的模型研究
仿真了心肌缺血过程中的高血钾、缺氧症和多酸症对心肌细胞动作电位的影响；根据实验数据重现了细胞透壁异质的电生理特征和力学特征；仿真了心肌缺血发生之后透壁异质细胞的选择性重建以及准心电图对应的变化。
2)心衰机制的模型研究
基于狗心室肌细胞的实验数据,构建了一个新的心室肌细胞模型。利用此模型仿真了发生心衰时伴有的动作电位延长、钙瞬态幅度降低、钠离子浓度升高以及alternans发生阈值降低等现象。采用定量分析的方法,我们发现了动作电位的延长主要是由钾电流的减少表达引起的,CaMKⅡ尽管影响了动作电位的形态,但是并没有改变动作电位长度；减少的基质网钙泵蛋白质表达在CaMKⅡ的调节作用下,对钙瞬态的影响并不是特别大,而增大的泄露电流则对降低的钙瞬态影响很大；增大的晚期钠电流自己并不能充分解释细胞内钠离子的上升幅度,应该考虑其他的因素；CaMKⅡ导致基质网释放电流和基质网内钙离子含量的关系变得更加的非线性陡峭,使alternans更容易发生；CaMKⅡ部分抑制结合基质网泄露电流的阻断有可能成为新的治疗心衰目标。
3)透壁心肌层异质特性的研究
瞬间外向钾电流对于动作电位长度的作用一直存在争议,长期以来实验上缺乏有效的瞬间外向钾电流特异性阻断剂使其作用更难以估计。我们基于模型发现瞬间外向钾电流并不会影响动作电位的长度；透壁分布的钠钾泵电流则对动作电位的透壁异质产生了明显的影响,同时钠钾泵电流对细胞内的钙瞬态影响特别大；透壁分布的钙离子和钠离子浓度可以造成透壁分布的钠钙交换电流,这解释了为什么实验测得的透壁钠钙交换电流的调控蛋白质密度均质而电流却异质。结合实验数据,我们构建了一个细胞平台,包含心外膜细胞、中间层细胞和心内膜细胞。我们成功仿真出中间层细胞更容易被诱发早后去极化(Early after depolarization,EAD),其根本原因在于中间层细胞拥有较长的动作电位平台期。这个平台可以很好的用来研究病态下电流的选择性重建以及不同的药物学反应。
4)心肌纤维动力学仿真
重现了实验上的前载荷-后载荷实验协议,仿真出了心脏工作的五个周期,充盈期、等容收缩期、射血期、等容舒张期以及等张舒张期。为将来的力学仿真提供了一个工具平台。
Cardiovascular diseases have become the killer to people's health and life. Common cardiovascular diseases such as myocardial ischemia and heart failure will damage the contraction-relaxation dynamics, which further affects the metabolism. Relative to the damage by disturbed cardiac mechanics, cardiac arrhythmias is more fatal because of its sudden and unexpected occurrence. Heart is a transmural heterogeneous tissue, with different properties in local regions. After cardiac disease, the transmural heterogeneous electrical properties will be selectively remodeled. The selective remodeling exaggerates the transmural action potential difference, proving the basis for cardiac arrhythmias like reentry. Therefore, it is really necessary for us to examine the ionic basis underlying the transmural heterogeneous electrical properties.
Cardiac myocyte is a biological system with many components interacting with each other. Due to their bi-directional coupling and the present level of experimental methods, it is difficult for researchers to explore the underlying mechanisms of some diseases. By using computer models, we can change the components in isolation, which has become an important tool to find the disease mechanisms.
In this thesis, based on experimental data, we developed cardiac models which can recreate the properties of cardiac dynamics. The models can be used to find the disease mechanisms and optimize the strategy to cure patients with cardiac diseases. It includes the following parts:
1) Investigating the mechanism of myocardial ischemia
The hyperkalemia, anoxia and acidosis of myocardial ischemia have been implemented to simulate their role in the shortened action potential duration. According to experimental data, the transmural heterogeneous electrical and mechanical properties of cardiac cells have been recreated. The selective changes of transmural distributed cardiac myocytes and ECG alterations after myocardial ischemia are simulated.
2) Theoretically investigating the mechanism of heart failure
Based on the available canine ventricular cell data, we developed a new canine ventricular cell model. The prolonged action potential, decreased Ca2+transient, Na+elevation and the alternans phenomenon are simulated. By quantitative analysis,we come to the following conclusions: Although CaMKⅡ affects the AP profile, it does not contribute to APD prolongation. The prolonged APD is caused by the down-regulation of K currents. The down-regulated SERCA protein plays a little role in decreased Ca2+transient due to the enhaced role of CaMKⅡ and prolonged APD. In contrary, increased SR Ca2+leak current makes a big contribution to the decreased Ca2+transient. Other Na+elevation factors should be considered because enhanced late Na+current alone could not account for the degree of Na+elevation. The enhanced CaMKⅡ makes the fractional SR Ca2+release more steepened, which facilitates the occurrence of alternans. Partial CaMKII inhibition combined with SR Ca2+leak current blockade may be a new way to cure patients with HF.
3) The ionic basis of transmural heterogeneous electrical properties and their different responsiveness to drugs
The contribution of the transient outward potassium current to ventricular repolarization has been controversial. It is difficult for experiments to identify its exact role because there is lack of selective Ito blockers. By computer models, we can find that Ito has little effect on canine ventricular repolarization in the physiological range. Transmural distributed Na+/K+pump current affects both the transmural APD dispersion and the regional Ca2+transients. Transmural heterogeneous Ca2+transient and Na+forms a different chemical gradient for local NCX. That accounts for why NCX is transmural different while the NCX protein is homogeneously distributed. According to experimental data, we have constructed a platform consisted of epicardial, midmyocardial and endocardial cells. We have simulated the easier EADs in the midmyocardial cells compared with epicardial and endocardial cells in response to AP prolonged factors such as E-4031. The essential underlying mechanism is the long plateau phase for midmyocardial cells. This platform could be used as a tool to study the selective remodeling and different responsiveness to drugs.
4) Cardiac fiber mechanics simulation
Cardiac fiber mechanics has been simulated to recreate the preload-afterload experiment. The five phases of cardiac work including filling, isovolumetric contraction, ejection, isovolumetric relaxation and isotonic relaxation are simulated. It provides a platform for the future cardiac mechanics simulation to test the effect of cardiac diseases.
心肌系统是一个很多成分相互作用的生理系统,由于实验技术发展水平的限制,目前实验方法对一些现象的背后机制都缺乏有效地研究。相对于实验方法,计算机模型由于可以独立控制各个成分,成为了辅助实验研究疾病机制的一种重要工具。
本论文立足于根据实验数据建立的能重现心脏活动特征的计算机模型,利用模型发现疾病机制,尝试更有效直接的治疗方案。内容有以下几个方面。
1)心肌缺血机制的模型研究
仿真了心肌缺血过程中的高血钾、缺氧症和多酸症对心肌细胞动作电位的影响；根据实验数据重现了细胞透壁异质的电生理特征和力学特征；仿真了心肌缺血发生之后透壁异质细胞的选择性重建以及准心电图对应的变化。
2)心衰机制的模型研究
基于狗心室肌细胞的实验数据,构建了一个新的心室肌细胞模型。利用此模型仿真了发生心衰时伴有的动作电位延长、钙瞬态幅度降低、钠离子浓度升高以及alternans发生阈值降低等现象。采用定量分析的方法,我们发现了动作电位的延长主要是由钾电流的减少表达引起的,CaMKⅡ尽管影响了动作电位的形态,但是并没有改变动作电位长度；减少的基质网钙泵蛋白质表达在CaMKⅡ的调节作用下,对钙瞬态的影响并不是特别大,而增大的泄露电流则对降低的钙瞬态影响很大；增大的晚期钠电流自己并不能充分解释细胞内钠离子的上升幅度,应该考虑其他的因素；CaMKⅡ导致基质网释放电流和基质网内钙离子含量的关系变得更加的非线性陡峭,使alternans更容易发生；CaMKⅡ部分抑制结合基质网泄露电流的阻断有可能成为新的治疗心衰目标。
3)透壁心肌层异质特性的研究
瞬间外向钾电流对于动作电位长度的作用一直存在争议,长期以来实验上缺乏有效的瞬间外向钾电流特异性阻断剂使其作用更难以估计。我们基于模型发现瞬间外向钾电流并不会影响动作电位的长度；透壁分布的钠钾泵电流则对动作电位的透壁异质产生了明显的影响,同时钠钾泵电流对细胞内的钙瞬态影响特别大；透壁分布的钙离子和钠离子浓度可以造成透壁分布的钠钙交换电流,这解释了为什么实验测得的透壁钠钙交换电流的调控蛋白质密度均质而电流却异质。结合实验数据,我们构建了一个细胞平台,包含心外膜细胞、中间层细胞和心内膜细胞。我们成功仿真出中间层细胞更容易被诱发早后去极化(Early after depolarization,EAD),其根本原因在于中间层细胞拥有较长的动作电位平台期。这个平台可以很好的用来研究病态下电流的选择性重建以及不同的药物学反应。
4)心肌纤维动力学仿真
重现了实验上的前载荷-后载荷实验协议,仿真出了心脏工作的五个周期,充盈期、等容收缩期、射血期、等容舒张期以及等张舒张期。为将来的力学仿真提供了一个工具平台。
Cardiovascular diseases have become the killer to people's health and life. Common cardiovascular diseases such as myocardial ischemia and heart failure will damage the contraction-relaxation dynamics, which further affects the metabolism. Relative to the damage by disturbed cardiac mechanics, cardiac arrhythmias is more fatal because of its sudden and unexpected occurrence. Heart is a transmural heterogeneous tissue, with different properties in local regions. After cardiac disease, the transmural heterogeneous electrical properties will be selectively remodeled. The selective remodeling exaggerates the transmural action potential difference, proving the basis for cardiac arrhythmias like reentry. Therefore, it is really necessary for us to examine the ionic basis underlying the transmural heterogeneous electrical properties.
Cardiac myocyte is a biological system with many components interacting with each other. Due to their bi-directional coupling and the present level of experimental methods, it is difficult for researchers to explore the underlying mechanisms of some diseases. By using computer models, we can change the components in isolation, which has become an important tool to find the disease mechanisms.
In this thesis, based on experimental data, we developed cardiac models which can recreate the properties of cardiac dynamics. The models can be used to find the disease mechanisms and optimize the strategy to cure patients with cardiac diseases. It includes the following parts:
1) Investigating the mechanism of myocardial ischemia
The hyperkalemia, anoxia and acidosis of myocardial ischemia have been implemented to simulate their role in the shortened action potential duration. According to experimental data, the transmural heterogeneous electrical and mechanical properties of cardiac cells have been recreated. The selective changes of transmural distributed cardiac myocytes and ECG alterations after myocardial ischemia are simulated.
