Biomechanics pp 165-219 | Cite as

Interaction of Red Cells with Vessel Wall, and Wall Shear with Endothelium

  • Yuan-Cheng Fung
Chapter

Abstract

The sizes of the viscometers cited in Chapter 3 are so large that blood can be treated as a homogeneous fluid in them. The size of the individual red cells is many orders of magnitude smaller than the dimensions of the viscometers. The same condition holds in large blood vessels. The diameters of the capillary blood vessels, however, are comparable with the dimensions of the red cells. Hence in the capillaries, red blood cells must be treated as individuals. Blood must be regarded as a two-phase fluid : a liquid plasma phase and a deformable solid phase of the blood cells.

Keywords

Wall Shear Stress Apparent Viscosity Tube Diameter Relative Viscosity Membrane Tension 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References to Blood Cells in Microcirculation

  1. Barbee, J. H. and Cokelet, G. R. (1971) The Fahreus effect. Microvasc. Res. 34, 6–21.CrossRefGoogle Scholar
  2. Braasch, D. and Jennett, W. (1986) Erythrozytenflexibilitat, Hämokonzen tration and Reibung swiderstand in Glascapillarem mit Durchmessern Zwischen 6 bis 50 p. Pfügers Archiv. Physiol. 302, 245–254.CrossRefGoogle Scholar
  3. Caro, C. G., Pedley, T. J., Schroter, R. C., and Seed, W. A. (1978) The Mechanics of Circulation. Oxford University Press, New York.Google Scholar
  4. Chien, S. (1972) Present status of blood rheology. In Hemodilution: Theoretical Basis and Clinical Application, K. Messmer and H. Schmid-Schönbein (eds.) Karger, Basel, pp. 1–45.Google Scholar
  5. Fahraeus, R. (1929) The suspension stability of blood. Physiol. Rev. 9, 241–274.Google Scholar
  6. Fahraeus, R. and Lindqvist, T. (1931) Viscosity of blood in narrow capillary tubes. Am. J. Physiol. 96, 562–568.Google Scholar
  7. Fitz-Gerald, J. M. (1969a) Mechanics of red cell motion through very narrow capillaries. Proc. Roy. Soc. London, B 174, 193–227.Google Scholar
  8. Fitz-Gerald, J. M. (1969b) Implications of a theory of erythrocyte motion in narrow capillaries. J. Appl. Physiol. 27, 912–918.Google Scholar
  9. Fitz-Gerald, J. M. (1972) In Cardiovascular Fluid Dynamics, D. H. Bergel (ed.) Academic, New York, Vol. 2, Chapter 16, pp. 205–241.Google Scholar
  10. Fung, Y. C. (1969a) Blood flow in the capillary bed. J. Biomechari. 2, 353–372.CrossRefGoogle Scholar
  11. Fung, Y. C. (1969b) Studies on the blood flow in the lung. Proc. Can. Congr. Appl. Mech., May, 1969. University of Waterloo, Canada, pp. 433–454Google Scholar
  12. Fung, Y. C. (1973) Stochastic flow in capillary blood vessels. Microvasc. Res. 5, 34–48.PubMedCrossRefGoogle Scholar
  13. Goldsmith, H. L. (1971) Deformation of human red cells in tube flow. Biorheology 7, 235–242.PubMedGoogle Scholar
  14. Goldsmith, H. L. and Skalak, R. (1975) Hemodynamics. Ann. Rev. Fluid Mech. 7 213–247.Google Scholar
