Stress, Strain, growth, and remodeling of living organisms

  • Yuan-Cheng Fung
Chapter

Abstract

Biomechanics deals with living organisms. In the beginning, biomechanics differed from the mechanics of ordinary engineering and physics mainly by the special geometric features of living organisms, by the usually large deformations, by the unusual constitutive equations, or by the very large range of Reynolds numbers of interest in biofluid motion. In dealing with the growth, disease, and healing in life, however, one encounters biological media whose chemical, cellular, and extracellular constitutions, geometrical structures, dimensions, and mechanical properties change with time. If we knew how a tissue would change under various chemical, physical, and mechanical conditions, then it is possible that we can learn to control and “engineer” the tissue to do what we want it to do. Thus began a new field of “tissue engineering”.

Keywords

Residual Stress Tissue Engineering Constitutive Equation Natural Tissue Blood Vessel Wall 
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.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    R. Skalak and C. F. Fox (eds.), Tissue Engineering. Alan R. Liss, Inc. New York 1988.Google Scholar
  2. [2]
    S. L-Y. Woo and Y. Seguchi (eds.), Tissue Engineering —1989. ASME Publications No. BED-Vol 14, Am. Soc. Mech. Eng., New York 1989.Google Scholar
  3. [3]
    E. Bell(ed.), Tissue Engineering: Current Perspectives. Birkhäuser, Boston 1993.Google Scholar
  4. [4]
    Y. C. Fung, Cellular growth in soft tissues affected by the stress level in service. In Tissue Engineering (ed. by R. Skalak and C. F. Fox), pp. 45–50. Alan Liss, New York 1988.Google Scholar
  5. [5]
    R. Nerem and D. Ingber (eds.), Keystone Symposium on Tissue Engineering: Abstracts. J. Cellular Biochemistry, Suppl. 18C, pp. 265–284. Wiley-Liss 1994.Google Scholar
  6. [6]
    D. E. Ingber and J. Falkman, Mechanochemical switching between growth and differentiation during fibroblast growth factor-stimulated angio genesis in vitro: role of extracellular matrix. J. Cell Biol. 109, 317–330 (1989).CrossRefGoogle Scholar
  7. [7]
    D. Ingber, The riddle of morphogenesis: A question of solution chemistry or molecular cell engineering? Cell 75, 1249–1252 (1993).CrossRefGoogle Scholar
  8. [8]
    N. Wang, J. P. Butler, and D. E. Ingber, Mechanotransduction across the cell surface and through the cytoskeleton. Science 260, 1124–1227 (1993).CrossRefGoogle Scholar
  9. [9]
    E. Evans, R. Merkel, K. Ritchie, S. Tha, and A. Ziler, Picoforce method to probe submicroscopic actions in biomembrane adhesion. In Methods for Studying Cell Adhesion (P. Bongrand, P. Claesson, A. Curtiss, eds.), pp. 123–137, Springer-Verlag, Berlin 1994. Also, Sensitive force technique to probe molecular adhesion and structural linkages at biological interfaces. Biophysical J. (in press).Google Scholar
  10. [10]
    N. Resnick, T. Collins, W. Atkinson, D. T. Bonthron, D. F. Dewey, Jr. and M. A. Gimbrone, Jr., Platelet-derived growth factor B chain promoter contains a cis-acting fluid shear-stress-responsive element. Proc. Nat. Acad. Sci., USA 90, 4591–4595 (1993).CrossRefGoogle Scholar
  11. [11]
    S. F. Badylak, A. C. Coffey, G. C. Lautz, and L. A. Geddes, A non-cellular biological substrate material for use as a vascular graft. (Abstract). J. Cellular Biochem. Suppl. 18C, 272 (1994).Google Scholar
  12. [12]
    H. Sage, R. B. Vernon, L. Iruela-Arispe, and T. F. Lane, Regulation of angiogenesis by copper/sparc and by traction-generated templates of collagen 1, E (Abstract). J. Cellular Biochem. Suppl. ISC, 272 (1994).Google Scholar
