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Complexity and Emergent Phenomena

Béla Suki, Jason H.T. Bates, Urs Frey

10.1002/cphy.c100022

Source: Volume 1, Issue 2, April 2011

Published online: April 2011

Full Article on Wiley Online Library



Abstract

Complex biological systems operate under non‐equilibrium conditions and exhibit emergent properties associated with correlated spatial and temporal structures. These properties may be individually unpredictable, but tend to be governed by power‐law probability distributions and/or correlation. This article reviews the concepts that are invoked in the treatment of complex systems through a wide range of respiratory‐related examples. Following a brief historical overview, some of the tools to characterize structural variabilities and temporal fluctuations associated with complex systems are introduced. By invoking the concept of percolation, the notion of multiscale behavior and related modeling issues are discussed. Spatial complexity is then examined in the airway and parenchymal structures with implications for gas exchange followed by a short glimpse of complexity at the cellular and subcellular network levels. Variability and complexity in the time domain are then reviewed in relation to temporal fluctuations in airway function. Next, an attempt is given to link spatial and temporal complexities through examples of airway opening and lung tissue viscoelasticity. Specific examples of possible and more direct clinical implications are also offered through examples of optimal future treatment of fibrosis, exacerbation risk prediction in asthma, and a novel method in mechanical ventilation. Finally, the potential role of the science of complexity in the future of physiology, biology, and medicine is discussed. © 2011 American Physiological Society. Compr Physiol 1:995‐1029, 2011.

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Figure 1. Figure 1.

Breathing irregularities in a preterm infant. Inter‐breath intervals (IBI) as a function of breath number at post‐conceptional ages of 39 (A) and 61 weeks (B). (C) Probability density distributions estimated from A and B and straight line fits on a log‐log graph; with permission from Reference 77.
Figure 2. Figure 2.

Color‐coded low attenuation areas (LAA) from a normal subject (left) and a patient with early emphysema (right). Different colors denote different contiguous but non‐overlapping clusters of LAA; with permission from Reference 138.
Figure 3. Figure 3.

Two sets of circles with different areas (A and B). The distribution of areas plotted on a double logarithmic graph in C demonstrates the difference between a Gaussian and a power law corresponding to the circles in A and B, respectively. The set of circles in B also shows schematically that as the scale (mean area corresponding to the rows) changes logarithmically, the ratio of the number of circles is preserved between scales.
Figure 4. Figure 4.

The scale (L) dependence of the number (N) of units in 1D (A) and in 2D (B).
Figure 5. Figure 5.

The scale dependence of the number of units in the Koch curve.
Figure 6. Figure 6.

Bond percolation on a square lattice (thin lines) for different values of the probability P. Thick line segments are occupied with probability P. The red curve marks the shortest percolating pathway at P = Pc = 0.5.
Figure 7. Figure 7.

Simulation of the progression of pulmonary fibrosis. The solid line shows the bulk modulus B of the elastic network versus the fraction of springs c randomly stiffened by a factor of 100. If all of the spring constants were uniformly stiffened in a gradual manner from the baseline value of 1 to 100, B would follow the dashed diagonal line. Shown at the top are the network configurations obtained when c = 0, c = 0.5, and c = 0.67 with thick line showing stiff springs; with permission from Reference 22.
Figure 8. Figure 8.

(A) A symmetrically bifurcating Weibel airway tree with each branch given a generation number starting at the trachea. (B) An asymmetrically branching Horsfield tree with each airway given an order number starting with the terminal bronchioles.
Figure 9. Figure 9.

A three‐dimensional branching model of the airway tree; with permission from 111.
Figure 10. Figure 10.

Laser scanning confocal microscopic image of the alveolar structure of a mouse lung fixed at 30 cmH2O airway pressure; with permission from 147.
Figure 11. Figure 11.

CT image of the lung of an emphysematous patient. Color clusters represent contiguous low attenuation areas; with permission from Reference 138.
Figure 12. Figure 12.

Exponent D of the cumulative distributions of cluster sizes as a function of the LAA% in normal (open symbols) and emphysematous (filled symbols) subjects. Solid line is model simulation. Based on Reference 138, with permission
Figure 13. Figure 13.

Network models mimicking emphysema. (A) Chemical breakdown of lung tissue. (B) Force‐based breakdown of lung tissue. Note that high forces (red) occur around the perimeter of the clusters especially in regions where a “thin wall” separates two clusters (arrow). (C) Size distributions of defect clusters from A and B as well as LAA cluster distribution from Fig. 10; with permission from Reference 187.
Figure 14. Figure 14.

Inter‐cell and intra‐cell networks. Metabolic function reflects the behavior of a dynamic cell‐cell network. The nodes of this network are the various different cell phenotypes that communicate via ligand‐receptor interactions involving both short‐range adhesion molecules and long‐range mediator molecules. The cell phenotypes themselves can be viewed as dynamic attractors of the gene regulatory network that determines which proteins are going to be produced within the cell nucleus. The cell‐cell and gene regulatory networks interact via the network of intra‐cellular signaling molecules that operates similarly to a multi‐layer perceptron.
Figure 15. Figure 15.

A representative time series of twice‐daily peak expiratory flow (PEF) during 6 months, showing self‐similar fluctuations at different time scales. The inset shows a shorter time scale in which the statistical properties of the PEF series are similar to those of the entire series. Despite the random‐looking appearance, the fluctuations are not random but ordered, which means that any particular value is dependent on previous values; with permission from Reference 75.
Figure 16. Figure 16.

(A) A four‐generation tree model of the airways. The numbers in brackets are segments opening in an avalanche (thick lines) when pressure P = 0.5. Thin lines are segments that have not opened. The numbers to the right of the segments are the normalized opening pressures. (B) Parallel model with the same segments arranged in an increasing order of their opening pressures. (C) Crackle events as a function of time from the tree model. Groups of crackles come from avalanches. (D) Crackle events from the parallel model. (E) Distribution of inter‐crackle intervals in the two models; with permission from Reference 181.
Figure 17. Figure 17.

Power‐law stress relaxation in response to a 10% step change in uniaxial stretching of an isolated lung tissue strip on a double logarithmic graph. The exponent β is the negative slope of a straight line fit to the data (not shown). Black line is control, and blue curve is following digestion with elastase, while the sample was held at the same length as before digestion. Red curve is obtained after adjusting the length of the sample so that the mean force was the same as before digestion.
Figure 18. Figure 18.

Immunofluorescently labeled collagen in alveolar walls at 20% (left) and at 40% (right) uniaxial stretch in the vertical direction. Notice that after 20% stretch, the same fibers become less wavy (black arrows). Bar denotes 5 μm.
Figure 19. Figure 19.

Modeling the repair of the fibrotic lung. The colors are related to the force the elements carry (red high force). The thick and thin lines denote stiff and soft springs, respectively. (A) The initial configuration with the concentration of stiff springs c = 0.649 and the bulk modulus B = 26.6. (B) The configuration of the network following random repair with c = 0.611 and B = 22.6. (C) The configuration of the network following targeted repair with c = 0.63 and B = 16; with permission from Reference 188.
Figure 20. Figure 20.

A possible approach to monitoring and treating chronic diseases aided by the tools of complexity analysis; with permission from Reference 78.
Figure 21. Figure 21.

