Nonlinear dynamics of microvascular blood flow

Annals of Biomedical Engineering

Volumn 28, Issue 6, 2000, Pages 641-652

  Carr, Russell T ^a   Lacoin, Marc ^b  

^a University of New Hampshire   (United States)

^b UNIVERSITY OF WASHINGTON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BLOOD; COMPUTER SIMULATION; FLUID DYNAMICS; LINEAR ALGEBRA; MATHEMATICAL MODELS; NONLINEAR EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING; RHEOLOGY;

BIOLOGICAL CONTROL; BLOOD FLOW OSCILLATIONS; FAHRAEUS-LINDQVIST EFFECT;

MICROCIRCULATION;

ARTICLE; BIOLOGICAL MODEL; BLOOD FLOW VELOCITY; BLOOD PRESSURE; BLOOD RHEOLOGY; BLOOD VISCOSITY; CIRCULATION; HEMATOCRIT; HOMEOSTASIS; HUMAN; MATHEMATICAL COMPUTING; MICROCIRCULATION; NONLINEAR SYSTEM; OSCILLOMETRY; PERIODICITY; PHYSIOLOGY; THERMODYNAMICS; TIME; VALIDATION STUDY;

BLOOD CIRCULATION; BLOOD FLOW VELOCITY; BLOOD PRESSURE; BLOOD VISCOSITY; CONVECTION; HEMATOCRIT; HEMORHEOLOGY; HOMEOSTASIS; HUMANS; MICROCIRCULATION; MODELS, CARDIOVASCULAR; NONLINEAR DYNAMICS; NUMERICAL ANALYSIS, COMPUTER-ASSISTED; OSCILLOMETRY; PERIODICITY; TIME FACTORS;

EID: 0033624376     PISSN: 00906964     EISSN: None     Source Type: Journal    
DOI: 10.1114/1.1306346     Document Type: Article

References (30)

1. Barbee, J. and G. R. Cokelet. Prediction of blood flow in tubes with diameters as small as 29 microns. Microvasc. Res. 5:17-21, 1971.
2. Bouskela, E. Vasomotion frequency and amplitude related to intaluminal pressure and temperature in the wing of the intact, unanesthetized bat. Microvasc. Res. 37:339-351, 1989.
3. Carr, R. T. and J. Xiao. Plasma skimming in vascular trees: Numerical estimates of symmetry recovery lengths. Microcirculation (Philadelphia) 2:345-353, 1995.
4. Cokelet, G. R. Blood flow through arterial microvascular bifurcations. In: Microvascular Networks: Experimental and Theoretical Studies, edited by A. S. Popel and P. C. Johnson. Basel, Switzerland: S. Karger AG. 1986, pp 155-167.
5. Cokelet, G. R. A commentary on the "in vivo viscosity law". Biorheology 34:363-367, 1997.
6. Fåhraeus, R. and T. Lindqvist. The viscosity of blood in narrow capillary tubes. Am. J. Physiol. 96:562-568, 1931.
7. Fenton, B. M., D. W. Wilson, and G. R. Cokelet. Analysis of the effects of measured white cell entrance times on hemodynamics in a computer model of microvascular bed. Pflueg. Arch. 403:396-401, 1985.
8. Fenton, B. M., R. T. Carr, and G. R. Cokelet. Nonuniform red cell distribution in 20 to 100 μm bifurcations. Microvasc. Res. 29:103-126, 1985.
9. Fung, Y. C. Biomechanics: Circulation. New York: Springer, 1996.
10. Goldsmith, H. L. Red cell motion and wall interaction in tube flow. Fed. Proc. 30:1578-1588, 1970.
11. Griffith, T. M. Temporal chaos in the microcirculation. Cardiovasc. Res. 31:342-358, 1996.
12. Helmke, B. P., S. N. Bremnr, B. W. Zweifach, R. Skalak, and G. W. Schmid-Schonbein. Mechanisms for increased flood flow resistance due to leukocytes. Am. J. Physiol. 273:H2884-H2890, 1997.
13. Hoffman, J. D. Numerical Methods for Engineers and Scientists. New York: McGraw-Hill, 1992, pp. 825.
14. House, S. D. and H. H Lipowsky. Leukocyte-endothelium adhesion: Microhemodynamics in mesentery of the cat. Microvasc. Res. 34:363-379, 1987.
15. Hsu, L. L. Mathematical Modeling of Blood Flow in Microcirculatory Networks-Relevance for Oxygen Transport. PhD thesis. New York: University of Rochester, 1988.
16. Intaglietta, M. Arteriolar vasomotion: implications for tissue ischaemia. Blood Vessels 28:1-7, 1991.
17. Johnson, P. C., and H. Wayland. Regulation of blood flow in single capillaries. Am. J. Physiol. 212:1405-1415, 1967.
18. Kiani, M. F. and A. G. Hudetz. A semi-empirical model of apparent blood viscosity as a function of vessel diameter and discharge hematocrit. Biorheology 28:65-73, 1991.
19. Kiani, M. F., A. R. Pries, L. L. Hsu, I. H. Sarelius, and G. R. Cokelet. Fluctuations in microvascular blood flow parameters caused by hemodynamic mechanisms. Am. J. Physiol. 266:H1822-H1828, 1994.
20. Krogh, A. Studies on the physiology of capillaries. II. The reactions to local stimuli of the blood vessels in the skin and web of the frog. J. Physiol. 55:414-422, 1921.
21. Minamiyama, M., and S. Hanai. Propagation properties of vasomotion at terminal arterioles and precapillaries in the rabbit mesentery. Biorheology 28:275-286, 1991.
22. Pries, A. R., K. Ley, M. Classen, and P. Gaehtgens. Red cell distribution at microvascular bifurcations. Microvasc. Res. 38:81-101, 1989.
23. Pries, A. R., T. W. Secomb, P. Gaehtgens, and J. F. Gross. Blood flow in microvascular networks. Experiments and simulation. Circ. Res. 67:826-834, 1990.
24. Pries, A. R., T. W. Secomb, T. Gessner, M. B. Sperandio, J. F. Gross, and P. Gaehtgens. Resistance to blood flow in microvessels in vivo. Circ. Res. 75:904-915, 1994.
25. Pries, A. R., D. Neuhaus, and P. Gaehtgens. Blood viscosity in tube flow: dependence on diameter and hematocrit. Am. J. Physiol. 263:H1770-H1778, 1992.
26. Rodgers, G. P., A. N. Schechter, C. T. Noguchi, H. G. Klein, A. W. Niehaus, and R. F. Bonner. Periodic microcirculatory flow in patients with sickle-cell disease. N. Engl. J. Med. 311:1534-1538, 1984.
27. Sainani, D., A. M. Barsoum, C. G. Ellis, M. F. Kiani, and G. R. Cokelet. Evidence of low dimensional chaos in a mathematical model of microvascular blood flow in the rat mesentery. FASEB J. 8:A1056 (Abstract M147), 1994.
28. Schechner, J. S. and I. M. Braverman. Synchronous vasomotion in the human cutaneous microvasculature periods evidence for central modulation. Microvasc. Res. 44:27-32, 1992.
29. Strogatz, S. H. Nonlinear Dynamics and Chaos. Reading, MA: Addison Wesley, 1994, p. 498.
30. Wayland, H. and P. C. Johnson. Erythrocyte velocity measurement in microvessels by a two slit photometric method. J. Appl. Physiol. 22:333-337, 1967.