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 Movies of Spiral Waves and Spiral Break-up
  in Reaction-Diffusion Equations


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2D Hodgkin-Huxley Double Spiral Wave à la (Art) Winfree





2D Mitchell-Shaeffer Spiral Break-up> Defribrilation à la (Jim) Keener


Spiral Break-up and Defribrillation
(Hi-Res/12.8MB)
Spiral Break-up and Defribrillation
(Lo-Res/6.4MB)
Spiral Break-up Close-up
(6.5MB)

Simulations were performed on a modified version of the two-variable (spatially-extended) Mitchell-Shaeffer model. Instabilities inherent in this model prevent a self-sustained spiral. Instead the sprial breaks-up, continually generating new spiral doublets which rapidly usurp the domain. Though it is not clear whether break-up of a spiral wave is the cause of fribrillation in heart tissue, it is thought that the field of doublets, generated in possibly a different way, is representative of fribrillation. Defribrillation is then the extinguishing of this self-sustained activity, which prevents the normal functioning of the heart, and is accomplished by the application of electrical currents to the surface of the body (the paddles). How such external currents manifest themselves within the heart to induce defribrillation remains a heated debate... i.e., a great mystery to be solved. The tail end of the movies demonstrate one approach to defribrillation, proposed by James P. Keener, which asserts that small-scale inhomogeneities in the tissue set up small dipole currents, whose size, relative to the spiral doublets' cores, is an important factor to explain the experimental data.


  Stefanos E. Folias
    10.01.2007