Computer modelling of the sinoatrial node

Over the past decades patch-clamp experiments have provided us with detailed information on the different types of ion channels that are present in the cardiac cell membrane. Sophisticated cardiac cell models based on these data can help us understand how the different types of ion channels act together to produce the cardiac action potential. In the field of biological pacemaker engineering, such models provide important instruments for the assessment of the functional implications of changes in density of specific ion channels aimed at producing stable pacemaker activity. In this review, an overview is given of the progress made in cardiac cell modelling, with particular emphasis on the development of sinoatrial (SA) nodal cell models. Also, attention is given to the increasing number of publicly available tools for non-experts in computer modelling to run cardiac cell models.

[1]  D. Noble A modification of the Hodgkin—Huxley equations applicable to Purkinje fibre action and pacemaker potentials , 1962, The Journal of physiology.

[2]  D. Noble,et al.  The Role of Sodium ‐ Calcium Exchange during the Cardiac Action Potential a , 1991, Annals of the New York Academy of Sciences.

[3]  A. Noma,et al.  A sustained inward current activated at the diastolic potential range in rabbit sino‐atrial node cells. , 1995, The Journal of physiology.

[4]  Michael R. Rosen,et al.  Biological pacemakers based on If , 2007, Medical & Biological Engineering & Computing.

[5]  Henggui Zhang,et al.  Sustained Inward Current and Pacemaker Activity of Mammalian Sinoatrial Node , 2002, Journal of cardiovascular electrophysiology.

[6]  C. Henriquez Simulating the electrical behavior of cardiac tissue using the bidomain model. , 1993, Critical reviews in biomedical engineering.

[7]  J. Myrheim,et al.  A theory for the membrane potential of living cells , 1998, European Biophysics Journal.

[8]  J. Clark,et al.  A mathematical model of a rabbit sinoatrial node cell. , 1994, The American journal of physiology.

[9]  Balth van der Pol Jun Docts. Sc.,et al.  LXXII. The heartbeat considered as a relaxation oscillation, and an electrical model of the heart , 1928 .

[10]  W. Giles,et al.  A mathematical model of action potential heterogeneity in adult rat left ventricular myocytes. , 2001, Biophysical journal.

[11]  D. Noble,et al.  Reconstruction of the electrical activity of cardiac Purkinje fibres. , 1975, The Journal of physiology.

[12]  Yoram Rudy,et al.  Rate Dependence and Regulation of Action Potential and Calcium Transient in a Canine Cardiac Ventricular Cell Model , 2004, Circulation.

[13]  R. Winslow,et al.  Mechanisms of altered excitation-contraction coupling in canine tachycardia-induced heart failure, II: model studies. , 1999, Circulation research.

[14]  C Antzelevitch,et al.  Phase resetting and annihilation in a mathematical model of sinus node. , 1985, The American journal of physiology.

[15]  R. Winslow,et al.  A computational model of the human left-ventricular epicardial myocyte. , 2004, Biophysical journal.

[16]  Mark Potse,et al.  A Comparison of Monodomain and Bidomain Reaction-Diffusion Models for Action Potential Propagation in the Human Heart , 2006, IEEE Transactions on Biomedical Engineering.

[17]  Hee-Sup Shin,et al.  Bradycardia and Slowing of the Atrioventricular Conduction in Mice Lacking CaV3.1/&agr;1G T-Type Calcium Channels , 2006, Circulation research.

[18]  Robert F Gilmour,et al.  Ionic mechanism of electrical alternans. , 2002, American journal of physiology. Heart and circulatory physiology.

[19]  D DiFrancesco,et al.  Reciprocal role of the inward currents ib, Na and if in controlling and stabilizing pacemaker frequency of rabbit sino-atrial node cells , 1992, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[20]  J. Jacklet,et al.  Neuronal and cellular oscillators , 1989 .

[21]  H Honjo,et al.  Characterisation of the transient outward K+ current in rabbit sinoatrial node cells. , 2000, Cardiovascular research.