Conditional probability π as a function of the long‐range correlation exponent α that given the current value of the peak expiratory flow (PEF), in this case 95% of the predicted value, PEF will drop to below 80% of the predicted value within a month. Notice that the risk is small, only 13%, if the time series is highly correlated (α = 0.8) compared to a nearly uncorrelated time series (α = 0.55) when the risk is 84%; with permission from Reference 78.
Figure 22. Figure 22.

Normalized pressure‐volume curve in a model of an atelectatic region of the lung. With conventional mechanical ventilation, pressure is cycled between P1 = 0.3 and P2 = 0.7, and the recruited volume is V2. During variable ventilation, end‐inspiratory pressure is varied from inflation to inflation sampling the Gaussian around P2. In one inflation, pressure increases to 0.65 losing volume, whereas for the next inflation, pressure increases to 0.75 gaining recruited volume. Because of the nonlinearity of the pressure‐volume curve, the “gain” is far greater than the “loss,” and the recruited volume available for gas exchange increases by ΔV from V2 to V3; with permission from Reference 182.
Figure 23. Figure 23.

Secretion phosphatidylcholine as a function of percent variability in stretch‐by‐stretch amplitude superimposed on 50% mean stretch amplitude. *denote P < 0.05 increase over cells exposed to monotonous stretch; with permission from Reference 10.


Figure 1.

Breathing irregularities in a preterm infant. Inter‐breath intervals (IBI) as a function of breath number at post‐conceptional ages of 39 (A) and 61 weeks (B). (C) Probability density distributions estimated from A and B and straight line fits on a log‐log graph; with permission from Reference 77.



Figure 2.

Color‐coded low attenuation areas (LAA) from a normal subject (left) and a patient with early emphysema (right). Different colors denote different contiguous but non‐overlapping clusters of LAA; with permission from Reference 138.



Figure 3.

Two sets of circles with different areas (A and B). The distribution of areas plotted on a double logarithmic graph in C demonstrates the difference between a Gaussian and a power law corresponding to the circles in A and B, respectively. The set of circles in B also shows schematically that as the scale (mean area corresponding to the rows) changes logarithmically, the ratio of the number of circles is preserved between scales.



Figure 4.

The scale (L) dependence of the number (N) of units in 1D (A) and in 2D (B).



Figure 5.

The scale dependence of the number of units in the Koch curve.



Figure 6.

Bond percolation on a square lattice (thin lines) for different values of the probability P. Thick line segments are occupied with probability P. The red curve marks the shortest percolating pathway at P = Pc = 0.5.



Figure 7.

Simulation of the progression of pulmonary fibrosis. The solid line shows the bulk modulus B of the elastic network versus the fraction of springs c randomly stiffened by a factor of 100. If all of the spring constants were uniformly stiffened in a gradual manner from the baseline value of 1 to 100, B would follow the dashed diagonal line. Shown at the top are the network configurations obtained when c = 0, c = 0.5, and c = 0.67 with thick line showing stiff springs; with permission from Reference 22.



Figure 8.

(A) A symmetrically bifurcating Weibel airway tree with each branch given a generation number starting at the trachea. (B) An asymmetrically branching Horsfield tree with each airway given an order number starting with the terminal bronchioles.



Figure 9.

A three‐dimensional branching model of the airway tree; with permission from 111.



Figure 10.

Laser scanning confocal microscopic image of the alveolar structure of a mouse lung fixed at 30 cmH2O airway pressure; with permission from 147.



Figure 11.

CT image of the lung of an emphysematous patient. Color clusters represent contiguous low attenuation areas; with permission from Reference 138.



Figure 12.

Exponent D of the cumulative distributions of cluster sizes as a function of the LAA% in normal (open symbols) and emphysematous (filled symbols) subjects. Solid line is model simulation. Based on Reference 138, with permission



Figure 13.

Network models mimicking emphysema. (A) Chemical breakdown of lung tissue. (B) Force‐based breakdown of lung tissue. Note that high forces (red) occur around the perimeter of the clusters especially in regions where a “thin wall” separates two clusters (arrow). (C) Size distributions of defect clusters from A and B as well as LAA cluster distribution from Fig. 10; with permission from Reference 187.



Figure 14.

Inter‐cell and intra‐cell networks. Metabolic function reflects the behavior of a dynamic cell‐cell network. The nodes of this network are the various different cell phenotypes that communicate via ligand‐receptor interactions involving both short‐range adhesion molecules and long‐range mediator molecules. The cell phenotypes themselves can be viewed as dynamic attractors of the gene regulatory network that determines which proteins are going to be produced within the cell nucleus. The cell‐cell and gene regulatory networks interact via the network of intra‐cellular signaling molecules that operates similarly to a multi‐layer perceptron.



Figure 15.

A representative time series of twice‐daily peak expiratory flow (PEF) during 6 months, showing self‐similar fluctuations at different time scales. The inset shows a shorter time scale in which the statistical properties of the PEF series are similar to those of the entire series. Despite the random‐looking appearance, the fluctuations are not random but ordered, which means that any particular value is dependent on previous values; with permission from Reference 75.



Figure 16.

(A) A four‐generation tree model of the airways. The numbers in brackets are segments opening in an avalanche (thick lines) when pressure P = 0.5. Thin lines are segments that have not opened. The numbers to the right of the segments are the normalized opening pressures. (B) Parallel model with the same segments arranged in an increasing order of their opening pressures. (C) Crackle events as a function of time from the tree model. Groups of crackles come from avalanches. (D) Crackle events from the parallel model. (E) Distribution of inter‐crackle intervals in the two models; with permission from Reference 181.



Figure 17.

Power‐law stress relaxation in response to a 10% step change in uniaxial stretching of an isolated lung tissue strip on a double logarithmic graph. The exponent β is the negative slope of a straight line fit to the data (not shown). Black line is control, and blue curve is following digestion with elastase, while the sample was held at the same length as before digestion. Red curve is obtained after adjusting the length of the sample so that the mean force was the same as before digestion.



Figure 18.

Immunofluorescently labeled collagen in alveolar walls at 20% (left) and at 40% (right) uniaxial stretch in the vertical direction. Notice that after 20% stretch, the same fibers become less wavy (black arrows). Bar denotes 5 μm.



Figure 19.

Modeling the repair of the fibrotic lung. The colors are related to the force the elements carry (red high force). The thick and thin lines denote stiff and soft springs, respectively. (A) The initial configuration with the concentration of stiff springs c = 0.649 and the bulk modulus B = 26.6. (B) The configuration of the network following random repair with c = 0.611 and B = 22.6. (C) The configuration of the network following targeted repair with c = 0.63 and B = 16; with permission from Reference 188.



Figure 20.

A possible approach to monitoring and treating chronic diseases aided by the tools of complexity analysis; with permission from Reference 78.



Figure 21.

Conditional probability π as a function of the long‐range correlation exponent α that given the current value of the peak expiratory flow (PEF), in this case 95% of the predicted value, PEF will drop to below 80% of the predicted value within a month. Notice that the risk is small, only 13%, if the time series is highly correlated (α = 0.8) compared to a nearly uncorrelated time series (α = 0.55) when the risk is 84%; with permission from Reference 78.



