Architecture and Hemodynamics of Microvascular Networks

  • T. W. Secomb
  • A. R. Pries
  • P. Gaehtgens


The main function of the circulation is to transport materials between different parts of the body. Transport over large distances is accomplished by convection, in blood flowing through large vessels. Exchange of materials between blood and tissues occurs mainly over short distances in the peripheral vascular beds, which consist of numerous very small vessels (the microcirculation). These microvessels provide a large surface area for exchange, and bring blood into close proximity to nearly all parts of most organs. Transport at this microscopic level occurs by diffusion, by active cellular transport, or by convective motion of water through microvessel walls.


Network Architecture Apparent Viscosity Parent Vessel Wall Shear Rate Microvascular Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Barnard, A.C.L., Lopez, L. and Heliums, J.D. (1968) Basic theory of blood flow in capillaries. Microvasc. Res. 1,23–34.CrossRefGoogle Scholar
  2. Burton, A.C. (1972) Physiology and Biophysics of the Circulation. 2nd ed. Chicago: Year Book Medical Publishers.Google Scholar
  3. Dawant, B. Levin, M. and Popel, A.S. (1986) Effect of dispersion of vessel diameters and lengths in stochastic networks. I. Modeling of microcirculatory flow. Microvasc. Res. 31, 203–222.PubMedCrossRefGoogle Scholar
  4. Davis, M.J. and Gore, R.W. (1986) Pressure distribution in the microvascular network of the hamster cheek pouch. In Microvascular Networks: Experimental and Theoretical Studies, ed. A.S. Popel and P.C. Johnson, pp. 142–154. Basel: Karger.Google Scholar
  5. Desjardins, C. and Duling, B.R. (1987) Microvessel hematocrit: measurement and implications for capillary oxygen transport. Am. J. Physiol. 252, H494–H503.PubMedGoogle Scholar
  6. Duling, B.R. and Damon, D.H. (1987) An examination of the measurement of flow heterogeneity in striated muscle. Circ. Res. 60, 1–13.PubMedCrossRefGoogle Scholar
  7. Engelson, E.T., Skalak, T.C. and Schmid-Schönbein, G.W. (1985) The microvasculature in skeletal muscle. I. Arteriolar network in the rat spinotrapezius muscle. Microvasc. Res. 30. 29–44.PubMedCrossRefGoogle Scholar
  8. Fåhraeus, R. (1928) Die Strömungsverhältnisse und die Verteilung der Blutzellen im Gefässsystem. Klin. Wschr. 7, 100–106.CrossRefGoogle Scholar
  9. Fahraeus, R. and Lindqvist, T. (1931) The viscosity of the blood in narrow capillary tubes. Am. J. Phvsiol. 96, 562–568.Google Scholar
  10. Fenton, B.M. and Zweifach, B.W. (1981) Microcirculatory model relating geometrical variation to changes in pressure and flow rate. Ann. Biomed. Eng. 9, 303–321.CrossRefGoogle Scholar
  11. Fenton, B.M., Wilson, D.W. and Cokelet, G.R. (1985) Analysis of the effects of measured white blood cell entrance times on hemodynamics in a computer model of a microvascular bed. Pflügers Arch. 403 396–401.PubMedCrossRefGoogle Scholar
  12. Frasher, W.G. and Wayland, H. (1972) A repeating modular organization of the microcirculation of cat mesentery. Microvasc. Res. 4, 62–76.PubMedCrossRefGoogle Scholar
  13. Fronek, K. and Zweifach, B.W. (1975) Microvascular pressure distribution in skeletal muscle and the effect of vasodilation. Am. J. Physiol. 228, 791–796.PubMedGoogle Scholar
  14. Fung, Y.C. (1984) Biodynamics: Circulation. New York: Springer.Google Scholar
  15. Gaehtgens, P. and Schmid-Schönbein, H. (1982) Mechanisms of dynamic flow adaptation of mammalian erythrocytes. Naturwissenschaften 69, 294–296.PubMedCrossRefGoogle Scholar
  16. Gaehtgens, P., Ley, K., and Pries, A.R. (1986) Topological approach to the analysis of microvessel structure and hematocrit distribution. In Microvascular Networks: Experimental and Theoretical Studies, ed. A.S. Popel and P.C. Johnson, pp. 52–60. Basel: Karger.Google Scholar
  17. Gore, R.W. (1974) Pressures in cat mesenteric arterioles and capillaries during changes in systemic blood pressure. Circ. Res. 34. 581–591.PubMedCrossRefGoogle Scholar
  18. Halpern, D. and Secomb, T.W. (1989) The squeezing of red blood cells through capillaries with near-minimal diameters. J. Fluid Mech. 203. 381–400.CrossRefGoogle Scholar
