Sudden Cardiac Death and Turbulence

  • Guillaume AttuelEmail author
  • Oriol Pont
  • Binbin Xu
  • Hussein Yahia
Part of the Understanding Complex Systems book series (UCS)


Data acquired from the electrical activity of human hearts during episodes of atrial fibrillation, a disordered arrhythmia that is a major cause of stroke, reveals intriguing features for an excitable media: highly skew symmetric probability distributions with heavy tails, long range correlations, and broad singularity spectra. Interestingly, the relevant exponents extracted from these empirical laws are stable over several minutes but not universal. Their stable values are distributed among patients and areas of the heart. The question of central clinical purpose is whether they might characterise locally the myocardium contingent pathology. To achieve clarification of these peculiar facts, we were led to devise a phenomenological model that departs from the conventional approach to fibrillation. Instead of a defect mediated spiral wave “turbulence” induced by front collisions, fibrillation is pictured here as a highly intermittent modulation of cardiac pulse trains. It is based on the physiology of inter-cellular ionic exchanges, which is associated with the natural degree of freedom of the inter-pulse duration. We infer an experimentally unknown slow dynamics of inter-cellular coupling, that may induce an inter-pulse effective coupling. This interaction creates a modulation that may lead to intermittency in various ways. The exchange of charges occurs at small scales in the model. They are passively advected at each interstitial junction on fast time scales and on average collectively driving the larger scales. In fact, a dimensionless number characterising the dynamics is an analogue of the Rayleigh number. Away from a rapidly beating source, random back scattering and front splitting make pulses follow random hierarchical “percolating” paths in 1D. We discuss very briefly the topological origin of these dynamics. In the light of this model, we don’t omit to mention some important physiological aspects of the pathology that are still not well understood and more possibilities for the case which comes to grip with sudden cardiac death.


Atrial Fibrillation Excitable Medium Spiral Wave Excess Charge Self Organise Criticality 
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.