Figure 22.

Normalized pressure‐volume curve in a model of an atelectatic region of the lung. With conventional mechanical ventilation, pressure is cycled between P1 = 0.3 and P2 = 0.7, and the recruited volume is V2. During variable ventilation, end‐inspiratory pressure is varied from inflation to inflation sampling the Gaussian around P2. In one inflation, pressure increases to 0.65 losing volume, whereas for the next inflation, pressure increases to 0.75 gaining recruited volume. Because of the nonlinearity of the pressure‐volume curve, the “gain” is far greater than the “loss,” and the recruited volume available for gas exchange increases by ΔV from V2 to V3; with permission from Reference 182.



Figure 23.

Secretion phosphatidylcholine as a function of percent variability in stretch‐by‐stretch amplitude superimposed on 50% mean stretch amplitude. *denote P < 0.05 increase over cells exposed to monotonous stretch; with permission from Reference 10.

References
 1. Akay M, Moodie KL, Hoopes PJ. Age related alterations in the complexity of respiratory patterns. J Integr Neurosci 2: 165–178, 2003.
 2. Akay M, Mulder EJ. Effects of maternal alcohol intake on fractal properties in human fetal breathing dynamics. IEEE Trans Biomed Eng 45: 1097–1103, 1998.
 3. Akay M, Sekine N. Investigating the complexity of respiratory patterns during recovery from severe hypoxia. J Neural Eng 1: 16–20, 2004.
 4. Albert R, Jeong H, and Barabasi AL. Error and attack tolerance of complex networks. Nature 406: 378–382, 2000.
 5. Alencar AM, Arold SP, Buldyrev SV, Majumdar A, Stamenovic D, Stanley HE, Suki B. Physiology: Dynamic instabilities in the inflating lung. Nature 417: 809–811, 2002.
 6. Alencar AM, Buldyrev SV, Majumdar A, Stanley HE, Suki B. Avalanche dynamics of crackle sound in the lung. Phys Rev Lett 87: 088101, 2001.
 7. Alencar AM, Hantos Z, Petak F, Tolnai J, Asztalos T, Zapperi S, Andrade JS Jr, Buldyrev SV, Stanley HE, Suki B. Scaling behavior in crackle sound during lung inflation. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 60: 4659–4663, 1999.
 8. Amin SD, Majumdar A, Frey U, Suki B. Modeling the dynamics of airway constriction: Effects of agonist transport and binding. J Appl Physiol 109: 553–563, 2010.
 9. Aon MA, Cortassa S, O'Rourke B. Percolation and criticality in a mitochondrial network. Proc Natl Acad Sci U S A 101: 4447–4452, 2004.
 10. Arold SP, Bartolak‐Suki E, Suki B. Variable stretch pattern enhances surfactant secretion in alveolar type II cells in culture. Am J Physiol Lung Cell Mol Physiol 296: L574–581, 2009.
 11. Arold SP, Mora R, Lutchen KR, Ingenito EP, Suki B. Variable tidal volume ventilation improves lung mechanics and gas exchange in a rodent model of acute lung injury. Am J Respir Crit Care Med 165: 366–371, 2002.
 12. Arold SP, Suki B, Alencar AM, Lutchen KR, Ingenito EP. Variable ventilation induces endogenous surfactant release in normal guinea pigs. Am J Physiol Lung Cell Mol Physiol 285: L370–375, 2003.
 13. Bak P. How nature Works: The Science of Self‐Organized Criticality. New York, NY, USA: Copernicus, 1996.
 14. Baldwin DN, Suki B, Pillow JJ, Roiha HL, Minocchieri S, Frey U. Effect of sighs on breathing memory and dynamics in healthy infants. J Appl Physiol 97: 1830–1839, 2004.
 15. Banavar JR, Maritan A, Rinaldo A. Size and form in efficient transportation networks. Nature 399: 130–132, 1999.
 16. Barabási A‐L, Stanley HE. Fractal Concepts in Surface Growth. New York, NY: Press Syndicate of the University of Cambridge, 1995.
 17. Barabasi AL, Buldyrev SV, Stanley HE, Suki B. Avalanches in the lung: A statistical mechanical model. Phys Rev Lett 76: 2192–2195, 1996.
 18. Barnes PJ. Chronic obstructive pulmonary disease. N Engl J Med 343: 269–280, 2000.
 19. Barnes PJ, Stockley RA. COPD: Current therapeutic interventions and future approaches. Eur Respir J 25: 1084–1106, 2005.
 20. Bassingthwaighte JB, Raymond GM. Evaluating rescaled ranged analysis for time series. Ann Biomed Eng 22: 432–444, 1994.
 21. Bates JH. A recruitment model of quasi‐linear power‐law stress adaptation in lung tissue. Ann Biomed Eng 35: 1165–1174, 2007.
 22. Bates JH, Davis GS, Majumdar A, Butnor KJ, Suki B. Linking parenchymal disease progression to changes in lung mechanical function by percolation. Am J Respir Crit Care Med 176: 617–623, 2007.
 23. Bates JHT. Nonlinear network theory of complex disease. In Bar‐Yam Y, editor. International Conference on Complex Systems. Boston, MA. New England Complex Systems Institute, 2006, p. 28.
 24. Bellardine CL, Hoffman AM, Tsai L, Ingenito EP, Arold SP, Lutchen KR, Suki B. Comparison of variable and conventional ventilation in a sheep saline lavage lung injury model. Crit Care Med 34: 439–445, 2006.
 25. Berisio R, Granata V, Vitagliano L, Zagari A. Imino acids and collagen triple helix stability: Characterization of collagen‐like polypeptides containing Hyp‐Hyp‐Gly sequence repeats. J Am Chem Soc 126: 11402–11403, 2004.
 26. Black LD, Allen PG, Morris SM, Stone PJ, Suki B. Mechanical and failure properties of extracellular matrix sheets as a function of structural protein composition. Biophys J 94: 1916–1929, 2008.
 27. Boker A, Haberman CJ, Girling L, Guzman RP, Louridas G, Tanner JR, Cheang M, Maycher BW, Bell DD, Doak GJ. Variable ventilation improves perioperative lung function in patients undergoing abdominal aortic aneurysmectomy. Anesthesiology 100: 608–616, 2004.
 28. Bonnet R, Jorres R, Heitmann U, Magnussen H. Circadian rhythm in airway responsiveness and airway tone in patients with mild asthma. J Appl Physiol 71: 1598–1605, 1991.
 29. Boser SR, Park H, Perry SF, Menache MG, Green FH. Fractal geometry of airway remodeling in human asthma. Am J Respir Crit Care Med 172: 817–823, 2005.
 30. Botros SM, Bruce EN. Neural network implementation of a three‐phase model of respiratory rhythm generation. Biol Cybern 63: 143–153, 1990.
 31. Bray D. Molecular networks: The top‐down view. Science 301: 1864–1865, 2003.
