Fractals in Physiology and Medicine

Chapter

Abstract

Calculus is a method of reasoning by computation of symbols and in medicine this has traditionally followed the path laid out by the physics of the nineteenth and twentieth century, with its smooth continuous functions and differential equations to make predictions. In the latter part of the twentieth century physical scientists began to look in earnest at complex phenomena and discovered to their surprise that the analytic functions they had touted for so long were not adequate for characterising the variations in any but the simplest of processes. This particular failing was discussed from a statistics perspective in an earlier chapter. It is now time to squarely face the general limitations of the traditional modelling techniques in medicine and address a calculus of medicine that is able to incorporate nonlinearity into its descriptions.

Keywords

Entropy Depression Cortisol Coherence Testosterone 

References

  1. 1.
    Weibel ER. Fractal geometry: a design principle for living organisms. Am J Physiol. 1991;261(6):L361–9.PubMedGoogle Scholar
  2. 2.
    Mandelbrot BB. The fractal geometry of nature. New York: W.H. Freeman and Company; 1982.Google Scholar
  3. 3.
    West BJ. Fractal physiology and the fractional calculus: a perspective. Front Physiol. 2010;1:12.PubMedGoogle Scholar
  4. 4.
    Bassingthwaighte JB, Liebovitch LS, West BJ. Fractal physiology. New York: Oxford University Press; 1994.Google Scholar
  5. 5.
    Beran J. Statistics for long-memory processes. New York: Chapman & Hall; 1994.Google Scholar
  6. 6.
    Schottky W. Uber spontane Stromschwaukungen in verschiedenen Elektrizitattslei-tern. Ann Phys. 1918;362:541–67.CrossRefGoogle Scholar
  7. 7.
    West BJ, Bologna M, Grigolini P. Maximizing information exchange between complex networks. Phys Rep. 2008;468:1–99.CrossRefGoogle Scholar
  8. 8.
    Task force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology. Heat rate variability: standards of measurement, physiological interpretation, and clinical use. Eur Heart J. 1996;17:354–81. and references cited therein.CrossRefGoogle Scholar
  9. 9.
    Alvarez-Ramirez J, Ibarra-Valdez C, Rodriguez E, Dagdug E. 1/f Noise structures in Pollocks’s drip paintings. Phys A. 2008;387:281–95.CrossRefGoogle Scholar
  10. 10.
    Grigolini P, Aquino G, Bologna M, Lukovic M, West BJ. A theory of 1/f noise in human cognition. Phys A. 2009;388:4192–204.CrossRefGoogle Scholar
  11. 11.
    Gilden DL. Cognitive emissions of 1/f noise. Psych Rev. 2001;108:33–56.CrossRefGoogle Scholar
  12. 12.
    Van Orden GC, Holden JG, Turvey MT. Human cognition and 1/f scaling. J Exp Psychol Gen. 2005;134:117–23.PubMedCrossRefGoogle Scholar
  13. 13.
    Kello CT, Beltz C, Holden JG, Van Orden GC. The emergent coordination of cognitive function. J Exp Psychol Gen. 2007;136:551–68.PubMedCrossRefGoogle Scholar
  14. 14.
    Liebovitch LS, Krekora P. The physical basis of ion channel kinetics: the importance of dynamics. In: Layton HE, Weinstein AM, editors. Institute for Mathematics and its Applications Volumes in Mathematics and its Applications, Membrane Transport and Renal Physiology, vol. 129. New York: Springer; 2002. p. 27–52.Google Scholar
  15. 15.
