Abstract
We show that the residual strain and stress in the blood vessels are not zero, and that the zero-stress state of a blood vessel consists of open-sector segments whose opening angles vary along the longitudinal axis of the vessel. When the homeostatic state of the blood vessel is changed, e.g., by a sudden hypertession, the opening angle will change. The time constant of the opening angle change is a few hours (e.g., in the pulmonary artery) or a few days (e.g., in the aorta). From a kinematic point of view, a change of opening angle is a bending of the blood vessel wall, which is caused by a nonuniformly distributed residual strain. From a mechanics point of view, changes of blood pressure and residual strain cause change of stress in the blood vessel wall. Correlating the stress with the change of residual strain yields a fundamental biological law relating the rate of growth or resorption of tissue with the stress in the tissue. Thus, residual stresses are related to the remodeling of the blood vessel wall. Our blood vessel remodels itself when stress changes. The stress-growth law provides a biomechanical foundation for tissue engineering.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Carter, D.R.; Fyhrie, D.P.; Whalen, R.T. Trabecular bone density and loading history: Regulation of connective tissue biology by mechanical energy. J. Biomech. 20:785–794; 1987.
Chuong, C.J.; Fung, Y.C. Three-dimensional stress distribution in arteries under the assumptions of incompressibility and homogeneity. In: van Buskirk, W.C.; Woo, S.L.-Y., eds. 1981 Biomechanics Symposium, AMD-43. New York: The American Society of Mechanical Engineers; 1981: pp. 125–128.
Chuong, C.J.; Fung, Y.C. Three-dimensional stress distribution in arteries. J. Biomech. Eng. 105:268–274; 1983.
Chuong, C.J.; Fung, Y.C. Compressibility and constitutive equation of arterial wall in radial compression experiments. J. Biomech. 17:35–40; 1984.
Chuong, C.J.; Fung, Y.C. Residual stress in arteries. In: Schmid-Schoenbein, G.W.; Woo, S.L.-Y. Zweifach, B.W., eds. Frontiers in Biomechanics. New York: Springer-Verlag; 1986: pp. 117–129.
Chuong, C.J.; Fung, Y.C. On residual stress in arteries. J. Biomech. Eng. 108:189–192; 1986.
Cowin, S.C. Wolff's law of trabecular architecture at remodeling equilibrium. J. Biomech. Eng. 108:83–88; 1986.
Fung, Y.C.; Fronek, K.; Patitucci, P. Pseudoelasticity of arteries and the choice of its mathematical expression. Am. J. Physiol. 237:H620-H631; 1979.
Fung, Y.C. Structure and stress-strain relationship of soft tissues. Am. Zool. 24:13–22; 1984.
Fung, Y.C. What principle governs the stress distribution in living organs. In: Fung, Y.C.; Fukada, E.; Wang, J.J., eds. Biomechanics in China, Japan, and USA. Proc. of an Intern. Conf. held in Wuhan, China, in May 1983. Beijing, China: Science Press; 1984: pp. 1–13.
Fung, Y.C. Biodynamics: Circulation. New York: Springer-Verlag; 1984.
Fung, Y.C. Biomechanics: Motion, flow, stress, and growth. New York: Springer-Verlag; 1990.
Fung, Y.C. Cellular growth in soft tissues affected by the stress level in service. In: Skalak, R.; Fox, D.F., eds. Tissue engineering. New York: Alan Liss; 1988: pp. 45–50.
Fung, Y.C. In search of a biomechanical foundation of tissue engineering. In: Woo, S.L.-Y.; Seguchi, Y., eds. Tissue engineering. New York: ASME Pub. No. BED-Vol. 14; 1989: pp. 11–14.
Fung, Y.C.; Liu, S.Q. Change of residual strains in arteries due to hypertrophy caused by aortic constriction. Circulation Res. 65:1340–1349; 1989.
Fung, Y.C.; Liu, S.Q. Changes of zero-stress state of rat pulmonary arteries in hypoxic hypertension. J. Appl. Physiol. (in press).
