Fractals and power law in pulmonary medicine. Implications for the clinician
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Lecturer in Intensive Care Medicine, Democritus University of Thrace, Alexandroupolis University Hospital, Intensive Care Unit, Greece
Professor of Intensive Care Medicine, Democritus University of Thrace, Alexandroupolis University Hospital, Intensive Care Unit, Greece
Corresponding author
Vasilios E. Papaioannou   

Polyviou 6-8, 55132, Thessaloniki, Greece
Pneumon 2010;23(3):250-259
Physiological data often display fluctuations, which have been traditionally considered as noise. However, as Goldberger has emphasized, biological systems are deterministic systems with noise. This noise reflects inherent dynamics and is responsible for the adaptation of the organism to its surroundings. Various techniques derived from statistical physics have already been applied to biological signals, especially in the field of cardiovascular medicine, unravelling potential pathogenetic mechanisms of disease and leading to the construction of more accurate prediction models. Recently, considerable effort has been devoted by several research groups to the assessment of the inherent variability and complexity of the respiratory system, concerning both structure and function. A few clinical studies, mainly involving patients with asthma and chronic obstructive pulmonary disease (COPD), have demonstrated that identification of loss of complexity of respiratory signals can be of significant value in both diagnosis of disease and monitoring of therapy. This review presents results from these studies and describes the basic methods for the assessment of dynamics that govern respiratory physiology in health and disease.
Suki B, Alencar AM. Fluctuations, noise and scaling in the cardio-pulmonary system. Fluctuations and Noise Letters. 2003; 3 (1): R1-R25.
Suki B. Fluctuations and power laws in pulmonary physiology. Am J Respir Crit Care Med 2002; 166: 133-137.
West BJ, Goldberger AL. Physiology in fractal dimensions. Am Sci 1987; 75: 354-365.
Seeley A, Macklem P. Complex systems and the technology of variability analysis. Critical Care 2004; 8: R367-R384 (doi: 10.1186/cc2948).
Goldberger AL. Non-linear dynamics for clinicians: chaos theory. Fractals and complexity at the bedside. Lancet 1996; 347: 1312-1314.
Thamrin C, Stern G, Frey U. Fractals for physicians. Ped Respir Review 2010; 11: 123-131.
Glenny RW, Robertson HT, Yamashiro S, Bassingthwaighte JB. Applications of fractal analysis to physiology. J Appl Physiol 1991; 70: 2351-2367.
Goldberger AL, Peng CK, Lipsitz LA. What is physiologic complexity and how does it change with aging and disease? Neurobiology of aging 2002; 23: 23-26.
West GB, Brown JH, Enquist BJ. The fourth dimension of life: fractal geometry and allometric scaling of organisms. Science 1999; 284: 1677-1679.
Weibel ER, Gomez DM. Architecture of the human lung. Use of quantitative methods establishes fundamental relations between size and number of lung structures. Science 1962; 137: 577-585.
Mandelbrot BB. The fractal geometry of nature. New York: W.H. Freeman; 1977.
Glenny RW, Polissar NL, Mckinney S, Robertson HT. Temporal heterogeneity of regional pulmonary perfusion is spatially clustered. J Appl Physiol 1995; 79: 986-1001.
Rigaut JP. An empirical formulation relating boundary lengths to resolution in specimens showing ‘non-ideally fractal’ dimensions. J Microsc 1984; 133: 41-54.
Suki B, Barabasi AL, Hantos Z, Petak F, Stanley HE. Avalanches and power-law behaviour in lung inflation. Nature 1994; 368: 615-618.
West BJ. Physiology in fractal dimensions: error tolerance. Ann Biomed Eng 1990; 18: 135-149.
Peng CK, Mietus JE, Liu Y, et al. Quantifying fractal dynamics of human respiration: age and gender effects. Ann Biomed Eng 2002; 30: 683-692.
Prakash KN, Ramakrishnan AG, Suresh S, Chow TW. Fetal lung maturity analysis using ultrasound image features. IEEE Trans Inf Technol Biomed 2002; 6: 38-45.