[22]  D. Noble,et al.  A model of sino-atrial node electrical activity based on a modification of the DiFrancesco-Noble (1984) equations , 1984, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[23]  D. Noble Cardiac Action and Pacemaker Potentials based on the Hodgkin-Huxley Equations , 1960, Nature.

[24]  Candido Cabo,et al.  Electrical remodeling of the epicardial border zone in the canine infarcted heart: a computational analysis. , 2003, American journal of physiology. Heart and circulatory physiology.

[25]  R. Winslow,et al.  Cardiac Ca2+ dynamics: the roles of ryanodine receptor adaptation and sarcoplasmic reticulum load. , 1998, Biophysical journal.

[26]  Catherine M Lloyd,et al.  CellML: its future, present and past. , 2004, Progress in biophysics and molecular biology.

[27]  D. Noble,et al.  Improved guinea-pig ventricular cell model incorporating a diadic space, IKr and IKs, and length- and tension-dependent processes. , 1998, The Canadian journal of cardiology.

[28]  C. Luo,et al.  A model of the ventricular cardiac action potential. Depolarization, repolarization, and their interaction. , 1991, Circulation research.

[29]  Semahat S. Demir,et al.  Interactive Cell Modeling Web-Resource, iCell, as a Simulation-Based Teaching and Learning Tool to Supplement Electrophysiology Education , 2006, Annals of Biomedical Engineering.

[30]  D. Noble,et al.  A model of the single atrial cell: relation between calcium current and calcium release , 1990, Proceedings of the Royal Society of London. B. Biological Sciences.

[31]  D DiFrancesco,et al.  A model of cardiac electrical activity incorporating ionic pumps and concentration changes. , 1985, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[32]  G. W. Beeler,et al.  Reconstruction of the action potential of ventricular myocardial fibres , 1977, The Journal of physiology.

[33]  S Nattel,et al.  Mathematical analysis of canine atrial action potentials: rate, regional factors, and electrical remodeling. , 2000, American journal of physiology. Heart and circulatory physiology.

[34]  Denis Noble,et al.  Comparative study of rabbit sino-atrial node cell models , 2002 .

[35]  R. FitzHugh Impulses and Physiological States in Theoretical Models of Nerve Membrane. , 1961, Biophysical journal.

[36]  N H Lovell,et al.  Vagal control of sinoatrial rhythm: a mathematical model. , 1996, Journal of theoretical biology.

[37]  R. Winslow,et al.  An integrative model of the cardiac ventricular myocyte incorporating local control of Ca2+ release. , 2002, Biophysical journal.

[38]  Marc A. Vos,et al.  Inhibition of cardiomyocyte automaticity by electrotonic application of inward rectifier current from Kir2.1 expressing cells , 2006, Medical and Biological Engineering and Computing.

[39]  R Wilders,et al.  Pacemaker activity of the rabbit sinoatrial node. A comparison of mathematical models. , 1991, Biophysical journal.

[40]  C. Luo,et al.  A dynamic model of the cardiac ventricular action potential. I. Simulations of ionic currents and concentration changes. , 1994, Circulation research.

[41]  M. Zaniboni,et al.  Beat-to-beat repolarization variability in ventricular myocytes and its suppression by electrical coupling. , 2000, American journal of physiology. Heart and circulatory physiology.

[42]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1952, The Journal of physiology.

[43]  Yasutaka Kurata,et al.  Dynamical description of sinoatrial node pacemaking: improved mathematical model for primary pacemaker cell. , 2002, American journal of physiology. Heart and circulatory physiology.

[44]  Henggui Zhang,et al.  Analysis of the Chronotropic Effect of Acetylcholine on Sinoatrial Node Cells , 2002, Journal of cardiovascular electrophysiology.

[45]  H Zhang,et al.  Mathematical models of action potentials in the periphery and center of the rabbit sinoatrial node. , 2000, American journal of physiology. Heart and circulatory physiology.

[46]  Ronald Wilders,et al.  Dynamic clamp: a powerful tool in cardiac electrophysiology , 2006, The Journal of physiology.