2) Theoretically investigating the mechanism of heart failure
Based on the available canine ventricular cell data, we developed a new canine ventricular cell model. The prolonged action potential, decreased Ca2+transient, Na+elevation and the alternans phenomenon are simulated. By quantitative analysis,we come to the following conclusions: Although CaMKⅡ affects the AP profile, it does not contribute to APD prolongation. The prolonged APD is caused by the down-regulation of K currents. The down-regulated SERCA protein plays a little role in decreased Ca2+transient due to the enhaced role of CaMKⅡ and prolonged APD. In contrary, increased SR Ca2+leak current makes a big contribution to the decreased Ca2+transient. Other Na+elevation factors should be considered because enhanced late Na+current alone could not account for the degree of Na+elevation. The enhanced CaMKⅡ makes the fractional SR Ca2+release more steepened, which facilitates the occurrence of alternans. Partial CaMKII inhibition combined with SR Ca2+leak current blockade may be a new way to cure patients with HF.
3) The ionic basis of transmural heterogeneous electrical properties and their different responsiveness to drugs
The contribution of the transient outward potassium current to ventricular repolarization has been controversial. It is difficult for experiments to identify its exact role because there is lack of selective Ito blockers. By computer models, we can find that Ito has little effect on canine ventricular repolarization in the physiological range. Transmural distributed Na+/K+pump current affects both the transmural APD dispersion and the regional Ca2+transients. Transmural heterogeneous Ca2+transient and Na+forms a different chemical gradient for local NCX. That accounts for why NCX is transmural different while the NCX protein is homogeneously distributed. According to experimental data, we have constructed a platform consisted of epicardial, midmyocardial and endocardial cells. We have simulated the easier EADs in the midmyocardial cells compared with epicardial and endocardial cells in response to AP prolonged factors such as E-4031. The essential underlying mechanism is the long plateau phase for midmyocardial cells. This platform could be used as a tool to study the selective remodeling and different responsiveness to drugs.
4) Cardiac fiber mechanics simulation
Cardiac fiber mechanics has been simulated to recreate the preload-afterload experiment. The five phases of cardiac work including filling, isovolumetric contraction, ejection, isovolumetric relaxation and isotonic relaxation are simulated. It provides a platform for the future cardiac mechanics simulation to test the effect of cardiac diseases.
引文
[1]http://enwikipediaorg/wiki/Circulatory_system.
[2]Hodgkin AL, Huxley AF. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol.1952;117:500-44.
[3]Cheng H, Lederer WJ, Cannell MB. Calcium sparks:elementary events underlying excitation-contraction coupling in heart muscle. Science.1993;262:740-4.
[4]Izu LT, Mauban JR, Balke CW, Wier WG.Large currents generate cardiac Ca2+ sparks. Biophys J.2001;80:88-102.
[5]Lu L, Xia L, Ye X, Cheng H. Simulation of the effect of rogue ryanodine receptors on a calcium wave in ventricular myocytes with heart failure. Phys Biol. 2010;7:026005.
[6]Gaur N, Rudy Y. Multiscale modeling of calcium cycling in cardiac ventricular myocyte:macroscopic consequences of microscopic dyadic function. Biophys J. 2011;100:2904-12.
[7]Sobie EA, Dilly KW, dos Santos Cruz J, Lederer WJ, Jafri MS. Termination of cardiac Ca(2+) sparks:an investigative mathematical model of calcium-induced calcium release. Biophys J.2002;83:59-78.
[8]Li Q, O'Neill SC, Tao T, Li Y, Eisner D, Zhang H. Mechanisms by which cytoplasmic calcium wave propagation and alternans are generated in cardiac atrial myocytes lacking T-tubules-insights from a simulation study. Biophys J. 2012; 102:1471-82.
[9]Tveito A, Lines GT, Edwards AG, Maleckar MM, Michailova A, Hake J, et al. Slow Calcium-Depolarization-Calcium waves may initiate fast local depolarization waves in ventricular tissue. Prog Biophys Mol Biol.2012;110:295-304.
[10]Swietach P, Spitzer KW, Vaughan-Jones RD. Modeling calcium waves in cardiac myocytes:importance of calcium diffusion. Front Biosci.2010;15:661-80.
[11]Noble D. A modification of the Hodgkin--Huxley equations applicable to Purkinje fibre action and pace-maker potentials. J Physiol.1962; 160:317-52.
[12]McAllister RE, Noble D, Tsien RW. Reconstruction of the electrical activity of cardiac Purkinje fibres. J Physiol.1975;251:1-59.
[13]Beeler GW, Reuter H. Reconstruction of the action potential of ventricular myocardial fibres. J Physiol.1977;268:177-210.
[14]Bristow DG, Clark JW. A mathematical model of primary pacemaking cell in SA node of the heart. Am J Physiol.1982;243:H207-18.
[15]Noble D, Noble SJ. A model of sino-atrial node electrical activity based on a modification of the DiFrancesco-Noble (1984) equations. Proc R Soc Lond B Biol Sci. 1984;222:295-304.
[16]DiFrancesco D, Noble D. A model of cardiac electrical activity incorporating ionic pumps and concentration changes. Philos Trans R Soc Lond B Biol Sci. 1985;307:353-98.
[17]Luo CH, Rudy Y. A model of the ventricular cardiac action potential. Depolarization, repolarization, and their interaction. Circ Res.1991;68:1501-26.
[18]Luo CH, Rudy Y. A dynamic model of the cardiac ventricular action potential. I. Simulations of ionic currents and concentration changes. Circ Res.1994;74:1071-96.
[19]Courtemanche M, Ramirez RJ, Nattel S. Ionic mechanisms underlying human atrial action potential properties:insights from a mathematical model. Am J Physiol. 1998;275:H301-21.
[20]Nygren A, Fiset C, Firek L, Clark JW, Lindblad DS, Clark RB, et al. Mathematical model of an adult human atrial cell:the role of K+ currents in repolarization. Circ Res.1998;82:63-81.
[21]Jafri MS, Rice JJ, Winslow RL. Cardiac Ca2+ dynamics:the roles of ryanodine receptor adaptation and sarcoplasmic reticulum load. Biophys J.1998;74:1149-68.
[22]Priebe L, Beuckelmann DJ. Simulation study of cellular electric properties in heart failure. Circ Res.1998;82:1206-23.
[23]Winslow RL, Rice J, Jafri S, Marban E, O'Rourke B. Mechanisms of altered excitation-contraction coupling in canine tachycardia-induced heart failure, Ⅱ:model studies. Circ Res.1999;84:571-86.
[24]Ramirez RJ, Nattel S, Courtemanche M. Mathematical analysis of canine atrial action potentials:rate, regional factors, and electrical remodeling. Am J Physiol Heart Circ Physiol.2000;279:H1767-85.
[25]Zhang H, Holden AV, Kodama I, Honjo H, Lei M, Varghese T, et al. Mathematical models of action potentials in the periphery and center of the rabbit sinoatrial node. Am J Physiol Heart Circ Physiol.2000;279:H397-421.
[26]Pandit SV, Clark RB, Giles WR, Demir SS. A mathematical model of action potential heterogeneity in adult rat left ventricular myocytes. Biophys J. 2001;81:3029-51.
[27]Puglisi JL, Bers DM. LabHEART:an interactive computer model of rabbit ventricular myocyte ion channels and Ca transport. Am J Physiol Cell Physiol. 2001;281:C2049-60.
[28]Bernus O, Wilders R, Zemlin CW, Verschelde H, Panfilov AV. A computationally efficient electrophysiological model of human ventricular cells. Am J Physiol Heart Circ Physiol.2002;282:H2296-308.
[29]ten Tusscher KH, Noble D, Noble PJ, Panfilov AV. A model for human ventricular tissue. Am J Physiol Heart Circ Physiol.2004;286:H1573-89.
[30]Iyer V, Mazhari R, Winslow RL. A computational model of the human left-ventricular epicardial myocyte. Biophys J.2004;87:1507-25.
[31]Hund TJ, Rudy Y. Rate dependence and regulation of action potential and calcium transient in a canine cardiac ventricular cell model. Circulation. 2004; 110:3168-74.
[32]Greenstein JL, Hinch R, Winslow RL. Mechanisms of excitation-contraction coupling in an integrative model of the cardiac ventricular myocyte. Biophys J. 2006;90:77-91.
[33]Grandi E, Pasqualini FS, Bers DM. A novel computational model of the human ventricular action potential and Ca transient. J Mol Cell Cardiol.2010;48:112-21.
[34]Inada S, Hancox JC, Zhang H, Boyett MR. One-dimensional mathematical model of the atrioventricular node including atrio-nodal, nodal, and nodal-his cells. Biophys J.2009;97:2117-27.
[35]Maleckar MM, Greenstein JL, Trayanova NA, Giles WR. Mathematical simulations of ligand-gated and cell-type specific effects on the action potential of human atrium. Prog Biophys Mol Biol.2008;98:161-70.
[36]Xia L, Gong YL, Zhu XW, Zhang Y, Sun Q, Zhang HG Mathematical models of canine right and left atria cardiomyocytes. J Zhejiang Univ Sci B.2010; 11:402-16.
[37]Koivumaki JT, Korhonen T, Tavi P. Impact of sarcoplasmic reticulum calcium release on calcium dynamics and action potential morphology in human atrial myocytes:a computational study. PLoS Comput Biol.2011;7:e1001067.
[38]O'Hara T, Virag L, Varro A, Rudy Y. Simulation of the undiseased human cardiac ventricular action potential:model formulation and experimental validation. PLoS Comput Biol.2011;7:e 1002061.
[39]Grandi E, Pandit SV, Voigt N, Workman AJ, Dobrev D, Jalife J, et al. Human atrial action potential and Ca2+ model:sinus rhythm and chronic atrial fibrillation. Circ Res.2011;109:1055-66.
[40]Heijman J, Volders PG, Westra RL, Rudy Y. Local control of beta-adrenergic stimulation:Effects on ventricular myocyte electrophysiology and Ca(2+)-transient. J Mol Cell Cardiol.2011;50:863-71.
[41]Zang Y, Dai L, Zhan H, Dou J, Xia L, Zhang H. Theoretical investigation of the mechanism of heart failure using a canine ventricular cell model:Especially the role of up-regulated CaMKII and SR Ca(2+) leak. J Mol Cell Cardiol.2013;56:34-43.
[42]Hill AV. The Heat of Shortening and the Dynamic Constants of Muscle. Proceedings of the Royal Society of London Series B-Biological Sciences. 1938;126:136-95.
[43]Huxley AF. Muscle structure and theories of contraction. Prog Biophys Biophys Chem.1957;7:255-318.
[44]Solovyova O, Katsnelson L, Guriev S, Nikitina L, Protsenko Y, Routkevitch S, et al. Mechanical inhomogeneity of myocardium studied in parallel and serial cardiac muscle duplexes:experiments and models. Chaos, Solitons & Fractals. 2002;13:1685-711.
