Evolution of spiral and scroll waves of excitation in a mathematical model of ischaemic border zone

PLoS ONE

Volumn 6, Issue 9, 2011, Pages

  Biktashev, Vadim N ^a   Biktasheva, Irina V ^a   Sarvazyan, Narine A ^b  

^a UNIVERSITY OF LIVERPOOL   (United Kingdom)

^b GEORGE WASHINGTON UNIVERSITY SCHOOL OF MEDICINE AND HEALTH SCIENCES   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CELL ADHESION; CELL HETEROGENEITY; ELECTRIC ACTIVITY; HEART AUTOMATICITY; HEART EXCITATION; HEART FIBRILLATION; HEART MUSCLE CELL; HEART MUSCLE ISCHEMIA; MATHEMATICAL MODEL; PREDICTION; SIMULATION; THEORETICAL MODEL; VORTEX MOTION; ACTION POTENTIAL; BIOLOGICAL MODEL; HEART; HEART ARRHYTHMIA; HUMAN; PATHOPHYSIOLOGY;

ACTION POTENTIALS; ARRHYTHMIAS, CARDIAC; HEART; HUMANS; MODELS, CARDIOVASCULAR; MODELS, THEORETICAL; MYOCARDIAL ISCHEMIA;

EID: 80052825832     PISSN: None     EISSN: 19326203     Source Type: Journal    
DOI: 10.1371/journal.pone.0024388     Document Type: Article

References (42)

