Article thumbnail

Evolution of Spiral and Scroll Waves of Excitation in a Mathematical Model of Ischaemic Border Zone

By Vadim N. Biktashev, Irina V. Biktasheva and Narine A. Sarvazyan


Abnormal electrical activity from the boundaries of ischemic cardiac tissue is recognized as one of the major causes in generation of ischemia-reperfusion arrhythmias. Here we present theoretical analysis of the waves of electrical activity that can rise on the boundary of cardiac cell network upon its recovery from ischaemia-like conditions. The main factors included in our analysis are macroscopic gradients of the cell-to-cell coupling and cell excitability and microscopic heterogeneity of individual cells. The interplay between these factors allows one to explain how spirals form, drift together with the moving boundary, get transiently pinned to local inhomogeneities, and finally penetrate into the bulk of the well-coupled tissue where they reach macroscopic scale. The asymptotic theory of the drift of spiral and scroll waves based on response functions provides explanation of the drifts involved in this mechanism, with the exception of effects due to the discreteness of cardiac tissue. In particular, this asymptotic theory allows an extrapolation of 2D events into 3D, which has shown that cells within the border zone can give rise to 3D analogues of spirals, the scroll waves. When and if such scroll waves escape into a better coupled tissue, they are likely to collapse due to the positive filament tension. However, our simulations have shown that such collapse of newly generated scrolls is not inevitable and that under certain conditions filament tension becomes negative, leading to scroll filaments to expand and multiply leading to a fibrillation-like state within small areas of cardiac tissue

Topics: Research Article
Publisher: Public Library of Science
OAI identifier:
Provided by: PubMed Central

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.

Suggested articles


  1. (2009). A geometric theory for scroll wave filaments in anisotropic excitable media.
  2. (1998). A three-dimensional autowave turbulence.
  3. (2010). Alternative stable scroll waves and conversion of autowave turbulence.
  4. (2010). Anomalous drift of spiral waves in heterogeneous excitable media.
  5. (2010). Computation of the drift velocity of spiral waves using response functions.
  6. (2009). Computation of the response functions of spiral waves in active media.
  7. (1992). Developmental increases in the inwardly rectifying potassium current of rat ventricular myocytes.
  8. (1983). Drift and interaction of vortices in twodimensional heterogeneous active medium.
  9. (2011). Effects of reduced discrete coupling on filament tension in excitable media.
  10. (1999). Evidence of three-dimensional scroll waves with ribbonshaped filament as a mechanism of ventricular tachycardia in the isolated rabbit heart.
  11. (2008). Generation and escape of local waves from the boundary of uncoupled cardiac tissue.
  12. (2005). Genesis of ectopic waves: role of coupling, automaticity, and heterogeneity.
  13. (2002). Initiation and propagation of ectopic waves: insights from an in vitro model of ischemia-reperfusion injury.
  14. (1993). Inwardly rectifying potassium current in rat fetal and neonatal ventricular cardiomyocytes.
  15. (2001). Localized injury in cardiomyocyte network: a new experimental model of ischemiareperfusion arrhythmias.
  16. (2008). Locations of ectopic beats coincide with spatial gradients of NADH in a regional model of low-ow reperfusion.
  17. (2003). Mechanism of pacemaking in (IK1)-downregulated myocytes.
  18. (2007). Negative filament tension of scroll rings in an excitable system.
  19. (1995). Nonstationary vortexlike reentrant activity as a mechanism of polymorphic ventricular tachycardia in the isolated rabbit heart.
  20. (2003). On a wave-particle dualism of spiral waves dynamics.
  21. (2010). Orbital movement of spiral waves.
  22. (2004). Pinning force in active media.
  23. (1977). Reconstruction of the action potential of ventricular myocardial fibres.
  24. (2003). Reentry in heterogeneous cardiac tissue described by the Luo-Rudy ventricular action potential model.
  25. (2001). Reperfusion arrhythmias and sudden cardiac death: a century of progress toward an understanding of the mechanisms.
  26. (1995). Resonant drift of autowave vortices in 2d and the effects of boundaries and inhomogeneities.
  27. (2008). Scroll wave instabilities in an excitable chemical medium.
  28. (1993). Spiral waves of excitation underlie reentrant activity in isolated cardiac muscle.
  29. (1997). Spirals, chaos, and new mechanisms of wave propagation.
  30. (2008). Stability of scroll ring orientation in an advective field.
  31. (2010). Steady motion of hairpin-shaped vortex filaments in excitable systems.
  32. (1994). Tension of organizing filaments of scroll waves. Phil Trans Roy Soc Lond ser A 347:
  33. (1988). The dynamics of 3-dimensional scroll waves in excitable media.
  34. (2005). The dynamics of cardiac fibrillation.
  35. (1989). The evolution of vortices in the excitable media.
  36. (2005). The inward rectifier current (IK1) controls cardiac excitability and is involved in arrhythmogenesis.
  37. (1986). Turbulent rings in 3-dimensional active media with diffusion by 2 components.
  38. (1987). Two regimes in scroll ring drift in the threedimensional active media.
  39. (1984). Vortex filament elasticity in active medium.
  40. (1984). Vortex ring in 3-dimensional active medium described by reaction-diffusion equations.
  41. (1987). Vortex rings in excitable media.