    Roy S, Mitra I, Llinas R. Non-Markovian noise mediated through anomalous diffusion with ion channels. Phys Rev E. 2008;78:041920.CrossRefGoogle Scholar
  16. 16.
    Das M, Gebber GL, Bauman SM, Lewis CD. Fractal properties of sympathetic nerve discharges. J Neurophysiol. 2003;89:833–40.PubMedCrossRefGoogle Scholar
  17. 17.
    West BJ. Where medicine went wrong; rediscovering the path to complexity. Singapore: World Scientific; 2006.Google Scholar
  18. 18.
    Goldberger A. Non-linear dynamics for clinicians: chaos theory, fractals, and complexity at the bedside. Lancet. 1996;347:1312–4.PubMedCrossRefGoogle Scholar
  19. 19.
    Haefeli-Bleuer B, Weibel ER. Morphometry of the human pulmonary acinus. Anat Rec. 1988;220(4):401–14.PubMedCrossRefGoogle Scholar
  20. 20.
    West BJ, Bargava V, Goldberger AL. Beyond the principle of similitude: renormalization in the bronchial tree. J Appl Physiol. 1986;60:1089–98.PubMedGoogle Scholar
  21. 21.
    Nelson TR, West BJ, Goldberger AL. The fractal lung: universal and species-related scaling patterns. Experientia. 1990;46:251–4.PubMedCrossRefGoogle Scholar
  22. 22.
    Goldberger AL, Bhargava V, West BJ, Mandell AJ. On a mechanism of cardiac electrical stability. The fractal hypothesis. Biophys J. 1985;48(3):525–8.PubMedCrossRefGoogle Scholar
  23. 23.
    Murray CD. The physiological principle of minimum work. I. The vascular system and the cost of blood. Proc Natl Acad Sci USA. 1926;12:207–14.PubMedCrossRefGoogle Scholar
  24. 24.
    Kassab GS. Scaling laws of vascular trees: of form and function. Am J Physiol Heart Circ Physiol. 2006;290(2):H894–903.PubMedCrossRefGoogle Scholar
  25. 25.
    Zhou Y, Kassab GS, Molloi S. On the design of the coronary arterial tree: a generalization of Murray’s law. J Phys Med Biol. 1999;44(12):2929–45.CrossRefGoogle Scholar
  26. 26.
    Vaillancourt DE, Newell KM. Changing complexity in human behavior and physiology through aging and disease. Neurobiol Aging. 2002;23(1):1–11.PubMedCrossRefGoogle Scholar
  27. 27.
    Lipsitz L, Goldberger A. Loss of ‘complexity’ and aging. potential applications of fractals and chaos theory to senescence. JAMA. 1992;267(13):1806–9.PubMedCrossRefGoogle Scholar
  28. 28.
    Scheibel AB. Falls, motor dysfunction, and correlative neurohistologic changes in the elderly. Clin Geriatr Med. 1985;1(3):671–6.PubMedGoogle Scholar
  29. 29.
    Mosekilde L. Age-related changes in vertebral trabecular bone architecture - assessed by a new method. Bone. 1988;9(4):247–50.PubMedCrossRefGoogle Scholar
  30. 30.
    Iyengar N, Peng CK, Morin R, Goldberger AL, Lipsitz LA. Age-related alterations in the fractal scaling of cardiac interbeat interval dynamics. Am J Physiol. 1996;271(4):R1078–84.PubMedGoogle Scholar
  31. 31.
    Kaplan DT, Furman MI, Pincus SM, Ryan SM, Lipsitz LA, Goldberger AL. Aging and the complexity of cardiovascular dynamics. Biophys J. 1991;59(4):915–49.CrossRefGoogle Scholar
  32. 32.
    Hausdorff JM, Mitchell SL, Firtion R, Peng CK, Cudkowicz ME, Wei JY, et al. Altered fractal dynamics of gait: reduced stride-interval correlations with aging and Huntington’s disease. J Appl Physiol. 1997;82(1):262–9.PubMedGoogle Scholar
  33. 33.
    Greenspan SL, Klibanski A, Rowe JW, Elahi D. Age-related alterations in pulsatile secretion of TSH: role of dopaminergic regulation. Am J Physiol. 1991;260(3):E486–91.PubMedGoogle Scholar