  1. 1.
    D.P. Zipes, H.J.J. Wellens, Circulation 98, 2334 (1998)CrossRefGoogle Scholar
  2. 2.
    A.L. Hodgkin, A.F. Huxley, J. Physiol. 117(4), 500 (1952)CrossRefGoogle Scholar
  3. 3.
    B. van der Pol, J. van der Mark, Philos. Mag. Suppl. (6), 763 (1928)Google Scholar
  4. 4.
    D. Noble, J. Physiol. 160, 317 (1962)CrossRefGoogle Scholar
  5. 5.
    R. Fitzhugh, in Mathematical Models of Excitation and Propagation in Nerve, ed. by H.P. Schwan. Biological Engineering (McGraw-Hill, New York, 1962)Google Scholar
  6. 6.
    J. Nagumo, S. Arimoto, S. Yoshizawa, Proc. IRE 50, 2061 (1962)CrossRefGoogle Scholar
  7. 7.
    M.R. Guevarra, L. Glass, J. Math. Biol. 14, 1 (1982)MathSciNetCrossRefGoogle Scholar
  8. 8.
    L. Glass, M.R. Guevarra, A. Shrier, R. Perez, Physica 7D 89 (1983)ADSGoogle Scholar
  9. 9.
    U. Parlitz, W. Lauterborn, Phys. Rev. A (36), 1428 (1987)Google Scholar
  10. 10.
    M.R., Guevarra, L. Glass, IEEE Comput. Cardiol. 167 (1984)Google Scholar
  11. 11.
    A. Karma, Chaos 4, 461 (1994)ADSCrossRefGoogle Scholar
  12. 12.
    P. Attuel et al., Int. J. Cardiol. 2, 179 (1982)CrossRefGoogle Scholar
  13. 13.
    M.A. Allessie, F.I.M. Bonke, F.J.G. Schopman, Circ. Res. 41(1), 9 (1977)CrossRefGoogle Scholar
  14. 14.
    E. Meron, P. Pelcé, Phys. Rev. Lett. 60(18), 1880 (1988)ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    A. Hagberg, E. Meron, Phys. Rev. Lett. 72(15), 2494 (1994)ADSCrossRefGoogle Scholar
  16. 16.
    I.S. Aranson, L. Kramer, Rev. Mod. Phys. 74(1), 99 (2002)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    J. Lajzerowicz, J.J. Niez, J. Phys. Lett. 40(7), 165 (1979)CrossRefGoogle Scholar
  18. 18.
    P. Coullet, J. Lega, B. Houchmanzadeh, J. Lajzerowicz, Phys. Rev. Lett. 65(11), 1352 (1990)ADSCrossRefGoogle Scholar
  19. 19.
    T. Frisch, S. Rica, P. Coullet, J.M. Gilli, Phys. Rev. Lett. 72(10), 1471 (1994)ADSCrossRefGoogle Scholar
  20. 20.
    A. Garfinkel et al., J. Clin. Investig. 99(2), 305 (1997)CrossRefGoogle Scholar
  21. 21.
    A. Karma, Phys. Rev. Lett. 71(7), 1103 (1993)ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    A.T. Winfree, Science 266(5187), 1003 (1994)ADSCrossRefGoogle Scholar
  23. 23.
    F.H. Fenton, E.M. Cherry, H.M. Hastings, S.J. Evans, Chaos 12(3), 852 (1993)ADSCrossRefGoogle Scholar
  24. 24.
    A. Hagberg, E. Meron, Chaos 4(3), 477 (1994)ADSCrossRefGoogle Scholar
  25. 25.
    P. Attuel, P. Coumel, M.J. Janse, The Atrium in Health and Disease, 1st edn. (Futura Publishing Co, Mount Kisco, 1989)Google Scholar
  26. 26.
    M.C. Wijffels, C.J. Kirchhof, R.M. Dorland, M. Allessie, Circulation 92, 1954 (1995)CrossRefGoogle Scholar
  27. 27.
    Y. Pomeau, Physica 23D 3 (1986)ADSGoogle Scholar
  28. 28.
    M. Argentina, P. Coullet, Phys. Rev. E 56(3), R2359 (1997)ADSCrossRefGoogle Scholar
  29. 29.
    K. Dahmen, J.P. Sethna, Phys. Rev. B 53(22), 14872 (1996)ADSCrossRefGoogle Scholar
  30. 30.
    J.C. McClure Jr., K. Schroder, C R C Crit. Rev. Solid State Sci. 6(1), 45 (1976)CrossRefGoogle Scholar
  31. 31.
    J.S. Urbach, R.C. Madison, J.T. Market, Phys. Rev. Lett. 75(2), 276 (1995)ADSCrossRefGoogle Scholar
  32. 32.
    C.J. Olson, C. Reichhardt, F. Nori, Phys. Rev. B 56(10), 6175 (1997)ADSCrossRefGoogle Scholar
  33. 33.
