Endogenous driving and synchronization in cardiac and uterine virtual tissues: Bifurcations and local coupling

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

Volumn 364, Issue 1842, 2006, Pages 1313-1327

  Benson, Alan P ^a   Clayton, Richard H ^b   Holden, Arun V ^a   Kharche, Sanjay ^a   Tong, Wing C ^a  

^a UNIVERSITY OF LEEDS   (United Kingdom)

^b UNIVERSITY OF SHEFFIELD   (United Kingdom)

Author keywords

Bifurcation; Ectopic focus; Excitable medium; Pacemaking

Indexed keywords

EID: 33646503508     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2006.1772     Document Type: Article

References (36)

1. Benson, A. P., Holden, A. V., Kharche, S. & Tong, W. C. 2005 From gene expression to tissue dynamics, via continuation algorithms: ectopic pacemaking in the heart. In Proc. Int. Workshop on Computational Methods in Systems Biology, Edinburgh, UK, 3-5 April 2005, pp. 192-203.
2. Biktasheva, I. V., Simitev, R. D., Suckley, R. & Biktashev, V. N. 2006 Asymptotic properties of mathematical models of excitability. Phil. Trans. R. Soc. A 364, 1283-1298. (doi:10.1098/rsta. 2006.1770)
3. Carey, P. A., Turner, M., Fry, C. H. & Sheridan, D. J. 2001 Reduced anisotropy of action potential conduction in left ventricular hypertrophy. J. Cardiovasc. Electrophysiol. 12, 830-835. (doi:10. 1046/j.l540-8167.2001.00830.x)
4. Carmeliet, E. 1999 Cardiac ionic currents and acute ischemia: from channels to arrhythmias. Physiol. Rev. 79, 917-1017.
5. Champneys, A. R., Kuznetsov, Y. A. & Sandstede, B. 1996 A numerical toolbox for homoclinic bifurcation analysis. Int. J. Bifurcat. Chaos 6, 867 887. (doi:10.1142/S0218127496000485)
6. DiFrancesco, D. & Noble, D. 1985 A model of cardiac electrical activity incorporating ionic pumps and concentration changes. Phil. Trans. R. Soc. D 307, 353-398.
7. Doedel, E. J. & Kernévez, J. P. 1986 AUTO: software for continuation and bifurcation problems in ordinary differential equations with applications. Technical report, Applied Mathematics, California Institute of Technology.
8. Ermentrout, B. 2002 Simulating, analyzing, and animating dynamical systems: a guide to XPPA UT for researchers and students. Philadelphia, PA: SIAM.
9. + currents to repolarization assessed using mathematical models of human ventricular myocytes. Phil. Trans. R. Soc. A 364, 1207-1222. (doi:10.1098/rsta.2006.1765)
10. FitzHugh, R. A. 1961 Impulses and physiological states in theoretical models of nerve membrane. Biophys. J. 1, 445-466.
11. Fozzard, H. A. & Schoenberg, M. 1972 Strength-duration curves in cardiac Purkinje fibres: effects of liminal length and charge distribution. J. Physiol. 226, 593-618.
12. Garlield, R. E., Ali, M., Yallampalli, C. & Izumi, H. 1995 Role of gap junctions and nitric oxide in control of myometrial contractility. Semin. Perinatal. 19, 41-51.
13. Gheorghiade, M., Adams, K. F. & Colucci, W. F. 2004 Digoxin in the management of cardiovascular disorders. Circulation 109, 2959-2964. (doi:10.1161/01.CIR.0000132482.95686.87)
14. Gima, K. & Rudy, Y. 2002 Ionic current basis of electrocardiographic waveforms: a model study. Circ. Res. 90, 889-896. (doi:10.1161/01.RES. 0000016960.61087.86)
15. Harrison, S. M., McCall, E. & Boyett, M. R. 1992 The relationship between contraction and intracellular sodium in rat and guinea-pig ventricular myocytes. J. Physiol. 449, 517-550.
16. 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.
