Biomechanics pp 261-301 | Cite as

Mechanical Properties of Blood Vessels

  • Y. C. Fung


Blood vessels belong to the class of soft tissues discussed in Chapter 7. They do not obey Hooke’s law. Figure 7.5:1 in Chapter 7, Sec. 7.5 demonstrates the nonlinearity of the stress-strain relationship and the existence of hysteresis. They also creep under constant stress and relax under constant strain. These mechanical properties must have a structural basis. In Sec. 8.2 we shall consider the structure of the blood vessel wall and its correlation with the mechanical properties. From Sec. 8.3 on, however, our attention will be concentrated on the mathematical description of the mechanical properties. In Secs. 8.3–8.5 we formulate a quasi-linear viscoelastic theory for blood vessels, using the pseudo-elasticity concept introduced in Chapter 7. In Sec. 8.6 we discuss the use of arterial pulse waves as a means to determine the mechanical properties of arteries. In Secs. 8.7–8.9 we consider the mechanical properties of arterioles, capillary blood vessels, venules, and veins. Finally, in Sec. 8.10, we discuss the long-term response of blood vessels to stresses: their reaction to hypertension, growth, regeneration, and resorption.


Blood Vessel Wall Transmural Pressure Strain Energy Function Stretch Ratio Uniaxial Test 


