As;Caos determinista, cinemâtica de fluidos y geometria fractal en el sistema carotideo

Revista de Neurologia

Volumn 25, Issue 148, 1997, Pages 2021-2031

  Martin Araguz, A ^a   Ruiz Alaez A ^a   De La Garcia Rocha, M L ^a   Fernandez Armayor V ^a   Delgado Reyes, S ^a   Moreno Martincz, J M ^a  

^a Hospital del Aire   (Spain)

Author keywords

Atherosclerosis; Carotid artery bifurcation; Determinist chaos; Fractal geometry; Kinematics of fluids; Nonequilibrium dynamics; Sciences of complexity

Indexed keywords

ARTERIOSCLEROSIS; BIOLOGICAL MODEL; BRAIN; CAROTID ARTERY OBSTRUCTION; ENTROPY; FRACTAL ANALYSIS; HOMEOSTASIS; HUMAN; NONLINEAR SYSTEM; PATHOLOGY; PHYSIOLOGY; REVIEW; TIME; VASCULARIZATION; ATHEROGENESIS; ATHEROMA; ATHEROSCLEROSIS; ATHEROSCLEROTIC PLAQUE; CAROTID ARTERY BIFURCATION; CINERADIOGRAPHY; FLOW; PATHOPHYSIOLOGY;

ARTERIOSCLEROSIS; BRAIN; CAROTID STENOSIS; ENTROPY; FRACTALS; HOMEOSTASIS; HUMANS; MODELS, BIOLOGICAL; NONLINEAR DYNAMICS; TIME FACTORS;

EID: 0031404561     PISSN: 02100010     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (122)

