The concept of nonlinearity in complex systems: An additional approach to understand the pathophysiology of severe trauma and shock

European Journal of Trauma

Volumn 29, Issue 1, 2003, Pages 11-22

  Willy, Christian ^a   Neugebauer, Edmund A M ^b   Gerngroß, Heinz ^a  

^a Military Hospital Ulm   (Germany)

^b UNIVERSITY HOSPITAL OF COLOGNE   (Germany)

Author keywords

Biosystem; Chaos control; Complexity; Linearity; Multiple organ failure; Reductionism; Trauma

Indexed keywords

BIOTECHNOLOGY; CELL FUNCTION; CELL RESPIRATION; CHEMOTAXIS; COMPUTER; CYBERNETICS; FEEDBACK SYSTEM; GROWTH RATE; LINEAR SYSTEM; MATHEMATICAL MODEL; MOLECULAR DYNAMICS; NONHUMAN; REVIEW; SHOCK; STIMULUS RESPONSE; THEORY; TRAUMATOLOGY;

EID: 0037328596     PISSN: 14390590     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00068-003-1248-x     Document Type: Review

References (88)

1. Haken H. Information and self-organization: a macroscopic approach to complex systems. Springer series in synergetics 1988. Berlin: Springer, 1988:1-227.
2. Moser J. Is the solar system stable? Math Intelligencer 1975;1:65-71.
3. Feigenbaum MJ. The universal properties of nonlinear transformations. J Stat Phys 1978;19:25-41.
4. Chirikov BV. A universal instability of many dimensional oscillator systems. Phys Rep 1980;52:463-72.
5. Lorenz EN. Deterministic nonperiodic flow. J Atmospher Sci 1963;20:130-41.
6. Ehlers CL. Chaos and complexity. Can it help us to understand mood and behavior? Arch Gen Psychiatry 1995;52:960-4.
7. Goldberger AL. Non-linear dynamics for clinicians: chaos theory, fractals, and complexity at the bedside. Lancet 1996;347:1312-4.
8. Griffiths F, Byrne D. General practice and the new science emerging from the theories of "chaos" and complexity. Br J Gen Pract 1998;48:1697-9.
9. Lipsitz LA, Goldberger AL. Loss of "complexity" and aging. Potential applications of fractals and chaos theory to senescence. JAMA 1992;267:1806-9.
10. Morinushi T, Kawasaki H, Masumoto Y, Shigeta K, Ogura T, Takigawa M. Self-organization, complexity and chaos: the new biology for medicine. Nat Med 1998;4:882-5.
11. Sandell HS, Bourne JR. Expert systems in medicine: a biomedical engineering perspective. Crit Rev Biomed Eng 1985;12:95-129.
12. Wagner CD, Mrowka R, Nafz B, Persson PB. Complexity and "chaos" in blood pressure after baroreceptor denervation of conscious dogs. Am J Physiol 1995;269:H1760-6.
13. Babloyantz A, Destexhe A. Is the normal heart a periodic oscillator? Biol Cybern 1988;58:203-11.
14. Boller F. Chaos in the cardiovascular system: an update. Cardiovasc Res 1998;40:257-64.
15. Bracic M, Stefanovska A. Nonlinear dynamics of the blood flow studied by Lyapunov exponents. Bull Math Biol 1998;60:417-33.
16. Christ F, Abicht JM, Athelogou M, Baschnegger H, Niklas M, Peter K, Messmer K. Cardiovascular monitoring of elective aortic aneurysm repair using methods of chaos analysis. Int J Microcirc Clin Exp 1997;17:374-84.
17. Goldberger AL, Bhargava V, West BJ, Mandell AJ. On a mechanism of cardiac electrical stability. The fractal hypothesis. Biophys J 1985;48:525-8.
18. Goldberger AL, West BJ. Applications of nonlinear dynamics to clinical cardiology. Ann NY Acad Sci 1987;504:195-213.
