Computational modelling of biological systems: Tools and visions

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 358, Issue 1766, 2000, Pages 579-610

  Kohl, Peter ^a   Noble, Denis ^a   Winslow, Raimond L ^b   Hunter, Peter J ^c  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b Johns Hopkins University   (United States)

^c NONE

Author keywords

Heart; In silico; Ion current; Mathematical model; Physiome

Indexed keywords

EID: 0346041902     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2000.0547     Document Type: Article

References (117)

1. Attwell, D., Cohen, I., Eisner, D., Ohba, M. & Ojeda, C. 1979 The steady state TTX-sensitive ('window') sodium current in cardiac Purkinje fibres. Pflüg. Arch. 379, 137-142.
2. Bassingthwaighte, J. B. 1995 Towards modeling the human physionome. In Molecular and subcellular cardiology: effects on structure and function (ed. S. Sideman & R. Beyar), pp. 331-339. New York: Plenum.
3. Bassingthwaighte, J. B., Li, Z. & Qian, H. 1998 Blood flows and metabolic components of the cardiome. Prog. Biophys. Molec. Biol. 69, 445-461.
4. Beeler, G. W. & Reuter, H. 1977 Reconstruction of the action potential of ventricular myocardial fibres. J. Physiol. 268, 177-210.
5. Bennett, P. B., Yazawa, K., Makita, N. & George, A. L. 1995 Molecular mechanism for an inherited cardiac arrhythmia. Nature 376, 683-685.
6. Biktashev, V. N. & Holden, A. V. 1996 Re-entrant activity and its control in a model of mammalian ventricular tissue. Proc. R. Soc. Lond. B 263, 1373-1382.
7. Bock, G. R. & Goode, J. A. (eds) 1998 The limits of reductionism in modern biology. In Novartis Foundation Symp. Wiley.
8. Boyd, C. A. R. & Noble, D. 1993 The logic of life. The challenge of integrative physiology. Oxford University Press.
9. Boyett, M. R., Clough, A., Dekanski, J. & Holden, A. V. 1997 Modelling cardiac excitation and excitability. In Computational biology of the heart (ed. A. V. Panfilov & A. V. Holden), pp. 1-47. Wiley.
10. Bradley, C. P., Pullan, A. J. & Hunter, P. J. 1997 Geometric modelling of the human torso using cubic Hermite elements. Ann. Biomed. Engng 25, 96-111.
11. Brady, F. (ed.) 1965 Pope: an essay on man. MacMillan.
12. Brown, H. F., Kimura, J., Noble, D., Noble, S. J. & Taupignon, A. 1984 The ionic currents underlying pacemaker activity in rabbit sino-atrial node: experimental results and computer simulations. Proc. R. Soc. Lond. B 222, 329-347.
13. Cabo, C., Pertsov, A. M., Baxter, W. T., Davidenko, J. M. & Jalife, J. 1995 Measurements of curvature in an ionic model of cardiac tissue. Chaos Solitons Fractals 5, 481-489.
14. Cai, D., Winslow, R. L. & Noble, D. 1994 Effects of gap junction conductance on dynamics of sinoatrial node cells: two cell and large-scale network models. IEEE Trans. Biomed. Engng 41, 217-231.
15. Cannon, S. C., Brown Jr, R. H. & Corey, D. P. 1993 Theoretical reconstruction of myotonia and paralysis caused by incomplete inactivation of sodium channels. Biophys. J. 65, 270-288.
16. CAST Investigators 1989 Preliminary report: effect of encainide and flecainide on mortality in a randomized trial of arrhythmia suppression after myocardial infarction. New England J. Med. 321, 406-412.
17. Chay, T. R. 1996 Modeling slowly bursting neurons via calcium store and voltage-independent calcium current. Neural Computat. 8, 951-978.