 32. Brenner M, McKenna RJ Jr, Gelb AF, Fischel RJ, Wilson AF. Rate of FEV1 change following lung volume reduction surgery. Chest 113: 652–659, 1998.
 33. Bruce EN. Temporal variations in the pattern of breathing. J Appl Physiol 80: 1079–1087, 1996.
 34. Buard B, Mahe G, Chapeau‐Blondeau F, Rousseau D, Abraham P, Humeau A. Generalized fractal dimensions of laser Doppler flowmetry signals recorded from glabrous and nonglabrous skin. Med Phys 37: 2827–2836, 2010.
 35. Buldyrev SV. Fractals in biology, In: Encyclopedia of Complexity and Systems Science, edited by Meyers RA. New York: Springer, 2009, p. 3779–‐3802
 36. Bunde A, Havlin S. Fractals and Disordered Systems. Berlin, NY: Springer, 1996.
 37. Burioka N, Miyata M, Endo M, Fukuoka Y, Suyama H, Nakazaki H, Igawa K, Shimizu E. Alteration of the circadian rhythm in peak expiratory flow of nocturnal asthma following nighttime transdermal beta2‐adrenoceptor agonist tulobuterol chronotherapy. Chronobiol Int 22: 383–390, 2005.
 38. Butler JP, Tsuda A. Comment on “interplay between geometry and flow distribution in an airway tree”. Phys Rev Lett 93: 049801; author reply 049802, 2004.
 39. Caldirola D, Bellodi L, Caumo A, Migliarese G, Perna G. Approximate entropy of respiratory patterns in panic disorder. Am J Psychiatry 161: 79–87, 2004.
 40. Cates ME. Reptation of living polymers: Dynamics of entangled polymers in the presence of reversible chain‐scission reactions. Macromolecules 20: 2289–2296, 1987.
 41. Cavalcante FS, Ito S, Brewer KK, Sakai H, Alencar AM, Almeida MP, Andrade JS Jr, Majumdar A, Ingenito EP, Suki B. Mechanical interactions between collagen and proteoglycans: Implications for the stability of lung tissue. J Appl Physiol 98: 672–679, 2005.
 42. Cernelc M, Suki B, Reinmann B, Hall GL, Frey U. Correlation properties of tidal volume and end‐tidal O2 and CO2 concentrations in healthy infants. J Appl Physiol 92: 1817–1827, 2002.
 43. Collard HR, Moore BB, Flaherty KR, Brown KK, Kaner RJ, King TE Jr, Lasky JA, Loyd JE, Noth I, Olman MA, Raghu G, Roman J, Ryu JH, Zisman DA, Hunninghake GW, Colby TV, Egan JJ, Hansell DM, Johkoh T, Kaminski N, Kim DS, Kondoh Y, Lynch DA, Muller‐Quernheim J, Myers JL, Nicholson AG, Selman M, Toews GB, Wells AU, Martinez FJ. Acute exacerbations of idiopathic pulmonary fibrosis. Am J Respir Crit Care Med 176: 636–643, 2007.
 44. Coughlin MF, Suki B, Stamenovic D. Dynamic behavior of lung parenchyma in shear. J Appl Physiol 80: 1880–1890, 1996.
 45. Coveney PV, Fowler PW. Modelling biological complexity: A physical scientist's perspective. J R Soc Interface 2: 267–280, 2005.
 46. Crawford AB, Cotton DJ, Paiva M, Engel LA. Effect of airway closure on ventilation distribution. J Appl Physiol 66: 2511–2515, 1989.
 47. D'Alonzo GE, Steinijans VW, Keller A. Measurements of morning and evening airflow grossly underestimate the circadian variability of FEV1 and peak expiratory flow rate in asthma. Am J Respir Crit Care Med 152: 1097–1099, 1995.
 48. Dawson CD, Krenz GS, Lineha JH. Complexity and structure‐function relationships in the pulmonary arterial tree. In: Hlastala M.P, Robertson HT, editors. Lung Biology in Health and Disease, Complexity in Structure and Function of the Lung. New York: Marcel Dekker, Inc., 1998, p. 401–427.
 49. de Gennes PG. Reptation of a polymer chain in the presence of fixed obstacles. J Chem Phys 55: 572–579, 1971.
 50. Dewey TG. Fractals in Molecular Biophysics. Oxford, NY: Oxford University Press, 1997.
 51. Diba C, Salome CM, Reddel HK, Thorpe CW, Toelle B, King GG. Short‐term variability of airway caliber‐a marker of asthma? J Appl Physiol 103: 296–304, 2007.
 52. Ding DJ, Martin JG, Macklem PT. Effects of lung volume on maximal methacholine‐induced bronchoconstriction in normal humans. J Appl Physiol 62: 1324–1330, 1987.
 53. Dirksen A, Holstein‐Rathlou NH, Madsen F, Skovgaard LT, Ulrik CS, Heckscher T, Kok‐Jensen A. Long‐range correlations of serial FEV1 measurements in emphysematous patients and normal subjects. J Appl Physiol 85: 259–265, 1998.
 54. Doi M, Edwards SF. The Theory of Polymer Dynamics. New York: Oxford University Press, 1986.
 55. Dreher D, Koller EA. Circadian rhythms of specific airway conductance and bronchial reactivity to histamine: The effects of parasympathetic blockade. Eur Respir J 3: 414–420, 1990.
 56. Ebihara T, Venkatesan N, Tanaka R, Ludwig MS. Changes in extracellular matrix and tissue viscoelasticity in bleomycin‐induced lung fibrosis. Temporal aspects. Am J Respir Crit Care Med 162: 1569–1576, 2000.
 57. Edelman GM. Topobiology : An Introduction to Molecular Embryology. New York: Basic Books, 1988.
 58. Engler AJ, Humbert PO, Wehrle‐Haller B, Weaver VM. Multiscale modeling of form and function. Science 324: 208–212, 2009.
 59. Engler AJ, Sen S, Sweeney HL, Discher DE. Matrix elasticity directs stem cell lineage specification. Cell 126: 677–689, 2006.
 60. Engoren M. Approximate entropy of respiratory rate and tidal volume during weaning from mechanical ventilation. Crit Care Med 26: 1817–1823, 1998.
 61. Engoren M, Courtney SE, Habib RH. Effect of weight and age on respiratory complexity in premature neonates. J Appl Physiol 106: 766–773, 2009.
 62. Fabry B, Maksym GN, Butler JP, Glogauer M, Navajas D, Fredberg JJ. Scaling the microrheology of living cells. Phys Rev Lett 87: 148102, 2001.
 63. Fadel PJ, Barman SM, Phillips SW, Gebber GL. Fractal fluctuations in human respiration. J Appl Physiol 97: 2056–2064, 2004.
 64. Farber JP. Medullary inspiratory activity during opossum development. Am J Physiol 254: R578–584, 1988.
 65. Felici M, Filoche M, Straus C, Similowski T, Sapoval B. Diffusional screening in real 3D human acini—a theoretical study. Respir Physiol Neurobiol 145: 279–293, 2005.
 66. Ferry J. Viscoelastic Properties of Polymers. New York: Wiley, 1980.
 67. Fetter LJ, Kiss AD, Pearson, DS, Quack GS, Vitus FJ. Rheological behavior of star‐shaped polymers. Macromolecules 26: 647–654, 1993.
