Anomalous drift of spiral waves in heterogeneous excitable media

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 82, Issue 5, 2010, Pages

  Sridhar, S ^a   Sinha, Sitabhra ^a   Panfilov, Alexander V ^b  

^a INSTITUTE OF MATHEMATICAL SCIENCES   (India)

^b UTRECHT UNIVERSITY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

EXCITABLE MEDIA; EXCITABLE MEDIUM; ION CHANNEL; REACTION-DIFFUSION MODELS; SPATIOTEMPORAL PATTERNS; SPIRAL WAVES;

WAVES;

EID: 78651277610     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.82.051908     Document Type: Article

References (42)

1. J. Keener and J. Sneyd, Mathematical Physiology (Springer, New York, 1998).
2. J. M. Davidenko, A. V. Pertsov, R. Salomonsz, W. Baxter, and J. Jalife, Nature (London) 355, 349 (1992). 10.1038/355349a0
3. A. V. Panfilov and A. V. Holden, J. Theor. Biol. 161, 271 (1993) 10.1006/jtbi.1993.1055
4. A. V. Panfilov and J. P. Keener, J. Theor. Biol. 163, 439 (1993). 10.1006/jtbi.1993.1129
5. S. Sinha, A. Pande, and R. Pandit, Phys. Rev. Lett. 86, 3678 (2001) 10.1103/PhysRevLett.86.3678
6. T. K. Shajahan, S. Sinha, and R. Pandit, Phys. Rev. E 75, 011929 (2007) 10.1103/PhysRevE.75.011929
7. S. Sridhar and S. Sinha, EPL 81, 50002 (2008). 10.1209/0295-5075/81/50002
8. D. J. Christini, M. L. Riccio, C. A. Culianu, J. J. Fox, A. Karma, and R. F. Gilmour Jr., Phys. Rev. Lett. 96, 104101 (2006). 10.1103/PhysRevLett.96. 104101
9. F. H. Fenton, S. Luther, E. M. Cherry, N. F. Otani, V. Krinsky, A. Pumir, E. Bodenschatz, and R. F. Gilmour Jr., Circulation 120, 467 (2009). 10.1161/CIRCULATIONAHA.108.825091
10. A. Garfinkel and Z. Qu, in Cardiac Eletrophysiology: From Cell to Bedside, edited by, D. P. Zipes, and, J. Jalife, (Saunders, Philadelphia, 2004), p. 327.
11. R. A. Gray, J. Jalife, A. Panfilov, W. T. Baxter, C. Cabo, J. M. Davidenko, and A. M. Pertsov, Circulation 91, 2454 (1995).
12. S. M. Cobbe and A. C. Rankin, in Oxford Textbook of Medicine, edited by, D. A. Warrell,,, T. M. Cox,,, J. D. Firth,, and, E. J. Benz, (Oxford University Press, USA, 2005), p. 975.
13. F. H. Fenton, E. M. Cherry, H. M. Hastings, and S. J. Evans, Chaos 12, 852 (2002). 10.1063/1.1504242
14. V. I. Krinsky, Problemy Kibernetiki 2, 59 (1968).
15. V. G. Fast and A. M. Pertsov, Biophysics (Oxf.) 35, 489 (1990).
16. M. Markus, Zh. Nagy-Ungavarai, and B. Hess, Science 257, 225 (1992). 10.1126/science.257.5067.225
17. A. N. Rudenko and A. V. Panfilov, Stud. Biophys. 98, 183 (1983)
18. A. V. Panfilov and B. N. Vasiev, Physica D 49, 107 (1991). 10.1016/0167-2789(91)90200-S
19. K. H. W. J. ten Tusscher and A. V. Panfilov, Am. J. Physiol. Heart Circ. Physiol. 284, H542 (2003).
20. G. R. Ivanitsky, V. I. Krinsky, A. V. Panfilov, and M. A. Tsiganov, Biofizika 34, 296 (1989).
21. A. S. Mikhailov, V. A. Davydov, and V. S. Zykov, Physica D 70, 1 (1994). 10.1016/0167-2789(94)90054-X
22. R. A. Gray, A. M. Pertsov, and J. Jalife, Circulation 94, 2649 (1996)
23. J. Jalife, O. Berenfeld, and M. Mansour, Cardiovasc. Res. 54, 204 (2002) 10.1016/S0008-6363(02)00223-7
24. R. H. Keldermann, K. H. W. J. ten Tusscher, M. P. Nash, C. P. Bradley, R. Hren, P. Taggart, and A. V. Panfilov, Am. J. Physiol. Heart Circ. Physiol. 296, H370 (2009). 10.1152/ajpheart.00952.2008
25. F. G. Akar and D. S. Rosenbaum, Circ. Res. 93, 638 (2003). 10.1161/01.RES.0000092248.59479.AE
26. G. Bub, A. Shrier, and L. Glass, Phys. Rev. Lett. 88, 058101 (2002). 10.1103/PhysRevLett.88.058101
27. D. Barkley, M. Kness, and L. S. Tuckerman, Phys. Rev. A 42, 2489 (1990). 10.1103/PhysRevA.42.2489
28. A. Pumir, S. Sinha, S. Sridhar, M. Argentina, M. Horning, S. Filippi, C. Cherubini, S. Luther, and V. Krinsky, Phys. Rev. E 81, 010901 (R) (2010). 10.1103/PhysRevE.81.010901
29. F. H. Fenton and A. Karma, Chaos 8, 20 (1998). 10.1063/1.166311
30. For a, b parameters where anomalous drift is observed, the period and wavelength of spiral wave exhibits a more rapid divergence with decreasing α compared to the parameter regime showing normal drift.
31. V. Hakim and A. Karma, Phys. Rev. E 60, 5073 (1999). 10.1103/PhysRevE.60. 5073
32. V. I. Krinsky, E. Hamm, and V. Voignier, Phys. Rev. Lett. 76, 3854 (1996). 10.1103/PhysRevLett.76.3854
33. A. V. Panfilov and A. N. Rudenko, Physica D 28, 215 (1987). 10.1016/0167-2789(87)90132-1
34. S. A. Alonso and A. V. Panfilov, Phys. Rev. Lett. 100, 218101 (2008). 10.1103/PhysRevLett.100.218101
35. H. Henry and V. Hakim, Phys. Rev. E 65, 046235 (2002). 10.1103/PhysRevE.65.046235
36. H. Henry, Phys. Rev. E 70, 026204 (2004). 10.1103/PhysRevE.70.026204
37. C. Luo and Y. Rudy, Circ. Res. 68, 1501 (1991).
38. K. H. W. J. ten Tusscher, D. Noble, P. J. Noble, and A. V. Panfilov, Am. J. Physiol. Heart Circ. Physiol. 286, H1573 (2004). 10.1152/ajpheart.00794.2003
39. G. Schram, M. Pourrier, P. Melnyk, and S. Nattel, Circ. Res. 90, 939 (2002). 10.1161/01.RES.0000018627.89528.6F
40. M. C. Boerlijst and P. Hogeweg, Physica D 88, 29 (1995). 10.1016/0167-2789(95)00178-7
41. A. Pumir, A. Arutunyan, V. Krinsky, and N. Sarvazyan, Biophys. J. 89, 2332 (2005). 10.1529/biophysj.105.061820
42. V. N. Biktashev, A. Arutunyan, and N. A. Sarvazyan, Biophys. J. 94, 3726 (2008). 10.1529/biophysj.107.117630