Origin choice and petal loss in the flower garden of spiral wave tip trajectories

Chaos

Volumn 19, Issue 3, 2009, Pages

  Gray, Richard A ^a,b   Wikswo, John P ^c   Otani, Niels F ^d  

^a CENTER FOR DEVICES AND RADIOLOGICAL HEALTH   (United States)

^b and Radiation Oncology   (United States)

^c VANDERBILT UNIVERSITY   (United States)

^d Cornell University ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; ARTICLE; BIOLOGICAL MODEL; BIOLOGICAL RHYTHM; COMPUTER SIMULATION; METHODOLOGY; NONLINEAR SYSTEM; OSCILLOMETRY; PHYSIOLOGY; SIGNAL PROCESSING;

ALGORITHMS; BIOLOGICAL CLOCKS; COMPUTER SIMULATION; MODELS, BIOLOGICAL; NONLINEAR DYNAMICS; OSCILLOMETRY; SIGNAL PROCESSING, COMPUTER-ASSISTED;

EID: 70349650795     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3204256     Document Type: Article

References (37)

1. A. Goldbeter, Nature (London) 0028-0836 253, 540 (1975). 10.1038/253540a0
2. A. T. Winfree, The Geometry of Biological Time (Springer-Verlag, Berlin, 1980), Vol. XIII, p. 530.
3. J. Lechleiter, S. Girard, E. Peralta, and D. Clapham, Science 0036-8075 252, 123 (1991). 10.1126/science.2011747
4. O. Steinbock, V. Zykov, and S. C. Muller, Nature (London) 0028-0836 366, 322 (1993). 10.1038/366322a0
5. G. Li, Q. Ouyang, V. Petrov, and H. L. Swinney, Phys. Rev. Lett. 0031-9007 77, 2105 (1996). 10.1103/PhysRevLett.77.2105
6. M. Vinson, S. Mironov, S. Mulvey, and A. Pertsov, Nature (London) 0028-0836 386, 477 (1997). 10.1038/386477a0 (Pubitemid 27164069)
7. M. Bazhenov, I. Timofeev, M. Steriade, and T. J. Sejnowski, Nat. Neurosci. 1097-6256 2, 168 (1999). 10.1038/5729 (Pubitemid 30491318)
8. V. S. Zykov, Biofizika 0006-3029 25, 906 (1986).
9. A. T. Winfree, Chaos 1054-1500 1, 303 (1991). 10.1063/1.165844
10. J. Beaumont, N. Davidenko, J. Davidenko, and J. Jalife, Biophys. J. 0006-3495 75, 1 (1998). 10.1016/S0006-3495(98)77490-9
11. Z. Qu, J. N. Weiss, and A. Garfinkel, Am. J. Physiol. 0002-9513 276, H269 (1999).
12. N. F. Otani, Chaos 1054-1500 12, 829 (2002). 10.1063/1.1503921
13. R. A. Gray, A. M. Pertsov, and J. Jalife, Nature (London) 0028-0836 392, 75 (1998). 10.1038/32164 (Pubitemid 28150591)
14. N. Copernicus, De Revolutionibus Orbium Caelestium, edited by, T. B. A. M. Duncan, (Newton Abbot, New York, 1976), p. 1543.
15. A. T. Winfree, When Time Breaks Down: The Three-Dimensional Dynamics of Electrochemical Waves and Cardiac Arrhythmias (Princeton University Press, Princeton, NJ, 1987), Vol. XIV, p. 339.
16. X. Huang, W. C. Troy, Q. Yang, H. Ma, C. R. Laing, S. J. Schiff, and J. -Y. Wu, J. Neurosci. 0270-6474 24, 9897 (2004). 10.1523/JNEUROSCI.2705-04.2004 (Pubitemid 39463570)