[47]  R L Winslow,et al.  Molecular Interactions Between Two Long-QT Syndrome Gene Products, HERG and KCNE2, Rationalized by In Vitro and In Silico Analysis , 2001, Circulation research.

[48]  Stanley Nattel,et al.  Time-dependent transients in an ionically based mathematical model of the canine atrial action potential. , 2002, American journal of physiology. Heart and circulatory physiology.

[49]  Yasutaka Kurata,et al.  Roles of L-type Ca2+ and delayed-rectifier K+ currents in sinoatrial node pacemaking: insights from stability and bifurcation analyses of a mathematical model. , 2003, American journal of physiology. Heart and circulatory physiology.

[50]  D. Noble,et al.  A model for human ventricular tissue. , 2004, American journal of physiology. Heart and circulatory physiology.

[51]  Yoram Rudy,et al.  Mechanism of Pacemaking in IK1-Downregulated Myocytes , 2003 .

[52]  A. Noma,et al.  Reconstruction of sino-atrial node pacemaker potential based on the voltage clamp experiments. , 1980, The Japanese journal of physiology.

[53]  Y Shinagawa,et al.  Sustained inward current during pacemaker depolarization in mammalian sinoatrial node cells. , 2000, Circulation research.

[54]  Satoshi Matsuoka,et al.  Role of individual ionic current systems in ventricular cells hypothesized by a model study. , 2003, The Japanese journal of physiology.

[55]  F. Fenton,et al.  Vortex dynamics in three-dimensional continuous myocardium with fiber rotation: Filament instability and fibrillation. , 1998, Chaos.

[56]  I. Hisatome,et al.  Dynamical mechanisms of pacemaker generation in IK1-downregulated human ventricular myocytes: insights from bifurcation analyses of a mathematical model. , 2005, Biophysical journal.

[57]  Satoshi Matsuoka,et al.  simBio: a Java package for the development of detailed cell models. , 2006, Progress in biophysics and molecular biology.

[58]  G. Bett,et al.  Computer model of action potential of mouse ventricular myocytes. , 2004, American journal of physiology. Heart and circulatory physiology.

[59]  F A Roberge,et al.  Revised formulation of the Hodgkin-Huxley representation of the sodium current in cardiac cells. , 1987, Computers and biomedical research, an international journal.

[60]  D. Noble,et al.  Rectifying Properties of Heart Muscle , 1960, Nature.

[61]  Y Shinagawa,et al.  The sustained inward current and inward rectifier K+ current in pacemaker cells dissociated from rat sinoatrial node , 2000, The Journal of physiology.

[62]  C Nordin,et al.  Computer model of membrane current and intracellular Ca2+ flux in the isolated guinea pig ventricular myocyte. , 1993, The American journal of physiology.

[63]  Alexander V Panfilov,et al.  Comparison of electrophysiological models for human ventricular cells and tissues. , 2006, Progress in biophysics and molecular biology.

[64]  J. Clark,et al.  Mathematical model of an adult human atrial cell: the role of K+ currents in repolarization. , 1998, Circulation research.

[65]  W. J. Hedley,et al.  A short introduction to CellML , 2001, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[66]  Denis Noble,et al.  Cellular Open Resource (COR): a Public CellML Based Environment for Modeling Biological Function , 2003, Int. J. Bifurc. Chaos.

[67]  J L Puglisi,et al.  LabHEART: an interactive computer model of rabbit ventricular myocyte ion channels and Ca transport. , 2001, American journal of physiology. Cell physiology.

[68]  P. Hunter,et al.  One‐Dimensional Rabbit Sinoatrial Node Models: , 2003, Journal of cardiovascular electrophysiology.

[69]  M. Courtemanche,et al.  Ionic mechanisms underlying human atrial action potential properties: insights from a mathematical model. , 1998, The American journal of physiology.

[70]  K. T. ten Tusscher,et al.  Alternans and spiral breakup in a human ventricular tissue model. , 2006, American journal of physiology. Heart and circulatory physiology.