  19. Hochmuth, R.M. and Waugh, R.E. (1987) Erythrocyte membrane elasticity and viscosity. Ann. Rev. Physiology 49, 209–219.CrossRefGoogle Scholar
  20. Horton, R.E. (1945) Erosional development of streams and their drainage basins: hydrophysical approach to quantitative morphology. Geol. Soc. Amer. Bull. 56, 275–370.CrossRefGoogle Scholar
  21. Hsu, R. and Secomb, T.W. (1989) Motion of non-axisymmetric red blood cells in cylindrical capillaries. J. Biomech. Eng. 111, 147–151.PubMedCrossRefGoogle Scholar
  22. Kiani, M.F., Cokelet, G.R. and Sarelius, I.H. (1993) Effect of diameter variability along a microvessel segment on pressure drop. Microvasc. Res. 45, 219–232.PubMedCrossRefGoogle Scholar
  23. Koller, A., Dawant, B, Liu, A., Popel, A.S., and Johnson, P.C. (1987) Quantitative analysis of arteriolar networkarchitecture in cat sartorius muscle. Am. J. Phvsiol. 253, H154–H164.Google Scholar
  24. Krogh, A. (1921) Studies on the physiology of capillaries. II. The reactions to local stimuli of blood vessels in the skin and web of the frog. J. Physiol. (London) 55, 412–422.Google Scholar
  25. Levin, M., Dawant, B. and Popel, A.S. (1986) Effect of dispersion of vessel diameters and lengths in stochastic networks. I. Modeling of microvascular hematocrit distribution. Microvasc. Res. 31, 223–234.PubMedCrossRefGoogle Scholar
  26. Ley, K., Pries, A.R. and Gaehtgens, P. (1986) Topological structure of rat mesenteric microvessel networks. Microvasc. Res. 32, 315–332.PubMedCrossRefGoogle Scholar
  27. Lighthill, M.J., (1968) Pressure-forcing of tightly fitting pellets along fluid-tilled elastic tubes. J. Fluid Mech. 34, 113–143.CrossRefGoogle Scholar
  28. Lipowsky, H.H. and Zweifach, B.W. (1974) Network analysis of microcirculation in rat mesentery. Microvasc. Res. 7, 73–83.PubMedCrossRefGoogle Scholar
  29. Lipowsky, H.H., Kovalcheck, S. and Zweifach, B.W. (1978) The distribution of blood rheological parameters in the microvasculature of cat mesentery. Circ. Res. 43, 738–749.PubMedCrossRefGoogle Scholar
  30. Mall, J.P. (1888) Die Blut-und Lymphwege im Dünndarm des Hundes. Königl. Sächs. Gesellsch. der Wissensch., Abhandlung der Math. Physikal. Klasse, Leipzig, Vol. XIV, 153-161.Google Scholar
  31. Martini, P., Pierach, A., and Schreyer, E. (1930) Die Strömung des blutes in engen Gefässen. Eine Abweichung vom Poiseuille’schen Gesetz. Dtsch. Arch. Klin. Med. 169, 212–222.Google Scholar
  32. Mayrovitz, H.N. (1986) Hemodynamic significance of microvascular arteriolar anastamosing. In Microvascular Networks: Experimental and Theoretical Studies, ed. A.S. Popel and P.C. Johnson, pp. 197–209. Basel: Karger.Google Scholar
  33. Mayrovitz, H.N. and Roy, J. (1983) Microvascular blood flow: evidence indicating a cubic dependence on arteriolar diameter. Am. J. Physiol. 245: H1031–H1038.PubMedGoogle Scholar
  34. Meilander, S. and Björnberg, J. (1992) Regulation of vascular smooth muscle tone and capillary pressure. News in Physiol. Sci. 7, 113–119.Google Scholar
  35. Popel, A.S. (1987) Network models of peripheral circulation. In Handbook of Bioengineering, ed. R. Skalak and S. Chien, pp. 20.1–20.24. New York: McGraw-Hill.Google Scholar
  36. Popel, A.S., Torres Filho, I.P., Johnson, P.C. and Bouskela, E. (1988) A new scheme for hierarchical classification of anastomosing vessels. Int. J. Microcirc. Clin. Exp. 7, 131–138.PubMedGoogle Scholar
  37. Potter, R.F., and Groom, A.C. (1983) Capillary diameter and geometry in cardiac and skeletal muscle studied by means of corrosion casts. Microvasc. Res. 25, 68–84.PubMedCrossRefGoogle Scholar
  38. Pries, A.R., Ley, K. and Gaehtgens, P. (1986) Generalization of the Fåhraeus principle for microvessel networks. Am. J. Physiol. 251, H1324–H1332.PubMedGoogle Scholar
  39. Pries, A.R., Ley, K., Claasen, M. and Gaehtgens, P. (1989) Red cell distribution at microvascular bifurcations. Microvasc. Res. 38, 81–101.PubMedCrossRefGoogle Scholar
  40. Pries, A.R., Secomb, T.W., Gaehtgens, P. and Gross, J.F. (1990) Blood flow in microvascular networks — Experiments and simulation. Circ. Res. 67: 826–834.PubMedCrossRefGoogle Scholar