[45]Rice JJ, Wang F, Bers DM, de Tombe PP. Approximate model of cooperative activation and crossbridge cycling in cardiac muscle using ordinary differential equations. Biophys J.s2008;95:2368-90.
[46]Panerai RB. A model of cardiac muscle mechanics and energetics. J Biomech. 1980; 13:929-40.
[47]Izakov V, Katsnelson LB, Blyakhman FA, Markhasin VS, Shklyar TF. Cooperative effects due to calcium binding by troponin and their consequences for contraction and relaxation of cardiac muscle under various conditions of mechanical loading. Circ Res.1991;69:1171-84.
[48]Peterson JN, Hunter WC, Berman MR. Estimated time course of Ca2+bound to troponin C during relaxation in isolated cardiac muscle. Am J Physiol. 1991;260:H1013-24.
[49]Landesberg A, Sideman S. Coupling calcium binding to troponin C and cross-bridge cycling in skinned cardiac cells. Am J Physiol.1994;266:H 1260-71.
[50]Landesberg A, Sideman S. Mechanical regulation of cardiac muscle by coupling calcium kinetics with cross-bridge cycling:a dynamic model. Am J Physiol. 1994;267:H779-95.
[51]Katsnelson LB, Markhasin VS. Mathematical modeling of relations between the kinetics of free intracellular calcium and mechanical function of myocardium. J Mol Cell Cardiol.1996;28:475-86.
[52]Hunter PJ, McCulloch AD, ter Keurs HE. Modelling the mechanical properties of cardiac muscle. Prog Biophys Mol Biol.1998;69:289-331.
[53]Guccione JM, Costa KD, McCulloch AD. Finite element stress analysis of left ventricular mechanics in the beating dog heart. J Biomech.1995;28:1167-77.
[54]Rice JJ, Winslow RL, Hunter WC. Comparison of putative cooperative mechanisms in cardiac muscle:length dependence and dynamic responses. Am J Physiol.1999;276:H1734-54.
[55]Rice JJ, Jafri MS, Winslow RL. Modeling short-term interval-force relations in cardiac muscle. Am J Physiol Heart Circ Physiol.2000;278:H913-31.
[56]Katsnelson LB, Nikitina LV, Chemla D, Solovyova O, Coirault C, Lecarpentier Y, et al. Influence of viscosity on myocardium mechanical activity:a mathematical model. J Theor Biol.2004;230:385-405.
[57]Niederer SA, Hunter PJ, Smith NP. A quantitative analysis of cardiac myocyte relaxation:a simulation study. Biophys J.2006;90:1697-722.
[58]Tran K, Smith NP, Loiselle DS, Crampin EJ. A metabolite-sensitive, thermodynamically constrained model of cardiac cross-bridge cycling:implications for force development during ischemia. Biophys J.2010;98:267-76.
[59]Campbell SG, Lionetti FV, Campbell KS, McCulloch AD. Coupling of adjacent tropomyosins enhances cross-bridge-mediated cooperative activation in a markov model of the cardiac thin filament. Biophys J.2010;98:2254-64.
[60]Dou J, Xia L, Zhang Y, Shou G, Wei Q, Liu F, et al. Mechanical analysis of congestive heart failure caused by bundle branch block based on an electromechanical canine heart model. Phys Med Biol.2009;54:353-71.
[61]Deng DD, Gong YL, Shou GF, Jiao PF, Zhang HG, Ye XS, et al. Simulation of biatrial conduction via different pathways during sinus rhythm with a detailed human atrial model. J Zhejiang Univ Sci B.2012; 13:676-94.
[62]Aslanidi OV, Colman MA, Zhao J, Smaill BH, Gilbert SH, Hancox JC, et al. Arrhythmogenic substrate for atrial fibrillation:Insights from an integrative computational model of pulmonary veins. Conf Proc IEEE Eng Med Biol Soc. 2012;2012:203-6.
[63]Gonzales MJ, Sturgeon G, Krishnamurthy A, Hake J, Jonas R, Stark P, et al. A three-dimensional finite element model of human atrial anatomy:New methods for cubic Hermite meshes with extraordinary vertices. Medical Image Analysis.
[64]Stevens C, Hunter PJ. Sarcomere length changes in a 3D mathematical model of the pig ventricles. Prog Biophys Mol Biol.2003;82:229-41.
[65]Vetter FJ, McCulloch AD. Mechanoelectric feedback in a model of the passively inflated left ventricle. Ann Biomed Eng.2001;29:414-26.
[66]Wang VY, Lam HI, Ennis DB, Cowan BR, Young AA, Nash MP. Modelling passive diastolic mechanics with quantitative MRI of cardiac structure and function. Med Image Anal.2009; 13:773-84.
[67]Henriquez CS. Simulating the electrical behavior of cardiac tissue using the bidomain model. Crit Rev Biomed Eng.1993;21:l-77.
[68]Dou J, Xia L, Deng D, Zang Y, Shou G, Bustos C, et al. A study of mechanical optimization strategy for cardiac resynchronization therapy based on an electromechanical model. Comput Math Methods Med.2012;2012:948781.
[69]Kerckhoffs RC, Neal ML, Gu Q, Bassingthwaighte JB, Omens JH, McCulloch AD. Coupling of a 3D finite element model of cardiac ventricular mechanics to lumped systems models of the systemic and pulmonic circulation. Ann Biomed Eng. 2007;35:1-18.
[70]Watanabe H, Sugiura S, Kafuku H, Hisada T. Multiphysics simulation of left ventricular filling dynamics using fluid-structure interaction finite element method. Biophys J.2004;87:2074-85.
[71]Magistrale edL. Numerical simulation of perfusion in the beating heart.硕士论文.2007.
[72]Baccani B, Domenichini F, Pedrizzetti G, Tonti G. Fluid dynamics of the left ventricular filling in dilated cardiomyopathy. J Biomech.2002;35:665-71.
[73]Hron J. Fluid structure interaction with applications in biomechanics.博士论文.2001.
[74]Nordsletten DA, Niederer SA, Nash MP, Hunter PJ, Smith NP. Coupling multi-physics models to cardiac mechanics. Prog Biophys Mol Biol.2011;104:77-88.
[75]Mirams GR, Cui Y, Sher A, Fink M, Cooper J, Heath BM, et al. Simulation of multiple ion channel block provides improved early prediction of compounds'clinical torsadogenic risk. Cardiovasc Res.2011;91:53-61.
[76]Withdrawal of troglitazone and cisapride. JAMA.2000;283:2228-.
[77]Gottlieb S. Antihistamine drug withdrawn by manufacturer. BMJ.1999;319:7.
[78]Davies MR, Mistry HB, Hussein L, Pollard CE, Valentin JP, Swinton J, et al. An in silico canine cardiac midmyocardial action potential duration model as a tool for early drug safety assessment. Am J Physiol Heart Circ Physiol.2012;302:H1466-80.
[79]Moreno JD, Zhu ZI, Yang PC, Bankston JR, Jeng MT, Kang C, et al. A computational model to predict the effects of class I anti-arrhythmic drugs on ventricular rhythms. Sci Transl Med.2011;3:98ra83.
[80]Romero L, Pueyo E, Fink M, Rodriguez B. Impact of ionic current variability on human ventricular cellular electrophysiology. Am J Physiol Heart Circ Physiol. 2009;297:H 1436-45.
[81]Trenor B, Cardona K, Gomez JF, Rajamani S, Ferrero JM, Jr., Belardinelli L, et al. Simulation and mechanistic investigation of the arrhythmogenic role of the late sodium current in human heart failure. PLoS One.2012;7:e32659.
[82]Boixel C, Gonzalez W, Louedec L, Hatem SN. Mechanisms of L-type Ca(2+) current downregulation in rat atrial myocytes during heart failure. Circ Res. 2001;89:607-13.
[83]Xiong W, Tian Y, DiSilvestre D, Tomaselli GF. Transmural heterogeneity of Na+-Ca2+ exchange:evidence for differential expression in normal and failing hearts. Circ Res.2005;97:207-9.
[84]O'Rourke B, Kass DA, Tomaselli GF, Kaab S, Tunin R, Marban E. Mechanisms of altered excitation-contraction coupling in canine tachycardia-induced heart failure, I:experimental studies. Circ Res.1999;84:562-70.
[85]Kohlhaas M, Zhang T, Seidler T, Zibrova D, Dybkova N, Steen A, et al. Increased sarcoplasmic reticulum calcium leak but unaltered contractility by acute CaMKII overexpression in isolated rabbit cardiac myocytes. Circ Res. 2006;98:235-44.
[86]Kerckhoffs RC, Bovendeerd PH, Kotte JC, Prinzen FW, Smits K, Arts T. Homogeneity of cardiac contraction despite physiological asynchrony of depolarization:a model study. Ann Biomed Eng.2003;31:536-47.
[87]Ashikaga H, Coppola BA, Hopenfeld B, Leifer ES, McVeigh ER, Omens JH. Transmural dispersion of myofiber mechanics:implications for electrical heterogeneity in vivo. J Am Coll Cardiol.2007;49:909-16.
[88]Walker JC, Ratcliffe MB, Zhang P, Wallace AW, Hsu EW, Saloner DA, et al. Magnetic resonance imaging-based finite element stress analysis after linear repair of left ventricular aneurysm. J Thorac Cardiovasc Surg.2008; 135:1094-102,102 e1-2.
[89]邓冬东.虚拟心脏正常电生理的仿真及房颤的研究.浙江大学博士论文.2012.
[90]Bers DM. Cardiac excitation-contraction coupling. Nature.2002;415:198-205.
[91]Tortora GJ, Derrickson BH. principles of anatomy and physiology. John Wiley&Sons.2006.
[92]Razumova MV, Bukatina AE, Campbell KB. Stiffness-distortion sarcomere model for muscle simulation. J Appl Physiol.1999;87:1861-76.
[93]Pruvot EJ, Katra RP, Rosenbaum DS, Laurita KR. Role of calcium cycling versus restitution in the mechanism of repolarization alternans. Circ Res.2004;94:1083-90.
[94]Hoffman BF, Suckling EE. Effect of heart rate on cardiac membrane potentials and the unipolar electrogram. Am J Physiol.1954; 179:123-30.
[95]Kleinfeld M, Stein E, Kossmann CE. Electrical alternans with emphasis on recent observations made by means of single-cell electrical recording. Am Heart J. 1963;65:495-500.
[96]Nolasco JB, Dahlen RW. A graphic method for the study of alternation in cardiac action potentials. J Appl Physiol.1968;25:191-6.
[97]Banville I, Gray RA. Effect of action potential duration and conduction velocity restitution and their spatial dispersion on alternans and the stability of arrhythmias. J Cardiovasc Electrophysiol.2002; 13:1141-9.