1. Wit AL, Janse MJ, (2001) Reperfusion arrhythmias and sudden cardiac death: a century of progress toward an understanding of the mechanisms. Circulation Research 89: 741-743.
2. Kay M, Swift L, Martell B, Arutunyan A, Sarvazyan N, (2008) Locations of ectopic beats coincide with spatial gradients of NADH in a regional model of low-ow reperfusion. Am J Physiol - Heart and Circ Physiol 294: H2400-H2405.
3. Arutunyan A, Webster DR, Swift LM, Sarvazyan N, (2001) Localized injury in cardiomyocyte network: a new experimental model of ischemia-reperfusion arrhythmias. Am J Physiol - Heart and Circ Physiol 280: H1905-H1915.
4. Arutunyan A, Swift LM, Sarvazyan N, (2002) Initiation and propagation of ectopic waves: insights from an in vitro model of ischemia-reperfusion injury. Am J Physiol - Heart and Circ Physiol 283: H741-H749.
5. Arutunyan A, Pumir A, Krinsky VI, Swift LM, Sarvazyan N, (2003) Behavior of ectopic surface: effects of beta-adrenergic stimulation and uncoupling. Am J Physiol - Heart and Circ Physiol 285: H2531-H2542.
6. Pumir A, Arutunyan A, Krinsky V, Sarvazyan N, (2005) Genesis of ectopic waves: role of coupling, automaticity, and heterogeneity. Biophys J 89: 2332-2349.
7. Biktashev VN, Arutunyan A, Sarvazyan NA, (2008) Generation and escape of local waves from the boundary of uncoupled cardiac tissue. Biophys J 94: 3726-3738.
8. Pertsov AM, Davidenko JM, Salomonsz R, Baxter WT, Jalife J, (1993) Spiral waves of excitation underlie reentrant activity in isolated cardiac muscle. Circulation Research 72: 631-650.
9. Gray RA, Jalife J, Pan_lov A, Baxter WT, Cabo C, et al. (1995) Nonstationary vortexlike reentrant activity as a mechanism of polymorphic ventricular tachycardia in the isolated rabbit heart. Circulation 91: 2454-2469.
10. Chen PS, Garfinkel A, Weiss JN, Karagueuzian HS, (1997) Spirals, chaos, and new mechanisms of wave propagation. PACE - Pacing and Clinical Electrophysiology 20: 414-421.
11. Efimov IR, (1999) Evidence of three-dimensional scroll waves with ribbon-shaped filament as a mechanism of ventricular tachycardia in the isolated rabbit heart. J Cardiovasc Electrophysiol 10: 1452-1462.
12. Weiss JN, Qu ZL, Chen PS, Lin SF, Karagueuzian HS, et al. (2005) The dynamics of cardiac fibrillation. Circulation 112: 1232-1240.
13. Biktasheva IV, Biktashev VN, (2003) On a wave-particle dualism of spiral waves dynamics. Phys Rev E 67: 026221.
14. Biktasheva IV, Barkley D, Biktashev VN, Bordyugov GV, Foulkes AJ, (2009) Computation of the response functions of spiral waves in active media. Phys Rev E 79: 056702.
15. Biktasheva IV, Barkley D, Biktashev VN, Foulkes AJ, (2010) Computation of the drift velocity of spiral waves using response functions. Phys Rev E 81: 066202.
16. Beeler GW, Reuter H, (1977) Reconstruction of the action potential of ventricular myocardial fibres. J Physiol 268: 177-210.
17. Silva J, Rudy Y, (2003) Mechanism of pacemaking in (IK1)-downregulated myocytes. Circulation Research 92: 261-263.
18. Dhamoon AS, Jalife J, (2005) The inward rectifier current (IK1) controls cardiac excitability and is involved in arrhythmogenesis. Heart Rhythm 2: 316-324.
19. Masuda H, Sperelakis N, (1993) Inwardly rectifying potassium current in rat fetal and neonatal ventricular cardiomyocytes. Am J Physiol 265: H1107-H1111.
20. Wahler GM, (1992) Developmental increases in the inwardly rectifying potassium current of rat ventricular myocytes. Am J Physiol 262: C1266-C1272.
21. Biktashev VN, (1989) The evolution of vortices in the excitable media. Ph.D. thesis, Moscow Institute of Physics and Technology.Http://www.maths.liv.ac.uk/~vadim/theses/Biktashev.pdf.
22. Biktashev VN, Holden AV, (1995) Resonant drift of autowave vortices in 2d and the effects of boundaries and inhomogeneities. Chaos, Solitons and Fractals 5: 575-622.
23. Foulkes AJ, Barkley D, Biktashev VN, Biktasheva IV, (2010) Alternative stable scroll waves and conversion of autowave turbulence. Chaos 20: 043136.
24. Yakushevich L, (1984) Vortex filament elasticity in active medium. Studia Biophysica 100: 195-200.
25. Panfilov AV, Pertsov AM, (1984) Vortex ring in 3-dimensional active medium described by reaction-diffusion equations. Doklady Akademii Nauk SSSR 274: 1500-1503.
26. Panfilov AV, Rudenko AN, Krinsky VI, (1986) Turbulent rings in 3-dimensional active media with diffusion by 2 components. Biofizika 31: 850-854.
27. Panfilov AV, Rudenko AN, (1987) Two regimes in scroll ring drift in the three-dimensional active media. Physica D 28: 215-218.
28. Bánsági T, Steinbock O, (2007) Negative filament tension of scroll rings in an excitable system. Phys Rev E 76: 045202.
29. Luengviriya C, Storb U, Lindner G, Müller SC, Bär M, et al. (2008) Scroll wave instabilities in an excitable chemical medium. Phys Rev Lett 100: 148302.
30. Luengviriya C, Hauser MJB, (2008) Stability of scroll ring orientation in an advective field. Phys Rev E 77: 056214.
31. Dutta S, Steinbock O, (2010) Steady motion of hairpin-shaped vortex filaments in excitable systems. Phys Rev E 81: 055202.
32. Keener J, (1988) The dynamics of 3-dimensional scroll waves in excitable media. Physica D 31: 269-276.
33. Biktashev VN, Holden AV, Zhang H, (1994) Tension of organizing filaments of scroll waves. Phil Trans Roy Soc Lond ser A 347: 611-630.
34. Dierckx H, Bernus O, Verschelde H, (2009) A geometric theory for scroll wave filaments in anisotropic excitable media. Physica D 238: 941-950.
35. Biktashev VN, Barkley D, Biktasheva IV, (2010) Orbital movement of spiral waves. Phys Rev Lett 104: 058302.
36. Sridhar S, Sinha S, Panfilov AV, (2010) Anomalous drift of spiral waves in heterogeneous excitable media. Phys Rev E 82: 051908.
37. Brazhnik PK, Davydov VA, Zykov VS, Mikhailov AS, (1987) Vortex rings in excitable media. Sov Phys JETP 66: 984.
38. Biktashev VN, (1998) A three-dimensional autowave turbulence. Int J of Bifurcation and Chaos 8: 677-684.
39. Rudenko AN, Panfilov AV, (1983) Drift and interaction of vortices in two-dimensional heterogeneous active medium. Studia Biophysica 98: 183-188.
40. Ten Tusscher KHWJ, Panfilov AV, (2003) Reentry in heterogeneous cardiac tissue described by the Luo-Rudy ventricular action potential model. Am J Physiol - Heart and Circ Physiol 284: H542-H548.
41. Pazó D, Kramer L, Pumir A, Kanani S, Efimov I, et al. (2004) Pinning force in active media. Phys Rev Lett 93: 168303.
42. Alonso S, Baer M, Panfilov AV, (2011) Effects of reduced discrete coupling on filament tension in excitable media. Chaos 21: 013118.