18. Chay, T. R. 1997 Effects of extracellular calcium on electrical bursting and intracellular and luminal calcium oscillations in insulin secreting pancreatic β-cells. Biophys. J. 73, 1673-1688.
19. Ch'en, F. F.-T., Vaughan-Jones, R. D., Clarke, K. & Noble, D. 1998 Modelling myocardial ischaemia and reperfusion. Prog. Biophys. Molec. Biol. 69, 515-538.
20. Chen, Q. (and 17 others) 1998 Genetic basis and molecular mechanism for idiopathic ventricular fibrillation. Nature 392, 293-296.
21. 31P nuclear magnetic resonance. J. Molec. Cellular Cardiol. 19, 1153-1160.
22. CONSENSUS Report 1987 Effects of enalapril on mortality in severe congestive heart failure: results of the coopertive North Scandinavian enalapril survival study (CONSENSUS). New England J. Med. 316, 1429-1435.
23. Costa, K. D., Hunter, P. J., Wayne, J. S., Waldman, L. K., Guccione, J. M. & McCulloch, A. D. 1996 A three-dimensional finite element method for large elastic deformations of ventricular myocardium. 2. Prolate spheroidal coordinates. J. Biomech. Engng 118, 464-472.
24. Cuthbertson, K. S. R. & Chay, T. R. 1991 Modelling receptor-controlled intracellular calcium oscillators. Cell Calcium 12, 97-109.
25. Demir, S. S., Clark, J. W., Murphey, C. R. & Giles, W. R. 1994 A mathematical model of a rabbit sinoatrial node cell. Am. J. Physiol. 266, C832-C852.
26. Dieudonne, J. M. 1969 The left ventricle as confocal spheroids. Bull. Math. Biophys. 31, 433-439.
27. DiFrancesco, D. & Noble, D. 1985 A model of cardiac electrical activity incorporating ionic pumps and concentration changes. Phil. Trans. R. Soc. Lond. B 307, 353-398.
28. Earm, Y. E. & Noble, D. 1990 A model of the single atrial cell: relation between calcium current and calcium release. Proc. R. Soc. Lond. B 240, 83-96.
29. Engels, F. 1879 Dialektik der Natur. (Published in 1995 in Karl Marx/Friedrich Engels Werke, vol. 20, pp. 305-570. Institut für Marxismus-Leninismus beim ZK der SED. Berlin: Dietz.)
30. Fast, V. G. & Kléber, A. G. 1995 Cardiac tissue geometry as a determinant of unidirectional conduction block: assessment of microscopic excitation spread by optical mapping in patterned cell cultures and in a computer model. Cardiovasc. Res. 29, 697-707.
31. FitzHugh, R. 1960 Thresholds and plateaus in the Hodgkin-Huxley nerve equations. J. General Physiol. 43, 867-896.
32. Gan, Q. & Wei, Y. 1992 Neural modeling with dynamically adjustable threshold and refractory period. Biosystems 27, 137-144.
33. Gould, P., Ghista, D. N., Brombolich, L. & Mirsky, I. 1972 In vivo stresses in the human left ventricular wall: analysis accounting for the irregular 3D geometry and comparison with idealized geometry analyses. J. Biomech. 5, 521-539.
34. Grindrod, P. 1995 One-way blocks in excitable media. Chaos Solitons Fractals 5, 555-565.
35. Gul'ko, F. B. & Petrov, A. A. 1972 Mechanism of the formation of closed propagation pathways in excitable media. Biofizika 17, 261-270.
36. Hancox, J. C., Witchel, H. J. & Varghese, A. 1998 Alteration of HERG current profile during the cardiac ventricular action potential, following a pore mutation. Biochem. Biophys. Res. Commun. 253, 719-724.
37. Hegel, G. W. F. 1830 Enzyklopädie der philosophischen Wissenschaften in Grundrisse. Mit den mündlichen Zusätzen. (Published in 1995 by Suhrkamp Verlag, Frankfurt.)
