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.


Topological Charge Spiral Wave Chaos Soliton Fractal Feedback Strategy American Physical Society 
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  1. 1.
    1.Gurvich PL.The Main Principles of Cardiac Defibrillation. Moscow: Meditsina; 1975Google Scholar
  2. 2.
    2.Krinsky VI, Agladze KI. Interaction of rotating waves in an active chemical mediumPhysica D1983;8:50–56CrossRefGoogle Scholar
  3. 3.
    3.Ermakova EA, Krinsky VI, Panfilov AV, Pertsov AM. Interaction between spiral and flat periodic waves in an active medium.Biofizika1986;31:318–323PubMedGoogle Scholar
  4. 4.
    Sinha S, Pande A, Pandit R. Defibrillation via the elimination of spiral turbulence in a model for ventricular fibrillation.Phys Rev Lett2001;86:3678–3681PubMedCrossRefGoogle Scholar
  5. 5.
    Pandit R, Pande A, Sinha S, Sen A. Spiral turbulence and spatiotemporal chaos:characterization and control in two excitable media.Physica A2002;306:211–219CrossRefGoogle Scholar
  6. 6.
    Davydov VA, Zykov VS, Mikhailov AS, Brazhnik PK. Drift and resonance of spiral waves in distributed media.Sov Phys Radiophys1988;31:574–582Google Scholar
  7. 7.
    Agladze KI, Davydov VA, Mikhailov AS. An observation of resonance of spiral waves in distributed excitable medium.Sov Phys JETP Lett1987;45:601–603Google Scholar
  8. 8.
    Mikhailov AS, Davydov VA, Zykov VS. Complex dynamics of spiral waves and motion of curves.Physica D.1994;70:1–39CrossRefGoogle Scholar
  9. 9.
    Biktashev VN, Holden AV. Control of re-entrant activity by resonant drift in a two-dimensional model of isotropic homogeneous atrial tissue.Proc Roy Soc Lond Ser B1995;260:211–217CrossRefGoogle Scholar
  10. 10.
    Biktashev VN, Holden AV. Resonant drift of the autowave vortex in abounded medium.Phys Lett A1993;181:216–224CrossRefGoogle Scholar
  11. 11.
    Biktashev VN, Holden AV. Resonant drift of autowave vortices in 2D and the effects of boundaries and inhomogeneities.Chaos Solitons Fractals1995;5:575–622CrossRefGoogle Scholar
  12. 12.
    Biktashev VN, Holden AV. Design principles of a low-voltage cardiac defibrillator based on the effect of feed-back resonant drift.J Theor Biol1994;169:101–112PubMedCrossRefGoogle Scholar
  13. 13.
    Zykov VS, Engel H. Feedback-mediated control of spiral waves.Physica D2004;199:243–263CrossRefGoogle Scholar
  14. 14.
    Zykov VS, Engel H. Feedback-mediated control of spiral waves In: Schimansky-Geier L, Fiedler B, Kurths J, Schoell E, eds.Analysis and Control of Complex Nonlinear Processes in Physics, Chemistry and Biology. Singapore: World Scientific;2007Google Scholar
  15. 15.
    Grill S, Zykov VS, Muller SC. Feedback-controlled dynamics of meandering spiral waves.Phys Rev Lett1995;75:3368–3371PubMedCrossRefGoogle Scholar
  16. 16.
    Sabbagh H. Stochastic properties of autowave turbulence elimination.Chaos Solitons Fractals2000;11:2141–2148CrossRefGoogle Scholar
  17. 17.
    Panfilov AV, Rudenko AN. 2 regimes of the scroll ring drift in the 3-dimensional active media.Physica D1987;28:215–218CrossRefGoogle Scholar
  18. 18.
    Brazhnik PK, Davydov VA, Zykov VS, Mikhailov AS. Vortex rings in excitable media.Zhurnal Eksperimentalnoi I Teoreticheskoi Fiziki1987;93:1725–1736Google Scholar
  19. 19.
    Yakushevich LV. Vortex filament elasticity in active medium.Studia Biophysica1984;100:195–200Google Scholar
  20. 20.
    Keener JP. The dynamics of 3-dimensional scroll waves in excitable media.Physica D1988;31:269–276CrossRefGoogle Scholar
  21. 21.
    Biktashev VN, Holden AV, Zhang H. Tension of organizing filaments of scroll waves.Philos Trans R Soc Lond Ser A1994;347:611–630CrossRefGoogle Scholar
  22. 22.
    Winfree AT. Electrical turbulence in three-dimensional heart muscle.Science1994;266:1003–1006PubMedCrossRefGoogle Scholar
  23. 23.
    Biktashev VN. A three-dimensional autowave turbulence.Int J Bifurcat Chaos1998;8:677–684CrossRefGoogle Scholar
  24. 24.
    Fenton FH, Cherry EM, Hastings HM, Evans SJ. Multiple mechanisms of spiral wave breakup in a model of cardiac electrical activity.Chaos2002;12:852–892PubMedCrossRefGoogle Scholar
  25. 25.
    Alonso S, Sagues F, Mikhailov AS. Negative-tension instability of scroll waves and Winfree turbulence in the Oregonator model.J Phys Chem A2006;110:12063–12071PubMedCrossRefGoogle Scholar
  26. 26.