1. Martin Araguz A. Actualizaciön del problema de la aterosclerosis carotidea y su relaciön con los accidentes cerebrovasculares isquémicos. Rev Esp Neurol 1992; 7: 5-26.
2. Schmid-Schombein H, Perktold K. Physical factors in the pathogenesis of atheroma formation. In Caplan LR, ed. Brain Ischemia. Basic Concepts and clinical relevance. London: Springer-Verlag; 1995. p. 185-213.
3. Ross R. The pathogenesis of atherosclerosis-an update. N Eng J Med 1986; 314: 488.
4. Fox JA, Hugh AE. Localization of atheroma: Theory based on boundary layer separation. Br Heart J 1966; 28: 388.
5. Caplan LR, Baker R. Extracranial occlusive vascular disease: Does size matter? Stroke 1980; 11: 66.
6. Capron L. Extra and intracranial atherosclerosis. In Vinken PJ, Bruyn GW, Klawans HL, eds. Handbook of Clinical Neurology (Revised Series). Amsterdam: Elsevier Publisher Co.; 1988. p. 91-106.
7. Friedmann MH, Deters OJ, Mark FF, Bargeron CB, Hutchins GM. Geometric effects on the hemodynamic environment of the arterial wall: A basis for geometric risk factors. In Schetter G, Nerem RM, Schimd-Schömbein H, Mörl H, Diehm C, eds. Fluid dynamics as a localizing factor for atherosclerosis. Berlin: Springer; 1983. p. 71.
8. Harrison MJG, Marshall J. Does the geometry of the carotid bifurcation affect its predisposition to atheroma? Stroke 1983; 14: 117.
9. Fisher CM, Pieman S. Geometric factors of the bifurcation in carotid atherogenesis. Stroke 1990; 21: 267-71.
10. Mandelbrot BB. The fractal geometry of nature. San Francisco: Freeman; 1983.
11. De Guzmân M, Martin MA, Morân M, Reyes M. Estructuras fractales y sus aplicaciones. Barcelona: Labor; 1993.
12. Murray CD. The physiological principle of minimum work: I. The vascular system and the cost of blood volume. Proc Natl Acad Sci USA 1926; 12:207-14.
13. Kaandorp JA. Fractal Modelling: Growth and form in Biology. Berlin-Heidelberg: Springer-Verlag; 1994.
14. Rossitti S, Löfgren J. Vascular dimension of the cerebral arteries follow the principle of minimun work. Stroke 1993; 24: 371-7.
15. Goldberger AL, West BJ. Fractals in physiology and medicine. Yale Journal of Biology and Medicine 1987; 60: 421-35.
16. Kamiya A, Toaawa T. Optimal branching structure of the vascular tree. Bull Math~Biophys 1972; 34: 431-8.
17. Coveney P. The second law of thermodynamics: Entropy, irreversibility, and dynamics. Nature 1988; 333: 409-15.
18. Coveney P, Highfield R. Antichaos: The arrow of time. London: Alien; 1990.
19. Sandau K. Kurz H. Modelling of vascular growth processes: A stochastic biophysical approach to embryonic angiogenesis. J Microsc 1994; 175: 205-13.
20. McMillan DE. Blood flow and the localization of atherosclerotic plaques. Stroke 1985; 16: 582-9.
21. Glagov S. Hemodynamic risk factors: Mechanical stress, cytoarchitecture, medial nutrition and the vulnerability of artery to aterosclerosis. In Wissler RW, Geer JC, eds. The Patogenesis of Atherosclerosis. Baltimore: Williams & Wilkins; 1972 p. 164-99.
22. Hugh AE, Fox JA. The precise localization of atheroma and its association with stasis at the origin of the internal carotid artery. A radiocraphic investigation. Br J Radiol 1970; 43: 377-83.
23. Phillips DJ, Greene FM Jr, Langlois Y, Roederer GO, Strandness DE Flow velocity patterns in the carotid bifurcations of young, presumed normal subjects. Ultrasound Med Biol 1983; 9: 39-49.
24. Mohr JP, Pessin MS. Extracranial carotid artery disease. In Barnett HJM, Mohr JP, Stein BM, Yatsu FM, eds. Stroke: Pathophysiology, diagnosis and management. New York: Churchill Livingstone; 1986. p. 293-336.
25. Wood CPI., Smith BR, McKinney CL, Toole JF. Non-invasive detection of boundary layer separation in the normal carotid artery bifurcation. Stroke 1982; 13: 120.
26. Perktold K, Resch M. Numerical flow studies in human carotid artery bifurcations: Basic discussion of the geometric factor in atheroaenesis. J Biomed Eng 1990; 12: 111-23.
27. Peterson LH. Physical factors which influence vascular caliber and blood flow. Circ Res 1960; 28 (Suppl 1): 3.