 68. Fiamma MN, Samara Z, Baconnier P, Similowski T, Straus C. Respiratory inductive plethysmography to assess respiratory variability and complexity in humans. Respir Physiol Neurobiol 156: 234–239, 2007.
 69. Florens M, Sapoval B, Filoche M. The optimal branching asymmetry of a bidirectional distribution tree. Computer Physics Communications, 2010, doi:10.1016/j.cpc.2010.11.008.
 70. Forgacs G. On the possible role of cytoskeletal filamentous networks in intracellular signaling: An approach based on percolation. J Cell Sci 108: (Pt 6): 2131–2143, 1995.
 71. Fratzl P, Daxer A. Structural transformation of collagen fibrils in corneal stroma during drying. x‐ray scattering study An. Biophys J 64: 1210–1214, 1993.
 72. Fredberg JJ, Inouye D, Miller B, Nathan M, Jafari S, Raboudi SH, Butler JP, Shore SA. Airway smooth muscle, tidal stretches, and dynamically determined contractile states. Am J Respir Crit Care Med 156: 1752–1759, 1997.
 73. Fredberg JJ, Jones KA, Nathan M, Raboudi S, Prakash YS, Shore SA, Butler JP, Sieck GC. Friction in airway smooth muscle: Mechanism, latch, and implications in asthma. J Appl Physiol 81: 2703–2712, 1996.
 74. Fredberg JJ, Kamm RD. Stress transmission in the lung: Pathways from organ to molecule. Annu Rev Physiol 68: 507–541, 2006.
 75. Frey U, Brodbeck T, Majumdar A, Taylor DR, Town GI, Silverman M, Suki B. Risk of severe asthma episodes predicted from fluctuation analysis of airway function. Nature 438: 667–670, 2005.
 76. Frey U, Hislop A, Silverman M. Branching properties of the pulmonary arterial tree during pre‐ and postnatal development. Respir Physiol Neurobiol 139: 179–189, 2004.
 77. Frey U, Silverman M, Barabasi AL, Suki B. Irregularities and power law distributions in the breathing pattern in preterm and term infants. J Appl Physiol 85: 789–797, 1998.
 78. Frey U, Suki B. Complexity of chronic asthma and chronic obstructive pulmonary disease: Implications for risk assessment, and disease progression and control. Lancet 372: 1088–1099, 2008.
 79. Fung YC. Biomechanics: Mechanical Properties of Living Tissues. New York: Springer‐Verlag, 1993.
 80. Gelb AF, McKenna RJ Jr, Brenner M, Schein MJ, Zamel N, Fischel R. Lung function 4 years after lung volume reduction surgery for emphysema. Chest 116: 1608–1615, 1999.
 81. Gillis HL, Lutchen KR. How heterogeneous bronchoconstriction affects ventilation distribution in human lungs: A morphometric model. Ann Biomed Eng 27: 14–22, 1999.
 82. Glenny R, Bernard S, Neradilek B, Polissar N. Quantifying the genetic influence on mammalian vascular tree structure. Proc Natl Acad Sci U S A 104: 6858–6863, 2007.
 83. Glenny RW. Spatial correlation of regional pulmonary perfusion. J Appl Physiol 72: 2378–2386, 1992.
 84. Glenny RW, Robertson HT. A computer simulation of pulmonary perfusion in three dimensions. J Appl Physiol 79: 357–369, 1995.
 85. Glenny RW, Robertson HT. Fractal modeling of pulmonary blood flow heterogeneity. J Appl Physiol 70: 1024–1030, 1991.
 86. Glenny RW, Robertson HT. Fractal properties of pulmonary blood flow: Characterization of spatial heterogeneity. J Appl Physiol 69: 532–545, 1990.
 87. Glenny RW, Robertson HT, Hlastala MP. Vasomotor tone does not affect perfusion heterogeneity and gas exchange in normal primate lungs during normoxia. J Appl Physiol 89: 2263–2267, 2000.
 88. Glenny RW, Robertson HT, Yamashiro S, Bassingthwaighte JB. Applications of fractal analysis to physiology. J Appl Physiol 70: 2351–2367, 1991.
 89. Goldberger AL, Amaral LA, Hausdorff JM, Ivanov P, Peng CK, Stanley HE. Fractal dynamics in physiology: Alterations with disease and aging. Proc Natl Acad Sci U S A 99: (Suppl 1): 2466–2472, 2002.
 90. Goldstein RH, Lucey EC, Franzblau C, Snider GL. Failure of mechanical properties to parallel changes in lung connective tissue composition in bleomycin‐induced pulmonary fibrosis in hamsters. Am Rev Respir Dis 120: 67–73, 1979.
 91. Grimmett GR, Stirzaker DR. Probability and Random Processes. New York: Oxford University Press, 1992.
 92. Hantos Z, Daroczy B, Suki B, Nagy S, Fredberg JJ. Input impedance and peripheral inhomogeneity of dog lungs. J Appl Physiol 72: 168–178, 1992.
 93. Hantos Z, Tolnai J, Asztalos T, Petak F, Adamicza A, Alencar AM, Majumdar A, Suki B. Acoustic evidence of airway opening during recruitment in excised dog lungs. J Appl Physiol 97: 592–598, 2004.
 94. Hart N, Polkey MI, Clement A, Boule M, Moxham J, Lofaso F, Fauroux B. Changes in pulmonary mechanics with increasing disease severity in children and young adults with cystic fibrosis. Am J Respir Crit Care Med 166: 61–66, 2002.
 95. Hayhurst MD, MacNee W, Flenley DC, Wright D, McLean A, Lamb D, Wightman AJ, Best J. Diagnosis of pulmonary emphysema by computerised tomography. Lancet 2: 320–322, 1984.
 96. Haykin SS. Neural Networks and Learning Machines. New York: Prentice Hall, 2009.
 97. Hetzel MR, Clark TJ. Comparison of normal and asthmatic circadian rhythms in peak expiratory flow rate. Thorax 35: 732–738, 1980.
 98. Hoop B, Burton MD, Kazemi H, Liebovitch LS. Correlation in stimulated respiratory neural noise. Chaos 5: 609–612, 1995.
 99. Horsfield K, Dart G, Olson DE, Filley GF, Cumming G. Models of the human bronchial tree. J Appl Physiol 31: 207–217, 1971.
 100. Hukins DWL. Connective Tissue Matrix. London: Macmillan, 1984.
 101. Irvin CG. Lung volume: A principle determinant of airway smooth muscle function. Eur Respir J 22: 3–5, 2003.
 102. Ito S, Majumdar A, Kume H, Shimokata K, Naruse K, Lutchen KR, Stamenovic D, Suki B. Viscoelastic and dynamic nonlinear properties of airway smooth muscle tissue: Roles of mechanical force and the cytoskeleton. Am J Physiol Lung Cell Mol Physiol 290: L1227–L1237, 2006.
 103. Ivanov PC, Amaral LA, Goldberger AL, Havlin S, Rosenblum MG, Struzik ZR, Stanley HE. Multifractality in human heartbeat dynamics. Nature 399: 461–465, 1999.
 104. Ivanov PC, Nunes Amaral LA, Goldberger AL, Havlin S, Rosenblum MG, Stanley HE, Struzik ZR. From 1/f noise to multifractal cascades in heartbeat dynamics. Chaos 11: 641–652, 2001.