[98]Saitoh H, Bailey JC, Surawicz B. Alternans of action potential duration after abrupt shortening of cycle length:differences between dog Purkinje and ventricular muscle fibers. Circ Res.1988;62:1027-40.
[99]Gilmour RF, Jr., Otani NF, Watanabe MA. Memory and complex dynamics in cardiac Purkinje fibers. Am J Physiol.1997;272:H 1826-32.
[100]Koller ML, Riccio ML, Gilmour RF, Jr. Dynamic restitution of action potential duration during electrical alternans and ventricular fibrillation. Am J Physiol. 1998;275:H 1635-42.
[101]Shannon TR, Ginsburg KS, Bers DM. Potentiation of fractional sarcoplasmic reticulum calcium release by total and free intra-sarcoplasmic reticulum calcium concentration. Biophys J.2000;78:334-43.
[102]Shiferaw Y, Watanabe MA, Garfinkel A, Weiss JN, Karma A. Model of intracellular calcium cycling in ventricular myocytes. Biophys J.2003;85:3666-86.
[103]Tao T, O'Neill SC, Diaz ME, Li YT, Eisner DA, Zhang H. Alternans of cardiac calcium cycling in a cluster of ryanodine receptors:a simulation study. Am J Physiol Heart Circ Physiol.2008;295:H598-609.
[104]Rovetti R, Cui X, Garfinkel A, Weiss JN, Qu Z. Spark-induced sparks as a mechanism of intracellular calcium alternans in cardiac myocytes. Circ Res. 2010;106:1582-91.
[105]Chudin E, Goldhaber J, Garfinkel A, Weiss J, Kogan B. Intracellular Ca(2+) dynamics and the stability of ventricular tachycardia. Biophys J.1999;77:2930-41.
[106]Wan X, Laurita KR, Pruvot EJ, Rosenbaum DS. Molecular correlates of repolarization alternans in cardiac myocytes. J Mol Cell Cardiol.2005;39:419-28.
[107]Huser J, Wang YG, Sheehan KA, Cifuentes F, Lipsius SL, Blatter LA. Functional coupling between glycolysis and excitation-contraction coupling underlies alternans in cat heart cells. J Physiol.2000;524 Pt 3:795-806.
[108]Livshitz LM, Rudy Y. Regulation of Ca2+and electrical alternans in cardiac myocytes:role of CAMKI1 and repolarizing currents. Am J Physiol Heart Circ Physiol.2007;292:H2854-66.
[109]Jordan PN, Christini DJ. Characterizing the contribution of voltage-and calcium-dependent coupling to action potential stability:implications for repolarization alternans. Am J Physiol Heart Circ Physiol.2007;293:H2109-18.
[110]Shiferaw Y, Sato D, Karma A. Coupled dynamics of voltage and calcium in paced cardiac cells. Phys Rev E Stat Nonlin Soft Matter Phys.2005;71:021903.
[111]Fox JJ, McHarg JL, Gilmour RF, Jr. Ionic mechanism of electrical alternans. Am J Physiol Heart Circ Physiol.2002;282:H516-30.
[112]ten Tusscher KH, Panfilov AV. Alternans and spiral breakup in a human ventricular tissue model. Am J Physiol Heart Circ Physiol.2006;291:H 1088-100.
[113]January CT, Chau V, Makielski JC. Triggered activity in the heart:cellular mechanisms of early after-depolarizations. Eur Heart J.1991;12 Suppl F:4-9.
[114]Orchard CH, Eisner DA, Allen DG. Oscillations of intracellular Ca2+in mammalian cardiac muscle. Nature.1983;304:735-8.
[115]Wier WG, Kort AA, Stern MD, Lakatta EG, Marban E. Cellular calcium fluctuations in mammalian heart:direct evidence from noise analysis of aequorin signals in Purkinje fibers. Proc Natl Acad Sci U S A.1983;80:7367-71.
[116]Iribe G, Kohl P, Noble D. Modulatory effect of calmodulin-dependent kinaseⅡ (CaMKII) on sarcoplasmic reticulum Ca2+ handling and interval-force relations:a modelling study. Philos Transact A Math Phys Eng Sci.2006;364:1107-33.
[117]Zygmunt AC, Eddlestone GT, Thomas GP, Nesterenko VV, Antzelevitch C. Larger late sodium conductance in M cells contributes to electrical heterogeneity in canine ventricle. Am J Physiol Heart Circ Physiol.2001;281:H689-97.
[118]Valdivia CR, Chu WW, Pu J, Foell JD, Haworth RA, Wolff MR, et al. Increased late sodium current in myocytes from a canine heart failure model and from failing human heart. J Mol Cell Cardiol.2005;38:475-83.
[119]Liu DW, Antzelevitch C. Characteristics of the delayed rectifier current (IKr and 1Ks) in canine ventricular epicardial, midmyocardial, and endocardial myocytes. A weaker IKs contributes to the longer action potential of the M cell. Circ Res. 1995;76:351-65.
[120]Liu D, Gintant G, Antzelevitch C. Ionic bases for electrophysiological distinctions among epicardial, midmyocardial, and endocardial myocytes from the free wall of the canine left ventricle. Circulation Research.1993;72:671-87.
[121]Xiong W, Tian Y, DiSilvestre D, Tomaselli GF. Transmural Heterogeneity of Na+-Ca2+ Exchange:Evidence for Differential Expression in Normal and Failing Hearts. Circ Res.2005;97:207-9.
[122]Laurita KR, Katra R, Wible B, Wan X, Koo MH. Transmural Heterogeneity of Calcium Handling in Canine. Circulation Research.2003;92:668-75.
[123]Li G-R, Lau C-P, Ducharme A, Tardif J-C, Nattel S. Transmural action potential and ionic current remodeling in ventricles of failing canine hearts. Am J Physiol Heart Circ Physiol.2002;283:H1031-41.
[124]Wilde AA, Escande D, Schumacher CA, Thuringer D, Mestre M, Fiolet JW, et al. Potassium accumulation in the globally ischemic mammalian heart. A role for the ATP-sensitive potassium channel. Circ Res.1990;67:835-43.
[125]Ferrero JM, Jr., Saiz J, Ferrero JM, Thakor NV. Simulation of action potentials from metabolically impaired cardiac myocytes. Role of ATP-sensitive K+ current. Circ Res.1996;79:208-21.
[126]Plonsey R BR. Bioelectricity:A Quantitative Approach.1988.
[127]Liu DW, Gintant GA, Antzelevitch C. Ionic bases for electrophysiological distinctions among epicardial, midmyocardial, and endocardial myocytes from the free wall of the canine left ventricle. Circ Res.1993;72:671-87.
[128]Cordeiro JM, Greene L, Heilmann C, Antzelevitch D, Antzelevitch C. Transmural heterogeneity of calcium activity and mechanical function in the canine left ventricle. Am J Physiol Heart Circ Physiol.2004;286:H1471-9.
[129]Sato R, Noma A, Kurachi Y, Irisawa H. Effects of intracellular acidification on membrane currents in ventricular cells of the guinea pig. Circ Res.1985;57:553-61.
[130]Harvey RD, Ten Eick RE. On the role of sodium ions in the regulation of the inward-rectifying potassium conductance in cat ventricular myocytes. J Gen Physiol. 1989;94:329-48.
[131]Tedesco C, Reigle J, Bergin J. Sudden Cardiac Death in Heart Failure. Journal of Cardiovascular Nursing.2000;14:38-56.
[132]Li GR, Lau CP, Ducharme A, Tardif JC, Nattel S. Transmural action potential and ionic current remodeling in ventricles of failing canine hearts. Am J Physiol Heart Circ Physiol.2002;283:H 1031-41.
[133]Maltsev VA, Reznikov V, Undrovinas NA, Sabbah HN, Undrovinas A. Modulation of late sodium current by Ca2+, calmodulin, and CaMKII in normal and failing dog cardiomyocytes:similarities and differences. Am J Physiol Heart Circ Physiol.2008;294:H 1597-608.
[134]Wagner S, Hacker E, Grandi E, Weber SL, Dybkova N, Sossalla S, et al. Ca/calmodulin kinase Ⅱ differentially modulates potassium currents. Circ Arrhythm Electrophysiol.2009;2:285-94.
[135]Wagner S, Dybkova N, Rasenack EC, Jacobshagen C, Fabritz L, Kirchhof P, et al. Ca2+/calmodulin-dependent protein kinase Ⅱ regulates cardiac Na+ channels. J Clin Invest.2006; 116:3127-38.
[136]Ai X, Curran JW, Shannon TR, Bers DM, Pogwizd SM. Ca2+/calmodul in-dependent protein kinase modulates cardiac ryanodine receptor phosphorylation and sarcoplasmic reticulum Ca2+ leak in heart failure. Circ Res. 2005;97:1314-22.
[137]Shannon TR, Ginsburg KS, Bers DM. Quantitative assessment of the SR Ca2+ leak-load relationship. Circ Res.2002;91:594-600.
[138]Shannon TR, Wang F, Bers DM. Regulation of cardiac sarcoplasmic reticulum Ca release by luminal [Ca] and altered gating assessed with a mathematical model. Biophys J.2005;89:4096-110.
[139]Cordeiro JM, Mazza M, Goodrow R, Ulahannan N, Antzelevitch C, Di Diego JM. Functionally distinct sodium channels in ventricular epicardial and endocardial cells contribute to a greater sensitivity of the epicardium to electrical depression. Am J Physiol Heart Circ Physiol.2008;295:H 154-62.
[140]Pu J, Boyden PA. Alterations of Na+ currents in myocytes from epicardial border zone of the infarcted heart. A possible ionic mechanism for reduced excitability and postrepolarization refractoriness. Circ Res.1997;81:110-9.
[141]Lue WM, Boyden PA. Abnormal electrical properties of myocytes from chronically infarcted canine heart. Alterations in Vmax and the transient outward current. Circulation.1992;85:1175-88.
[142]Xiao L, Coutu P, Villeneuve LR, Tadevosyan A, Maguy A, Le Bouter S, et al. Mechanisms underlying rate-dependent remodeling of transient outward potassium current in canine ventricular myocytes. Circ Res.2008; 103:733-42.
[143]Greenstein JL, Wu R, Po S, Tomaselli GF, Winslow RL. Role of the calcium-independent transient outward current I(to1) in shaping action potential morphology and duration. Circ Res.2000;87:1026-33.
[144]Akar FG, Wu RC, Deschenes I, Armoundas AA, Piacentino V,3rd, Houser SR, et al. Phenotypic differences in transient outward K+ current of human and canine ventricular myocytes:insights into molecular composition of ventricular Ito. Am J Physiol Heart Circ Physiol.2004;286:H602-9.
[145]Rubart M, Lopshire JC, Fineberg NS, Zipes DP. Changes in left ventricular repolarization and ion channel currents following a transient rate increase superimposed on bradycardia in anesthetized dogs. J Cardiovasc Electrophysiol. 2000; 11:652-64.