  15. Gross, J. F. and Aroesty, J. (1972) Mathematical models of capillary flow: A critical review. Biorheology 9, 255–264.Google Scholar
  16. Haynes, R. H. (1960) Physical basis of the dependence of blood viscosity on tube radius. Am. J. Physiol. 198, 1193–1200.PubMedGoogle Scholar
  17. Hochmuth, R. M., Marple, R. N., and Sutera, S. P. (1970) Capillary blood flow. 1. Erythrocyte deformation in glass capillaries. Microvasc. Res. 2, 409–419.PubMedCrossRefGoogle Scholar
  18. Jay, A. W. C., Rowlands, S., and Skibo, L. (1972) Cand. J. Physiol. Pharmacol. 5, 1007–1013.CrossRefGoogle Scholar
  19. Johnson, P. C. and Wayland, H. (1967) Regulation of blood flow in single capillaries. Am. J. Physiol. 212, 1405–1415.PubMedGoogle Scholar
  20. Kot, P. (1971) Motion picture shown at the Annual Meeting of the Microcirculatory Society, Atlantic City, N. J., April 1971.Google Scholar
  21. Kuethe, A. M. and Chow, C. Y. (1986). Foundations of Aerodynamics 4th Edn. Wiley, N.Y.Google Scholar
  22. Lee, J. S. (1969) Slow viscous flow in a lung alveoli model. J. Biomech. 2, 187–198.PubMedCrossRefGoogle Scholar
  23. Lee, J. S. and Fung Y. C. (1969). Modeling experiments of a single red blood cell moving in a capillary blood vessel. Microvasc. Res. 1, 221–243.PubMedCrossRefGoogle Scholar
  24. Lew, H. S. and Fung, Y. C. (1969a) The motion of the plasma between the red cells in the bolus flow. Biorheology, 6, 109–119.PubMedGoogle Scholar
  25. Lew, H. S. and Fung, Y. C. (1969b) On the low-Reynolds-number entry flow into a circular cylindrical tube. J. Biomech. 2, 105–119.PubMedCrossRefGoogle Scholar
  26. Lew, H. S. and Fung, Y. C. (1969c) Flow in an occluded circularly cylindrical tube with permeable wall. Zeit. angew. Math. Physik 20, 750–766.Google Scholar
  27. Lew, H. S. and Fung, Y. C. (1970a) Entry flow into blood vessels at arbitrary Reynolds number. J. Biomech. 3, 23–38.PubMedCrossRefGoogle Scholar
  28. Lew, H. S. and Fung, Y. C. (1970b) Plug effect of erythrocytes in capillary blood vessels. Biophys. J. 10, 80–99.PubMedCrossRefGoogle Scholar
  29. Lighthill, M. J. (1968) Pressure forcing of tightly fitting pellets along fluid-filled elastic tubes. J. Fluid Mech. 34, 113–143.CrossRefGoogle Scholar
  30. Mason, S. G. and Goldsmith, H. L. (1969) The flow behavior of particulate suspensions. In Circulatory and Respiratory Mass Transport. A Ciba Foundation Symposium, G. E. W. Wolstenholme and J. Knight (eds.) Churchill, London, p. 105.Google Scholar
  31. Prothero, J. and Burton, A. C. (1961) The physics of blood flow in capillaries. Biophys.Google Scholar
  32. J. 1 565–579; 2 199–212; 2 213–222 (1962).Google Scholar
  33. Secomb, T. W., Skalak, R., Özkaya, N., and Gross, J. F. (1986) Flow of axisymmetric red blood cells in narrow capillaries. J. Fluid Mech. 163, 405–423.CrossRefGoogle Scholar
  34. Segre, G. and Silberberg, A. (1962) Behavior of macroscopic rigid spheres in Poiseuille flow. J. Fluid Mech. 14, 136–157.CrossRefGoogle Scholar
