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Resonance and Feedback Strategies for Low-Voltage Defibrillation

  • Vadim N. Biktashev

Early experiments on defibrillation revealed that it is sometimes possible to achieve defib-rillation by lower voltage pulses, if they are applied several times and are properly timed.1 This chapter will review some ideas about detailed mechanisms and how this method may work. Most of these ideas are theoretical and tested only in numerical simulations or in a chemical model of the cardiac tissue, the Belousov—Zhabotinsky (BZ) reaction medium; only in some cases have experimentalists attempted a direct verification in cardiac preparations. The literature on the subject is vast; as the space allocated for this review is limited, the focus here will be on a few cornerstone ideas and somewhat arbitrarily selected examples.

Multiple wave sources in an excitable medium compete with one another. During such competition, the fastest source entrains increasingly more of the tissue. If the faster source is the stimulating electrode and it entrains the whole of the cardiac tissue, it would have expelled the reentrant circuits and perhaps stopped the fibrillation. However, the success of that depends on what happens to the reentry source when the high-frequency waves reach it. This was first investigated in the chemical model of excitable tissues, the BZ reaction medium,2 and then subsequently in more details in numerical simulations of a variant of the FitzHugh—Nagumo model.3 Figure 1 illustrates the main concept. The first panels show the process of entrainment of the medium by the faster source, which in this particular case is the electrode located at the lower boundary of the model medium. When the entrained region reaches the spiral wave, the latter changes its nature: it is no longer a rotating source of waves, but is a dislocation in the otherwise regular field of waves emitted by the fast source. Notice that it cannot disappear completely for topological reasons, as it carries a topological charge. When the approximately periodic waves are passing through a certain point in the medium, one observes oscillations of the dynamic variables at that point and can assign a phase to those oscillations. The increment of change of the phase of oscillations around a contour encircling the spiral or that is the dislocation is the same for both of them, as it cannot change as long as the oscillations persist, which they do unless the contour is crossed by the dislocation. Hence the dislocation carries this topological charge of the spiral wave. Typically it does not stay but drifts; this is sometimes called high-frequency induced drift of spirals, to distinguish it from drift caused by other mechanisms. The direction of drift depends on the parameters of the problem, in particular on the frequency of the entraining source. When the entraining source stops, the dislocation immediately turns back into a spiral wave, which locates in a new place. If the duration and direction of the induced drift are such that the dislocation reaches the place where the regular oscillations are not observed (e.g., the inexcitable border or a Wenckebach block zone), then the topological restriction is lifted and the dislocation may be eliminated, so when the high-frequency source stops, the spiral wave does not resume, and the reentry is stopped.

Keywords

Topological Charge Spiral Wave Chaos Soliton Fractal Feedback Strategy American Physical Society 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC. 2009

Authors and Affiliations

  • Vadim N. Biktashev
    • 1
  1. 1.Department of MathematicsUniversity of LiverpoolUK

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