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  1. Anliker, M., Histand, M. B., and Ogden, E. (1968) Circulation Res. 23, 539–551.Google Scholar
  2. Anliker, M., Wells, M. K., and Ogden, E. (1969) IEEE Trans. Biomed. Eng. BME-16 262–273.Google Scholar
  3. Anliker, M. (1972) In Biomechanics: Its Foundations and Objectives, Fung, Y. C., Perrone, N., and Anliker, M. (eds.). Prentice-Hall, Englewood Cliffs, N.J., 1972, pp. 337–380.Google Scholar
  4. Ayorinde, O. A., Kobayashi, A. S., and Merati, J. K. (1975) In 1975 Biomechanics Symposium. ASME, New York, p. 79.Google Scholar
  5. Azuma, T., Hasegawa, M., and Matsuda, T. (1970) In Proceedings of the 5th International Congress on Rheology, Onogi, S. (ed.) University of Tokyo Press, Tokyo and University Park Press, Baltimore, pp. 129–141.Google Scholar
  6. Azuma, T., and Hasegawa, M. (1971) Japan J. Physiol. 21 37–47. Azuma, T., and Hasegawa, M. (1973) Biorheology 10,469–479.Google Scholar
  7. Baez, S., Lamport, H., and Baez, A. (1960)•In Flow Properties of Blood and Other Biological Systems,Copley, A. L., and Stainsby, G. (eds.). Pergamon Press, Oxford, pp. 122–136.Google Scholar
  8. Bauer, R. D., and Pasch, T. (1971) Pflügers Arch. 330, 335–346.CrossRefGoogle Scholar
  9. Bergel, D. H. (1972) In Biomechanics: Its Foundations and Objectives, Fung, Y. C., Perrone, N., and Anliker, M. (eds.). Prentice-Hall, Englewood Cliffs, N.J. Chap. 5, pp. 105–140.Google Scholar
  10. Bevan, J. A., Bevan, R. D., Chang, P. C., Pegram, B. L., Purdy, R. E., and Su, C. (1975) Circulation Res. 37, 183–190.CrossRefGoogle Scholar
  11. Bevan, R. D. (1976) Blood Vessels 13, 100–124.Google Scholar
  12. Bohr, D. F., Somlyo, A. P., and Sparks, H. V., Jr. (eds.) (1980) Handbook of Physiology. Sec. 2. The Cardiovascular System. Vol. 2: Vascular Smooth Muscle. American Physiological Society, Bethesda, Md.Google Scholar
  13. Bouskela, E. and Wiederhielm, C. (1979) Microvascular Res. 17,No. 3, Part 2, p. 51, (abstract).Google Scholar
  14. Burton, A. C. (1966) Fed. Proc. 25, 1753–1760.Google Scholar
  15. Brankov, G., Rachev, A., and Stoychev, S. (1974) Biomechanica (Bulgarian Academy of Sciences, Sofia) 1, 27–35.Google Scholar
  16. Brankov, G., Rachev, A., and Stoychev, S. (1976) Biomechanica (Bulgarian Academy of Sciences, Sofia) 3, 3–11.Google Scholar
  17. Carew, T. E., Vaishnav, R. N., and Patel, D. J. (1968) Circulation Res. 23, 61–68.CrossRefGoogle Scholar
  18. Caro, C. G., Pedley, T. J., Schroter, R. C., and Seed, W. A. (1978) The Mechanics of the Circulation Oxford University Press, Oxford, 1978.Google Scholar
  19. Cox, R. H. (1976–1978) Am. J. Physiol. 230, 462–470, 1976; 231, 420–425, 1976; 233, H243—H255, 1977; 234, H280–288, 1978.Google Scholar
  20. Crystal, R. G. (1974) Fed. Proc. 33, 2248–2255.Google Scholar
  21. Demiray, H. J. (1972) J. Biomechanics 5,309–311.Google Scholar
  22. Doyle, J. M., and Dobrin, P. B. (1971) Microvascular Res. 3, 400–415. Doyle, J. M., and Dobrin, P. B. (1973) J. Biomechanics 6 631–639, 1973. Fisher, G. M., and Llaurado, J. G. (1967) Arch. Pathol. 84 95–98. Frank, O. (1920) J. Biol. 71,255–272.Google Scholar
  23. Frasher, W. G. (1966) In Biomechanics, Proc. Symp., Fung, Y. C. (eds.). ASME, New York, 1966.Google Scholar
  24. Fry, D. L. (1968) Circulation Res. 22, 165–197. Fry, D. L. (1969) Circulation Res. 24, 93–108.Google Scholar
  25. Fung, Y. C. (1966a) In Biomechanics, Proc. of a Symp.Google Scholar
  26. Fung, Y. C. (ed.). ASME, New York. pp. 151–166.Google Scholar
  27. Fung, Y. C. (1966b) Fed. Proc. 25, 1761–1772.Google Scholar
  28. Fung, Y. C. (1967) Am. J. Physiol. 28, 1532–1544.Google Scholar
  29. Fung, Y. C. (1972) In Biomechanics: Its Foundations and Objectives, Fung, Y. C., Perrone, N., and Anliker, M. (eds.). Prentice-Hall, Englewood Cliffs, N.J., pp. 181–208.Google Scholar
  30. Fung, Y. C. (1973) Biorheology 10, 139–155.Google Scholar
  31. Fung, Y. C. (1975) Mechanika Polymerov LSSR, 10, 850–867.Google Scholar
  32. Fung, Y. C. (1975) Circulation Res. 37, 481–496.CrossRefGoogle Scholar
  33. Fung, Y. C., and Sobin, S. S. (1969) J. Appl. Physiol. 26, 472–488.Google Scholar
  34. Fung, Y. C., and Sobin S. S. (1972) Circulation Res. 30, 451–469; 470–490.Google Scholar
  35. Fung, Y. C., and Sobin, S. S. (1977) In Bioengineering Aspects of Lung Biology, West, J. B. (ed.). Marcel Dekker, New York, Chapter 4, pp. 267–358.Google Scholar