  35. Seshadri, V., Hochmuth, R. M., Croce, P. A., and Sutera, A. P. (1970) Capillary blood flow. III. Deformable model cells compared to erythrocytes in vito. Microvasc. Res. 2, 434–442.PubMedCrossRefGoogle Scholar
  36. Skalak, R. (1972) Mechanics of the microcirculation. In Biomechanics: Its Foundations and Objectives, Y. C., Fung, N. Perrone, and M. Anliker (eds.) Prentice-Hall, Englewood Cliffs, NJ, pp. 457–500.Google Scholar
  37. Skalak, R. (1973) Modeling the mechanical behavior of red blood cells. Biorheology 10, 229–238.PubMedGoogle Scholar
  38. Skalak, R. Chen, P. H. and Chien, S. (1972) Effect of hematocrit and rouleau on apparent viscosity in capillaries. Biorheology 9 67–82.Google Scholar
  39. Skalak, R. and Chien, S. (1983) Theoretical models of rouleau formation and dis-aggregation. Ann. New York Academy of Sciences. Part 1, Vol 416, pp. 138–148.Google Scholar
  40. Skalak, R. (1990) Capillary flow: history, experiments, and theory Biorheology 27, 277–293.PubMedGoogle Scholar
  41. Sobin, S. S., Tremer, H. M., and Fung, Y. C. (1970) Morphometric basis of the sheet-flow concept of the pulmonary alveolar microcircumation in the cat. Circulation Res. 26, 397–414.PubMedCrossRefGoogle Scholar
  42. Sobin, S. S., Fung, Y. C., Tremer, H. M., and Rosenquist, T. H. (1972) Elasticity of the pulmonary alveolar microvascular sheet in the cat. Circulation Res. 30, 440–450.PubMedCrossRefGoogle Scholar
  43. Sutera, S. P. (1978) Red cell motion and deformation in the microcirculation. J. Biomech. Eng. 100, 139–148.CrossRefGoogle Scholar
  44. Sutera, S. P. and Hochmuth, R. M. (1968) Large scale modeling of blood flow in the capillaries. Biorheology 5, 45–78.PubMedGoogle Scholar
  45. Sutera, S. P., Seshadri, V., Croce, P. A., and Hochmuth, R. M. (1970) Capillary blood flow. II. Deformable model cells in tube flow. Microvasc. Res. 2, 420–433.PubMedCrossRefGoogle Scholar
  46. Svanes, K. and Zweifach, B. W. (1968) Variations in small blood vessel hematocrits produced in hypothermic rats by micro-occlusion. Microvasc. Res. 1, 210–220.CrossRefGoogle Scholar
  47. Tong, P. and Fung, Y. C. (1971) Slow particulate viscous flow in channels and tubes—Application to biomechanics. J. Appl. Mech. 38, 721–728.CrossRefGoogle Scholar
  48. Warrell, D. A., Evans, J. W., Clarke, R. O., Kingaby, G. P., and West, J. B. (1972) Patterns of filling in the pulmonary capillary bed. J. Appl. Physiol. 32, 346–356.PubMedGoogle Scholar
  49. Yen, R. T. and Fung, Y. C. (1973) Model experiments on apparent blood viscosity and hematocrit in pulmonary alveoli. J. Appl. Physiol. 35, 510–517.PubMedGoogle Scholar
  50. Yen, R. T. and Fung, Y. C. (1977) Inversion of Fahraeus effect and effect of mainstream flow on capillary hematocrit. J. Appl. Physiol. 42 (4), 578–586.PubMedGoogle Scholar
  51. Yen, R. T. and Fung, Y. C. (1978) Effect of velocity distribution on red cell distribution in capillary blood vessels. Am. J. Physiol. 235 (2), H251–H257.PubMedGoogle Scholar

