Bulletin of Mathematical Biology

, Volume 75, Issue 8, pp 1351–1376 | Cite as

Negative Tension of Scroll Wave Filaments and Turbulence in Three-Dimensional Excitable Media and Application in Cardiac Dynamics

  • Sergio AlonsoEmail author
  • Markus Bär
  • Alexander V. Panfilov
Review Article


Scroll waves are vortices that occur in three-dimensional excitable media. Scroll waves have been observed in a variety of systems including cardiac tissue, where they are associated with cardiac arrhythmias. The disorganization of scroll waves into chaotic behavior is thought to be the mechanism of ventricular fibrillation, whose lethality is widely known. One possible mechanism for this process of scroll wave instability is negative filament tension. It was discovered in 1987 in a simple two variables model of an excitable medium. Since that time, negative filament tension of scroll waves and the resulting complex, often turbulent dynamics was studied in many generic models of excitable media as well as in physiologically realistic models of cardiac tissue. In this article, we review the work in this area from the first simulations in FitzHugh–Nagumo type models to recent studies involving detailed ionic models of cardiac tissue. We discuss the relation of negative filament tension and tissue excitability and the effects of discreteness in the tissue on the filament tension. Finally, we consider the application of the negative tension mechanism to computational cardiology, where it may be regarded as a fundamental mechanism that explains differences in the onset of arrhythmias in thin and thick tissue.


Reaction–diffusion systems Cardiac tissue 



Financial support by the Deutsche Forschungs-gemeinschaft (DFG) within the framework of SFB 910 (Control of Self-Organizing Nonlinear Systems) is acknowledged. We are grateful to A.S. Mikhailov, F. Sagués, H. Engel, and M.J.B. Hauser for valuable discussions about scroll wave dynamics.


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Copyright information

© Society for Mathematical Biology 2012

Authors and Affiliations

  • Sergio Alonso
    • 1
    Email author
  • Markus Bär
    • 1
  • Alexander V. Panfilov
    • 2
  1. 1.Physikalisch-Technische BundesanstaltBerlinGermany
  2. 2.Department of Physics and AstronomyGent UniversityGentBelgium

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