[146]Hua F, Gilmour RF, Jr. Contribution of IKr to rate-dependent action potential dynamics in canine endocardium. Circ Res.2004;94:810-9.
[147]Gao J, Wang W, Cohen IS, Mathias RT. Transmural gradients in Na/K pump activity and [Na+]I in canine ventricle. Biophys J.2005;89:1700-9.
[148]Sipido KR, Volders PG, de Groot SH, Verdonck F, Van de Werf F, Wellens HJ, et al. Enhanced Ca(2+) release and Na/Ca exchange activity in hypertrophied canine ventricular myocytes:potential link between contractile adaptation and arrhythmogenesis. Circulation.2000; 102:2137-44.
[149]Lou Q, Fedorov VV, Glukhov AV, Moazami N, Fast VG, Efimov IR. Transmural heterogeneity and remodeling of ventricular excitation-contraction coupling in human heart failure. Circulation.2011;123:1881-90.
[150]Akar FG Rosenbaum DS. Transmural electrophysiological heterogeneities underlying arrhythmogenesis in heart failure. Circ Res.2003;93:638-45.
[151]Despa S, Islam MA, Weber CR, Pogwizd SM, Bers DM. Intracellular Na(+) concentration is elevated in heart failure but Na/K pump function is unchanged. Circulation.2002;105:2543-8.
[152]Verdonck F, Volders PG, Vos MA, Sipido KR. Increased Na+ concentration and altered Na/K pump activity in hypertrophied canine ventricular cells. Cardiovasc Res. 2003;57:1035-43.
[153]Baartscheer A, Schumacher CA, van Borren MM, Belterman CN, Coronel R, Fiolet JW. Increased Na+/H+-exchange activity is the cause of increased [Na+]i and underlies disturbed calcium handling in the rabbit pressure and volume overload heart failure model. Cardiovasc Res.2003;57:1015-24.
[154]Grandi E, Puglisi JL, Wagner S, Maier LS, Severi S, Bers DM. Simulation of Ca-calmodulin-dependent protein kinase Ⅱ on rabbit ventricular myocyte ion currents and action potentials. Biophys J.2007;93:3835-47.
[155]Bers DM. Excitation-contraction coupling and cardiac contractile force. Kluwer Academic Press.2001:427.
[156]Wilson LD, Jeyaraj D, Wan X, Hoeker GS, Said TH, Gittinger M, et al. Heart failure enhances susceptibility to arrhythmogenic cardiac alternans. Heart Rhythm. 2009;6:251-9.
[157]Shannon TR, Lew WY. Diastolic release of calcium from the sarcoplasmic reticulum:a potential target for treating triggered arrhythmias and heart failure. J Am Coll Cardiol.2009;53:2006-8.
[158]Bossuyt J, Ai X, Moorman JR, Pogwizd SM, Bers DM. Expression and phosphorylation of the na-pump regulatory subunit phospholemman in heart failure. Circ Res.2005;97:558-65.
[159]Lukas A, Antzelevitch C. Differences in the electrophysiological response of canine ventricular epicardium and endocardium to ischemia. Role of the transient outward current. Circulation.1993;88:2903-15.
[160]Zygmunt AC, Goodrow RJ, Antzelevitch C. I(NaCa) contributes to electrical heterogeneity within the canine ventricle. Am J Physiol Heart Circ Physiol. 2000;278:H1671-8.
[161]Kaab S, Nuss HB, Chiamvimonvat N, O'Rourke B, Pak PH, Kass DA, et al. Ionic mechanism of action potential prolongation in ventricular myocytes from dogs with pacing-induced heart failure. Circ Res.1996;78:262-73.
[162]Sun X, Wang HS. Role of the transient outward current (Ito) in shaping canine ventricular action potential--a dynamic clamp study. J Physiol.2005;564:411-9.
[163]Decker KF, Heijman J, Silva JR, Hund TJ, Rudy Y. Properties and ionic mechanisms of action potential adaptation, restitution, and accommodation in canine epicardium. Am J Physiol Heart Circ Physiol.2009;296:H1017-26.
[164]Akar FG, Wu RC, Juang GJ, Tian Y, Burysek M, Disilvestre D, et al. Molecular mechanisms underlying K+current downregulation in canine tachycardia-induced heart failure. Am J Physiol Heart Circ Physiol.2005;288:H2887-96.
[165]Jost N. A szivizom repolarizaciojaban reszt vevo kulonbozo kaliumcsatornak kolcsonhatasanak vizsgalata emlos kamraizmon-A repolarizacios tartalek jelentosege. Cardiologia Hungarica.2008:10-6.
[166]Xiao L, Zhang L, Han W, Wang Z, Nattel S. Sex-based transmural differences in cardiac repolarization and ionic-current properties in canine left ventricles. Am J Physiol Heart Circ Physiol.2006;291:H570-80.
[167]Szabo G, Szentandrassy N, Biro T, Toth BI, Czifra G, Magyar J, et al. Asymmetrical distribution of ion channels in canine and human left-ventricular wall: epicardium versus midmyocardium. Pflugers Arch.2005;450:307-16.
[168]Laurita KR, Katra R, Wible B, Wan X, Koo MH. Transmural heterogeneity of calcium handling in canine. Circ Res.2003;92:668-75.
[169]Obreztchikova MN, Patberg KW, Plotnikov AN, Ozgen N, Shlapakova IN, Rybin AV, et al. I(Kr) contributes to the altered ventricular repolarization that determines long-term cardiac memory. Cardiovasc Res.2006;71:88-96.
[170]Flaim SN, Giles WR, McCulloch AD. Contributions of sustained INa and IKv43 to transmural heterogeneity of early repolarization and arrhythmogenesis in canine left ventricular myocytes. Am J Physiol Heart Circ Physiol. 2006;291:H2617-29.
[171]Benson AP, Aslanidi OV, Zhang H, Holden AV. The canine virtual ventricular wall:a platform for dissecting pharmacological effects on propagation and arrhythmogenesis. Prog Biophys Mol Biol.2008;96:187-208.
[172]Kuijpers NH, Ten Eikelder HM, Bovendeerd PH, Verheule S, Arts T, Hilbers PA. Mechanoelectric feedback as a trigger mechanism for cardiac electrical remodeling:a model study. Ann Biomed Eng.2008;36:1816-35.
[173]Solovyova O, Katsnelson L, Guriev S, Nikitina L, Protsenko Y, Routkevitch S, et al. Mechanical inhomogeneity of myocardium studied in parallel and serial cardiac muscle duplexes:experiments and models. Chaos, Solitons & Fractals. 2002;13:1685-711.
[2]Hodgkin AL, Huxley AF. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol.1952;117:500-44.
[3]Cheng H, Lederer WJ, Cannell MB. Calcium sparks:elementary events underlying excitation-contraction coupling in heart muscle. Science.1993;262:740-4.
[4]Izu LT, Mauban JR, Balke CW, Wier WG.Large currents generate cardiac Ca2+ sparks. Biophys J.2001;80:88-102.
[5]Lu L, Xia L, Ye X, Cheng H. Simulation of the effect of rogue ryanodine receptors on a calcium wave in ventricular myocytes with heart failure. Phys Biol. 2010;7:026005.
[6]Gaur N, Rudy Y. Multiscale modeling of calcium cycling in cardiac ventricular myocyte:macroscopic consequences of microscopic dyadic function. Biophys J. 2011;100:2904-12.
[7]Sobie EA, Dilly KW, dos Santos Cruz J, Lederer WJ, Jafri MS. Termination of cardiac Ca(2+) sparks:an investigative mathematical model of calcium-induced calcium release. Biophys J.2002;83:59-78.
[8]Li Q, O'Neill SC, Tao T, Li Y, Eisner D, Zhang H. Mechanisms by which cytoplasmic calcium wave propagation and alternans are generated in cardiac atrial myocytes lacking T-tubules-insights from a simulation study. Biophys J. 2012; 102:1471-82.
[9]Tveito A, Lines GT, Edwards AG, Maleckar MM, Michailova A, Hake J, et al. Slow Calcium-Depolarization-Calcium waves may initiate fast local depolarization waves in ventricular tissue. Prog Biophys Mol Biol.2012;110:295-304.
[10]Swietach P, Spitzer KW, Vaughan-Jones RD. Modeling calcium waves in cardiac myocytes:importance of calcium diffusion. Front Biosci.2010;15:661-80.
[11]Noble D. A modification of the Hodgkin--Huxley equations applicable to Purkinje fibre action and pace-maker potentials. J Physiol.1962; 160:317-52.
[12]McAllister RE, Noble D, Tsien RW. Reconstruction of the electrical activity of cardiac Purkinje fibres. J Physiol.1975;251:1-59.
[13]Beeler GW, Reuter H. Reconstruction of the action potential of ventricular myocardial fibres. J Physiol.1977;268:177-210.
[14]Bristow DG, Clark JW. A mathematical model of primary pacemaking cell in SA node of the heart. Am J Physiol.1982;243:H207-18.
[15]Noble D, Noble SJ. A model of sino-atrial node electrical activity based on a modification of the DiFrancesco-Noble (1984) equations. Proc R Soc Lond B Biol Sci. 1984;222:295-304.
[16]DiFrancesco D, Noble D. A model of cardiac electrical activity incorporating ionic pumps and concentration changes. Philos Trans R Soc Lond B Biol Sci. 1985;307:353-98.
[17]Luo CH, Rudy Y. A model of the ventricular cardiac action potential. Depolarization, repolarization, and their interaction. Circ Res.1991;68:1501-26.
[18]Luo CH, Rudy Y. A dynamic model of the cardiac ventricular action potential. I. Simulations of ionic currents and concentration changes. Circ Res.1994;74:1071-96.
[19]Courtemanche M, Ramirez RJ, Nattel S. Ionic mechanisms underlying human atrial action potential properties:insights from a mathematical model. Am J Physiol. 1998;275:H301-21.
[20]Nygren A, Fiset C, Firek L, Clark JW, Lindblad DS, Clark RB, et al. Mathematical model of an adult human atrial cell:the role of K+ currents in repolarization. Circ Res.1998;82:63-81.
[21]Jafri MS, Rice JJ, Winslow RL. Cardiac Ca2+ dynamics:the roles of ryanodine receptor adaptation and sarcoplasmic reticulum load. Biophys J.1998;74:1149-68.
[22]Priebe L, Beuckelmann DJ. Simulation study of cellular electric properties in heart failure. Circ Res.1998;82:1206-23.
[23]Winslow RL, Rice J, Jafri S, Marban E, O'Rourke B. Mechanisms of altered excitation-contraction coupling in canine tachycardia-induced heart failure, Ⅱ:model studies. Circ Res.1999;84:571-86.