References to Endothelial Cells

  1. Caro, C. G., Fitz-Gerald, J. M., and Schroter, R. C. (1971) Atheroma and arterial wall shear—observation, correlation, and proposal of a shear-dependent mass-transfer mechanism for atherogenesis. Proc. Roy. Soc. London (Biol.) 177, 109–159.CrossRefGoogle Scholar
  2. Curry, F-R. E. (1988) Mechanics and thermodynamics of transcapillary exchange. In Handbook of Physiology—Cardiovascular System IV. American Physiological Society, Bethesda, MD, Part I, pp. 309–374.Google Scholar
  3. Davies, P. F., Remuzzi, A., Gordon, E. F., Dewey, C. F., Jr., and Gimbrone, M. A., Jr. (1986) Turbulent fluid shear stress iduces vascular endothelial cell turnover in vitro. Proc. Natl. Acad. Sci. 83, 2114–2117.CrossRefGoogle Scholar
  4. Dewey, C. F., Bussolari, S. R., Gimbrone, M. A., and Davies, P. F. (1981) The dynamic response of vascular endothelial cells to fluid shear stress. J. Biomech. Eng. 103, 177–185.PubMedCrossRefGoogle Scholar
  5. Dewey, C. F., Bussolari, S. R., Gimbrone, M. A., Jr., and Davies, P. F. (1981) The dynamic response of vascular endothelial cells to fluid shear stress. J. Biomech. Eng. 103, 177–185.PubMedCrossRefGoogle Scholar
  6. Flaherty, J. T., Pierce, J. E., Ferrans, V. J., Patel, D. J., Tucker, W. K., and Fry, D. L. (1972) Endothelial nuclear patterns in the canine arterial tree with particular reference to hemodynamic events. Circulation Res. 30, 23–33.PubMedCrossRefGoogle Scholar
  7. Fry D. L. (1968) Acute vascular endothelial changes associated with increased blood velocity gradients. Circulation Res. 22, 165–197.PubMedCrossRefGoogle Scholar
  8. Fry D. L. (1969) Certain histological and chemical responses of the vascular interface to acutely induced mechanical stress in the aorta of the dog. Circulation Res. 24, 93–108.PubMedCrossRefGoogle Scholar
  9. Fung, Y. C. (1965) Foundations and Solid Mechanics. Prentice-Hall, Englewood Cliffs, N.J.Google Scholar
  10. Fung, Y. C., and Liu, S. Q. (1993) Elementary mechanics of the endothelium of blood vessels. J. Biomech. Eng. 115, 1-12.Google Scholar
  11. Gau, G. S., Ryder, T. A., and MacKenzie, M. L. (1980) The effect of blood flow on the surface morphology of the human endothelium. J. Pathol. 131, 55–60.PubMedCrossRefGoogle Scholar
  12. Giddens, D. P., Zarins, C. K., and Glagov, S. (1990) Response of arteries to near-wall fluid dynamic behavior. Appl. Mech. Rev. 43, S98–5102.CrossRefGoogle Scholar
  13. Hammersen, F. and Lewis, D. H. (eds.) (1985) Endothelial Cell Vesicles. Proc. Workshop, Karger, Basel, 1985.Google Scholar
  14. Helmlinger, G., Geiger, R. V., Schreck, S., and Nerem, R. M. (1991) Effects of pulsatile flow on cultured vascular endothelial cell morphology. J. Biomech. Eng. 113, 123–131.PubMedCrossRefGoogle Scholar
  15. Hsiung, C. C. and Skalak, R. (1984) Hydrodynamic and mechanical aspects of endothelial permeability. Biorheology 21, 207–221.Google Scholar
  16. Kamiya, A. and Togawa, T. (1980) Adaptive regulation of wall shear stress to flow change in the canine carotid artery. Am. J. Physiol. 239, H14 — H21.PubMedGoogle Scholar
  17. Kamiya, A., Bukhari, R., and Togawa, T. (1984) Adaptive regulation of wall shear stress optimizing vascular tree function. Bull. Math. Biol. 46, 127–137.PubMedGoogle Scholar
  18. Kim, D. W., Gotlieb, A. L., and Langille, B. L. (1989) In vivo modulation of enthothelial F-actin microfilaments by experimental alterations in shear stress. Arteriosclerosis 9, 439–445.Google Scholar
  19. Kim, D. W., Langille, B. L., Wong, M. K. K., and Gotlieb, A. L. (1989) Patterns of endothelial microfilament distribution in the rabbit aorta in situ. Circulation Res. 64, 21–31.PubMedCrossRefGoogle Scholar
  20. Koslow, A. R., Stromberg, R. R., Friedman, L. I., Lutz, R. J., Hilbert, S. L., and Schuster, P. (1986) A flow system for the study of shear forces upon cultured endothelial cells. J. Biomech. Eng. 108, 338–341.PubMedCrossRefGoogle Scholar
  21. Levesque, M. J. and Nerem, R. M. (1985) The elongation and orientation of cultured endothelial cells in response to shear stress. J. Biomech. Eng. 107, 341–347.Google Scholar
  22. Markin, V. S. and Martinac, B. (1991) Mechano sensitive ion channels as reporters of bilayer expansion. A theoretical model. Biophys. J. 60, 1-8.Google Scholar