Szeto HH, Cheng PY, Decena JA, Cheng Y, Wu DL, Dwyer G. Fractal properties in fetal breathing dynamics. Am J Physiol 1992; 263: 141-147.
Mackey MC, Glass L. Oscillation and chaos in physiological control systems. Science 1977; 197: 287-289.
Peng CK, Havlin S, Stanley HE, Goldberger AL. Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. Chaos 1995; 5: 82-87.
Goldberger AL, Amaral LAN, Hausdorff JM, Ivanov PC, Peng CK, Stanley HE. Fractal dynamics in physiology: Alterations with disease and aging. Proc Natl Acad Sci USA 2002; 99: 2466-2472.
Seely AJE, Christou NV. Multiple organ dysfunction syndrome: exploring the paradigm of complex nonlinear systems. Crit Care Med 2000; 28: 2193-2200.
Penzel T, Kantelhardt JW, Grote L, Peter JH, Bunde A. Comparison of detrended fluctuation analysis and spectral analysis for heart rate variability in sleep and sleep apnea. IEEE Trans Biomed Eng 2003; 50: 1143-1151.
Macklem PT. Can airway function be predicted? Am J Respir Crit Care Med 1996; 153: 19-20.
Que CL, Kenyon CM, Olivenstein R, Macklem PT, Maksym GN. Homeokinesis and short-term variability of human airway caliber. J Appl Physiol 2001; 91: 1131-1141.
Frey U, Brodbeck T, Majumdar A, et al. Risk of severe asthma episodes predicted from fluctuation analysis of airway function. Nature 2005; 438: 667-670.
Suki B, Barabasi AL, Hantos Z, Petak F, Stanley HE. Avalanches and poer law behaviour in lung inflation. Nature 1994; 368: 615-618.
Forgacs P. Crackles and wheezes. Lancet 1967; 2: 203-205.
Boser S, Park H, Perry S, Menache M, Green F. Fractal geometry of airway remodelling in human asthma. Am J Respir Crit Care Med 2005; 172: 817-823.
Venegas JG, Schroeder T, Harris S, Winkler RT, Melo MF. The distribution of ventilation during bronchoconstriction is patchy and bimodal: a PET imaging study. Respir Physiol Neurobiol 2005; 148: 57-64.
Venegas JG, Winkler T, Musch G. Self-organized patchiness in asthma as a prelude to catastrophic shifts. Nature 2005; 434: 777-782.
Frey U, Suki B. Complexity of chronic asthma and chronic obstructive pulmonary disease: implications for risk assessment, and disease progression and control. Lancet 2008; 372:1088-1099.
Sujeer MK, Buldyrev SV, Zapperi S, Andrade JS, Stanley HE, Suki B. Volume distributions of avalanches in lung inflation: a statistical mechanical approach. Phys Rev E 1997; 56: 3385- 3394.
Martynowicz MA, Walters BJ, Hubmayr RD. Mechanisms of recruitment in oleic-acid injured lungs. J Appl Physiol 2001; 90: 1744-1753.
Gattinoni L, Dandrea L, Pelosi P, Vitale G, Pesenti A, Fumagalli R. Regional effects and mechanism of positive end-expiratory pressure in early adult respiratory distress syndrome. JAMA 1993; 269: 2122-2127.
Mishima M, Hirai T, Itoh H, et al. Complexity of terminal airspace geometry assessed by lung computed tomography in normal subjects and patients with chronic obstructive pulmonary disease. Proc Natl Acad USA 1999; 96: 8829-8834.
Mutch WA, Harms S, Ruth Graham M, Kowalski SE, Girling LG, Lefevre GR. Biologically variable or naturally noisy mechanical ventilation recruits atelectatic lung. Am J Respir Crit Care Med. 2000; 162: 319-323.
Suki B, Alencar AM, Sujeer MK, et al. Life-support system benefits from noise. Nature 1998; 393: 127-128.
Macklem PT. Emergent phenomena and the secrets of life. J Appl Physiol 2008; 104: 1844-1846.
Goldberger AL, Amaral LAN, Glass L, et al. PhysioBank, PhysioToolkit, and PhysioNet: Components of a new research resource for complex physiologic signals. Circulation 2000; 101: 215-220.
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