    E. Altshuler et al., Phys. Rev. B 70, 140505 (2004)ADSCrossRefGoogle Scholar
  34. 34.
    J.M. Beggs, D. Plenz, J. Neurosci. 23(35), 1167 (2003)Google Scholar
  35. 35.
    C.-W. Shin, S. Kim, Phys. Rev. E 74, 045101(R) (2006)Google Scholar
  36. 36.
    L. de Arcangelis, C. Perrone-Capano, H.J. Herrmann, Phys. Rev. Lett. 96, 028107 (2006)ADSCrossRefGoogle Scholar
  37. 37.
    J. Hesse, T. Gross, Front. Syst. Neurosci. 8, 166 (2014)CrossRefGoogle Scholar
  38. 38.
    S. Ciliberto, P. Bigazzi, Phys. Rev. Lett. 60(4), 286 (1988)ADSCrossRefGoogle Scholar
  39. 39.
    U. Frisch, Turbulence: The legacy of Kolmogorov (Cambridge University Press, Cambridge, 1995)zbMATHGoogle Scholar
  40. 40.
    B. Hille, Ion Channels of Excitable Membranes, 3d edn. (Sinauer Sunderland, 2001)Google Scholar
  41. 41.
    A. Panfilov, P. Hogeweg, Phys. Lett. A 176, 295 (1993)ADSCrossRefGoogle Scholar
  42. 42.
    L. Landau, E.M. Lifchitz, Physique Statistique, 4th édn. (Mir ellipse, Moscow, 1994)Google Scholar
  43. 43.
    Y.J. Chen, S.A. Chen, M.S. Chang, C.I. Lin, Cardiovasc. Res. 48, 265 (2000)CrossRefGoogle Scholar
  44. 44.
    G. Bub, A. Shrier, L. Glass, Phys. Rev. Lett. 88(5), 058101 (2002)ADSCrossRefGoogle Scholar
  45. 45.
    G. Bub, A. Shrier, L. Glass, Phys. Rev. Lett. 94, 028105 (2005)ADSCrossRefGoogle Scholar
  46. 46.
    H.-Z. Wang, J.L. Jian, F.L. Lemanski, R.D. Veenstra, Biophys. J. 63, 39 (1992)Google Scholar
  47. 47.
    J. Neyton, A. Trautmann, J. Exp. Biol. 124, 93 (1986)Google Scholar
  48. 48.
    M.C. Cross, P.C. Hohenberg, Rev. Mod. Phys. 65(3), 851 (1993)ADSCrossRefGoogle Scholar
  49. 49.
    P. Glansdorff, I. Prigogine, Thermodynamic Theory of Structure, Stability and Fluctuations. (Wiley-Interscience & Wiley, New York, 1971)Google Scholar
  50. 50.
    I. Prigogine, G. Nicolis, Q. Rev. Biophys. 4(2 & 3), 107 (1971)CrossRefGoogle Scholar
  51. 51.
    P. Bergé, M. Dubois, J. Phys. Lett. 46(10), 431 (1985)CrossRefGoogle Scholar
  52. 52.
    E.G. Daoud et al., Circulation 94, 1600 (1996)CrossRefGoogle Scholar
  53. 53.
    H. Fukuyama, P.A. Lee, Phys. Rev. B 17(2), 535 (1978)ADSCrossRefGoogle Scholar
  54. 54.
    P.A. Lee, T.M. Rice, Phys. Rev. B 19(8), 3970 (1979)ADSCrossRefGoogle Scholar
  55. 55.
    M.J. Rice, Phys. Rev. Lett. 36(8), 432 (1976)ADSCrossRefGoogle Scholar
  56. 56.
    G. Grüner, Rev. Mod. Phys. 60(4), 3970 (1979)Google Scholar
  57. 57.
    P.C. Hohenberg, P.C. Hohenberg, Rev. Mod. Phys. 49(3), 435 (1977)ADSCrossRefGoogle Scholar
  58. 58.
    C.R. Myers, J.P. Sethna, Phys. Rev. B 47(17), 11171 (1993)ADSCrossRefGoogle Scholar
  59. 59.
    D.S. Fisher, Phys. Rev. Lett. 50(19), 1486 (1983)ADSCrossRefGoogle Scholar
  60. 60.
    H. Hinrichsen, Adv. Phys. 49(7), 815–958 (2000)ADSMathSciNetCrossRefGoogle Scholar
  61. 61.
    G. Grinstein, D. Mukamel, R. Seidin, C.H. Bennett, Phys. Rev. Lett. 70(23), 3607 (1993)ADSCrossRefGoogle Scholar
  62. 62.
    P. Grassberger, Phys. Rev. E 59(3), R2520 (1999)ADSCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Guillaume Attuel
    • 1
    Email author
  • Oriol Pont
    • 1
  • Binbin Xu
    • 1
  • Hussein Yahia
    • 1
  1. 1.GeoStat, “Geometry and Statistics in acquisition data”Centre de recherche INRIA Bordeaux Sud-OuestTalence CedexFrance

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