[24]Ramirez RJ, Nattel S, Courtemanche M. Mathematical analysis of canine atrial action potentials:rate, regional factors, and electrical remodeling. Am J Physiol Heart Circ Physiol.2000;279:H1767-85.
[25]Zhang H, Holden AV, Kodama I, Honjo H, Lei M, Varghese T, et al. Mathematical models of action potentials in the periphery and center of the rabbit sinoatrial node. Am J Physiol Heart Circ Physiol.2000;279:H397-421.
[26]Pandit SV, Clark RB, Giles WR, Demir SS. A mathematical model of action potential heterogeneity in adult rat left ventricular myocytes. Biophys J. 2001;81:3029-51.
[27]Puglisi JL, Bers DM. LabHEART:an interactive computer model of rabbit ventricular myocyte ion channels and Ca transport. Am J Physiol Cell Physiol. 2001;281:C2049-60.
[28]Bernus O, Wilders R, Zemlin CW, Verschelde H, Panfilov AV. A computationally efficient electrophysiological model of human ventricular cells. Am J Physiol Heart Circ Physiol.2002;282:H2296-308.
[29]ten Tusscher KH, Noble D, Noble PJ, Panfilov AV. A model for human ventricular tissue. Am J Physiol Heart Circ Physiol.2004;286:H1573-89.
[30]Iyer V, Mazhari R, Winslow RL. A computational model of the human left-ventricular epicardial myocyte. Biophys J.2004;87:1507-25.
[31]Hund TJ, Rudy Y. Rate dependence and regulation of action potential and calcium transient in a canine cardiac ventricular cell model. Circulation. 2004; 110:3168-74.
[32]Greenstein JL, Hinch R, Winslow RL. Mechanisms of excitation-contraction coupling in an integrative model of the cardiac ventricular myocyte. Biophys J. 2006;90:77-91.
[33]Grandi E, Pasqualini FS, Bers DM. A novel computational model of the human ventricular action potential and Ca transient. J Mol Cell Cardiol.2010;48:112-21.
[34]Inada S, Hancox JC, Zhang H, Boyett MR. One-dimensional mathematical model of the atrioventricular node including atrio-nodal, nodal, and nodal-his cells. Biophys J.2009;97:2117-27.
[35]Maleckar MM, Greenstein JL, Trayanova NA, Giles WR. Mathematical simulations of ligand-gated and cell-type specific effects on the action potential of human atrium. Prog Biophys Mol Biol.2008;98:161-70.
[36]Xia L, Gong YL, Zhu XW, Zhang Y, Sun Q, Zhang HG Mathematical models of canine right and left atria cardiomyocytes. J Zhejiang Univ Sci B.2010; 11:402-16.
[37]Koivumaki JT, Korhonen T, Tavi P. Impact of sarcoplasmic reticulum calcium release on calcium dynamics and action potential morphology in human atrial myocytes:a computational study. PLoS Comput Biol.2011;7:e1001067.
[38]O'Hara T, Virag L, Varro A, Rudy Y. Simulation of the undiseased human cardiac ventricular action potential:model formulation and experimental validation. PLoS Comput Biol.2011;7:e 1002061.
[39]Grandi E, Pandit SV, Voigt N, Workman AJ, Dobrev D, Jalife J, et al. Human atrial action potential and Ca2+ model:sinus rhythm and chronic atrial fibrillation. Circ Res.2011;109:1055-66.
[40]Heijman J, Volders PG, Westra RL, Rudy Y. Local control of beta-adrenergic stimulation:Effects on ventricular myocyte electrophysiology and Ca(2+)-transient. J Mol Cell Cardiol.2011;50:863-71.
[41]Zang Y, Dai L, Zhan H, Dou J, Xia L, Zhang H. Theoretical investigation of the mechanism of heart failure using a canine ventricular cell model:Especially the role of up-regulated CaMKII and SR Ca(2+) leak. J Mol Cell Cardiol.2013;56:34-43.
[42]Hill AV. The Heat of Shortening and the Dynamic Constants of Muscle. Proceedings of the Royal Society of London Series B-Biological Sciences. 1938;126:136-95.
[43]Huxley AF. Muscle structure and theories of contraction. Prog Biophys Biophys Chem.1957;7:255-318.
[44]Solovyova O, Katsnelson L, Guriev S, Nikitina L, Protsenko Y, Routkevitch S, et al. Mechanical inhomogeneity of myocardium studied in parallel and serial cardiac muscle duplexes:experiments and models. Chaos, Solitons & Fractals. 2002;13:1685-711.
[45]Rice JJ, Wang F, Bers DM, de Tombe PP. Approximate model of cooperative activation and crossbridge cycling in cardiac muscle using ordinary differential equations. Biophys J.s2008;95:2368-90.
[46]Panerai RB. A model of cardiac muscle mechanics and energetics. J Biomech. 1980; 13:929-40.
[47]Izakov V, Katsnelson LB, Blyakhman FA, Markhasin VS, Shklyar TF. Cooperative effects due to calcium binding by troponin and their consequences for contraction and relaxation of cardiac muscle under various conditions of mechanical loading. Circ Res.1991;69:1171-84.
[48]Peterson JN, Hunter WC, Berman MR. Estimated time course of Ca2+bound to troponin C during relaxation in isolated cardiac muscle. Am J Physiol. 1991;260:H1013-24.
[49]Landesberg A, Sideman S. Coupling calcium binding to troponin C and cross-bridge cycling in skinned cardiac cells. Am J Physiol.1994;266:H 1260-71.
[50]Landesberg A, Sideman S. Mechanical regulation of cardiac muscle by coupling calcium kinetics with cross-bridge cycling:a dynamic model. Am J Physiol. 1994;267:H779-95.
[51]Katsnelson LB, Markhasin VS. Mathematical modeling of relations between the kinetics of free intracellular calcium and mechanical function of myocardium. J Mol Cell Cardiol.1996;28:475-86.
[52]Hunter PJ, McCulloch AD, ter Keurs HE. Modelling the mechanical properties of cardiac muscle. Prog Biophys Mol Biol.1998;69:289-331.
[53]Guccione JM, Costa KD, McCulloch AD. Finite element stress analysis of left ventricular mechanics in the beating dog heart. J Biomech.1995;28:1167-77.
[54]Rice JJ, Winslow RL, Hunter WC. Comparison of putative cooperative mechanisms in cardiac muscle:length dependence and dynamic responses. Am J Physiol.1999;276:H1734-54.
[55]Rice JJ, Jafri MS, Winslow RL. Modeling short-term interval-force relations in cardiac muscle. Am J Physiol Heart Circ Physiol.2000;278:H913-31.
[56]Katsnelson LB, Nikitina LV, Chemla D, Solovyova O, Coirault C, Lecarpentier Y, et al. Influence of viscosity on myocardium mechanical activity:a mathematical model. J Theor Biol.2004;230:385-405.
[57]Niederer SA, Hunter PJ, Smith NP. A quantitative analysis of cardiac myocyte relaxation:a simulation study. Biophys J.2006;90:1697-722.
[58]Tran K, Smith NP, Loiselle DS, Crampin EJ. A metabolite-sensitive, thermodynamically constrained model of cardiac cross-bridge cycling:implications for force development during ischemia. Biophys J.2010;98:267-76.
[59]Campbell SG, Lionetti FV, Campbell KS, McCulloch AD. Coupling of adjacent tropomyosins enhances cross-bridge-mediated cooperative activation in a markov model of the cardiac thin filament. Biophys J.2010;98:2254-64.
[60]Dou J, Xia L, Zhang Y, Shou G, Wei Q, Liu F, et al. Mechanical analysis of congestive heart failure caused by bundle branch block based on an electromechanical canine heart model. Phys Med Biol.2009;54:353-71.
[61]Deng DD, Gong YL, Shou GF, Jiao PF, Zhang HG, Ye XS, et al. Simulation of biatrial conduction via different pathways during sinus rhythm with a detailed human atrial model. J Zhejiang Univ Sci B.2012; 13:676-94.
[62]Aslanidi OV, Colman MA, Zhao J, Smaill BH, Gilbert SH, Hancox JC, et al. Arrhythmogenic substrate for atrial fibrillation:Insights from an integrative computational model of pulmonary veins. Conf Proc IEEE Eng Med Biol Soc. 2012;2012:203-6.
[63]Gonzales MJ, Sturgeon G, Krishnamurthy A, Hake J, Jonas R, Stark P, et al. A three-dimensional finite element model of human atrial anatomy:New methods for cubic Hermite meshes with extraordinary vertices. Medical Image Analysis.
[64]Stevens C, Hunter PJ. Sarcomere length changes in a 3D mathematical model of the pig ventricles. Prog Biophys Mol Biol.2003;82:229-41.
[65]Vetter FJ, McCulloch AD. Mechanoelectric feedback in a model of the passively inflated left ventricle. Ann Biomed Eng.2001;29:414-26.
[66]Wang VY, Lam HI, Ennis DB, Cowan BR, Young AA, Nash MP. Modelling passive diastolic mechanics with quantitative MRI of cardiac structure and function. Med Image Anal.2009; 13:773-84.
[67]Henriquez CS. Simulating the electrical behavior of cardiac tissue using the bidomain model. Crit Rev Biomed Eng.1993;21:l-77.
[68]Dou J, Xia L, Deng D, Zang Y, Shou G, Bustos C, et al. A study of mechanical optimization strategy for cardiac resynchronization therapy based on an electromechanical model. Comput Math Methods Med.2012;2012:948781.
[69]Kerckhoffs RC, Neal ML, Gu Q, Bassingthwaighte JB, Omens JH, McCulloch AD. Coupling of a 3D finite element model of cardiac ventricular mechanics to lumped systems models of the systemic and pulmonic circulation. Ann Biomed Eng. 2007;35:1-18.
[70]Watanabe H, Sugiura S, Kafuku H, Hisada T. Multiphysics simulation of left ventricular filling dynamics using fluid-structure interaction finite element method. Biophys J.2004;87:2074-85.
[71]Magistrale edL. Numerical simulation of perfusion in the beating heart.硕士论文.2007.
[72]Baccani B, Domenichini F, Pedrizzetti G, Tonti G. Fluid dynamics of the left ventricular filling in dilated cardiomyopathy. J Biomech.2002;35:665-71.
[73]Hron J. Fluid structure interaction with applications in biomechanics.博士论文.2001.
[74]Nordsletten DA, Niederer SA, Nash MP, Hunter PJ, Smith NP. Coupling multi-physics models to cardiac mechanics. Prog Biophys Mol Biol.2011;104:77-88.
[75]Mirams GR, Cui Y, Sher A, Fink M, Cooper J, Heath BM, et al. Simulation of multiple ion channel block provides improved early prediction of compounds'clinical torsadogenic risk. Cardiovasc Res.2011;91:53-61.
[76]Withdrawal of troglitazone and cisapride. JAMA.2000;283:2228-.
[77]Gottlieb S. Antihistamine drug withdrawn by manufacturer. BMJ.1999;319:7.