 105. Kamm RD. Airway wall mechanics. Annu Rev Biomed Eng 1: 47–72, 1999.
 106. Kang H, Koh YY, Yoo Y, Yu J, Kim DK, Kim CK. Maximal airway response to methacholine in cough‐variant asthma: Comparison with classic asthma and its relationship to peak expiratory flow variability. Chest 128: 3881–3887, 2005.
 107. Kauffman SA. At Home in the Universe: The Search for Laws of Self‐Organization and Complexity. New York: Oxford University Press, 1995.
 108. Kerr HD. Diurnal variation of respiratory function independent of air quality: Experience with an environmentally controlled exposure chamber for human subjects. Arch Environ Health 26: 144–152, 1973.
 109. Kirkpatrick S, Gelatt CD, Vecchi MP Jr. Optimization by simulated annealing. Science 220: 671–680, 1983.
 110. Kitaoka H, Suki B. Branching design of the bronchial tree based on a diameter‐flow relationship. J Appl Physiol 82: 968–976, 1997.
 111. Kitaoka H, Takaki R, Suki B. A three‐dimensional model of the human airway tree. J Appl Physiol 87: 2207–2217, 1999.
 112. Kleiber M. Body size and metabolism. Hilgardia 6: 315–353, 1932.
 113. Koh YY, Kang H, Yoo Y, Yu J, Nah KM, Kim CK. Peak expiratory flow variability and exercise responsiveness in methacholine‐hyperresponsive adolescents with asthma remission. J Asthma 42: 17–23, 2005.
 114. Kolokotrones T, Van S, Deeds EJ, Fontana W. Curvature in metabolic scaling. Nature 464: 753–756, 2010.
 115. Kononov S, Brewer K, Sakai H, Cavalcante FS, Sabayanagam CR, Ingenito EP, Suki B. Roles of mechanical forces and collagen failure in the development of elastase‐induced emphysema. Am J Respir Crit Care Med 164: 1920–1926., 2001.
 116. Kronick PL, Sacks MS. Matrix macromolecules that affect the viscoelasticity of calfskin. J Biomech Eng 116: 140–145, 1994.
 117. Lall CA, Cheng N, Hernandez P, Pianosi PT, Dali Z, Abouzied A, Maksym GN. Airway resistance variability and response to bronchodilator in children with asthma. Eur Respir J 30: 260–268, 2007.
 118. Larsen PD, Elder DE, Tzeng YC, Campbell AJ, Galletly DC. Fractal characteristics of breath to breath timing in sleeping infants. Respir Physiol Neurobiol 139: 263–270, 2004.
 119. Lefevre GR, Kowalski SE, Girling LG, Thiessen DB, Mutch WA. Improved arterial oxygenation after oleic acid lung injury in the pig using a computer‐controlled mechanical ventilator. Am J Respir Crit Care Med 154: 1567–1572, 1996.
 120. Lefevre J. Teleonomical optimization of a fractal model of the pulmonary arterial bed. J Theor Biol 102: 225–248, 1983.
 121. Liebovitch LS, Fischbarg J, Koniarek JP. Ion channel kinetics: A model based on fractal scaling rather than multistate Markov processes. Math Biosci 84: 37–68, 1987.
 122. Lum H, Mitzner W.A species comparison of alveolar size and surface forces. J Appl Physiol 62: 1865–1871, 1987.
 123. Macklem PT. Can airway function be predicted? Am J Respir Crit Care Med 153: S19–20, 1996.
 124. Macklem PT, Seely, A. Towards a definition of life. Perspect Biol Med 53(3): 330–‐340, 2010.
 125. Majumdar A, Alencar AM, Buldyrev SV, Hantos Z, Lutchen KR, Stanley HE, Suki B. Relating airway diameter distributions to regular branching asymmetry in the lung. Phys Rev Lett 95: 168101, 2005.
 126. Majumdar A, Hantos Z, Tolnai J, Parameswaran H, Tepper R, Suki B. Estimating the diameter of airways susceptible for collapse using crackle sound. J Appl Physiol 107: 1504–1512, 2009.
 127. Maksym GN, Bates JH. A distributed nonlinear model of lung tissue elasticity. J Appl Physiol 82: 32–41, 1997.
 128. Maksym GN, Fredberg JJ, Bates JH. Force heterogeneity in a two‐dimensional network model of lung tissue elasticity. J Appl Physiol 85: 1223–1229, 1998.
 129. Mandelbrot BB. The Fractal Geometry of Nature. San Francisco: W.H. Freeman, 1983.
 130. Matsuoka S, Kurihara Y, Yagihashi K, Nakajima Y. Morphological progression of emphysema on thin‐section CT: Analysis of longitudinal change in the number and size of low‐attenuation clusters. J Comput Assist Tomogr 30: 669–674, 2006.
 131. Mauroy B, Filoche M, Weibel ER, Sapoval B. An optimal bronchial tree may be dangerous. Nature 427: 633–636, 2004.
 132. McCullagh CM, Jamieson AM, Blackwell J, Gupta R. Viscoelastic properties of human tracheobronchial mucin in aqueous solution. Biopolymers 35: 149–159, 1995.
 133. McDonnell MD, Abbott D. What is stochastic resonance? Definitions, misconceptions, debates, and its relevance to biology. PLoS Comput Biol 5: e1000348, 2009.
 134. McNamee JE. Fractal perspectives in pulmonary physiology. J Appl Physiol 71: 1–8, 1991.
 135. Meyers LA, Newman ME, Pourbohloul B. Predicting epidemics on directed contact networks. J Theor Biol 240: 400–418, 2006.
 136. Mijailovich SM, Butler JP, Fredberg JJ. Perturbed equilibria of myosin binding in airway smooth muscle: Bond‐length distributions, mechanics, and ATP metabolism. Biophys J 79: 2667–2681, 2000.
 137. Mijailovich SM, Stamenovic D, Fredberg JJ. Toward a kinetic theory of connective tissue micromechanics. J Appl Physiol 74: 665–681, 1993.
 138. Mishima M, Hirai T, Itoh H, Nakano Y, Sakai H, Muro S, Nishimura K, Oku Y, Chin K, Ohi M, Nakamura T, Bates JH, Alencar AM, and Suki B. Complexity of terminal airspace geometry assessed by lung computed tomography in normal subjects and patients with chronic obstructive pulmonary disease. Proc Natl Acad Sci U S A 96: 8829–8834, 1999.
 139. Mortola JP. Breathing around the clock: An overview of the circadian pattern of respiration. Eur J Appl Physiol 91: 119–129, 2004.
 140. Murray CD. The physiological principle of minimum work: I. The vascular system and the cost of blood volume. Proc Natl Acad Sci U S A 12: 207–214, 1926.
 141. Muskulus M, Slats AM, Sterk PJ, Verduyn‐Lunel S. Fluctuations and determinism of respiratory impedance in asthma and chronic obstructive pulmonary disease. J Appl Physiol 109: 1582–1591, 2010.
 142. Nelson TR, Manchester DK. Modeling of lung morphogenesis using fractal geometries. IEEE Trans Med Imaging 7: 321–327, 1988.