28. Young DF, Tsai FY. Flow characteristics in models of arterial stenoses I: Steady flow. J Biomech 1973; 6: 395-546.
29. Young DF, Tsai FY. Flow characteristics of models of arterial stenoses II. Unsteady flow. J Biomech 1973; 6: 547-81.
30. Glagov S, Weisenberg E, Zarins CK, et al. Compensatory enlargement of human atherosclerotic coronary arteries. N Engl J Med 1987; 316: 1371-5.
31. Fry DL. Responses of the arterial wall to certain physical factors. Ciba FndSymp 1973; 12:93.
32. Wilens SL. The nature of diffuse intimai thickening of arteries. Am J Pathol 1951; 27: 825-9.
33. Zarins CK, Glagov S. Artery wall pathology in atherosclerosis. In Rutherford R, ed. Vascular Surgery vol I. Philadelphia: Saunders Co.; 1989. p. 164-99.
34. McDonald DA. Blood flow in arteries. 2 ed. Baltimore: Williams & Wilkins Co.; 1974.
35. Burton AC. Physiology and biophysics of circulation. 2 ed. Chicago: Year Book Medical Publishers; 1972.
36. Crutchfield JP, Fanner JD, Packard NH, Shaw RS. Caos. Sci Am 1986; 12: 17-49.
37. Cromer AH. Physics for the Life Sciences. 2 ed. New York: McGrawHill; 1994.
38. Berga L, Vives JL, Feliu E, Woessner S, Rozman C. Hemorreologia: bases teôricas y aplicaciones clinicas. Barcelona: Salvat; 1983.
39. Peterson LH, Jensen RE, Parnell J. Mechanical properties of arteries in vivo. Circ Res 1960; 8: 622-9.
40. May AG, de Weese JA, Rob CA. Hemodynamic effects of arterial stenosis. Surgery 1963; 53: 239-49.
41. May AG, Van de Berg L, de Weese JA, et al. Critical arterial stenosis. Surgery 1963:54:250-6.
42. Zarins CK, Zatina MA, Giddens DP, et al. Shear stress regulation of artery lumen diameter in experimental atherocenesis. J Vase Surg 1986; 5:413-9.
43. Wolinsky H, Glagow S. A lamellar unit of aortic medial structure and function in marnais. Cir Res 1967; 20: 99-103.
44. Ku DN, Giddens DP, Zarins CK, et al. Pulsatile flow atherosclerosis in the human carotid bifurcation: Possible relation between plaque location and low and oscillation stress. Arteriosclerosis 1985; 5: 293-302.
45. Ku DN, Zarins CK, Giddens DP, et al. Reduced atherosclerosis distal to stenosis despite turbulence and hypertension. Circulation 1986; 74 (Suppl): (abstract).
46. Dobrin PB. Mechanical properties of arteries. Physiol Rev 1973; 58: 397-415.
47. Furchgott RF. Role of endothelium in responses of vascular smooth muscle. Cir Res 1983:53:557.
48. Brice JG, Dowsett DJ, Löwe RD. Hemodynamic effects of carotid artery stenosis. Br Med J (Clin Res) 1964; 2: 1362-6.
49. Stehbens WE. Changes in the cross-sectional area of the arterial fork. Angiology 1974; 25: 561-75.
50. Fisher CM, Ojemann RG. A clinico-pathologic study of carotid endarterectomy plaques. Rev Neurol (Paris) 1986; 142: 573-89.
51. Veterans Administration Cooperative Study. Role of carotid endarterectomy in asymptomatic carotid stenosis. Stroke 1986; 17: 534-9.
52. Hart RG, Easton DF. Dissections of cervical and cerebral arteries. Ncurol Clin North Am 1983; 1: 155.
53. Toronto Cerebrovascular Study Group. Risk of carotid endarterectomy. Stroke 1986; 17: 848-52.
54. O'Holleran LW, Kennelly MM, McClurken M, Johnson JM. Natural History of asymptomatic carotid plaque: Five year follow-study. Am J Surg 1987; 154: 659-62.
55. Gômez CR. Carotid plaque morpholocy and risk for stroke. Stroke 1990; 21: 148-51.
56. Mayrovitz HN. An optimal flow-radius equation for microvessels nonNewtonian blood flow. Microvasc Res 1987; 34: 380-4.
57. Martin Araguz A, Moreno Martinez JM, Revilla Valle B, et al. Manejo de los accidentes cerebrovasculares en el anciano. Pren Med Argent 1994; 81: 787-803.
58. Azuma T, Fukushuma T. Flow patterns in stenotic blood vessel models. Biorheology 1976; 13: 337-55.
59. LeVeen HH, Moon I, Ahmed N, et al. Lowering blood viscosity to overcrome vascular resistance. Surg Gynecol Obstet 1980; 150: 139-50.
60. Yellin EL. Laminar-turbulent transition process in pulsation flow. Circ Res 1966; 19: 791-4.
61. Meakin P. A new model for biological pattern formation. J Theor Biol 1986; 118: 101-13.
