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Elastic Behavior of Porcine Coronary Artery Tissue Under Uniaxial and Equibiaxial Tension

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Abstract

The aim of this study was to characterize the nonlinear anisotropic elastic behavior of healthy porcine coronary arteries under uniaxial and equibiaxial tension. Porcine coronary tissue was chosen for its availability and similarity to human arterial tissue. A biaxial test device previously used to test human femoral arterial tissue samples (Prendergast, P. J., C. Lally, S. Daly, A. J. Reid, T. C. Lee, D. Quinn, and F. Dolan. ASME J. Biomech. Eng., Vol. 125, pp. 692–699, 2003) was further developed to test porcine coronary tissue specimens. The device applies an equal force to the four sides of a square specimen and therefore creates a biaxial stretch that demonstrates the anisotropy of arterial tissue. The nonlinear elastic behavior was marked in both uniaxial and biaxial tests. The tissue demonstrated higher stiffness in the circumferential direction in four out of eight cases subjected to biaxial tension. Even though anisotropy is demonstrated it is proposed that an isotropic hyperelastic model may adequately represent the properties of an artery, provided that an axial stretch is applied to the vessel to simulate the in vivo longitudinal tethering on the vessel. Isotropic hyperelastic models based on the Mooney-Rivlin constitutive equation were derived from the test data by averaging the longitudinal and circumferential equibiaxial data. Three different hyperelastic models were established to represent the test specimens that exhibited a high stiffness, an average stiffness, and a low stiffness response; these three models allow the analyst to account for the variability in the arterial tissue mechanical properties. These models, which take account of the nonlinear elastic behavior of coronary tissue, may be implemented in finite element models and used to carry out preclinical tests of intravascular devices. The errors associated with the hyperelastic models when fitting to both the uniaxial and equibiaxial data for the low stiffness, average stiffness, and high stiffness models were found to be 0.836, 5.206, and 2.980, respectively.

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REFERENCES

  1. Auricchio, F., M. Di Loreto, and E. Sacco. Finite-element analysis of a stenotic artery revascularization through a stent insertion. Comput. Methods Biomech. Biomed. Eng. 4:249-263, 2001.

    Google Scholar 

  2. Burton, A. C. Physical principles of circulatory phenomena: The physical equilibria of the heart and blood vessels. In: Handbook of Physiology, Section 2, Circulation 1. Washington, DC: American Physiological Society, 1962, pp. 94.

    Google Scholar 

  3. Carew, T. E., R. N. Vaishnav, and D. J. Patel. Compressibility of the arterial wall. Circ. Res. 22:61-68, 1968.

    Google Scholar 

  4. Carmines, D. V., J. H. McElhaney, and R. Stack. A piece-wise non-linear elastic stress expression of human and pig coronary arteries tested in vitro. J. Biomech. 24:899-906, 1992.

    Google Scholar 

  5. Dobrin, P. B., and A. A. Rovick. Influence of vascular smooth muscle on contractile mechanics and elasticity of arteries. Am. J. Physiol. 217:1644-1651, 1969.

    Google Scholar 

  6. Fung, Y. C. Biomechanics. Mechanical Behaviour of Living Tissues, 2nd ed. New York: Springer, 1993, pp. 261-262.

    Google Scholar 

  7. Holzapfel, G. A., T. C. Gasser, and M. Stadler. A structural model for the viscoelastic behavior of arterial walls: Continuum formulation and finite element analysis. Eur. J. Mech. A-Solids 21:441-463, 2002.

    Google Scholar 

  8. Humphrey, J. D. Cardiovascular Solid Mechanics. Cells, Tissues and Organs. New York: Springer, 2002, pp. 329.

    Google Scholar 

  9. James, A. G., A. Green, and G. M. Simpson. Strain energy functions of Rubber. I. Characterization of gum valcanizates. J. Appl. Polym. Sci. 19:2033-2058, 1972.