[78]Davies MR, Mistry HB, Hussein L, Pollard CE, Valentin JP, Swinton J, et al. An in silico canine cardiac midmyocardial action potential duration model as a tool for early drug safety assessment. Am J Physiol Heart Circ Physiol.2012;302:H1466-80.
[79]Moreno JD, Zhu ZI, Yang PC, Bankston JR, Jeng MT, Kang C, et al. A computational model to predict the effects of class I anti-arrhythmic drugs on ventricular rhythms. Sci Transl Med.2011;3:98ra83.
[80]Romero L, Pueyo E, Fink M, Rodriguez B. Impact of ionic current variability on human ventricular cellular electrophysiology. Am J Physiol Heart Circ Physiol. 2009;297:H 1436-45.
[81]Trenor B, Cardona K, Gomez JF, Rajamani S, Ferrero JM, Jr., Belardinelli L, et al. Simulation and mechanistic investigation of the arrhythmogenic role of the late sodium current in human heart failure. PLoS One.2012;7:e32659.
[82]Boixel C, Gonzalez W, Louedec L, Hatem SN. Mechanisms of L-type Ca(2+) current downregulation in rat atrial myocytes during heart failure. Circ Res. 2001;89:607-13.
[83]Xiong W, Tian Y, DiSilvestre D, Tomaselli GF. Transmural heterogeneity of Na+-Ca2+ exchange:evidence for differential expression in normal and failing hearts. Circ Res.2005;97:207-9.
[84]O'Rourke B, Kass DA, Tomaselli GF, Kaab S, Tunin R, Marban E. Mechanisms of altered excitation-contraction coupling in canine tachycardia-induced heart failure, I:experimental studies. Circ Res.1999;84:562-70.
[85]Kohlhaas M, Zhang T, Seidler T, Zibrova D, Dybkova N, Steen A, et al. Increased sarcoplasmic reticulum calcium leak but unaltered contractility by acute CaMKII overexpression in isolated rabbit cardiac myocytes. Circ Res. 2006;98:235-44.
[86]Kerckhoffs RC, Bovendeerd PH, Kotte JC, Prinzen FW, Smits K, Arts T. Homogeneity of cardiac contraction despite physiological asynchrony of depolarization:a model study. Ann Biomed Eng.2003;31:536-47.
[87]Ashikaga H, Coppola BA, Hopenfeld B, Leifer ES, McVeigh ER, Omens JH. Transmural dispersion of myofiber mechanics:implications for electrical heterogeneity in vivo. J Am Coll Cardiol.2007;49:909-16.
[88]Walker JC, Ratcliffe MB, Zhang P, Wallace AW, Hsu EW, Saloner DA, et al. Magnetic resonance imaging-based finite element stress analysis after linear repair of left ventricular aneurysm. J Thorac Cardiovasc Surg.2008; 135:1094-102,102 e1-2.
[89]邓冬东.虚拟心脏正常电生理的仿真及房颤的研究.浙江大学博士论文.2012.
[90]Bers DM. Cardiac excitation-contraction coupling. Nature.2002;415:198-205.
[91]Tortora GJ, Derrickson BH. principles of anatomy and physiology. John Wiley&Sons.2006.
[92]Razumova MV, Bukatina AE, Campbell KB. Stiffness-distortion sarcomere model for muscle simulation. J Appl Physiol.1999;87:1861-76.
[93]Pruvot EJ, Katra RP, Rosenbaum DS, Laurita KR. Role of calcium cycling versus restitution in the mechanism of repolarization alternans. Circ Res.2004;94:1083-90.
[94]Hoffman BF, Suckling EE. Effect of heart rate on cardiac membrane potentials and the unipolar electrogram. Am J Physiol.1954; 179:123-30.
[95]Kleinfeld M, Stein E, Kossmann CE. Electrical alternans with emphasis on recent observations made by means of single-cell electrical recording. Am Heart J. 1963;65:495-500.
[96]Nolasco JB, Dahlen RW. A graphic method for the study of alternation in cardiac action potentials. J Appl Physiol.1968;25:191-6.
[97]Banville I, Gray RA. Effect of action potential duration and conduction velocity restitution and their spatial dispersion on alternans and the stability of arrhythmias. J Cardiovasc Electrophysiol.2002; 13:1141-9.
[98]Saitoh H, Bailey JC, Surawicz B. Alternans of action potential duration after abrupt shortening of cycle length:differences between dog Purkinje and ventricular muscle fibers. Circ Res.1988;62:1027-40.
[99]Gilmour RF, Jr., Otani NF, Watanabe MA. Memory and complex dynamics in cardiac Purkinje fibers. Am J Physiol.1997;272:H 1826-32.
[100]Koller ML, Riccio ML, Gilmour RF, Jr. Dynamic restitution of action potential duration during electrical alternans and ventricular fibrillation. Am J Physiol. 1998;275:H 1635-42.
[101]Shannon TR, Ginsburg KS, Bers DM. Potentiation of fractional sarcoplasmic reticulum calcium release by total and free intra-sarcoplasmic reticulum calcium concentration. Biophys J.2000;78:334-43.
[102]Shiferaw Y, Watanabe MA, Garfinkel A, Weiss JN, Karma A. Model of intracellular calcium cycling in ventricular myocytes. Biophys J.2003;85:3666-86.
[103]Tao T, O'Neill SC, Diaz ME, Li YT, Eisner DA, Zhang H. Alternans of cardiac calcium cycling in a cluster of ryanodine receptors:a simulation study. Am J Physiol Heart Circ Physiol.2008;295:H598-609.
[104]Rovetti R, Cui X, Garfinkel A, Weiss JN, Qu Z. Spark-induced sparks as a mechanism of intracellular calcium alternans in cardiac myocytes. Circ Res. 2010;106:1582-91.
[105]Chudin E, Goldhaber J, Garfinkel A, Weiss J, Kogan B. Intracellular Ca(2+) dynamics and the stability of ventricular tachycardia. Biophys J.1999;77:2930-41.
[106]Wan X, Laurita KR, Pruvot EJ, Rosenbaum DS. Molecular correlates of repolarization alternans in cardiac myocytes. J Mol Cell Cardiol.2005;39:419-28.
[107]Huser J, Wang YG, Sheehan KA, Cifuentes F, Lipsius SL, Blatter LA. Functional coupling between glycolysis and excitation-contraction coupling underlies alternans in cat heart cells. J Physiol.2000;524 Pt 3:795-806.
[108]Livshitz LM, Rudy Y. Regulation of Ca2+and electrical alternans in cardiac myocytes:role of CAMKI1 and repolarizing currents. Am J Physiol Heart Circ Physiol.2007;292:H2854-66.
[109]Jordan PN, Christini DJ. Characterizing the contribution of voltage-and calcium-dependent coupling to action potential stability:implications for repolarization alternans. Am J Physiol Heart Circ Physiol.2007;293:H2109-18.
[110]Shiferaw Y, Sato D, Karma A. Coupled dynamics of voltage and calcium in paced cardiac cells. Phys Rev E Stat Nonlin Soft Matter Phys.2005;71:021903.
[111]Fox JJ, McHarg JL, Gilmour RF, Jr. Ionic mechanism of electrical alternans. Am J Physiol Heart Circ Physiol.2002;282:H516-30.
[112]ten Tusscher KH, Panfilov AV. Alternans and spiral breakup in a human ventricular tissue model. Am J Physiol Heart Circ Physiol.2006;291:H 1088-100.
[113]January CT, Chau V, Makielski JC. Triggered activity in the heart:cellular mechanisms of early after-depolarizations. Eur Heart J.1991;12 Suppl F:4-9.
[114]Orchard CH, Eisner DA, Allen DG. Oscillations of intracellular Ca2+in mammalian cardiac muscle. Nature.1983;304:735-8.
[115]Wier WG, Kort AA, Stern MD, Lakatta EG, Marban E. Cellular calcium fluctuations in mammalian heart:direct evidence from noise analysis of aequorin signals in Purkinje fibers. Proc Natl Acad Sci U S A.1983;80:7367-71.
[116]Iribe G, Kohl P, Noble D. Modulatory effect of calmodulin-dependent kinaseⅡ (CaMKII) on sarcoplasmic reticulum Ca2+ handling and interval-force relations:a modelling study. Philos Transact A Math Phys Eng Sci.2006;364:1107-33.
[117]Zygmunt AC, Eddlestone GT, Thomas GP, Nesterenko VV, Antzelevitch C. Larger late sodium conductance in M cells contributes to electrical heterogeneity in canine ventricle. Am J Physiol Heart Circ Physiol.2001;281:H689-97.
[118]Valdivia CR, Chu WW, Pu J, Foell JD, Haworth RA, Wolff MR, et al. Increased late sodium current in myocytes from a canine heart failure model and from failing human heart. J Mol Cell Cardiol.2005;38:475-83.
[119]Liu DW, Antzelevitch C. Characteristics of the delayed rectifier current (IKr and 1Ks) in canine ventricular epicardial, midmyocardial, and endocardial myocytes. A weaker IKs contributes to the longer action potential of the M cell. Circ Res. 1995;76:351-65.
[120]Liu D, Gintant G, Antzelevitch C. Ionic bases for electrophysiological distinctions among epicardial, midmyocardial, and endocardial myocytes from the free wall of the canine left ventricle. Circulation Research.1993;72:671-87.
[121]Xiong W, Tian Y, DiSilvestre D, Tomaselli GF. Transmural Heterogeneity of Na+-Ca2+ Exchange:Evidence for Differential Expression in Normal and Failing Hearts. Circ Res.2005;97:207-9.
[122]Laurita KR, Katra R, Wible B, Wan X, Koo MH. Transmural Heterogeneity of Calcium Handling in Canine. Circulation Research.2003;92:668-75.
[123]Li G-R, Lau C-P, Ducharme A, Tardif J-C, Nattel S. Transmural action potential and ionic current remodeling in ventricles of failing canine hearts. Am J Physiol Heart Circ Physiol.2002;283:H1031-41.
[124]Wilde AA, Escande D, Schumacher CA, Thuringer D, Mestre M, Fiolet JW, et al. Potassium accumulation in the globally ischemic mammalian heart. A role for the ATP-sensitive potassium channel. Circ Res.1990;67:835-43.
[125]Ferrero JM, Jr., Saiz J, Ferrero JM, Thakor NV. Simulation of action potentials from metabolically impaired cardiac myocytes. Role of ATP-sensitive K+ current. Circ Res.1996;79:208-21.
[126]Plonsey R BR. Bioelectricity:A Quantitative Approach.1988.
[127]Liu DW, Gintant GA, Antzelevitch C. Ionic bases for electrophysiological distinctions among epicardial, midmyocardial, and endocardial myocytes from the free wall of the canine left ventricle. Circ Res.1993;72:671-87.
