Electrical Activity in Cardiac Tissue, Modeling of
S.L. Cloherty
University of New South Wales, Graduate School of Biomedical Engineering, Sydney, Australia
University of Newcastle, School of Engineering, Callaghan, Australia
Search for more papers by this authorS. Dokos
University of New South Wales, Graduate School of Biomedical Engineering, Sydney, Australia
Search for more papers by this authorN.H. Lovell
University of New South Wales, Graduate School of Biomedical Engineering, Sydney, Australia
Australian Technology Park, National ICT Australia (NICTA), Eveleigh, Australia
Search for more papers by this authorS.L. Cloherty
University of New South Wales, Graduate School of Biomedical Engineering, Sydney, Australia
University of Newcastle, School of Engineering, Callaghan, Australia
Search for more papers by this authorS. Dokos
University of New South Wales, Graduate School of Biomedical Engineering, Sydney, Australia
Search for more papers by this authorN.H. Lovell
University of New South Wales, Graduate School of Biomedical Engineering, Sydney, Australia
Australian Technology Park, National ICT Australia (NICTA), Eveleigh, Australia
Search for more papers by this authorAbstract
The heart is a complex organ, exhibiting significant variation in both structural and functional characteristics from one region to another. Mathematical modeling represents a powerful tool for improving our understanding of the mechanisms underlying both normal and abnormal cardiac function. This article describes the techniques routinely employed in modeling the electrical activity of the heart at the cellular and tissue scales. These techniques have proven useful in modeling the structural and functional characteristics in all areas of the heart and provide a foundation for constructing integrated models of the entire heart.
Bibliography
- 1D. Noble, Modeling the heart: Insights, failures, and progress. Bioessays. 2002; 24: 1155–1163.
- 2A. L. Hodgkin and A. F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 1952; 117: 500–544.
- 3J. J. B. Jack, D. Noble, and R. W. Tsien, Electric Current Flow in Excitable Cells. Oxford: Clarendon Press, 1975.
- 4D. Noble, A modification of the Hodgkin–Huxley equations applicable to Purkinje fibre action and pace-maker potentials. J. Physiol. 1962; 160: 317–352.
- 5R. E. McAllister, D. Noble, and R. W. Tsien, Reconstruction of the electrical activity of cardiac Purkinje fibres. J. Physiol. 1975; 251: 1–59.
- 6G. W. Beeler and H. Reuter, Reconstruction of the action potential of ventricular fibres. J. Physiol. 1977; 268: 177–210.
- 7K. Yanagihara, A. Noma, and H. Irisawa, Reconstruction of sino-atrial node pacemaker potential based on the voltage clamp experiments. Jpn. J. Physiol. 1980; 30: 841–857.
- 8D. G. Bristow and J. W. Clark, A mathematical model of primary pacemaking cell in sa node of the heart. Am. J. Physiol. 1982; 243: H207–H218.
- 9D. DiFrancesco and D. Noble, A model of cardiac electrical activity incorporating ionic pumps and concentration changes. Phil. Trans. R. Soc. Lond. B. 1985; 307: 353–398.
- 10S. Dokos, B. G. Celler, and N. H. Lovell, Vagal control of sinoatrial rhythm: a mathematical model. J. Theor. Biol. 1996; 182: 21–44.
- 11A. Michailova and A. D. McCulloch, Model study of ATP and ADP buffering, transport of Ca2+ and Mg2+, and regulation of ion pumps in ventricular myocytes. Biophys. J. 2001; 81: 614–629.
- 12A. Garny, D. Noble, and P. Kohl, Dimensionality in cardiac modelling. Prog. Biophys. Mol. Biol. 2005; 87: 47–66.
- 13R. FitzHugh, Impulses and physiological states in theoretical models of nerve membrane. Biophys. J. 1961; 1: 445–466.
- 14S. Sato, S. Doi, and T. Nomura, Bonhoeffer-van der Pol oscillator model of the sino-atrial node: A possible mechanism of heart rate regulation. Meth. Inform. Med. 1994; 33: 116–119.
- 15J. Nagumo, S. Arimoto, and S. Yoshizawa, An active pulse transmission line simulating nerve axon. Proc. IRE. 1962; 50: 2061–2071.
- 16J. M. Rogers and A. D. McCulloch, A collocation-galerkin finite element model of cardiac action potential propagation. IEEE Trans. Biomed. Eng. 1994; 41: 743–757.