17. Holden, A. V. & Yoda, M. 1981 Ionic channel density of excitable membranes can act as a bifurcation parameter. Biol. Cybern. 42, 29-38. (doi:10.1007/BF00335156)
18. Joyner, R. W., Wang, Y., Wilders, R., Golod, D. A., Wagner, M. B., Kumar, R. & Goolsby, W. N. 2000 A spontaneously active focus drives a model atrial sheet more easily than a model ventricular sheet. Am. J. Physiol. 279, H752-H763.
19. Kass, R. S., Tsien, R. W. & Weingart, R. 1978 Ionic basis of transient inward current induced by strophanthidin in cardiac Purkinje fibres. J. Physiol. 281, 209-226.
20. Kleber, A. G. & Rudy, Y. 2004 Basic mechanisms of cardiac impulse propagation and associated arrhythmias. Physiol. Rev. 84, 431-488. (doi:10.1152/physrev.00025.2003)
21. Lindemans, F. W. & Vandergon, J. J. D. 1978 Current thresholds and liminal size in excitation of heart-muscle. Cardiovasc. Res. 12, 477-485.
22. Luo, C. H. & Rudy, Y. 1994 A dynamic model of the cardiac ventricular action potential. I. Simulations of ionic currents and concentration changes. Circ. Res. 74, 1071-1096.
23. Miake, J., Marban, E. & Nuss, H. B. 2002 Biological pacemaker created by gene transfer. Nature. 419, 132 133. (doi:10.1038/419132b)
24. Miake, J., Marban, E. & Nuss, H. B. 2003 Functional role of inward rectifier current in heart probed by Kir2.1 over expression and dominant-negative suppression. J. Clin. Invest. 111, 1529-1536. (doi:10.1172/JCI200317959)
25. Nagumo, J., Animoto, S. & Yoshizawa, S. 1962 An active pulse transmission line simulating nerve axon. Proc. Inst. Radio Engrs 50, 2061-2070.
26. K1-downregulated myocytes. Circ. Res. 92, 261-263. (doi:10.1161/01.RES.0000057996.20414.C6)
27. ten Tusscher, K. H. W. J., Noble, D., Noble, P. J. & Panfilov, A. V. 2004 A model for human ventricular tissue. Am. J. Physiol. 286, H1573-H1589.
28. Tong, W. C. & Holden, A. V. 2005 Induced pacemaker activity in virtual mammalian ventricular cells. Lect. Notes Comput. Sci. 3504, 226-235.
29. Tristani-Firouzi, M. et al. 2002 Functional and clinical characterization of KCNJ2 mutations associated with LQT7 (Andersen syndrome). J. Clin. Invest. 110, 381-388. (doi:10.1172/ JCI200215183)
30. Varghese, A. & Winslow, R. L. 1993 Dynamics of the calcium subsystem in cardiac Purkinje fibers. Physica 68D, 364-386.
31. Varghese, A. & Winslow, R. L. 1994 Dynamics of abnormal pacemaking activity in cardiac Purkinje fibers. J. Theor. Biol. 168, 407-420. (doi:10.1006/jtbi.1994.1121)
32. Wilders, R., Wagner, M. B., Golod, D. A., Kumar, R., Wang, Y., Goolsby, W. N., Joyner, R. W. & Jongsma, H. J. 2000 Effects of anisotropy on the development of cardiac arrhythmias associated with focal activity. Pflügers Arch. 441, 301-312. (doi:10.1007/s004240000413)
33. Winslow, R. L., Varghese, A., Noble, D., Adlakha, C. & Hoythya, A. 1993 Generation and propagation of ectopic beats induced by spatially localized Na-K pump inhibition in atrial network models. Proc. R. Soc. B 254, 55-61.
34. Wray, S. 1993 Uterine contraction and physiological mechanisms of modulation. Am. J. Physiol. 264, C1-C18.
35. Yan, G. X., Shimizu, W. & Antzelevitch, C. 1998 Characteristics and distribution of M cells in arterially perfused canine left ventricular wedge preparations. Circulation 98, 1921-1927.
36. Zhang, H., Holden, A. V., Kodama, I., Honjo, H., Lei, M., Varghese, T. & Boyett, M. R. 2000 Mathematical models of action potentials in the periphery and center of the rabbit sinaotrial node. Am. J. Physiol. 279, H397-H421.