62. Milnor WR. Pulsatile blood flow. N Eng J Med 1972; 287: 27-35.
63. Zarins CK, Taylor KE, Bomberger RA, et al. Endothelial integrity at ostial flow dividers. Scanning Electr Microsc 1980; 3: 249-54.
64. Ku DN, Giddens DP. Pulsatile flow in a model carotid bifurcation. Arteriosclerosis 1983; 3: 31-4.
65. Ku DN, Giddens DP, Phillips DJ, Strandness DE Hemodynamics of the normal human carotid bifurcation: In vivo and in vitro studies. Ultrasound Med Biol 1985; 11: 13-25.
66. Attincer EO. Flow patterns and vascular geometry. In Pulsatile Blood Flow. New York: McGraw-Hill; 1964. p. 179-200.
67. Zarins CK, Giddens DP, Bharadvaj BK, Sottiurai VS, Mabon RF, Glagov S. Carotid bifurcation atherosclerosis: Quantitative correlation of plaque localization with flow velocity profiles and wall shear stress. Circ Res 1983; 53: 502-14.
68. Lorenz EN. La Esencia del Caos. Madrid: Debate; 1995.
69. Gleick J. Chaos. Making a New Science. Munich: Droehmer-Knauer; 1988.
70. Glass L, Kaplan D. Time series analysis of complex dynamics in physiology and medicine. Med Prog Technol 1993; 19: 115-28.
71. Javid H, Ostermiller WE Jr, Hengesh JW, et al. Natural history of carotid bifurcation atheroma. Surgery 1970; 67: 80-8.
72. Norrving B, Nilsson B, Olsson JE. Progression of carotid disease after endarterectomy: A Doppler ultrasound study. Ann Neurol 1982; 12: 548-53.
73. Weinberger J, Ramos L, Ambrose JA, Foster V. Morphologic and dynamic changes of atherosclerotic plaque at the carotid artery bifurcation: Sequential imaging by real time B-mode ultrasonography. J Am Coll Cardiol 1988; 12: 1515-21.
74. Lusby RJ, Ferrell LD, Ehrenfeld WK, et al. Carotid plaque hemorrhage. Its role in production of cerebral ischemia. Arch Surg 1982; 117: 1479-84.
75. Hennerici M, Rautemberg W, Trockel U, Kladetzky I. Spontaneous progression and regression of small carotid atheroma. Lancet 1985; I: 1415-19.
76. Martin Araguz A, Zaragoza Garcia E. Tipos de ateroma carotideo e isquemia cerebral. Ponencia presentada en el Symposium Estenosis carotidea e isquemia cerebral. Madrid 1985, 31 de marzo.
77. Meyer Y. La expresion matemâtica del conocimiento. Anuario de Ciencia, Tecnologia y Medio Ambiente. Madrid: Ediciones El Pat's; 1996. p. 162-5.
78. Nicolis G, Prigogine I. Self-Organization in Non-Equilibrium Systems. New York: WIIey Interscience; 1977.
79. Prigogine I. Introduction to thermodynamics of irreversible processes. New York: Wiley Interscience; 196I.
80. Stewart I. Juega Dios a los dados? La nueva matemâtica del caos. Barcelona: Critica; 1996.
81. Sole RV, Bascompte J, Delgado J, Luque B, Manrubia SC. Complejidad en la frontera del caos. Investigaciön y Ciencia 1996; 236: 14-21.
82. Kauffman SA. Anti-chaos and adaptation. Sci Am 1992; 1: 46-53.
83. Lewin R. Complejidad: el caos como generador de orden. Barcelona: Tusquets; 1995.
84. Kauffman SA. The Origins of Order. Oxford: University Press; 1992.
85. Goldsmith HL, Turitto VT. Rheological aspects of thrombosis and haemostasis. Basic principles and applications. Thromb Haemost 1986; 55: 415-35.
86. Summer DS. Essential Hemodynamic Principles. In Rutherford, ed. Vascular Surgery. Vol. I. Philadelphia: Saunders Co.; 1989. p. 178-93.
87. Nicholls SC, Phillips DJ, Primozich JF, Lawrence RL, Kohler TR, Rudd TG, et al. Diacnostic sienificance of flow separation in the carotid bulb. Stroke 1989; 20: 175-82.
88. Patel DJ, Vaishnav RN. Basic hemodynamics and its role in disease processes. Baltimore: University Park Press; 1980.
89. Motomiya M, Karino T. Flow patterns in the human carotid artery bifurcation. Stroke 1984; 15: 50-6.
90. Hènon M, Pomeau Y. Two strange attractors with a simple structure. In Teman R, éd. Turbulence and thé Navier-Stokes Equations. New York: Springer-Verlag; 1977.
91. Ruelle D. Strange attractors. Mathematical Intelligencer 1980; 2: 126-37.
92. Ruelle D, Takens F. On the nature of turbulence. Commun Math Phys 1971; 20: 167-92.