[128]Cordeiro JM, Greene L, Heilmann C, Antzelevitch D, Antzelevitch C. Transmural heterogeneity of calcium activity and mechanical function in the canine left ventricle. Am J Physiol Heart Circ Physiol.2004;286:H1471-9.
[129]Sato R, Noma A, Kurachi Y, Irisawa H. Effects of intracellular acidification on membrane currents in ventricular cells of the guinea pig. Circ Res.1985;57:553-61.
[130]Harvey RD, Ten Eick RE. On the role of sodium ions in the regulation of the inward-rectifying potassium conductance in cat ventricular myocytes. J Gen Physiol. 1989;94:329-48.
[131]Tedesco C, Reigle J, Bergin J. Sudden Cardiac Death in Heart Failure. Journal of Cardiovascular Nursing.2000;14:38-56.
[132]Li GR, Lau CP, Ducharme A, Tardif JC, Nattel S. Transmural action potential and ionic current remodeling in ventricles of failing canine hearts. Am J Physiol Heart Circ Physiol.2002;283:H 1031-41.
[133]Maltsev VA, Reznikov V, Undrovinas NA, Sabbah HN, Undrovinas A. Modulation of late sodium current by Ca2+, calmodulin, and CaMKII in normal and failing dog cardiomyocytes:similarities and differences. Am J Physiol Heart Circ Physiol.2008;294:H 1597-608.
[134]Wagner S, Hacker E, Grandi E, Weber SL, Dybkova N, Sossalla S, et al. Ca/calmodulin kinase Ⅱ differentially modulates potassium currents. Circ Arrhythm Electrophysiol.2009;2:285-94.
[135]Wagner S, Dybkova N, Rasenack EC, Jacobshagen C, Fabritz L, Kirchhof P, et al. Ca2+/calmodulin-dependent protein kinase Ⅱ regulates cardiac Na+ channels. J Clin Invest.2006; 116:3127-38.
[136]Ai X, Curran JW, Shannon TR, Bers DM, Pogwizd SM. Ca2+/calmodul in-dependent protein kinase modulates cardiac ryanodine receptor phosphorylation and sarcoplasmic reticulum Ca2+ leak in heart failure. Circ Res. 2005;97:1314-22.
[137]Shannon TR, Ginsburg KS, Bers DM. Quantitative assessment of the SR Ca2+ leak-load relationship. Circ Res.2002;91:594-600.
[138]Shannon TR, Wang F, Bers DM. Regulation of cardiac sarcoplasmic reticulum Ca release by luminal [Ca] and altered gating assessed with a mathematical model. Biophys J.2005;89:4096-110.
[139]Cordeiro JM, Mazza M, Goodrow R, Ulahannan N, Antzelevitch C, Di Diego JM. Functionally distinct sodium channels in ventricular epicardial and endocardial cells contribute to a greater sensitivity of the epicardium to electrical depression. Am J Physiol Heart Circ Physiol.2008;295:H 154-62.
[140]Pu J, Boyden PA. Alterations of Na+ currents in myocytes from epicardial border zone of the infarcted heart. A possible ionic mechanism for reduced excitability and postrepolarization refractoriness. Circ Res.1997;81:110-9.
[141]Lue WM, Boyden PA. Abnormal electrical properties of myocytes from chronically infarcted canine heart. Alterations in Vmax and the transient outward current. Circulation.1992;85:1175-88.
[142]Xiao L, Coutu P, Villeneuve LR, Tadevosyan A, Maguy A, Le Bouter S, et al. Mechanisms underlying rate-dependent remodeling of transient outward potassium current in canine ventricular myocytes. Circ Res.2008; 103:733-42.
[143]Greenstein JL, Wu R, Po S, Tomaselli GF, Winslow RL. Role of the calcium-independent transient outward current I(to1) in shaping action potential morphology and duration. Circ Res.2000;87:1026-33.
[144]Akar FG, Wu RC, Deschenes I, Armoundas AA, Piacentino V,3rd, Houser SR, et al. Phenotypic differences in transient outward K+ current of human and canine ventricular myocytes:insights into molecular composition of ventricular Ito. Am J Physiol Heart Circ Physiol.2004;286:H602-9.
[145]Rubart M, Lopshire JC, Fineberg NS, Zipes DP. Changes in left ventricular repolarization and ion channel currents following a transient rate increase superimposed on bradycardia in anesthetized dogs. J Cardiovasc Electrophysiol. 2000; 11:652-64.
[146]Hua F, Gilmour RF, Jr. Contribution of IKr to rate-dependent action potential dynamics in canine endocardium. Circ Res.2004;94:810-9.
[147]Gao J, Wang W, Cohen IS, Mathias RT. Transmural gradients in Na/K pump activity and [Na+]I in canine ventricle. Biophys J.2005;89:1700-9.
[148]Sipido KR, Volders PG, de Groot SH, Verdonck F, Van de Werf F, Wellens HJ, et al. Enhanced Ca(2+) release and Na/Ca exchange activity in hypertrophied canine ventricular myocytes:potential link between contractile adaptation and arrhythmogenesis. Circulation.2000; 102:2137-44.
[149]Lou Q, Fedorov VV, Glukhov AV, Moazami N, Fast VG, Efimov IR. Transmural heterogeneity and remodeling of ventricular excitation-contraction coupling in human heart failure. Circulation.2011;123:1881-90.
[150]Akar FG Rosenbaum DS. Transmural electrophysiological heterogeneities underlying arrhythmogenesis in heart failure. Circ Res.2003;93:638-45.
[151]Despa S, Islam MA, Weber CR, Pogwizd SM, Bers DM. Intracellular Na(+) concentration is elevated in heart failure but Na/K pump function is unchanged. Circulation.2002;105:2543-8.
[152]Verdonck F, Volders PG, Vos MA, Sipido KR. Increased Na+ concentration and altered Na/K pump activity in hypertrophied canine ventricular cells. Cardiovasc Res. 2003;57:1035-43.
[153]Baartscheer A, Schumacher CA, van Borren MM, Belterman CN, Coronel R, Fiolet JW. Increased Na+/H+-exchange activity is the cause of increased [Na+]i and underlies disturbed calcium handling in the rabbit pressure and volume overload heart failure model. Cardiovasc Res.2003;57:1015-24.
[154]Grandi E, Puglisi JL, Wagner S, Maier LS, Severi S, Bers DM. Simulation of Ca-calmodulin-dependent protein kinase Ⅱ on rabbit ventricular myocyte ion currents and action potentials. Biophys J.2007;93:3835-47.
[155]Bers DM. Excitation-contraction coupling and cardiac contractile force. Kluwer Academic Press.2001:427.
[156]Wilson LD, Jeyaraj D, Wan X, Hoeker GS, Said TH, Gittinger M, et al. Heart failure enhances susceptibility to arrhythmogenic cardiac alternans. Heart Rhythm. 2009;6:251-9.
[157]Shannon TR, Lew WY. Diastolic release of calcium from the sarcoplasmic reticulum:a potential target for treating triggered arrhythmias and heart failure. J Am Coll Cardiol.2009;53:2006-8.
[158]Bossuyt J, Ai X, Moorman JR, Pogwizd SM, Bers DM. Expression and phosphorylation of the na-pump regulatory subunit phospholemman in heart failure. Circ Res.2005;97:558-65.
[159]Lukas A, Antzelevitch C. Differences in the electrophysiological response of canine ventricular epicardium and endocardium to ischemia. Role of the transient outward current. Circulation.1993;88:2903-15.
[160]Zygmunt AC, Goodrow RJ, Antzelevitch C. I(NaCa) contributes to electrical heterogeneity within the canine ventricle. Am J Physiol Heart Circ Physiol. 2000;278:H1671-8.
[161]Kaab S, Nuss HB, Chiamvimonvat N, O'Rourke B, Pak PH, Kass DA, et al. Ionic mechanism of action potential prolongation in ventricular myocytes from dogs with pacing-induced heart failure. Circ Res.1996;78:262-73.
[162]Sun X, Wang HS. Role of the transient outward current (Ito) in shaping canine ventricular action potential--a dynamic clamp study. J Physiol.2005;564:411-9.
[163]Decker KF, Heijman J, Silva JR, Hund TJ, Rudy Y. Properties and ionic mechanisms of action potential adaptation, restitution, and accommodation in canine epicardium. Am J Physiol Heart Circ Physiol.2009;296:H1017-26.
[164]Akar FG, Wu RC, Juang GJ, Tian Y, Burysek M, Disilvestre D, et al. Molecular mechanisms underlying K+current downregulation in canine tachycardia-induced heart failure. Am J Physiol Heart Circ Physiol.2005;288:H2887-96.
[165]Jost N. A szivizom repolarizaciojaban reszt vevo kulonbozo kaliumcsatornak kolcsonhatasanak vizsgalata emlos kamraizmon-A repolarizacios tartalek jelentosege. Cardiologia Hungarica.2008:10-6.
[166]Xiao L, Zhang L, Han W, Wang Z, Nattel S. Sex-based transmural differences in cardiac repolarization and ionic-current properties in canine left ventricles. Am J Physiol Heart Circ Physiol.2006;291:H570-80.
[167]Szabo G, Szentandrassy N, Biro T, Toth BI, Czifra G, Magyar J, et al. Asymmetrical distribution of ion channels in canine and human left-ventricular wall: epicardium versus midmyocardium. Pflugers Arch.2005;450:307-16.
[168]Laurita KR, Katra R, Wible B, Wan X, Koo MH. Transmural heterogeneity of calcium handling in canine. Circ Res.2003;92:668-75.
[169]Obreztchikova MN, Patberg KW, Plotnikov AN, Ozgen N, Shlapakova IN, Rybin AV, et al. I(Kr) contributes to the altered ventricular repolarization that determines long-term cardiac memory. Cardiovasc Res.2006;71:88-96.
[170]Flaim SN, Giles WR, McCulloch AD. Contributions of sustained INa and IKv43 to transmural heterogeneity of early repolarization and arrhythmogenesis in canine left ventricular myocytes. Am J Physiol Heart Circ Physiol. 2006;291:H2617-29.
[171]Benson AP, Aslanidi OV, Zhang H, Holden AV. The canine virtual ventricular wall:a platform for dissecting pharmacological effects on propagation and arrhythmogenesis. Prog Biophys Mol Biol.2008;96:187-208.
[172]Kuijpers NH, Ten Eikelder HM, Bovendeerd PH, Verheule S, Arts T, Hilbers PA. Mechanoelectric feedback as a trigger mechanism for cardiac electrical remodeling:a model study. Ann Biomed Eng.2008;36:1816-35.
[173]Solovyova O, Katsnelson L, Guriev S, Nikitina L, Protsenko Y, Routkevitch S, et al. Mechanical inhomogeneity of myocardium studied in parallel and serial cardiac muscle duplexes:experiments and models. Chaos, Solitons & Fractals. 2002;13:1685-711.