38. Hilgemann, D. W. & Noble, D. 1987 Excitation-contraction coupling and extracellular calcium transients in rabbit atrium: reconstruction of basic cellular mechanisms. Proc. R. Soc. Lond. B 230, 163-205.
39. Hodgkin, A. L. & Huxley, A. F. 1952 A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117, 500-544.
40. Holden, A. V. 1997 The restless heart of a spiral. Nature 387, 655-657.
41. Holden, A. V. & Panfilov, A. V. 1997 Modelling propagation in excitable media. In Computational biology of the heart (ed. A. V. Panfilov & A. V. Holden), pp. 65-99. Wiley.
42. Hudson, T. J. 1998 The Human Genome Project: tools for the identification of disease genes. Clin. Investigative Med. 21, 267-276.
43. Hunter, P. J. 1995 Myocardial constitutive laws for continuum models of the heart. In Molecular and subcellular cardiology (ed. S. Sideman & R. Beyar), pp. 303-318. New York: Plenum.
44. Hunter, P. J. & Smaill, B. H. 1989 The analysis of cardiac function - a continuum approach. Prog. Biophys. Molec. Biol. 52, 101-164.
45. Hunter, P. J., Nash, M. P. & Sands, G. B. 1997 Computational electromechanics of the heart. In Computational biology of the heart (ed. A. V. Panfilov & A. V. Holden), pp. 345-407. Wiley.
46. Hunter, P. J., McCulloch, A. D. & ter Keurs, H. E. D. J. 1998 Modelling the mechanical properties of cardiac muscle. Prog. Biophys. Molec. Biol. 69, 289-331.
47. 2+ dynamics: the roles of ryanodine receptor adaptation and sarcoplasmic reticulum load. Biophys. J. 74, 1149-1168.
48. Janse, M. J. 1997 Why does atrial fibrillation occur? Eur. Heart J. 18, C12-C18.
49. Janse, M. J. & Wit, A. 1989 Electrophysiological mechanisms of ventricular arrhythmias resulting from myocardial ischaemia and infarction. Physiol. Rev. 69, 1049-1169.
50. Janz, R. F. & Grimm, A. F. 1973 Deformation of the diastolic left ventricle. I. Non-linear elastic effects. Biophys. J. 13, 689-704.
51. Jongsma, H. J. 1998 Sudden cardiac death: a matter of faulty ion channels? Curr. Biol. 8, R568-R571.
52. Kassab, G. S., Rider, C. A., Tang, N. J. & Fung, Y. C. 1993 Morphometry of pig coronary arterial trees. Am. J. Physiol 265, H350-H365.
53. Kauppinen, P., Hyttinen, J., Heinonen, T. & Malmivuo, J. 1998 Detailed model of the thorax as a volume conductor based on the visible human man data. J. Med. Engng Technol. 22, 126-133.
54. Knudsen, Z., Holden, A. V. & Brindley, J. 1997 Qualitative modeling of mechanoelectrical feedback in a ventricular cell. Bull. Math. Biol 59, 1155-1181.
55. Kohl, P. & Noble, D. 1996 Mechanosensitive connective tissue: potential influence on heart rhythm. Cardiovasc. Res. 32, 62-68.
56. Kohl, P., Kamkin, A. G., Kiseleva, I. S. & Noble, D. 1994 Mechanosensitive fibroblasts in the sino-atrial node region of rat heart: interaction with cardiomyocytes and possible role. Experimental Physiol 79, 943-956.
57. Kohl, P., Varghese, A. & Noble, D. 1997 Retrograde conduction in a 2-D cardiac scar model. Biophys. J. 72, A370 (abstract).
58. Kohl, P., Day, K. & Noble, D. 1998 Cellular mechanisms of cardiac mechano-electric feedback in a mathematical model. Can. J. Cardiol 14, 111-119.