Fung, Y.C.; Liu, S.Q. Strain distribution in small blood vessels with zero-stress state taken into consideration. Am. J. Physiol. Heart and Circulation. Submitted. 1990.
Guyton, A.C.; Coleman, T.G.; Cowley Jr., A.W.; Laird, J.F.; Norman, R.A.; Manning Jr., R.D. Systems analysis of arterial pressure regulation and hypertension. Annals of Biomed. Eng. 1:254–281; 1972. ALZA Lecture. Baltimore, MD, April 7, 1972.
Han, H.C.; Fung, Y.C. Species dependence on the zero-stress state of aorta: pig vs rat. J. Biomech. Eng. (in press).
Han, H.C.; Fung, Y.C. Residual strains in porcine and canine trachea. J. Biomech. Accepted. 1990.
Hayashi, K.; Takamizawa, K. Stress and strain distributions in residual stresses in arterial walls. In: Fung, Y.C.; Hayashi, K.; Seguchi, Y., eds. Progress and new directions of biomechanics. Tokyo, Japan: MITA Press; 1989: pp. 185–192.
Janz, R.F.; Grimm, A.F. Deformation of the diastolic left ventricle. I. Nonlinear elastic effects. Biophys. J. 13:689–704; 1973.
Liu, S.Q.; Fung, Y.C. Zero-stress states of arteries. J. Biomech. Eng. 110:82–84; 1988.
Liu, S.Q.; Fung, Y.C. Relationship between hypertension, hypertrophy, and opening angle of zero-stress state of arteries following aortic constriction. J. Biomech. Eng. 111:325–335; 1989.
Liu, S.Q.; Fung, Y.C. Influence of streptozocin-diabetes on zero-stress states of rat pulmonary and systemic arteries. Diabetes. Submitted. 1990.
Meyrick, B.; Reid, L. Hypoxia-induced structural changes in the media and adventitia of the rat hillar pulmonary artery and their regression. Am. J. Pathol. 100:151–178; 1980.
Mirsky, I. Ventricular and arterial wall stresses based on large deformation theories. Biophys. J. 13:1141–1159; 1973.
Omens, J.H.; Fung, Y.C. Residual strain in rat left ventricle. Circulation Res. 66(1):37–45; 1990.
Patel, D.J.; Vaishnav, R.N., eds. Basic hemodynamics and its role in disease process. Baltimore, MD.: University Park Press; 1980.
Skalak, R.; Fox, D.F., eds. Tissue engineering. New York: Alan Liss; 1988.
Takamizawa, K.; Hayashi, K. Strain energy density function and uniform strain hypothesis for arterial mechanics. J. Biomech. 20:7–17; 1987.
Takamizawa, K.; Hayashi, K. Uniform strain hypothesis and thin-walled theory in arterial mechanics. Biorheology 25:555–565; 1988.
Vaishnav, R.N.; Vossoughi, J. Estimation of residual strains in aortic segments. In: Hall, C.W., ed. Biomedical engineering, II. Recent developments. New York: Pergamon Press; 1983: pp. 330–333.
Vaishnav, R.N.; Vossoughi, J. Residual stress and strain in aortic segments. J. Biomech. 20:235–239; 1987.
Vossoughi, J.; Weizsacker, H.E.; Vaishnav, R.N. Variation of aortic geometry in various animal species. Biomedizinische Technik 30:48–54; 1985.
Wolff, J. Über die innere Architektur der Knochen und ihre Bedeutung für die Frage vom Knochenwachstum. Archiv für pathologische Anatomie und Physiologie und für Klinische Medizin (Virchows Archiv). 50:389–453; 1870.
Xie, J.P.; Yang, R.F.; Liu, S.Q.; Fung, Y.C. The zero-stress state of rat vena cava. J. Biomech. Eng. 113:36–41; 1991.
Yin, F.C.P. Ventricular wall stress. Circulation Res. 49:829–842; 1981.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Fung, Y.C. What are the residual stresses doing in our blood vessels?. Ann Biomed Eng 19, 237–249 (1991). https://doi.org/10.1007/BF02584301
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02584301