 143. Nichols JE, Cortiella J. Engineering of a complex organ: Progress toward development of a tissue‐engineered lung. Proc Am Thorac Soc 5: 723–730, 2008.
 144. Nicolis G, Proigogine I. Exploring Complexity: An Introduction. New York: W.H. Freeman & Company, 1989.
 145. Oosterhoff Y, Koeter GH, De Monchy JG, Postma DS. Circadian variation in airway responsiveness to methacholine, propranolol, and AMP in atopic asthmatic subjects. Am Rev Respir Dis 147: 512–517, 1993.
 146. Painter PR, Eden P, Bengtsson HU. Pulsatile blood flow, shear force, energy dissipation and Murray's Law. Theor Biol Med Model 3: 31, 2006.
 147. Parameswaran H, Majumdar A, Ito S, Alencar AM, Suki B. Quantitative characterization of airspace enlargement in emphysema. J Appl Physiol 100: 186–193, 2006.
 148. Paydarfar D, Buerkel DM. Dysrhythmias of the respiratory oscillator. Chaos 5: 18–29, 1995.
 149. Peng CK, Buldyrev SV, Goldberger AL, Havlin S, Sciortino F, Simons M, Stanley HE. Long‐range correlations in nucleotide sequences. Nature 356: 168–170, 1992.
 150. Peng CK, Havlin S, Stanley HE, Goldberger AL. Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. Chaos 5: 82–87, 1995.
 151. Peng CK, Mietus JE, Liu Y, Lee C, Hausdorff JM, Stanley HE, Goldberger AL, Lipsitz LA. Quantifying fractal dynamics of human respiration: Age and gender effects. Ann Biomed Eng 30: 683–692, 2002.
 152. Politi AZ, Donovan GM, Tawhai MH, Sanderson MJ, Lauzon AM, Bates JH, Sneyd J. A multiscale, spatially distributed model of asthmatic airway hyper‐responsiveness. J Theor Biol 266: 614–624.
 153. Poon CS, Barahona M. Titration of chaos with added noise. Proc Natl Acad Sci U S A 98: 7107–7112, 2001.
 154. Presson RG Jr, Okada O, Hanger CC, Godbey PS, Graham JA, Glenny RW, Capen RL, Wagner WW Jr. Stability of alveolar capillary opening pressures. J Appl Physiol 77: 1630–1637, 1994.
 155. Prigogine I, Stengers I. Order Out of Chaos: Man's New Dialogue with Nature. New York, N.Y.: Bantam Books, 1984.
 156. Que CL, Kenyon CM, Olivenstein R, Macklem PT, Maksym GN. Homeokinesis and short‐term variability of human airway caliber. J Appl Physiol 91: 1131–1141, 2001.
 157. Redaelli A, Vesentini S, Soncini M, Vena P, Mantero S, Montevecchi FM. Possible role of decorin glycosaminoglycans in fibril to fibril force transfer in relative mature tendons–a computational study from molecular to microstructural level. J Biomech 36: 1555–1569, 2003.
 158. Ribeiro AS, Kauffman SA. Noisy attractors and ergodic sets in models of gene regulatory networks. J Theor Biol 247: 743–755, 2007.
 159. Richter DW, Ballantyne, D. A Three Phase Theory About the Basic Respiratory Pattern Generator. Berlin: Springer‐Verlag, 1983.
 160. Ritter MC, Jesudason R, Majumdar A, Stamenovic D, Buczek‐Thomas JA, Stone PJ, Nugent MA, Suki B. A zipper network model of the failure mechanics of extracellular matrices. Proc Natl Acad Sci U S A 106: 1081–1086, 2009.
 161. Robertson HT, Altemeier WA, Glenny RW. Physiological implications of the fractal distribution of ventilation and perfusion in the lung. Ann Biomed Eng 28: 1028–1031, 2000.
 162. Robertson HT, Hlastala MP. Microsphere maps of regional blood flow and regional ventilation. J Appl Physiol 102: 1265–1272, 2007.
 163. Romero FJ, Pastor A, Lopez J, Romero PV. A recruitment‐based rheological model for mechanical behavior of soft tissues. Biorheology 35: 17–35, 1998.
 164. Rostig S, Kantelhardt JW, Penzel T, Cassel W, Peter JH, Vogelmeier C, Becker HF, Jerrentrup A. Nonrandom variability of respiration during sleep in healthy humans. Sleep 28: 411–417, 2005.
 165. Sachis PN, Armstrong DL, Becker LE, Bryan AC. Myelination of the human vagus nerve from 24 weeks postconceptional age to adolescence. J Neuropathol Exp Neurol 41: 466–472, 1982.
 166. Sapoval B, Filoche M. Role of diffusion screening in pulmonary diseases. Adv Exp Med Biol 605: 173–178, 2008.
 167. Sapoval B, Filoche M, Weibel ER. Smaller is better—but not too small: A physical scale for the design of the mammalian pulmonary acinus. Proc Natl Acad Sci U S A 99: 10411–10416, 2002.
 168. Sasaki N, Shukunami N, Matsushima N, Izumi Y. Time‐resolved X‐ray diffraction from tendon collagen during creep using synchrotron radiation. J Biomech 32: 285–292, 1999.
 169. Sato A, Hirai T, Imura A, Kita N, Iwano A, Muro S, Nabeshima Y, Suki B, Mishima M. Morphological mechanism of the development of pulmonary emphysema in klotho mice. Proc Natl Acad Sci U S A 104: 2361–2365, 2007.
 170. Savage VM, Deeds EJ, Fontana W. Sizing up allometric scaling theory. PLoS Comput Biol 4: e1000171, 2008.
 171. Schmidt‐Nielsen K. Scaling, why is animal size so important? Cambridge, New York: Cambridge University Press, 1984.
 172. Schmidt A, Zidowitz S, Kriete A, Denhard T, Krass S, Peitgen HO. A digital reference model of the human bronchial tree. Comput Med Imaging Graph 28: 203–211, 2004.
 173. Seely AJ, Macklem PT. Complex systems and the technology of variability analysis. Crit Care 8: R367–384, 2004.
 174. Shibata H, Horie O, Sugita M. [Studies on the deviation of short‐term FRC measurements with He closed‐circuit method and on diurnal variation of FRC]. Rinsho Byori 38: 463–467, 1990.
 175. Shin'oka T, Matsumura G, Hibino N, Naito Y, Watanabe M, Konuma T, Sakamoto T, Nagatsu M, Kurosawa H. Midterm clinical result of tissue‐engineered vascular autografts seeded with autologous bone marrow cells. J Thorac Cardiovasc Surg 129: 1330–1338, 2005.
 176. Small M, Judd K, Lowe M, Stick S. Is breathing in infants chaotic? Dimension estimates for respiratory patterns during quiet sleep. J Appl Physiol 86: 359–376, 1999.
 177. Stanley HE, Amaral LA, Buldyrev SV, Gopikrishnan P, Plerou V, Salinger MA. Self‐organized complexity in economics and finance. Proc Natl Acad Sci U S A 99: (Suppl 1): 2561–2565, 2002.
 178. Stanley HE, Amaral LA, Goldberger AL, Havlin S, Ivanov P, Peng CK. Statistical physics and physiology: Monofractal and multifractal approaches. Physica A 270: 309–324, 1999.