  34. 34.
    Pincus SM, Mulligan T, Iranmanesh A, Gheorghiu S, Godschalk M, Veldhuis JD. Older males secrete luteinizing hormone and testosterone more irregularly, and jointly more asynchronously, than younger males. Proc Natl Acad Sci. 1996;93(24):14100–5.PubMedCrossRefGoogle Scholar
  35. 35.
    Roelfsema F, Pincus SM, Veldhuis JD. Patients with Cushing’s disease secrete adrenocorticotropin and cortisol jointly more asynchronously than healthy subjects. J Clin Endocrinol Metab. 1998;83(2):688–92.PubMedCrossRefGoogle Scholar
  36. 36.
    Siragy HM, Vieweg WV, Pincus S, Veldhuis JD. Increased disorderliness and amplified basal and pulsatile aldosterone secretion in patients with primary aldosteronism. J Clin Endocrinol Metab. 1995;80(1):28–33.PubMedCrossRefGoogle Scholar
  37. 37.
    Hartman ML, Pincus SM, Johnson ML, Matthews DH, Faunt LM, Vance ML, et al. Enhanced basal and disorderly growth hormone secretion distinguish acromegalic from normal pulsatile growth hormone release. J Clin Invest. 1994;94(3):1277–88.PubMedCrossRefGoogle Scholar
  38. 38.
    Frolkis VV, Bezrukov VV. Aging of the central nervous system. Interdiscip Top Gerontol. 1979;16:87–9.Google Scholar
  39. 39.
    Mader S. Hearing impairment in elderly persons. J Am Geriatr Soc. 1984;2(7):548–53.Google Scholar
  40. 40.
    Scafetta N, Griffin L, West BJ. Holder exponent spectra for human gait. Phys A. 2003;328:561–83.CrossRefGoogle Scholar
  41. 41.
    West BJ, Scafetta N. Nonlinear dynamical model of human gait. Phys Rev E. 2003;67:051917-1.CrossRefGoogle Scholar
  42. 42.
    Goldberger AL. Fractal mechanisms in the electrophysiology of the heart. IEEE Eng Med Biol Mag. 1992;11(2):47–52.PubMedCrossRefGoogle Scholar
  43. 43.
    Jian-Jun Z, Xin-Bao N, Xiao-Dong Y, Fang-Zhen H, Cheng-Yu H. Decrease in Hurst exponent of human gait with aging and neurodegenerative diseases. Chin Phys B. 2008;17:852.CrossRefGoogle Scholar
  44. 44.
    Scafetta N, Moon RE, West BJ. Fractal response of physiological signals to stress conditions, environmental changes and neurodegenerative diseases. Complexity. 2005;12:13–7.Google Scholar
  45. 45.
    Peng C-K, Havlin S, Stanley HE, Goldberger AL. Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. Chaos. 1995;5:82.PubMedCrossRefGoogle Scholar
  46. 46.
    Churruca J, Vigil L, Luna E, Ruiz-Galiana J, Varela M. The route to diabetes: Loss of complexity in the glycemic profile from health through the metabolic syndrome to type 2 diabetes. Diabetes Metab Syndr Obes. 2008;1:3–11.PubMedGoogle Scholar
  47. 47.
    Katerndahl DA. Power laws in covariability of anxiety and depression among newly diagnosed patients with major depressive episode, panic disorder and controls. J Eval Clin Pract. 2009;15(3):565–70.PubMedCrossRefGoogle Scholar
  48. 48.
    Gottschalk A, Bauer MS, Whybrow PC. Evidence of chaotic mood variation in bipolar disorder. Arch Gen Psychiatry. 1995;52(11):947–59.PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of General PracticeMonash UniversityMelbourneAustralia
  2. 2.The Newcastle University, NewcastleWamberalAustralia
  3. 3.Army Research OfficeResearch Triangle ParkUSA

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