19. Kroll MH. Chaotic dynamics in medicine. Wiad Lek 1998;51:525-30.
20. Mitchinson MJ, Stephens NG, Parsons A, Bligh E, Schofield PM, Brown MJ. Origin of chaos in the circulation: open loop analysis with an artificial heart. ASAIO J 1998;44:M700-3.
21. Silke B, Riddell JG. Heart rate variability effects of an agonist or antagonists of the beta-adrenoceptor assessed with scatterplot and sequence analysis. Clin Auton Res 1998;8:145-53.
22. Wagner CD, Persson PB. Chaos in the cardiovascular system: an update. Cardiovasc Res 1998;40:257-64.
23. De la Fuente IM, Martinez L, Veguillas J. Intermittency route to chaos in a biochemical system. Biosystems 1996;39:87-92.
24. Demling L. Immune network at the edge of chaos. J Theor Biol 1997;186:173-87.
25. Feigenbaum MJ. Universal behavior in nonlinear systems. Los Alamos Science 1980;1:4-27.
26. Glass L, Mackey MC. Pathological conditions resulting from instabilities in physiological control systems. Ann NY Acad Sci 1979;316:214-35.
27. Glenny RW, Robertson HT, Yamashiro S, Bassingthwaighte JB. Applications of fractal analysis to physiology. J Appl Physiol 1991;70:2351-67.
28. Goldberger AL, West BJ. Fractals in physiology and medicine. Yale J Biol Med 1987;60:421-35.
29. Persson C. Discoveries in complex biosystems. Nat Biotechnol 1997;15:927.
30. Pool R. Is it healthy to be chaotic? Science 1989;243:604-7.
31. Sugihara G, May RM. Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series. Nature 1990;344:734-41.
32. Neugebauer E, Rixen D, Raum M, Schäfer U. Thirty years of antimediator treatment in sepsis and septic shock-what have we learned? Langenbecks Arch Surg 1998;383:26-34.
33. Opal SM. Criticisms of clinical trials in sepsis and organ dysfunction. In: Gullo A, ed. Organ Failure Academy - Sepsis and organ failure. Fogliazza Milano Italy, 1996:29-41.
34. May RM. Simple mathematical models with very complicated dynamics. Nature 1976;261:459-67.
35. Maynard Smith J. Population regulations. In: Maynard Smith J, ed. Mathematical ideas in biology. London-Cambridge: University Press, 1968:39-56.
36. Dewey TG. Fractal analysis of proton exchange kinetics in lysozyme. Proc Natl Acad Sci U S A 1994;91:12101-4.
37. Ansari A, Berendzen J, Bowne SF, Frauenfelder H, Iben IE, Sauke TB, Shyamsunder E, Young RD. Protein states and proteinquakes. Proc Natl Acad Sci U S A 1985;82:5000-4.
38. Donati A, Bellik L, Picchi MP, Bonechi C. Complexity at the molecular level. A dynamic view of biomolecules obtained by NMR. Ann NY Acad Sci 1999;879:235-40.
39. Frauenfelder H. Function and dynamics of myoglobin. Ann N Y Acad Sci 1987;504:151-67.
40. Liebovitch LS, Fisch barg J, Koniarek JP, Todorova I, Wang M. Fractal model of ion-channel kinetics. Biochim Biophys Acta 1987;896:173-80.
41. De Boer RJ, Perelson AS, Kevrekidis IG. Immune network behavior - I. From stationary states to limit cycle oscillations. Bull Math Biol 1993;55:745-80.
42. Shen P, Larter R. Chaos in intracellular Ca2+ oscillations in a new model for non-excitable cells. Cell Calcium 1995;17:225-32.
43. Sinha S, Ramaswamy R. On the dynamics of controlled metabolic network and cellular behaviour. Biosystems 1987;20:341-54.
44. Watkins JC, Woessner B. Diffusion models for chemotaxis: a statistical analysis of noninteractive unicellular movement. Math Biosci 1991;104:271-303.