17. R. H. Clayton and A. V. Holden, IEEE Trans. Biomed. Eng. 0018-9294 51, 28 (2004). 10.1109/TBME.2003.820356 (Pubitemid 38009960)
18. A. V. Panfilov, Heart Rhythm 1547-5271 3, 862 (2006). 10.1016/j.hrthm.2005.12.022 (Pubitemid 43960531)
19. R. A. Gray, J. Jalife, A. V. Panfilov, W. T. Baxter, C. Cabo, J. M. Davidenko, A. M. Pertsov, Science 0036-8075 270, 1222 (1995). 10.1126/science.270.5239.1222
20. R. A. Gray, J. Jalife, A. Panfilov, W. T. Baxter, C. Cabo, J. M. Davidenko, and A. M. Pertsov, Circulation 0009-7322 91, 2454 (1995).
21. M. A. Bray and J. P. Wikswo, Phys. Rev. Lett. 0031-9007 90, 238303 (2003). 10.1103/PhysRevLett.90.238303
22. R. A. Gray and N. Chattipakorn, Proc. Natl. Acad. Sci. U.S.A. 0027-8424 102, 4672 (2005). 10.1073/pnas.0407860102 (Pubitemid 40471513)
23. R. H. Clayton, E. A. Zhuchkova, and A. V. Panfilov, Prog. Biophys. Mol. Biol. 0079-6107 90, 378 (2006). 10.1016/j.pbiomolbio.2005.06.011 (Pubitemid 41721060)
24. V. G. Fast and A. M. Pertsov, Biofizika 0006-3029 35, 478 (1990).
25. F. Fenton and A. Karma, Chaos 1054-1500 8, 20 (1998). 10.1063/1.166311 (Pubitemid 128045675)
26. R. Mandapati, Circulation 0009-7322 98, 1688 (1998).
27. M. A. Bray, S. -F. Lin, R. R. Aliev, B. J. Roth, and J. P. Wikswo, Jr., J. Cardiovasc. Electrophysiol. 1045-3873 12, 716 (2001). 10.1046/j.1540-8167. 2001.00716.x
28. S. Puwal, B. J. Roth, and S. Kruk, IMA J. Math. Appl. Med. Biol. 0265-0746 22, 335 (2005). 10.1093/imammb/dqi013 (Pubitemid 43118444)
29. Y. B. Liu, A. Peter, S. T. Lamp, J. N. Weiss, P. -S. Chen, and S. -F. Lin, J. Cardiovasc. Electrophysiol. 1045-3873 14, 1103 (2003). 10.1046/j.1540-8167.2003.03218.x (Pubitemid 37412089)
30. A. N. Iyer and R. A. Gray, Ann. Biomed. Eng. 0090-6964 29, 47 (2001). 10.1114/1.1335538 (Pubitemid 32251395)
31. F. H. Fenton, E. M. Cherry, H. M. Hastings, and S. J. Evans, Chaos 1054-1500 12, 852 (2002). 10.1063/1.1504242
32. J. M. Davidenko, A. V. Pertsov, R. Salomonsz, W. Baxter, and J. Jalife, Nature (London) 0028-0836 355, 349 (1992). 10.1038/355349a0
33. D. Barkley, Phys. Rev. Lett. 0031-9007 68, 2090 (1992). 10.1103/PhysRevLett.68.2090
34. D. Barkley, M. Kness, and L. S. Tuckerman, Phys. Rev. A 1050-2947 42, 2489 (1990). 10.1103/PhysRevA.42.2489
35. V. N. Biktashev and A. V. Holden, Proc. R. Soc. London, Ser. B 0962-8452 263, 1373 (1996). 10.1098/rspb.1996.0201 (Pubitemid 26370888)
36. F. Takens, in Dynamical Systems and Turbulence, edited by, D. A. Rand, and, L. S. Young, (Springer-Verlag, Berlin, 1981), pp. 366-381.
37. A. Iyer and R. A. Gray, Pacing Clin. Electrophysiol. 0147-8389 24, 692 (2001).