  41. Pries, A.R., Neuhaus, D. and Gaehtgens, P. (1992a) Blood viscosity in tube flow: dependence on diameter and hematocrit. Am: J. Physiol. 263, H1770–1778.Google Scholar
  42. Pries, A.R., Fritzsche, A., Ley, K., and Gaehtgens, P. (1992b) Redistribution of red blood cell flow in microcirculatory networks by hemodilution. Circ. Res. 70, 1113–1121.PubMedCrossRefGoogle Scholar
  43. Pries, A.R., Secomb, T.W., Gessner, T., Sperandio, M.B., Gross, J.F. and Gaehtgens, P. (1994) Resistance to blood flow in microvessels in vivo. Circ. Res. 75: 904–915.CrossRefGoogle Scholar
  44. Reinke, W., Gaehtgens, P. and Johnson, P.C. (1987) Blood viscosity in small tubes: effect of shear rate, aggregation and sedimentation. Am. J. Physiol. 253, H540–H547.PubMedGoogle Scholar
  45. Renkin, E.M. (1985) Regulation of the microcirculation. Microvasc. Res. 30, 251–263.PubMedCrossRefGoogle Scholar
  46. Richardson, D.R. and Zweifach B.W. (1970) Pressure relationships in the macro-and microcirculation of the mesentery. Microvasc. Res. 2, 474–488.PubMedCrossRefGoogle Scholar
  47. Schmid-Schönbein, G.W., Skalak, R., Usami, S. and Chien, S. (1980) Cell distribution in capillary networks. Microvasc. Res. 19, 18–44.PubMedCrossRefGoogle Scholar
  48. Schmid-Schönbein, G.W., Sung, K.-R, Tözeren, H., Skalak, R. and Chien, S. (1981) Passive mechanical properties of human leukocytes. Biophys. J. 36, 243–256.PubMedCentralPubMedCrossRefGoogle Scholar
  49. Secomb, T.W. (1987) Flow-dependent rheological properties of blood in capillaries. Microvasc. Res. 34, 46–58.PubMedCrossRefGoogle Scholar
  50. Secomb, T.W. (1991) Red blood cell mechanics and capillary blood rheology. Cell Biophysics 18: 23 1–251.Google Scholar
  51. Secomb, T.W. (1995) Mechanics of blood flow in the microcirculation. To appear in Biological Fluid Dynamics, ed. C.P. Ellington and T.J. Pedley. Cambridge, Company of Biologists.Google Scholar
  52. Secomb, T.W., Skalak, R., üzkaya, N. and Gross, J.F. (1986) Flow of axisymmetric red blood cells in narrow capillaries. J. Fluid Mech. 163, 405–423.CrossRefGoogle Scholar
  53. Secomb, T.W., Pries, A.R., Gaehtgens, P. and Gross, J.F. Theoretical and experimental analysis of hematocrit distribution in microcirculatory networks. In Microvascular Mechanics, ed. J.S. Lee and T.C. Skalak, Springer, New York, 1989, pp. 40–49.Google Scholar
  54. Skalak, R. (1976) Rheology of red blood cell membrane. In Microcirculation, Vol. I, ed. J. Grayson and W. Zingg, pp. 53–70. New York: Plenum.Google Scholar
  55. Strahler, A.N. (1952) Hypsometric (area-altitude) analysis of erosional topography. Geol. Soc. Amer. Bull. 63, 1117–1142.CrossRefGoogle Scholar
  56. Vicaut, E. (1986) Statistical estimation of parameters in microcirculation. Microvasc. Res. 32, 244–247.PubMedCrossRefGoogle Scholar
  57. Warnke, K.C. and Skalak, T.C. (1990) The effects of leukocytes on blood flow in a model skeletal muscle capillary network. Microvasc. Res. 40, 118–136.PubMedCrossRefGoogle Scholar
  58. Wiedeman, M.P., Turna, R.F. and Mayrovitz, H.N. (1981) An Introduction to Microcirculation. New York: Academic Press.Google Scholar
  59. Zarda, P.R., Chien, S. and Skalak, R. (1977) Interaction of viscous incompressible fluid with an elastic body. In Computational Methods for Fluid-Solid Interaction Problems, ed. T. Belytschko and T.L. Geers, pp. 65–82. New York: American Society of Mechanical Engineers.Google Scholar
  60. Zweifach, B.W. (1937) The structure and reactions of the small blood vessels in Amphibia. Am. J. Anat. 60, 473–514.CrossRefGoogle Scholar
  61. Zweifach, B.W. (1974) Quantitative studies of microcirculatory structure and function. I. Analysis of pressure distribution in the terminal vasculature in cat mesentery. Circ. Res. 34, 843–857.PubMedGoogle Scholar
  62. Zweifach, B.W. and Lipowsky, H.H. (1977) Quantitative studies of microcirculatory structure and function. III. Microvascular hemodynamics of cat mesentery and rabbit omentum. Circ. Res. 41, 380–390.PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • T. W. Secomb
    • 1
  • A. R. Pries
    • 2
  • P. Gaehtgens
    • 2
  1. 1.Department of PhysiologyUniversity of Arizona TucsonArizonaUSA
  2. 2.Dept. of PhysiologyFreie Universität BerlinBerlinGermany

Personalised recommendations