45. De Boer RJ, Perelson AS, Kevrekidis IG. Immune network behavior -II. From oscillations to chaos and stationary states. Bull Math Biol 1993;55:781-816.
46. Byrne HM, Cave G, McElwain DL. The effect of chemotaxis and chemokinesis on leukocyte locomotion: a new interpretation of experimental results. IMAJ Math Appl Med Biol 1998;15:235-56.
47. James A, Swann K, Recce M. Cell behaviour as a dynamic attractor in the intracellular signalling system. J Theor Biol 1999;196:269-88.
48. Roeder I, de Haan G, Engel C, Nijhof W, Dontje B, Loeffler M. Interactions of erythropoietin, granulocyte colony-stimulating factor, stem cell factor, and interleukin-11 on murine hematopoiesis during simultaneous administration. Blood 1998;91:3222-9.
49. Schimz A, Hildebrand E. Nonrandom structures in the locomotor behavior of Halobacterium: a bifurcation route to chaos? Proc Natl Acad Sci U S A 1992;89:457-60.
50. Paulus MP, Geyer MA, Gold LH, Mandell AJ. Application of entropy measures derived from the ergodic theory of dynamical systems to rat locomotor behavior. Proc Natl Acad Sci U S A 1990;87:723-7.
51. Melarvie S, Jeevanandam M, Holaday NJ, Petersen SR. Pulsatile nature of growth hormone levels in critically ill trauma victims. Surgery 1995;117:402-8.
52. Neugebauer EA, Willy C, Sauerland S. Complexity and non-linearity in shock research: reductionism or synthesis? Shock 2001;16:252-8.
53. Prank K, Harms H, Dämmig M, Brabant G, Mitschke F, Hesch RD. Is there low-dimensional chaos in pulsatile secretion of parathyroid hormone in normal human subjects? Am J Physiol 1994;266:E653-8.
54. Goldberger AL, Bhargava V, West BJ, Mandell AJ. Some observations on the question: is ventricular fibrillation "chaos"? Physica 1986;19D:282-9.
55. Goldberger AL. On the meaning and measurement of affective instability: clues from chaos theory. Biol Psychiatry 1999;45:261-9.
56. Mantica G, Sloan A. Chaotic optimization and the construction of fractals: solution of the inverse problem. Complex Syst 1989;3:37-62.
57. Ito K, Gunji YP. Self-organisation of living systems towards criticality at the edge of chaos. Biosystems 1994;33:17-24.
58. Broomhead DS, King GP. Extracting qualitative dynamics from experimental data. Physica 1986;20D:217-36.
59. Gilden DL, Thornton T, Mallon MW. 1/f noise in human cognition. Science 1995;267:1837-9.
60. Goldberger AL, Kobalter K, Bhargava V. 1/f-like scaling in normal neutrophil dynamics: implications for hematologic monitoring. IEEE Trans Biomed Eng 1986;33:874-6.
61. Theiler J. Two tools to test time series data for evidence of chaos and/or nonlinearity. Integr Physiol Behav Sci 1994;29:211-6.
62. Sugihara G, Grenfell B, May RM. Distinguishing error from chaos in ecological time series. Philos Trans R Soc Lond B Biol Sci 1990;330:235-51.
63. Grassberger P, Procaccia I. Characterization of strange attractors. Phys Rev Lett 1983;50:346-9.
64. Skinner JE, Carpeggiani C, Landisman CE, Fulton KW. Correlation dimension of heartbeat intervals is reduced in conscious pigs by myocardial ischemia. Circ Res 1991;68:966-76.
65. Weiss JN, Garfinkel A, Spano ML, Ditto WL. Chaos and chaos control in biology. J Clin Invest 1994;93:1355-60.