[71]  D. Beuckelmann,et al.  Simulation study of cellular electric properties in heart failure. , 1998, Circulation research.

[72]  Mary B. Wagner,et al.  Propagation of pacemaker activity , 2007, Medical & Biological Engineering & Computing.

[73]  R Wilders,et al.  Beating irregularity of single pacemaker cells isolated from the rabbit sinoatrial node. , 1993, Biophysical journal.

[74]  J. Clark,et al.  A model of the action potential and underlying membrane currents in a rabbit atrial cell. , 1996, The American journal of physiology.

[75]  John W. Clark,et al.  Parasympathetic modulation of sinoatrial node pacemaker activity in rabbit heart: a unifying model. , 1999, American journal of physiology. Heart and circulatory physiology.

[76]  Elizabeth M Cherry,et al.  Real-time computer simulations of excitable media: JAVA as a scientific language and as a wrapper for C and FORTRAN programs. , 2002, Bio Systems.

[77]  H. Brown,et al.  Cardiac pacemaking in the sinoatrial node. , 1993, Physiological reviews.

[78]  N Lovell,et al.  Ion currents underlying sinoatrial node pacemaker activity: a new single cell mathematical model. , 1996, Journal of theoretical biology.

[79]  A C van Ginneken,et al.  Considerations in studying the transient outward K(+) current in cells exhibiting the hyperpolarization-activated current. , 2001, Cardiovascular research.

[80]  H Honjo,et al.  The sinoatrial node, a heterogeneous pacemaker structure. , 2000, Cardiovascular research.

[81]  Satoshi Matsuoka,et al.  Role of individual ionic current systems in the SA node hypothesized by a model study. , 2003, The Japanese journal of physiology.

[82]  D. Noble,et al.  Excitation-contraction coupling and extracellular calcium transients in rabbit atrium: reconstruction of basic cellular mechanisms , 1987, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[83]  A. V. Holden,et al.  Control of the pacemaker activity of the sinoatrial node by intracellular Ca2+. Experiments and modelling , 2001, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[84]  Trine Krogh-Madsen,et al.  An ionic model for rhythmic activity in small clusters of embryonic chick ventricular cells. , 2005, American journal of physiology. Heart and circulatory physiology.

[85]  Michael D Stern,et al.  Diastolic calcium release controls the beating rate of rabbit sinoatrial node cells: numerical modeling of the coupling process. , 2004, Biophysical journal.

[86]  R Wilders,et al.  A computationally efficient electrophysiological model of human ventricular cells. , 2002, American journal of physiology. Heart and circulatory physiology.

[87]  M. Guevara,et al.  A minimal single-channel model for the regularity of beating in the sinoatrial node. , 1995, Chaos.

[88]  J W Clark,et al.  A mathematical model of primary pacemaking cell in SA node of the heart. , 1982, The American journal of physiology.

[89]  Akinori Noma,et al.  Pacemaker Mechanisms of Rabbit Sinoatrial Node Cells , 1982 .

[90]  Habo J. Jongsma,et al.  Cardiac rate and rhythm : physiological, morphological, and developmental aspects , 1982 .

[91]  Donald M Bers,et al.  A mathematical treatment of integrated Ca dynamics within the ventricular myocyte. , 2004, Biophysical journal.

[92]  M Lei,et al.  Two components of the delayed rectifier potassium current, IK, in rabbit sino‐atrial node cells , 1996, Experimental physiology.

[93]  D Durrer,et al.  Computer Simulation of Arrhythmias in a Network of Coupled Excitable Elements , 1980, Circulation research.

[94]  Socrates Dokos,et al.  A gradient model of cardiac pacemaker myocytes. , 2004, Progress in biophysics and molecular biology.

[95]  P. C. Viswanathan,et al.  Recreating an artificial biological pacemaker: insights from a theoretical model. , 2006, Heart rhythm.

[96]  Aamir Shabbir,et al.  Experiments and Modeling , 1991 .