  36. Fung, Y. C., Zweifach, B. W., and Intaglietta, M. (1966) Circulation Res. 19, 441–461, 1966.CrossRefGoogle Scholar
  37. Fung, Y. C., Fronek, K., and Patitucci, P. (1979) Am. J. Physiol. 237(5): H620–H631. or Am. J. Physiol.: Heart and Circulation, 6 (5): H620–H631.Google Scholar
  38. Gaehtgens, P., and Uekermann, U. (1971) Pflügers Arch. 330, 206–216. Gore, R. W. (1972) Am. J. Physiol. 222 (1), 82–91.Google Scholar
  39. Gore, R. W. (1974) Circulation Res. 34, 581–591.ADSCrossRefGoogle Scholar
  40. Gou, P. E. (1970) J. Biomechanics 3, 547–550.CrossRefGoogle Scholar
  41. Hardung, V. (1953) Hely. Physiol. Pharmacol. Acta 11, 194–211.Google Scholar
  42. Harkness, M. L. R., Harkness, R. D., McDonald, D. A. (1957) Proc. Roy. Soc. B 146, 541–51.ADSCrossRefGoogle Scholar
  43. Hayashi, K., Handa, H., Mori, K., and Moritake, K. (1971) J. Soc. Material Sci. (Japan) 20 1001–1011.Google Scholar
  44. Hayashi, J., Sato, M., Handa, H., and Moritake, K. (1974) Exper. Mech. 14, 440–444.CrossRefGoogle Scholar
  45. Intaglietta, M., and Plomb, E. P. (1973) Microvascular Res. 7, 153–168.CrossRefGoogle Scholar
  46. Johnson, P. C. (1968) Circulation Res. 22, 199–212.CrossRefGoogle Scholar
  47. Johnson, P. C. (ed.) (1978) Peripheral Circulation. Wiley, New York.Google Scholar
  48. Johnson, P. C. (1980). The myogenic response. In Bohr et al. (1980) loc. cit.,pp. 409–442.Google Scholar
  49. Kasyanov, V. (1974) Mechanika Polymerov LSSR,874–884.Google Scholar
  50. Kasyanov, V., and Knets, I. (1974) Mechanica Polymerov. LSSR,122–128.Google Scholar
  51. Kenner, T. (1967) Arch. Kreislaufforschung 54, 68–139.CrossRefGoogle Scholar
  52. Laszt, L. (1968) Angiologica. 5, 14–27.Google Scholar
  53. Lee, J. S., Frasher, W. G., and Fung, Y. C. (1967) Two-dimensional finite deformation experiments on dog’s arteries and veins. Rept. No. AFOSR 67–198, Dept. of Applied Mechanics and Engineering Science—Bioengineering, University of California, San Diego, Calif.Google Scholar
  54. Marquart, D. W. (1963) J. Soc. Indust. Appl. Math. 2, 431–441.Google Scholar
  55. McDonald, D. A. (1968) J. Appl. Physiol. 24, 73–78.Google Scholar
  56. Moritake, K., Handa, H., Hayashi, K., and Sato, M. (1973) Japan J. Brain Surg. 1 (2), 115–123.Google Scholar
  57. Patel, D. J., and Vaishnav, R. N. (1972) In Cardiovascular Fluid Dynamics, Bergel, D. H. (ed.) Academic Press, New York, Vol. 2, Chapter 11, pp. 2–65.Google Scholar
  58. Roach, M. R., and Burton, A. C. (1957) Canad. J. Biochem. Physiol. 35, 681–690.CrossRefGoogle Scholar
  59. Rushmer, R. F. (1970) Cardiovascular Dynamics, 3rd edn. W. B. Saunders, Philadelphia, p. 196.Google Scholar
  60. Schmid-Schoenbein, G. W., Fung, Y. C., and Zweifach, B. W. (1975) Circulation Res. 36, 173–184.CrossRefGoogle Scholar
  61. Sharma, M. G. (1974) Biorheology 11, 279–291.Google Scholar
  62. Shepherd, J. T., and Vanhoutte, P. M. (1975) Veins and Their Control. W. B. Saunders, Philadelphia.Google Scholar
  63. Snyder, R. W. (1972) J. Biomechanics 5, 601–606.CrossRefGoogle Scholar
  64. Sobin, P. (1977) Mechanical Properties of Human Veins. M. S. Thesis, University of California, San Diego, Calif.Google Scholar
  65. Sobin, S., Fung, Y. C., Tremer, H. M., and Rosenquist, T. H. (1972) Circulation Res. 30, 440–450.Google Scholar
  66. Tanaka, T. T., and Fung, Y. C. (1974) J. Biomechanics. 7, 357–370.CrossRefGoogle Scholar
  67. Vaishnav, R. N., Young, J. T., Janicki, J. S., and Patel, D. J. (1972) Biophysical J. 12, 1008–1027.Google Scholar
  68. Wesley, R. L. R., Vaishnav, R. N., Fuchs, J. C. A., Patel, D. J., and Greenfield, J. C., Jr. (1975) Circulation Res. 37, 509–520.CrossRefGoogle Scholar
  69. Wetterer, E., and Kenner, T. (1968) Grundlagen der Dynamik des arterienpulses. Springer-Verlag, Berlin.Google Scholar
  70. Wetterer, E., Bauer, R. D., and Busse, R. (1978) In The Arterial System, Bauer, R. D. and Busse, R. (eds.) Springer-Verlag, New York.Google Scholar
  71. Wylie, E. B. (1966) in Biomechanics, Proc. ASME Symp., Fung, Y. C. (ed.). American Society of Mechanical Engineers, New York. pp. 82–95.Google Scholar
  72. Zweifach, B. W., and Intaglietta, M. (1968) Microvascular Res. 1, 83–101.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1981

Authors and Affiliations

  • Y. C. Fung
    • 1
  1. 1.University of California, San DiegoLa JollaUSA

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