    Alonso S, Panfilov AV. Negative filament tension in the Luo—Rudy model of cardiac tissue.Chaos2007;17:015102PubMedCrossRefGoogle Scholar
  27. 27.
    Fenton F, Karma A. Vortex dynamics in three-dimensional continuous myocardium with fiber rotation: filament instability and fibrillation.Chaos1998;8:20–47PubMedCrossRefGoogle Scholar
  28. 28.
    Fenton F, Karma A. Fiber-rotation-induced vortex turbulence in thick myocardium.Phys Rev Lett1998;81:481–484CrossRefGoogle Scholar
  29. 29.
    Verschelde H, Dierckx H, Bernus O. Covariant string dynamics of scroll wave filaments in anisotropic cardiac tissue.Phys Rev Lett2007;99:168104PubMedCrossRefGoogle Scholar
  30. 30.
    Alonso S, Sagues F, Mikhailov AS. Taming Winfree turbulence of scroll waves in excitable media.Science2003;299:1722–1725PubMedCrossRefGoogle Scholar
  31. 31.
    Alonso S, Sagues F, Mikhailov AS. Periodic forcing of scroll rings and control of Winfree turbulence in excitable media.Chaos2006;16:023124PubMedCrossRefGoogle Scholar
  32. 32.
    Vinson M, Pertsov A, Jalife J. Anchoring of vortex filaments in 3D excitable media.Physical D1994;72:119–134CrossRefGoogle Scholar
  33. 33.
    Nikolaev EV, Biktashev VN, Holden AV. On feedback resonant drift and interaction with the boundaries in circular and annular excitable media.Chaos Solitons Fractals1998;9:363–376CrossRefGoogle Scholar
  34. 34.
    Pazo D, Kramer L, Pumir A, Kanani S, Efimov I, Krinsky V. Pinning force in active media.Phys Rev Lett2004;93:168303PubMedCrossRefGoogle Scholar
  35. 35.
    Biktasheva IV, Holden AV, Biktashev VN. Localization of response functions of spiral waves in the FitzHugh–Nagumo system.Int J Bifurcat Chaos2006;16(5):1547–1555CrossRefGoogle Scholar
  36. 36.
    Biktasheva IV, Elkin Yu E, Biktashev VN. Localised sensitivity of spiral waves in the complex Ginzburg—Landau equation.Phys Rev E1998;57:2656–2659CrossRefGoogle Scholar
  37. 37.
    Sambelashvili AT, Nikolski VP, Efimov IR. Nonlinear effects in subthreshold virtual electrode polarization.Am J Physiol Heart Circ Physiol2003;284:H2368–H2374PubMedGoogle Scholar
  38. 38.
    Takagi S, Pumir A, Efimov I, Pazó D, Nikolski V, Krinsky V. Unpinning and removal of a rotating wave in cardiac muscle.Phys Rev Lett2004;93:058101PubMedCrossRefGoogle Scholar
  39. 39.
    Krinsky VI, Biktashev VN, Pertsov AM. Autowave approaches to cessation of reentrant arrhythmias.Ann N Y Acad Sci1990;591:232–246PubMedCrossRefGoogle Scholar
  40. 40.
    Huyet G, Dupont C, Corriol T, Krinsky V. Unpinning of a vortex in a chemical excitable medium.Int J Bifurcat Chaos1998;8:1315–1323CrossRefGoogle Scholar
  41. 41.
    Pumir A, Krinsky V. Unpinning of a rotating wave in cardiac muscle by an electric field.J Theor Biol1999;199:311–319PubMedCrossRefGoogle Scholar
  42. 42.
    Takagi S, Pumir A, Pazó D, Efimov I, Nikolski V, Krinsky V. A physical approach to remove anatomical reentries: a bidomain study.J Theor Biol2004;230:489–497PubMedCrossRefGoogle Scholar
  43. 43.
    Ripplinger CM, Krinsky VI, Nikolski VP, Efimov IR. Mechanisms of unpinning and termination of ventricular tachycardia.Am J Physiol Heart Circ Physiol2006;291:H184–H192PubMedCrossRefGoogle Scholar
  44. 44.
    Alekseev VV, Loskutov AY. Control of a system with a strange attractor through periodic parametric action.Sov Phys Dokl1987;32:270–271Google Scholar
  45. 45.
    Loskutov AY, Cheremin RV, Vysotskii SA. Stabilization of turbulent dynamics in excitable media by an external point action.Dokl Phys2005;50:490–493CrossRefGoogle Scholar
  46. 46.
    Loskutov AY, Vysotskii SA. New approach to the defibrillation problem: suppression of the spiral wave activity of cardiac tissue.JETP Lett2006;84:524–529CrossRefGoogle Scholar
  47. 47.
    Ott E, Grebogi C, Yorke JA. Controlling chaos.Phys Rev Lett1990;64:1196–1199PubMedCrossRefGoogle Scholar
  48. 48.
    Garfinkel A, Spano ML, Ditto WL, Weiss JN. Controlling cardiac chaos.Science1992;257:1230–1235PubMedCrossRefGoogle Scholar
  49. 49.
    Pak HN, Liu YB, Hayashi H, Okuyama Y, Chen PS, Lin SF. Synchronization of ventricular fibrillation with real-time feedback pacing: implication to low-energy defibrillationAm J Physiol2003;285:H2704–H2711Google Scholar

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© Springer Science+Business Media, LLC. 2009

Authors and Affiliations

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

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