    Google Scholar 

  10. Lally, C., and P. J. Prendergast. An investigation into the applicability of a Mooney-Rivlin constitutive equation for modelling vascular tissue in cardiovascular stenting procedures. Proceedings of the First International Congress on Computational Biomechanics, Zaragoza, Spain, September 24–26, 2003, pp. 542-550.

  11. Loree, H. M., R. D. Kamm, R. G. Stringfellow, and R. T. Lee. Effects of fibrous cap thickness on peak circumferential stress in model atherosclerotic vessels. Circ. Res. 71:850-858, 1992.

    Google Scholar 

  12. Marc/Mentat Manuals. Santa Ana, CA: MscSoftware.

  13. Mooney, M. A theory of large elastic deformation. J. Appl. Phys. 11:582-592, 1940.

    Google Scholar 

  14. Ogden, R. W., and C. A. J. Schulze-Bauer. Phenomenological and structural aspects of the mechanical response of arteries. In: Mechanics in Biology, edited by J. Casey and G. Bao, BED-Vol. 46, 2000, pp. 25-140.

  15. Patel, D. J., and R. N. Vaishnav. The rheology of large blood vessels. In: Cardiovascular Fluid Dynamics, edited by D. H. Bergel. London: Academic Press, Vol. 2, 1972, pp. 2-65.

    Google Scholar 

  16. Prendergast, P. J., C. Lally, S. Daly, A. J. Reid, T. C. Lee, D. Quinn, and F. Dolan. Analysis of prolapse in cardiovascular stents: A constitutive equation for vascular tissue and finite element modelling. ASME J. Biomechan. Eng. 125:692-699, 2003.

    Google Scholar 

  17. Rogers, C., D. Y. Tseng, J. C. Squire, and E. R. Edelman. Balloon-artery interactions during stent placement. A finite element analysis approach to pressure, compliance, and stent design as contributors to vascular injury. Circ. Res. 84:378-383, 1999.

    Google Scholar 

  18. Sacks, M. S. Biaxial mechanical evaluation of biological materials. J. Elasticity 61:199-246, 2000.

    Google Scholar 

  19. Schulze-Bauer, C. A. J., C. Mörth, and G. A. Holzapfel. Passive biaxial response of aged human iliac arteries. ASME J. Biomech. Eng. 125:395-406, 2003.

    Google Scholar 

  20. Swindle, M. Swine as Models in Biomedical Research. Ames: Iowa State University Press, 1992, pp. 165.

    Google Scholar 

  21. Truesdell, C. A. The mechanical foundations of elasticity and fluid dynamics. J. Ration. Mech. Anal. 1:173-182, 1952.

    Google Scholar 

  22. Weizsacker, H. W., H. Lambert, and K. Pascale. Analysis of the passive mechanical properties of rat carotid arteries. J. Biomech. 16:703-715, 1983.

    Google Scholar 

  23. Weisacker, H. W., and J. G. Pinto. Isotropy and anisotropy of the arterial wall. J. Biomech. 21:477-487, 1988.

    Google Scholar 

  24. Yamada, H. Strength of Biological Materials. Baltimore: Williams and Wilkins, 1970, pp. 113.

    Google Scholar 

  25. van Andel, C. J., P. V. Pistecky, and C. Borst. Mechanical properties of porcine and human arteries: Implications for coronary anastomotic connectors. Ann. Thorac. Surg. 76:58-65, 2003.

    Google Scholar 

  26. Vito, R. P., and S. A. Dixon. Blood vessel constitutive models 1995–2002. Annu. Rev. Biomed. Eng. 5:413-439, 2003.

    Google Scholar 

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Lally, C., Reid, A.J. & Prendergast, P.J. Elastic Behavior of Porcine Coronary Artery Tissue Under Uniaxial and Equibiaxial Tension. Annals of Biomedical Engineering 32, 1355–1364 (2004). https://doi.org/10.1114/B:ABME.0000042224.23927.ce

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