59. Kohl, P., Hunter, P. & Noble, D. 1999 Stretch-induced changes in heart rate and rhythm: clinical observations, experiments and mathematical models. Prog. Biophys. Molec. Biol. 71, 91-138.
60. Kotter, R. & Wickens, J. 1998 Striatal mechanisms in Parkinson's disease: new insights from computer modeling. Artificial Intell. Med. 13, 37-55.
61. Lab, M. J. 1982 Contraction-excitation feedback in myocardium: physiological basis and clinical relevance. Circulation Res. 50, 757-766.
62. LeGrice, I. J., Hunter, P. J. & Smaill, B. H. 1997 Laminar structure of the heart: a mathematical model. Am. J. Physiol. 272, H2466-H2476.
63. Lei, M. & Kohl, P. 1998 Swelling-induced decrease in spontaneous pacemaker activity of rabbit isolated sino-atrial node cells. Acta Physiol Scand. 164, 1-12.
64. Lindblad, D. S., Murphey, C. R., Clark, J. W. & Giles, W. R. 1996 A model of the action potential and underlying membrane currents in a rabbit atrial cell. Am. J. Physiol. 271, H1666-H1696.
65. Luo, C.-H. & Rudy, Y. 1994 A dynamic model of the cardiac ventricular action potential. I. Simulations of ionic currents and concentration changes. Circulation Res. 74, 1071-1096.
66. Malik, M., Smits, K. F. A. A. & Lindemans, F. 1997 Computer modelling of transthoracic electric field during defibrillation shocks: an efficient finite difference implementation. Computers Cardiol. 24, 255-258.
67. Mall, F. P. 1911 On the muscular architecture of the ventricles of the human heart. Am. J. Anatomy 11, 211-266.
68. Marban, E., Yamagishi, T. & Tomaselli, F. 1998 Structure and function of voltage-gated sodium channels. J. Physiol. 508, 647-657.
69. Meijler, F. L. & Janse, M. J. 1988 Morphology and electrophysiology of the mammalian atrioventricular node. Physiol. Rev. 68, 608-647.
70. Nagumo, J. & Sato, S. 1972 On a response characteristic of a mathematical neuron model. Kybernetik 10, 155-164.
71. Nielsen, P. M. F., LeGrice, I. J., Smaill, B. H. & Hunter, P. J. 1991 A mathematical model of the geometry and fibrous structure of the heart. Am. J. Physiol. 29, H1365-H1378.
72. Noble, D. 1960 Cardiac action and pacemaker potentials based on the Hodgkin-Huxley equations. Nature 188, 495-497.
73. Noble, D. 1962 A modification of the Hodgkin-Huxley equation applicable to Purkinje fibre action and pace-maker potentials. J. Physiol. 160, 317-352.
74. Noble, D. 1995 The development of mathematical models of the heart. Chaos Solitons Fractals 5, 321-333.
75. Noble, D. 1997 Transcript, 80th Meeting of the Cardiovascular and Renal Drugs Advisory Committee, NDA 20-689. New Drug Application Hearing, NIH.
76. Noble, D. & Noble, P. J. 1999 Reconstruction of a cellular mechanism of a human genetically-based arrhythmia. J. Physiol. 518, 2P.
77. Noble, D. & Varghese, A. 1998 Modelling of sodium-overload arrhythmias and their suppression. Can. J. Cardiol. 14, 97-100.
78. Noble, D. & Winslow, R. L. 1997 Reconstructing the heart: network models of SA node-atrial interaction. In Computational biology of the heart (ed. A. V. Panfilov & A. V. Holden), pp. 49-64. Wiley.
79. f in controlling and stabilizing pacemaker frequency of rabbit sino-atrial node cells. Proc. R. Soc. Lond. B 250, 199-207.
80. Ks, and length-and tension-dependent processes. Can. J. Cardiol. 14, 123-134.
81. + currents in repolarization. Circulation Res. 82, 63-81.
