Fail Small, Fail Often: An Outsider’s View of Physiologic Complexity

  • Bruce J. WestEmail author


We examine the hypothesis that the robustness of physiological time series results from allowing the underlying process to fail in small ways, and on a fairly regular basis. The notion of controlling such complex time series by suppressing their natural variability is argued to increase the likelihood of failure being catastrophic when it does occur. We also examine the hypothesis that the statistics of heart rate variability (HRV) are given by a tempered Lévy probability density function. Herein, we use the fractional probability calculus to frame our arguments as a new way to understand complex physiological dynamics. A self-induced nonlinear control is shown to induce a tempered Lévy process and is consistent with the hypothesis of disease being the loss of physiologic complexity made over 25 years ago.


  1. 1.
    Bernard C. Introduction to experimental medicine. New York: Dover Publications; 1865.Google Scholar
  2. 2.
    Cannon WB. The wisdom of the body. New York: W W Norton & Co.; 1932.CrossRefGoogle Scholar
  3. 3.
    Peng C-K, Mietus J, Hausdorff JM, Havlin S, Stanley HE, Goldberger AL. Long-range anticorrelations and non-Gaussian behavior of the heartbeat. Phys Rev Lett. 1993;70(9):1343–6.CrossRefGoogle Scholar
  4. 4.
    Goldberger AL, West BJ. Fractals in physiology and medicine. Yale J Biol Med. 1987;60(5):421–35 and references therein.Google Scholar
  5. 5.
    Shlesinger MF, West BJ. Asymmetric branching of the mammalian lung. Phys Rev Lett. 1991;67:2106.CrossRefGoogle Scholar
  6. 6.
    West BJ. Fractal physiology and chaos in medicine, 2nd ed. New Jersey: World Scientific; 2013.CrossRefGoogle Scholar
  7. 7.
    Hausdorff JF, Peng CK, Ladin Z, Ladin JY, Wei JY, Goldberger AL. Is walking a random walk? Evidence for long-range correlations in stride interval of human gait. J Appl Physiol. 1995;78(1):349–58.CrossRefGoogle Scholar
  8. 8.
    Griffin L, West DJ, West BJ. Random stride intervals with memory. J Biol Phys. 2000;26(3):185–202.CrossRefGoogle Scholar
  9. 9.
    Peng CK, Meus J, Li Y, Lee C, Hausdorff JM, Stanley HE, Goldberger AL, Lipsitz LA. Quantifying fractal dynamics of human respiration: age and gender effects. Ann Biomed Eng. 2002;30(5):683–92.CrossRefGoogle Scholar
  10. 10.
    West BJ, Griffin LA, Freerick HJ, Moon RE. The independently fractal nature of respiration and heart rate during exercise under normobaric and hyperbaric conditions. Respir Physiol Neurobiol. 2005;145(2–3):219–33.CrossRefGoogle Scholar
  11. 11.
    Costa MD, Peng CK, Goldberger AL. Multiscale analysis of heart rate dynamics: entropy and time irreversibility measures. Cardiovasc Eng. 2008;8(2):88–93.CrossRefGoogle Scholar
  12. 12.
    Yaniv Y, Lyaskov AE, Lakatta EG. The fractal-like complexity of heart rate variability beyond neurotransmitters and autonomic receptors: signaling intrinsic to sinoatrial node pacemaker cells. Cardiovasc Pharm Open Access. 2013;2:111.CrossRefGoogle Scholar
  13. 13.
    Goldberger AL, Rigney DR, West BJ. Chaos and fractals in human physiology. Sci Am. 1990;262(2):42–9.CrossRefGoogle Scholar
  14. 14.
    West BJ. Where medicine west wrong. Singapore: World Scientific; 2006.CrossRefGoogle Scholar
  15. 15.
    Bassigthwaighte JB, Liebowitch LS, West BJ. Fractal physiology. Oxford: Oxford University Press; 1994.CrossRefGoogle Scholar
  16. 16.
    Mandelbrot BB. Fractals, form, chance and dimension. San Francisco: W.H. Freeman & Co; 1977.Google Scholar
  17. 17.
    West BJ. A mathematics for medicine: the network effect. Front Physiol. 2014;5:456.CrossRefGoogle Scholar
  18. 18.
    Bacry E, Delour J, Muzy JF. Multifractal random walk. Phys Rev E. 2001;64(2):026103.CrossRefGoogle Scholar
  19. 19.
    West BJ. Fractional calculus view of complexity: tomorrow’s science. Boca Raton: CRC Press; 2016.CrossRefGoogle Scholar
  20. 20.
    West BJ, Latka M, Glaubic-Latka M, Latka D. Multifractality of cerebral blood flow. Physica A. 2003;318(3–4):453–60.CrossRefGoogle Scholar
  21. 21.
    Hayano J, Kiyono K, Struzik ZR, Yamamoto Y, Watanabe E, Stein PK, Watkins LL, Blumenthal JA, Carney RM. Increased non-Gaussianity of heart rate variability predicts cardiac mortality after an acute myocardial infarction. Front Physiol. 2011;2:65.CrossRefGoogle Scholar
  22. 22.
    Mora T, Bialek W. Are biological systems poised at criticality? J Stat Phys. 2011;144(2):268–302.CrossRefGoogle Scholar
  23. 23.
    Chechkin AV, Gonchar YY, Klafter J, Metzler R. Natural cutoff in Lévy caused by dissipative nonlinearity. Phys Rev E. 2005;72(1 Pt 1):010101.CrossRefGoogle Scholar
  24. 24.
    West BJ, Turalska M. Hypothetical control of HRV (under review).Google Scholar
  25. 25.
    Kiyono K, Struzik ZR, Aoyagi N, Sakata S, Hayano J, Yamamoto Y. Critical scale invariance in a healthy human heart rate. Phys Rev Lett. 2004;93(17):178103.CrossRefGoogle Scholar
  26. 26.
    Kiyono K, Struzik ZR, Aoyagi N, Yamamoto Y. Multiscale probability density function analysis: non-Gaussian and scale-invariant fluctuations of healthy human heart rate. IEEE Trans Biomed Eng. 2006;53(1):95–102.CrossRefGoogle Scholar
  27. 27.
    Taleb NN, Blyth M. The black swan of Cairo: how suppressing volatility makes the world less predictable and more dangerous. Foreign Aff. 2011;90(3):33–9.Google Scholar
  28. 28.
    Taleb NN. The black swan: the impact of the highly improbable. New York: Random House; 2007.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Information Science Directorate, Army Research OfficeResearch Triangle ParkUSA

Personalised recommendations