66. Spano ML, Ditto WL. The fundamentals of controlling chaos. Integr Physiol Behav Sci 1994;29:235-45.
67. Schiff SJ, Jerger K, Duong DH, Chang T, Spano ML, Ditto WL. Controlling chaos in the brain. Nature 1994;370:615-20.
68. Garfinkel A, Spano ML, Ditto WL, Weiss JN. Controlling cardiac chaos. Science 1992;257:1230-5.
69. Huang JW, Roy RJ. Multiple-drug hemodynamic control using fuzzy decision theory. IEEE Trans Biomed Eng 1998;45:213-28.
70. Lab MJ. Fibrillation, chaos and clinical control. Nat Med 1997;3:385-6.
71. Rundell AE, DeCarlo R, Balakrishnan V, HogenEsch H. Systematic method for determining intravenous drug treatment strategies aiding the humoral immune response. IEEE Trans Biomed Eng 1998;45:429-39.
72. Petrov V, Peng B, Showalter K. A map-based algorithm for controlling low-dimensional chaos. J Chem Phys 1992;96:7506-13.
73. Ott E, Grebogi C, Yorke JA. Controlling chaos. Phys Rev Lett 1990;64:1196-9.
74. Singer J, Wang YZ, Bau HH. Controlling a chaotic system. Phys Rev Lett 1991;66:1123-5.
75. Klar R, Zaiss A. Medical expert systems: design and applications in pulmonary medicine. Lung 1990;168:Suppl:1201-9.
76. Petersen J, Kochs E, Kochs HD. Expert systems in medicine: possible uses in anesthesia. Anasthesiol Intensivmed Notfallmed Schmerzther 1994;29:74-89.
77. Ogryzko VV. A quantum-theoretical approach to the phenomenon of directed mutations in bacteria (hypothesis). Biosystems 1997;43:83-95.
78. Goldfeld MG, Lobysheva II, Mikoyan VD, Chernavskii DS. Non-linear effects in phosphorylation induced by an alkaline shift in chloroplast membranes. J Nonlinear Biol 1990;1:19-35.
79. Papavasiliou SS, Brue T, Jaquet P, Castanas E. Pattern of prolactin diurnal secretion in normal humans: evidence for nonlinear dynamics. Neuroendocrinology 1995;62:444-53.
80. Cherruault Y, Sarin VB. A six-compartment model to study the kinetics of 14C-labelled glucose. Kybernetes 1991;20:29-34.
81. Barenghi CF, Lakshminarayanan V. Spontaneous symmetry breaking and the onset of chaos in a muscle model. Neurol Res 1992;14:228-32.
82. Cowin SC, Arramon YP, Luo GM, Sadegh AM. Chaos in the discrete-time algorithm for bone-density remodeling rate equations. J Biomech 1993;26:1077-89.
83. Dry IB, Moore AL, Day DA, Wiskich JT. Regulation of alternative pathway activity in plant mitochondria: nonlinear relationship between electron flux and the redox poise of the quinone pool. Arch Biochem Biophys 1989;273:148-57.
84. Sharan M, Selvakumar S. The effects of chemical kinetics on oxygen delivery to tissue. Math Biosci 1992;108:253-77.
85. Bates JH. A micromechanical model of lung tissue rheology. Ann Biomed Eng 1998;26:679-87.
86. Khanin MA, Semenov VV. A mathematical model of the kinetics of blood coagulation. J Theor Biol 1989;136:127-34.
87. Schmid Schönbein H, Ziege S, Grebe R, Blazek V, Spielmann R, Linzenich F. Synergetic interpretation of patterned vasomotor activity in microvascular perfusion: discrete effects of myogenic and neurogenic vasoconstriction as well as arterial and venous pressure fluctuations. Int J Microcirc Clin Exp 1997;17:346-59.
88. Czock D, Giehl M. Aminoglycoside pharmacokinetics and dynamics: a nonlinear approach. Int J Clin Pharmacol Ther 1995;33:537-9.