82. Onuchic, J. N., Luthey-Schulten, Z. & Wolynes, P. G. 1997 Theory of protein folding: the energy landscape perspective. A. Rev. Phys. Chem. 48, 545-600.
83. Oosthoek, P. W., Viragh, S., Mayen, A. E. M., Kempen, M. J. Av., Lamers, W. H. & Moorman, A. F. M. 1993 Immunohistochemical delineation of the conduction system. I. The sinoatrial node. Circulation Res. 73, 473-481.
84. Opthof, T., de Jonge, B., Jongsma, H. J. & Bouman, L. N. 1987 Functional morphology of the mammalian sinoatrial node. Eur. Heart J. 8, 1249-1259.
85. Packer, M., Bristow, M. R., Cohn, J. N., Colucci, W. S., Fowler, M. B., Gilbert, E. M. & Shusterman, N. H. 1996 The effect of carvedilol on morbidity and mortality in patients with chronic heart failure. New England J. Med. 334, 1349-1355.
86. Panfilov, A. & Holden, A. 1993 Computer simulation of re-entry sources in myocardium in two and three dimensions. J. Theor. Biol. 161, 271-285.
87. Panfilov, A. & Keener, J. 1993 Re-entry generation in anisotropic twisted myocardium. J. Cardiovasc. Electrophysiol. 4, 412-421.
88. Rice, J. J., Winslow, R. L., Dekanski, J. & McVeigh, E. 1998 Model studies of the role of mechano-sensitive currents in the generation of cardiac arrhythmias. J. Theor. Biol. 190, 295-312.
89. Rice, J. J., Winslow, R. L. & Hunter, W. C. 1999 Comparison of putative cooperative mechanisms in cardiac muscle: length-dependence and dynamic responses. Am. J. Physiol. 45, H1734-H1754.
90. Sachs, F. 1994 Modeling mechanical-electrical transduction in the heart. In Cell mechanics and cellular engineering (ed. V. Mow, F. Guliac, R. Tran-son-Tray & R. Hochmuth), pp. 308-328. Springer.
91. Sahakian, A. V., Myers, G. A. & Maglaveras, N. 1992 Unidirectional block in cardiac fibres -effects of discontinuities in coupling resistance and spatial changes in resting membrane potential in a computer simulation study. IEEE Trans. Biomed. Engng 39, 510-522.
92. Sands, G. B. 1998 Mathematical model of ventricular activation in an anatomically accurate deforming heart. Department of Engineering Science, Auckland, University of Auckland.
93. Smith, N. P. 1999 An anatomically based mathematical model of coronary blood flow coupled to cardiac contraction. Department of Engineering Science, Auckland, University of Auckland.
94. Streeter Jr, D. D. & Bassett, D. L. 1966 An engineering analysis of myocardial fiber orientation in pig's left ventricle in systole. Anatom. Record 155, 503-511.
95. Thompson, D. (ed.) 1995 The concise Oxford dictionary of current English. Oxford: Clarendon.
96. Trabka-Janik, E., Coombs, W., Lemanski, L. L., Delmar, M. & Jalife, J. 1994 Immunohistochemical localization of gap junction protein channels in hamster sinoatrial node in correlation with electrophysiologic mapping of the pacemaker region. J. Cardiovasc. Electrophysiol. 5, 125-137.
97. Tuckwell, H. C. & Rodriguez, R. 1998 Analytical and simulation results for stochastic Fitzhugh-Nagumo neurons and neural networks. J. Computational Neurosci. 5, 91-113.
98. Ursell, P. C., Gardner, P. I., Albala, A., Fenoglio, J. J. J. & Wit, A. L. 1985 Structural and electrophysiological changes in the epicardial border zone of canine myocardial infarcts during infarct healing. Circulation Res. 56, 436-451.
99. van Capelle, F. J. L. & Durrer, D. 1980 Computer simulation of arrhythmias in a network of coupled excitable elements. Circulation Res. 47, 454-466.
