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Chaos / Volume 22 / Issue 1 / REGULAR ARTICLES

Chaos 22, 013108 (2012); http://dx.doi.org/10.1063/1.3675622 (7 pages)

Fractal variability: An emergent property of complex dissipative systems

Andrew J. E. Seely1,2,3 and Peter Macklem4

1Ottawa Hospital Research Institute, Ottawa, ON, K1H 8L6, Canada
2Division of Thoracic Surgery, University of Ottawa, Ottawa, ON, Canada
3Department of Critical Care Medicine, University of Ottawa, Ottawa, ON, Canada
4Respiratory Medicine, McGill University, Montreal, QC, Canada

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(Received 13 October 2011; accepted 13 December 2011; published online 19 January 2012)

The patterns of variation of physiologic parameters, such as heart and respiratory rate, and their alteration with age and illness have long been under investigation; however, the origin and significance of scale-invariant fractal temporal structures that characterize healthy biologic variability remain unknown. Quite independently, atmospheric and planetary scientists have led breakthroughs in the science of non-equilibrium thermodynamics. In this paper, we aim to provide two novel hypotheses regarding the origin and etiology of both the degree of variability and its fractal properties. In a complex dissipative system, we hypothesize that the degree of variability reflects the adaptability of the system and is proportional to maximum work output possible divided by resting work output. Reductions in maximal work output (and oxygen consumption) or elevation in resting work output (or oxygen consumption) will thus reduce overall degree of variability. Second, we hypothesize that the fractal nature of variability is a self-organizing emergent property of complex dissipative systems, precisely because it enables the system’s ability to optimally dissipate energy gradients and maximize entropy production. In physiologic terms, fractal patterns in space (e.g., fractal vasculature) or time (e.g., cardiopulmonary variability) optimize the ability to deliver oxygen and clear carbon dioxide and waste. Examples of falsifiability are discussed, along with the need to further define necessary boundary conditions. Last, as our focus is bedside utility, potential clinical applications of this understanding are briefly discussed. The hypotheses are clinically relevant and have potential widespread scientific relevance.

© 2012 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. THERMODYNAMICS
    1. Entropy
      1. Thermodynamic definition
      2. Probabilistic definition
      3. Information definition
      4. Energy dispersal definition
    2. The second law of thermodynamics
    3. Entropy production and non-equilibrium thermodynamics
    4. Principle of maximum entropy production
    5. Work cycles
    6. Spontaneous self-organization of entropy producing work cycles
  3. ORIGINS OF VARIABILITY
    1. Variability revisited
    2. Hypothesis: Fractal variability reflects self-organizing optimal entropy production
    3. Therapeutic value of maximizing entropy production
    4. Overall degree of variability
    5. Therapeutic value of optimizing proportion of maximal work expended
  4. CONCLUSION

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KEYWORDS and PACS

Keywords

cardiology, emergent phenomena, fractals, lung, maximum entropy methods, oxygen, pneumodynamics

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3675622

PUBLICATION DATA

ISSN

1054-1500 (print)  
1089-7682 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    M. Costa, A. L. Goldberger, and C. K. Peng, Phys. Rev. Lett. 89(6), 068102 (2002).

    E. T. Jaynes, Phys. Rev. 108, 171 (1957).



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