Fractals in physiology and medicine

Handbook of Systems and Complexity in Health

Volumn , Issue , 2013, Pages 171-192

  Sturmberg, Joachim P ^a,b   West, Bruce J ^c  

^a MONASH UNIVERSITY   (Australia)

^b UNIVERSITY OF NEWCASTLE   (Australia)

^c U S ARMY RESEARCH OFFICE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84923043164     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-1-4614-4998-0_11     Document Type: Chapter

References (48)

1. Weibel ER. Fractal geometry: a design principle for living organisms. Am J Physiol. 1991;261(6): L361-9.
2. Mandelbrot BB. The fractal geometry of nature. New York: W.H. Freeman and Company; 1982.
3. West BJ. Fractal physiology and the fractional calculus: a perspective. Front Physiol. 2010;1:12.
4. Bassingthwaighte JB, Liebovitch LS, West BJ. Fractal physiology. New York: Oxford University Press; 1994.
5. Beran J. Statistics for long-memory processes. New York: Chapman & Hall; 1994.
6. Schottky W. Uber spontane Stromschwaukungen in verschiedenen Elektrizitattslei-tern. Ann Phys. 1918;362:541-67.
7. West BJ, Bologna M, Grigolini P. Maximizing information exchange between complex networks. Phys Rep. 2008;468:1-99.
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.
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.
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.
11. Gilden DL. Cognitive emissions of 1/f noise. Psych Rev. 2001;108:33-56.
12. Van Orden GC, Holden JG, Turvey MT. Human cognition and 1/f scaling. J Exp Psychol Gen. 2005;134:117-23.
13. Kello CT, Beltz C, Holden JG, Van Orden GC. The emergent coordination of cognitive function. J Exp Psychol Gen. 2007;136:551-68.
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.
15. Roy S, Mitra I, Llinas R. Non-Markovian noise mediated through anomalous diffusion with ion channels. Phys Rev E. 2008;78:041920.
16. Das M, Gebber GL, Bauman SM, Lewis CD. Fractal properties of sympathetic nerve discharges. J Neurophysiol. 2003;89:833-40.
17. West BJ. Where medicine went wrong; rediscovering the path to complexity. Singapore: World Scientific; 2006.
18. Goldberger A. Non-linear dynamics for clinicians: chaos theory, fractals, and complexity at the bedside. Lancet. 1996;347:1312-4.
19. Haefeli-Bleuer B, Weibel ER. Morphometry of the human pulmonary acinus. Anat Rec. 1988;220(4): 401-14.
20. West BJ, Bargava V, Goldberger AL. Beyond the principle of similitude: renormalization in the bronchial tree. J Appl Physiol. 1986;60:1089-98.
21. Nelson TR, West BJ, Goldberger AL. The fractal lung: universal and species-related scaling patterns. Experientia. 1990;46:251-4.
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.
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.
24. Kassab GS. Scaling laws of vascular trees: of form and function. Am J Physiol Heart Circ Physiol. 2006;290(2): H894-903.
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.
26. Vaillancourt DE, Newell KM. Changing complexity in human behavior and physiology through aging and disease. Neurobiol Aging. 2002;23(1): 1-11.
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.
28. Scheibel AB. Falls, motor dysfunction, and correlative neurohistologic changes in the elderly. Clin Geriatr Med. 1985;1(3): 671-6.
29. Mosekilde L. Age-related changes in vertebral trabecular bone architecture - assessed by a new method. Bone. 1988;9(4): 247-50.
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.
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.
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.
33. Greenspan SL, Klibanski A, Rowe JW, Elahi D. Agerelated alterations in pulsatile secretion of TSH: role of dopaminergic regulation. Am J Physiol. 1991;260(3): E486-91.
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.
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.
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.
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.
38. Frolkis VV, Bezrukov VV. Aging of the central nervous system. Interdiscip Top Gerontol. 1979;16: 87-9.
39. Mader S. Hearing impairment in elderly persons. J Am Geriatr Soc. 1984;2(7): 548-53.
40. Scafetta N, Griffin L, West BJ. Holder exponent spectra for human gait. Phys A. 2003;328:561-83.
41. West BJ, Scafetta N. Nonlinear dynamical model of human gait. Phys Rev E. 2003;67:051917-1.
42. Goldberger AL. Fractal mechanisms in the electrophysiology of the heart. IEEE Eng Med Biol Mag. 1992;11(2): 47-52.
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.
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.
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.
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.
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.
48. Gottschalk A, Bauer MS, Whybrow PC. Evidence of chaotic mood variation in bipolar disorder. Arch Gen Psychiatry. 1995;52(11): 947-59.