  13. [13]
    Y. C. Fung, A First Course in Continuum Mechanics, for Physical and Biological Engineers and Scientists. Prentice-Hall, New Jersey, 3rd edition 1993.Google Scholar
  14. [14]
    T. T. Tanaka and Y. C. Fung, Elastic and inelastic properties of the canine aorta and their variation along the aortic tree. J. Biomech 7, 357–370 (1974).CrossRefGoogle Scholar
  15. [15]
    J. P. Yu, J. Zhou and Y. C. Fung, Neutral axis location in bending and the Young’s modulus of different layers of arterial wall. Am. J. Physiology 265: Heart and Circulatory Physiology 34, H52-H60 (1993).Google Scholar
  16. [16]
    J. P. Xie, J. Zhou and Y. C. Fung, Bending of blood vessel wall: Stress-strain laws of the intima-medial and adventital layers. J. Biomech. Eng. (in press).Google Scholar
  17. [17]
    Y. C. Fung, S. Q. Liu and J. B. Zhou, Remodeling of the constitutive equation while a blood vessel remodels itself under stress. J. Biomech. Eng. 115, 453–459 (1993).CrossRefGoogle Scholar
  18. [18]
    J. Zhou, Theoretical analysis of bending experiments on aorta and determination of constitutive equations of materials in different layers of arterial walls. Ph.D. Dissertation, UC, San Diego. 1992.Google Scholar
  19. [19]
    Y. Lanir and Y. C. Fung, Two-dimensional mechanical properties of the rabbit skin. I. Experimental system. J. Biomechanics 7, 29–34 (1974).CrossRefGoogle Scholar
  20. [20]
    D. L. Vawter, Y. C. Fung and J. B. West, Elasticity of excised dog lung parenchyma. J. Applied Physiology 45, 261–269 (1978).Google Scholar
  21. [21]
    J. Zhou and Y. C. Fung, Biaxial testing of canine aorta. J. Biomechanics (in press).Google Scholar
  22. [22]
    S. X. Deng, J. Tomioka, J. C. Debes and Y. C. Fung, New experiments on shear modulus of elasticity of arteries. American J. of Physiology 266, H1-H10 (1994).Google Scholar
  23. [23]
    Y. C. Fung, Biorheology of soft tissues. Biorheology 10, 139–155 (1973).Google Scholar
  24. [24]
    P. Tong and Y. C. Fung, The stress-strain relationship for the skin. J. Biomechanics 9, 649–657 (1976).CrossRefGoogle Scholar
  25. [25]
    C. J. Chuong and Y. C. Fung, Three-dimensional stress distribution in arteries. J. Biomech. Eng. 105, 268–274 (1983).CrossRefGoogle Scholar
  26. [26]
    Y. C. Fung, What principle governs the stress distribution in living organs? Biomechanics in China, Japan, and USA. Proc. of Wuhan Conf., Science Press, Beijing, China, May 1983.Google Scholar
  27. [27]
    Y. C. Fung, Biodynamics: Circulation. Springer-Verlag, New York 1984.Google Scholar
  28. [28]
    R. N. Vaishnav and J. Vossoughi, Estimation of residual strains in aortic segments. In Biomedical Engineering, II. Recent Developments (C. W. Hall, ed.), pp. 330–333. Pergamon Press, New York 1983.Google Scholar
  29. [29]
    R. Vaishnav and J. Vossoughi, Residual stress and strain in aortic segments. J. Biomech. 20, 235–239 (1987).CrossRefGoogle Scholar
  30. [30]
    Y. C. Fung and S. Q. Liu, Change of residual strains in arteries due to hypertrophy caused by aortic constriction. Circ. Res. 65, 1340–1349 (1989).Google Scholar
  31. [31]
    Y. C. Fung and S. Q. Liu, Changes of zero-stress state of rat pulmonary arteries in hypoxic hypertension. J. Appl. Physiol. 70, 2455–2470 (1991).CrossRefGoogle Scholar
  32. [32]
    Y. C. Fung and S. Q. Liu, Strain distribution in small blood vessels with zero-stress state taken into consideration. Am. J. Physiol. 262, H544-H552 (1992).Google Scholar
  33. [33]