 179. Stanley HE, Buldyrev SV, Goldberger AL, Hausdorff JM, Havlin S, Mietus J, Peng CK, Sciortino F, Simons M. Fractal landscapes in biological systems: Long‐range correlations in DNA and interbeat heart intervals. Physica A 191: 1–12, 1992.
 180. Stauffer D, Aharony A. Introduction to percolation theory. London; Washington, DC: Taylor & Francis, 1992.
 181. Suki B. Fluctuations and power laws in pulmonary physiology. Am J Respir Crit Care Med 166: 133–137, 2002.
 182. Suki B, Alencar AM, Sujeer MK, Lutchen KR, Collins JJ, Andrade JS Jr, Ingenito EP, Zapperi S, Stanley HE. Life‐support system benefits from noise. Nature 393: 127–128, 1998.
 183. Suki B, Alencar AM, Tolnai J, Asztalos T, Petak F, Sujeer MK, Patel K, Patel J, Stanley HE, Hantos Z. Size distribution of recruited alveolar volumes in airway reopening. J Appl Physiol 89: 2030–2040, 2000.
 184. Suki B, Barabasi AL, Hantos Z, Petak F, Stanley HE. Avalanches and power‐law behaviour in lung inflation. Nature 368: 615–618, 1994.
 185. Suki B, Barabasi AL, and Lutchen KR. Lung tissue viscoelasticity: A mathematical framework and its molecular basis. J Appl Physiol 76: 2749–2759, 1994.
 186. Suki B, Frey U. Temporal dynamics of recurrent airway symptoms and cellular random walk. J Appl Physiol 95: 2122–2127, 2003.
 187. Suki B, Lutchen KR, Ingenito EP. On the progressive nature of emphysema: Roles of proteases, inflammation, and mechanical forces. Am J Respir Crit Care Med 168: 516–521, 2003.
 188. Suki B, Majumdar A, Nugent MA, Bates JH. In silico modeling of interstitial lung mechanics: Implications for disease development and repair. Drug Discov Today Dis Models 4: 139–145, 2007.
 189. Szeto HH, Cheng PY, Decena JA, Cheng Y, Wu DL, Dwyer G. Fractal properties in fetal breathing dynamics. Am J Physiol 263: R141–147, 1992.
 190. Thamrin C, Stern G, Strippoli MP, Kuehni CE, Suki B, Taylor DR, and Frey U. Fluctuation analysis of lung function as a predictor of long‐term response to beta2‐agonists. Eur Respir J 33: 486–‐493, 2009.
 191. Thamrin C, Taylor DR, Jones AD, Suki B, Frey U. Variability of lung function predicts loss of asthma control following withdrawal of inhaled corticosteroid treatment. Thorax 65(5): 403–‐408, 2010.
 192. Troyanov S, Ghezzo H, Cartier A, Malo JL. Comparison of circadian variations using FEV1 and peak expiratory flow rates among normal and asthmatic subjects. Thorax 49: 775–780, 1994.
 193. Trubel H, Banikol WK. Variability analysis of oscillatory airway resistance in children. Eur J Appl Physiol 94: 364–370, 2005.
 194. Tsuda A, Rogers RA, Hydon PE, Butler JP. Chaotic mixing deep in the lung. Proc Natl Acad Sci U S A 99: 10173–10178, 2002.
 195. Venegas JG, Winkler T, Musch G, Vidal Melo MF, Layfield D, Tgavalekos N, Fischman AJ, Callahan RJ, Bellani G, Harris RS. Self‐organized patchiness in asthma as a prelude to catastrophic shifts. Nature 434: 777–782, 2005.
 196. Vlahakis NE, Hubmayr RD. Cellular stress failure in ventilator‐injured lungs. Am J Respir Crit Care Med 171: 1328–1342, 2005.
 197. Wagner WW Jr, Todoran TM, Tanabe N, Wagner TM, Tanner JA, Glenny RW, Presson RG Jr. Pulmonary capillary perfusion: Intra‐alveolar fractal patterns and interalveolar independence. J Appl Physiol 86: 825–831, 1999.
 198. Wang Y, Bai C, Li K, Adler KB, Wang X. Role of airway epithelial cells in development of asthma and allergic rhinitis. Respir Med 102: 949–955, 2008.
 199. Weibel ER. Fractal geometry: A design principle for living organisms. Am J Physiol 261: L361–369, 1991.
 200. Weibel ER. Morphometry of the human lung. New York: Academic Press, 1963.
 201. Weibel ER. What makes a good lung? Swiss Med Wkly 139: 375–386, 2009.
 202. Weiss DJ. Stem cells and cell therapies for cystic fibrosis and other lung diseases. Pulm Pharmacol Ther 21: 588–594, 2008.
 203. West BJ. Physiology in fractal dimensions: Error tolerance. Ann Biomed Eng 18: 135–149, 1990.
 204. West GB, Brown JH, Enquist BJ. A general model for the origin of allometric scaling laws in biology. Science 276: 122–126, 1997.
 205. West GB, Woodruff WH, Brown JH. Allometric scaling of metabolic rate from molecules and mitochondria to cells and mammals. Proc Natl Acad Sci U S A 99: (Suppl 1): 2473–2478, 2002.
 206. White EP, Enquist BJ, Green JL. On estimating the exponent of power‐law frequency distributions. Ecology 89: 905–912, 2008.
 207. Wirtz HR, Dobbs LG. Calcium mobilization and exocytosis after one mechanical stretch of lung epithelial cells. Science 250: 1266–1269, 1990.
 208. Witten ML, Tinajero JP, Sobonya RE, Lantz RC, Quan SF, Lemen RJ. Human alveolar fractal dimension in normal and chronic obstructive pulmonary disease subjects. Res Commun Mol Pathol Pharmacol 98: 221–230, 1997.
 209. Wysocki M, Fiamma MN, Straus C, Poon CS, Similowski T. Chaotic dynamics of resting ventilatory flow in humans assessed through noise titration. Respir Physiol Neurobiol 153: 54–65, 2006.
 210. Yernault JC, de Jonghe M, de Coster A, Englert M. Pulmonary mechanics in diffuse fibrosing alveolitis. Bull Physiopathol Respir (Nancy) 11: 231–244, 1975.
 211. Yoo Y, Choung JT, Yu J, Kim do K, Koh YY. Acute effects of Asian dust events on respiratory symptoms and peak expiratory flow in children with mild asthma. J Korean Med Sci 23: 66–71, 2008.
 212. Yoo Y, Kim DK, Yu J, Choi SH, Kim CK, Koh YY. Relationships of methacholine and AMP responsiveness with peak expiratory flow variability in children with asthma. Clin Exp Allergy 37: 1158–1164, 2007.
 213. Zamir M. Fractal dimensions and multifractility in vascular branching. J Theor Biol 212: 183–190, 2001.
 214. Zapperi S, Ray P, Stanley HE, Vespignani A. Avalanches in breakdown and fracture processes. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 59: 5049–5057, 1999.

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Article Title: Complexity and Emergent Phenomena
 

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Béla Suki, Jason H.T. Bates, Urs Frey. Complexity and Emergent Phenomena. Compr Physiol 2011, 1: 995-1029. doi: 10.1002/cphy.c100022