100. van der Pol, B. & van der Mark, J. 1928 The heartbeat considered as a relaxation oscillation, and an electrical model of the heart. Lond. Edinb. Dublin Phil. Mag. J. Sci. 6, 763-775.
101. Varghese, A. & Winslow, R. L. 1994 Dynamics of abnormal pacemaking activity in cardiac Purkinje fibers. J. Theor. Biol. 168, 407-420.
102. Wang, Q., Shen, J., Splawski, I., Atkinson, D., Li, Z., Robinson, J. L., Moss, A. J., Towbin, J. A. & Keating, M. J. 1995 SCN5A mutations associated with an inherited cardiac arrhythmia, long QT syndrome. Cell 80, 805-811.
103. Wilders, R., Jongsma, H. J. & van Ginneken, A. C. G. 1993 Membrane currents underlying pacemaker depolarization in rabbit sinoatrial node cells: a model approach. Prog. Pharmacol. Res. 2, 35-44.
104. Wilders, R., Kumar, R., Joyner, R. W., Jongsma, H. J., Verheijck, E. E., Golod, D., van Ginneken, A. C. G. & Goolsby, W. N. 1990 Action potential conduction between a ventricular cell model and an isolated ventricular cell. Biophys. J. 70, 281-295.
105. Winfree, A. T. 1994 Electrical turbulence in three-dimensional heart muscle. Science 266, 1003-1006.
106. Winslow, R. L. 1998 Quantitative modeling of electrical activity: has it helped us to understand arrhythmia? Network and organ models. In 71st Scientific Session of the American Heart Association, Dallas, TX.
107. Winslow, R. L. & Jongsma, H. J. 1995 Role of tissue geometry and spatial localization of gap junctions in generation of the pacemaker potential. J. Physiol. 487, 126P.
108. Winslow, R. L. & Scollan, D. 1997 Modelling normal and abnormal electrical activity in the canine ventricle: from single cells to whole heart. In XXXIII Int. Congr. IUPS, St Petersburg, L017.08 (abstract).
109. Winslow, R. L. & Varghese, A. 1994 Modeling the functional role of SA node - atrial interdigitation. Computers Cardiol. 1994, 649-652.
110. Winslow, R. L., Kimball, A., Varghese, A. & Noble, D. 1993 Simulating cardiac sinus and atrial network dynamics on the connection machine. Physica D 64, 281-298.
111. Winslow, R. L., Cai, D., Varghese, A. & Lai, Y. C. 1995 Generation and propagation of normal and abnormal pacemaker activity in network models of cardiac sinus node and atrium. Chaos Solitons Fractals 5, 491-512.
112. Winslow, R. L., Rice, J. J. & Jafri, M. S. 1998 Modeling the cellular basis of altered excitation-contraction coupling in heart failure. Prog. Biophys. Molec. Biol. 69, 497-517.
113. Winslow, R. L., Rice, J., Jafri, S., Marbán, E. & O'Rourke, B. 1999 Mechanisms of altered excitation-contraction coupling in canine tachycardia-induced heart failure. II. Model studies. Circulation Res. 84, 571-586.
114. Young, A. A., Fayad, Z. A. & Axel, L. 1996 Right ventricular midwall surface motion and deformation using magnetic resonance tagging. Am. J. Physiol. 271, H2677-H2688.
115. Zerhouni, E. A., Parish, D. M., Rogers, W. J., Yang, A. & Shapiro, E. P. 1988 Human heart: tagging with MR imaging - a method for noninvasive assessment of myocardial motion. Radiology 169, 59-63.
116. Zhang, H. & Patel, N. 1995 Spiral wave breakdown in an excitable medium model of cardiac tissue. Chaos Solitons Fractals 5, 635-643.
117. Zoll, P. M., Belgard, A. H., Weintraub, M. J. & Frank, H. A. 1976 External mechanical cardiac stimulation. New England J. Med. 294, 1274-1275.