93. Karino T, Goldsmith HL. Particle flow behavior in models of branching vessels II. Effects of branching angle and diameter ratio on flow patterns. Biorheology 1985; 22: 87-104.
94. Andereck CD, Liu SS, Swinney HL. Flow regimes in a circular Couette system with independently rotating cylinders. Journal of Fluid Mechanics 1986; 164: 155-83.
95. Swinney HL, Gollub JP. Hydrodynamic instabilities and the transition to turbulence. Berlin: Springer-Verlag; 1987.
96. Gollub JP, Swinney HL. Onset of turbulence in a rotating fluid. Physical Review Letters 1975; 35: 927.
97. Kosko B. Pensamiento borroso: la nueva ciencia de la lôgica borrosa. Barcelona: Grijalbo Mondadori; 1995.
98. Roux JC, Rossi A, Bachelart S, Vidai C. Representation of a strange attractor from an experimental study of chemical turbulence. Physics Letters 1980; 77A: 391-3.
99. Barenblatt GI, looss G, Joseph DD. Non linear dynamics and turbulence. London: Pitman; 1983.
100. Chirikov BV, Izrailev FM. Degeneration of turbulence in Simple System. PhysicaD 1981; 2: 30-7.
101. Lorenz EN. Deterministic nonperiodic flow. Journal oh the Atmospheric Sciences 1963; 20: 130-41.
102. Herzel H, Ebeling W. Effects of noise and inhomogeneous attractors in biochemical systems. Biomed Biochim Acta 1990; 49: 941-9.
103. Sole RV, Manrubia B, Luque J, Delgado J, Bascompte J. Phase transitions and complex systems. Complexity 1996; I: 13-26.
104. Sole RV, Miramontes O. Information at the edge of chaos in fluid neural networks. Physica D 1995; 80: 171-80.
105. Poincaré JH. Sur le problème des trois corps et les équations de la dynamique. Acta Mathematica 1890; 13: 1-270.
106. Karino T, Goldsmith H. Microscopic structure of disturbed flow in the arterial and venous systems. Haemostasiology 1989; 9: 53-65.
107. Berge P, Pomeau Y, Vidai C. L'ordre dans le chaos. Paris: Herman; 1984.
108. Hayles NK. Chaos Bound. Orderly disorder in Contemporary Literature and Science. Cornell: University Press; 1990.
109. Martin Araguz A, Femdndez Armayor V, Moreno Martinez, et al. Neurobiologia del cortex frontal e hipôtesis sobre su papel como 'procesador natural' del caos determinista. Rev Esp Neurol 1995; 10: 269-89.
110. May RM. Simple mathematical models with very complicated dynamics. Nature 1976; 261: 459-67.
111. Goldberger AL, Rigney DR, West BJ. Chaos and fractals in human physiology. Sci Am 1990; 262: 34-41.
112. West BJ, Goldberger AL. Physiolocy in facial dimensions. Am Sci 1987; 75: 354-65.
113. Rossitti S, Stephensen H. Temporal heterogeneity of the blood flow velocity at the middle cerebral artery in the normal human characterized by fractal analysis. Acta Physiol Scand 1994; 151: 191-8.
114. Keunen RW, Pijlman HC, Visée HF, Tavy DL, Stam KJ. Dynamical chaos determines the variability of transcranial Doppler signals. Neurol Res 1994; 16: 353-8.
115. De Groot S, Mazur P. Non-equilibrium thermodynamics. Amsterdam: North-Holland; 1962.
116. Fry DL. Hemodynamic forces in atherogenesis. In Steinbcrg P, cd. Cerebrovascular Diseases. New York: Raven Press; 1976. p. 77-85.
117. Hutchison KL, Karpinski E. Stability of flow patterns in the vivo postestenotic velocity field. Ultrasound Med Biol 1988; 14: 269-75.
118. Naumann RM, Schmid-Schönbein H. A fluid-dynamicist's and a physiologist's look at arterial flow and arteriosclerosis. In Schettler G, Nerem RM, Schmid-Schömbein H, Mörl H, Diehm C, eds. Fluid Dynamics as a localizing factor for atherosclerosis. Berlin: Sprincer: 1983. p. 9-37.
119. Nicolis G, Prigogine I. La estructura de lo complejo: en el camino hacia una nueva comprensiön de las ciencias. Madrid: Alianza Universidad (Alianza Editorial); 1994.
120. Ranada AF. Movimiento Caötico. En Ranada AF, ed. Orden y Caos. Libros de Investigaciön y Ciencia (Scientific American). Barcelona: La Prensa Cientifica; 1990. p. 66-77.
121. Uylings HBM. Optimization of diameters and bifurcation angles in lung and vascular tree structures. Bull Math Biol 1977; 39: 509-20.
122. Witten TA, Gates ME. Tenuous structures from disorderly crowth processes. Science 1986: 232; 1607-12.