- 17F. J. L. van Capelle and D. Dürrer, Computer simulation of arrhythmias in a network of coupled excitable elements. Circ. Res. 1980; 47: 454–466.
- 18L. P. Endresen, A theory for the membrane potential of living cells. Ph.D. dissertation, Norwegian University of Science and Technology, June 2000.
- 19G. C. L. Bett and R. L. Rasmusson, Computer models of ion channels. In: C. Cabo and D. S. Rosenbaum, eds., Qualitative Cardiac Electrophysiology. New York: Marcel Dekker, 2002, pp. 1–60.
10.1201/b14064-2 Google Scholar
- 20B. Hille, Ion Channels of Excitable Membranes, 3rd ed. Sunderland, MA: Sinauer Associates, 2001.
10.1111/j.1540-8167.1998.tb01847.x Google Scholar
- 21L. A. Irvine, M. S. Jafri, and R. L. Winslow, Cardiac sodium channel Markov model with temperature dependence and recovery from inactivation. Biophys. J. 1999; 76: 1868–1885.
- 22D. Colquhoun and A. G. Hawkes, On the stochastic properties of bursts of single ion channel openings and of clusters of bursts. Phil. Trans. R. Soc. Lond. B. 1982; 300: 1–59.
- 23N. H. Lovell, S. L. Cloherty, B. G. Celler, and S. Dokos, A gradient model of cardiac pacemaker myocytes. Prog. Biophys. Mol. Biol. 2004; 85: 301–323.
- 24Y. E. Earm and D. Noble, A model of the single atrial cell: relation between calcium current and calcium release. Proc. R. Soc. Lond. B. 1990; 240: 83–96.
- 25G. M. Faber and Y. Rudy, Action potential and contractility changes in [na+]i overloaded cardiac myocytes: A simulation study. Biophys. J. 2000; 78: 2392–2404.
- 26D. W. Hilgemann and D. Noble, Excitation-contraction coupling and extracellular calcium transients in rabbit atrium: Reconstruction of basic cellular mechanisms. Proc. R. Soc. Lond. B. 1987; 230: 63–205.
- 27C.-H. Luo and Y. Rudy, A dynamic model of the cardiac ventricular action potential: I. simulations of ionic currents and concentration changes. Circ. Res. 1994; 74: 1071–1096.
- 28G. K. Moe, W. C. Rheinboldt, and J. A. Abildskov, A computer model of atrial fibrillation. Am. Heart J. 1964; 67: 200–220.
- 29P. Siregar, J. Sinteff, M. Chahine, and P. Lebeux, A cellular automata model of the heart and its coupling with a qualitative model. Comp. Biomed. Res. 1996; 29: 222–246.
- 30H. Zhu, Y. Sun, G. Rajagopal, A. Mondry, and P. Dhar, Facilitating arrhythmia simulation: The method of quantitative cellular automata modeling and parallel running. Biomed. Eng. Online. 2004; 3.
- 31C. S. Henriquez, Simulating the electrical behaviour of cardiac tissue using the bidomain model. Crit. Rev. Biomed. Eng. 1993; 21: 1–77.
- 32O. H. Schmidtt, Biological information processing using the concept of interpenetrating domains. In: K. N. Leibovic, ed., Information Processing in the Nervous System. New York: Springer-Verlag, 1969, pp. 325–331.
- 33I. J. Le Grice, B. H. Smaill, L. Z. Chai, S. G. Edgar, J. B. Gavin, and P. J. Hunter, Laminar structure of the heart: ventricular myocyte arrangement and connective tissue architecture in the dog. Am. J. Physiol. 1995; 269: H571–H582.
- 34E. J. Vigmond, F. Aguel, and N. A. Trayanova, Computational techniques for solving the bidomain equations in three dimensions. IEEE Trans. Biomed. Eng. 2003; 49: 1260–1269.
- 35J. P. Wikswo Jr., S.-F. Lin, and R. A. Abbas, Virtual electrodes in cardiac tissue: A common mechanism for anodal and cathodal stimulation. Biophys. J. 1995; 69: 2195–2210.
- 36S. Dokos and N. H. Lovell, Parameter estimation in cardiac ionic models. Prog. Biophys. Mol. Biol. 2004; 85: 407–431.
- 37P. J. Hunter and T. K. Borg, Integration from proteins to organs: The Physiome Project. Nature Rev. 2003; 4: 237–243.
- 38Y. Rudy, From genome to physiome: Integrative models of cardiac excitation. Ann. Biomed. Eng. 2000; 28: 945–950.