    H. C. Han and Y. C. Fung. Species dependence of the zero-stress state of aorta: Pig versus rat. J. Biomech. Eng. 113, 446–451 (1991).CrossRefGoogle Scholar
  34. [34]
    S. Q. Liu and Y. C. Fung, Relationship between hypertension, hypertrophy, and opening angle of zero-stress state of arteries following aortic constriction. J. Biomech. Eng. 111, 325–335 (1989).CrossRefGoogle Scholar
  35. [35]
    S. Q. Liu and Y. C. Fung, Influence of STZ-diabetes on zero-stress state of rat pulmonary and systemic arteries. Diabetes 41, 136–146 (1992).CrossRefGoogle Scholar
  36. [36]
    S. Q. Liu and Y. C. Fung, Changes in rheological properties of the blood vessels due to tissue remodeling in the course of the development of diabetes. Biorheology 29, 443–457 (1992).Google Scholar
  37. [37]
    S. Q. Liu and Y. C. Fung, Material coefficients of the strain energy function of pulmonary arteries in normal and cigarette smoke-exposed rats. J. Biomech. 26, 1261–1269 (1993).CrossRefGoogle Scholar
  38. [38]
    S. Q. Liu and Y. C. Fung, Changes in the structure and mechanical properties of pulmonary arteries in rats exposed to cigarette smoke. Am. Rev. Respir. Dis. 148, 768–777 (1993).CrossRefGoogle Scholar
  39. [39]
    Y. C. Fung, Biomechanics: Mechanical Properties of Living Tissues. Springer-Verlag, New York, 1st ed. 1981, 2nd ed. 1993.Google Scholar
  40. [40]
    Y. C. Fung. Biomechanics: Motion, Flow, Stress, and Growth. Springer-Verlag, New York 1990.MATHGoogle Scholar
  41. [41]
    S. C. Cowin. Wolffs law of trabecular architecture at remodeling equilibrium. J. Biomech. Eng. 108, 83–88 (1986).CrossRefGoogle Scholar
  42. [42]
    B. K. Kummer, Biomechanics of bone: Mechanical properties, functional structure, functional adaptation. In: Biomechanics: Its Foundation and Objectives (Y. C. Fung, N. Perrone, M. Anliker, eds.), pp. 237–271. Prentice-Hall, New Jersey 1972.Google Scholar
  43. [43]
    K. Hayashi, Experimental approaches on measuring the mechanical properties and constitutive laws of arterial walls. J. Biomechanical Eng. 115, 481–488 (1993).CrossRefGoogle Scholar
  44. [44]
    H. Demiray and R. P. Vitor, A layered cylindrical shell model for an aorta. Int. J. Engineering Science 29, 47–54 (1991).MATHCrossRefGoogle Scholar
  45. [45]
    W.-W von Maltzahn, R. G. Warrinyar and W. F. Keitzer, Experimental measurements of elastic properties of media and adventitia of bovine carotid arteries. J. Biomechanics 17, 839–847 (1984).CrossRefGoogle Scholar
  46. [46]
    W. M. Lai, V. C. Mow and W. Zhu, Constitutive modeling of articular cartilage and biomacromolec-ular solutions. J. Biomechanical Eng. 115, 474–480 (1993).CrossRefGoogle Scholar
  47. [47]
    S. L-Y. Woo, G. A. Johnson and B. A. Smith, Mathematical modeling of ligaments and tendons. J. Biomechanical Eng. 115, 468–473 (1993).CrossRefGoogle Scholar
  48. [48]
    Y. C. Fung and S. Q. Liu, Elementary mechanics of the endothelium of blood vessels. J. Biomechanical Engineering 115, 1–12 (1993).CrossRefGoogle Scholar
  49. [49]
    S. Q. Liu, M. Yen and Y. C. Fung, On measuring the third-dimension of cultured endothelial cells in shear flow. Proc. Nat. Acad. Sci. USA 91, 8782–8786 (1994).CrossRefGoogle Scholar
  50. [50]
    Y. C. Fung and S. Q. Liu, Determination of the mechanical properties of the different layers of blood vessels in vivo. Proc. Nat. Acad. Sci. USA (in press).Google Scholar

Copyright information

© Birkhäuser Basel/Switzerland 1995

Authors and Affiliations

  • Yuan-Cheng Fung
    • 1
  1. 1.University of CaliforniaSan Diego, La JollaUSA

Personalised recommendations