Electrical Singular Filaments in the Heart Wall

  • Arthur T. Winfree
Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 12)


Thus Homer first described a graphic recording from a normal, healthy ventricular wall, presumably ending with fibrillation 3500 years ago during the siege of Bronze-Age Troy by bloodthirsty heroes from Mycenaean Greece.


Action Potential Duration Excitable Medium Spiral Wave Activation Front Phase Gradient 
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  1. 1.
    Equivalent in some respects but not all: the main difference is that the resetting curves of a driven oscillator may have an abrupt jump at the moment when the driving periodicity hits it. This could be modeled as a discontinuity, deflating all topological arguments. In fact nothing discontinuous happens in real physiology, and the size of the abrupt place can only be discovered in the lab, where also one finds out whether or not idealized conceptual arguments pointed the way to discovery or to confusion.Google Scholar
  2. 2.
    Classical notions of spatially random parametric inhomogeneity as the basis of fibrillation might be mirrored more accurately in the processes of electrical defibrillation. At this writing, real hearts and uniform tissue models do not respond to electric shock in quantitatively comparable ways. But if inhomogeneities of resistivity are strewn throughout the modeled tissue, it becomes more responsive, and simulated fibrillation can be erased with shocks of reasonable energy. For a review see papers in the March 1998 issue of Chaos. Google Scholar
  3. 3.
    Unless quite close to a boundary, a localized stimulus in a continuous medium can produce only adjacent mirror-image rotors, as stressed in Winfree (1974f, 1978a, and 1983b about myocardium): this fact rather than the symmetry of large-electrode initial conditions is probably the origin of the pattern that eventually acquired the memorable name “figure of eight.”Google Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Arthur T. Winfree
    • 1
  1. 1.Department of Ecology and Evolutionary BiologyUniversity of ArizonaTucsonUSA

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