  23. Nerem, R. M. and Girard, P. R. (1990) Hemodynamic influence on vascular endothelial biology. Toxicologic Pathol. 18, 572–582.Google Scholar
  24. Nollert, M. U., Diamond, S. L., and McIntire, L. V. (1991) Hydrodynamic shear stress and mass transport modulation of endothelial cell metabolism. Biotech. Bioeng. 38, 588–602.CrossRefGoogle Scholar
  25. Pappenheimer, J. R. (1953) Passage of molecules through capillary walls. Physiol. Rev. 33, 387–423.PubMedGoogle Scholar
  26. Repin, V. S., Dolgov, V. V., Zaikina, O. E., Novikov, I. A., Antonov, A. S., Nikolaeva, N. A., and Smirnov, V. N. (1984) Heterogeneity of endothelium in human aorta. Atherosclerosis 50, 35–52.Google Scholar
  27. Rhodin, J. A. G. (1980) Architecture of the vessel wall. In Handbook of Physiology, Sec 2, Vascular Smooth Muscle, D. F. Bohr, A. P. Samlyo, and H. V. Sparks, Jr. (eds.) American Physiological Society, Bethesda, MA Chap. 1, pp. 1–32.Google Scholar
  28. Rodbard, S. (1970) Negative feedback mechanisms in the architecture and function of the connective and cardiovascular tissues. Perspective Biol. Med. 13, 507–527.Google Scholar
  29. Sakariassen, K. S., Aarts, P. A. M. M., Degroot, P. G., Houdijk, W. P. M., and Sixma, J. J. (1983) A perfusion chamber developed to investigate platelet interaction in flowing blood with human vessel wall cells. J. Lab. Clin. Med. 102, 522–535.PubMedGoogle Scholar
  30. Sato, M., Levesque, M. J., and Nerem, R. M. (1987) Application of the micropipette technique to the measurement of the mechanical properties of cultured bovine endothelial cells. J. Biomech. Eng. 109, 27–34.PubMedCrossRefGoogle Scholar
  31. Sato, M., Theret, D. P., Wheeler, L. T., Ohshima, N., and Nerem, R. M. (1990) Application of the micropipette technique to the measurement of cultured porcine aortic endothelial cell viscoelastic properties. J. Biomech. Eng. 112, 263–268.Google Scholar
  32. Simionescu, M. Simionescu, N., and Palade, G. E. (1975) Segmental differentiations of cell junctions in the vascular endothelium. The microvasculature. J. Cell Biol. 67 863–885.Google Scholar
  33. Simionescu, N., Simionescu, M., and Palade, G. E. (1976) Segmental differentiations of cell junctions in the vascular endothelium. Arteries and veins. J. Cell Biol. ’68, 705–723.Google Scholar
  34. Simionescu, N. and Simionescu, M. (eds.) (1988) Endothelial Cell Biology in Health and Disease. Plenum Press, New York.Google Scholar
  35. Singer, S. J. and Nicolson, G. L. (1972) The fluid mosaic model of the structure of cell membranes. Science 175, 720–731.Google Scholar
  36. Skalak, R., Tözeren, A., Zahalak, G., Elson, E., and Chien, D. (Scheduled 1993 ) Biomechanics of Cells. Springer-Verlag, New York.Google Scholar
  37. Sprague, E. A., Steinbach, B. L., Nerem, R. M., and Schwartz, C. J. (1987) Influence of a laminar steady-state fluid-imposed wall shear stress on the binding, internalization, and degradation of low-density lipoproteins by cultured arterial endothelium. Circulation 76, 648–656.PubMedCrossRefGoogle Scholar
  38. Strong, A. B., Absolom, D. R., Zingg, W., Hum, O., Ledain, C., and Thompson, B. E. (1982) A new cell for platelet adhesion studies. Animals Biomed. Eng. 10, 71–82.Google Scholar
  39. Theret, D. Levesque, M. J. Sato, M., Nerem, R. M., and Wheeler, L. T. (1988) The application of homogeneous half-space model in the analysis of endothelial cell micropipette measurements. J. Biomech. Eng. 110 190–199.Google Scholar
  40. Thilo-Korner, D. G. S. and Freshney, R. I. (eds.) (1983) International Endothelial Cell Symposium. Karger, Basel.Google Scholar
  41. Viggers, R. F., Wechezak, A. R., and Sauvage, L. R. (1986) An apparatus to study the response of cultured endothelium to shear stress. J. Biomech. Eng. 108, 332–337.PubMedCrossRefGoogle Scholar
  42. Zarins, C. K., Zatina, M. A., Giddens, D. P., Ku, D. N., and Glagov, S. (1987) Shear stress regulation of artery lumen diameter in experimental atherogenesis. J. Vascular Surg. 5, 413–420.Google Scholar

Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Yuan-Cheng Fung
    • 1
  1. 1.Department of BioengineeringUniversity of California, San DiegoLa JollaUSA

Personalised recommendations