Annals of Biomedical Engineering

, Volume 44, Issue 4, pp 993–1007 | Cite as

On the Compressibility of Arterial Tissue

  • D. R. Nolan
  • J. P. McGarryEmail author


Arterial tissue is commonly assumed to be incompressible. While this assumption is convenient for both experimentalists and theorists, the compressibility of arterial tissue has not been rigorously investigated. In the current study we present an experimental-computational methodology to determine the compressibility of aortic tissue and we demonstrate that specimens excised from an ovine descending aorta are significantly compressible. Specimens are stretched in the radial direction in order to fully characterise the mechanical behaviour of the tissue ground matrix. Additionally biaxial testing is performed to fully characterise the anisotropic contribution of reinforcing fibres. Due to the complexity of the experimental tests, which entail non-uniform finite deformation of a non-linear anisotropic material, it is necessary to implement an inverse finite element analysis scheme to characterise the mechanical behaviour of the arterial tissue. Results reveal that ovine aortic tissue is highly compressible; an effective Poisson’s ratio of 0.44 is determined for the ground matrix component of the tissue. It is also demonstrated that correct characterisation of material compressibility has important implications for the calibration of anisotropic fibre properties using biaxial tests. Finally it is demonstrated that correct treatment of material compressibility has significant implications for the accurate prediction of the stress state in an artery under in vivo type loading.


Compressibility Anisotropy Hyperelasticity Arterial tissue Mechanical properties 



The authors wish to acknowledge funding from Science Foundation Ireland under project SFI-12/IP/1723. Furthermore we acknowledge funding from the Irish Research Council and the College of Engineering and Informatics at NUI, Galway. The authors wish to thank Noel Reynods and Prof. Michel Destrade for insightful discussions on this topic.


  1. 1.
    Anderson, T. L. Fracture mechanics: fundamentals and applications. Boca Raton: CRC press, 2005.Google Scholar
  2. 2.
    Boutouyrie, P., D. P. Germain, A.-I. Tropeano, B. Laloux, F. Carenzi, M. Zidi, X. Jeunemaitre, and S. Laurent. Compressibility of the carotid artery in patients with pseudoxanthoma elasticum. Hypertension. 38:1181–1184, 2001.CrossRefPubMedGoogle Scholar
  3. 3.
    Canham, P. B., H. M. Finlay, J. G. Dixon, D. R. Boughner, and A. Chen. Measurements from light and polarised light microscopy of human coronary arteries fixed at distending pressure. Cardiovasc. Res. 23:973–982, 1989.CrossRefPubMedGoogle Scholar
  4. 4.
    Carew, T. E., R. N. Vaishnav, and D. J. Patel. Compressibility of the arterial wall. Circ. Res. 23:61–68, 1968.CrossRefPubMedGoogle Scholar
  5. 5.
    Chuong, C., and Y. Fung. Three-dimensional stress distribution in arteries. J. Biomech. Eng. 105:268–274, 1983.CrossRefPubMedGoogle Scholar
  6. 6.
    Chuong, C., and Y. Fung. Compressibility and constitutive equation of arterial wall in radial compression experiments. J. Biomech. 17:35–40, 1984.CrossRefPubMedGoogle Scholar
  7. 7.
    Conway, C., F. Sharif, J. McGarry, and P. McHugh. A computational test-bed to assess coronary stent implantation mechanics using a population-specific approach. Cardiovasc. Eng. Technol. 3:374–387, 2012.CrossRefGoogle Scholar
  8. 8.
    Di Puccio, F., S. Celi, and P. Forte. Review of experimental investigations on compressibility of arteries and introduction of a new apparatus. Exp. Mech. 52:895–902, 2012.CrossRefGoogle Scholar
  9. 9.
    Dobrin, P., and A. Rovick. Static elastic properties of dog carotid arterial wall. Fed. Proc. 26:439, 1967.Google Scholar
  10. 10.
    Dobrin, P. B. Biaxial anisotropy of dog carotid artery: estimation of circumferential elastic modulus. J. Biomech. 19:351–358, 1986.CrossRefPubMedGoogle Scholar
  11. 11.
    Elliott, D. M., and L. A. Setton. Anisotropic and inhomogeneous tensile behavior of the human anulus fibrosus: experimental measurement and material model predictions. J. Biomech. Eng. 123:256–263, 2001.CrossRefPubMedGoogle Scholar
  12. 12.
    Finlay, H., L. McCullough, and P. Canham. Three-dimensional collagen organization of human brain arteries at different transmural pressures. J. Vasc. Res. 32:301–312, 1995.PubMedGoogle Scholar
  13. 13.
    Finlay, H. M., P. Whittaker, and P. B. Canham. Collagen organization in the branching region of human brain arteries. Stroke 29: 1595–1601, 1998.CrossRefPubMedGoogle Scholar
  14. 14.
    Gasser, T. C., R. W. Ogden, and G. A. Holzapfel. Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. J. R. Soc. Interface 3:15–35, 2006.CrossRefPubMedPubMedCentralGoogle Scholar
  15. 15.
    Ghriallais, R. N., and M. Bruzzi. Effects of knee flexion on the femoropopliteal artery: a computational study. Med. Eng. Phys. 35: 1620–1628, 2013.CrossRefGoogle Scholar
  16. 16.
    Hayashi, K., H. Handa, S. Nagasawa, A. Okumura, and K. Moritake. Stiffness and elastic behavior of human intracranial and extracranial arteries, J. Biomech. 13:175–184, 1980.CrossRefPubMedGoogle Scholar
  17. 17.
    Holzapfel, G. A. Nonlinear solid mechanics: a continuum approach for engineers. Wiley: Chichester, 2000.Google Scholar
  18. 18.
    Holzapfel, G. A., and R. W. Ogden. On planar biaxial tests for anisotropic nonlinearly elastic solids. A continuum mechanical framework. Math. Mech. Solids 14:474–489, 2009.CrossRefGoogle Scholar
  19. 19.
    Holzapfel, G. A., T. C. Gasser, and R. W. Ogden. A new constitutive framework for arterial wall mechanics and a comparative study of material models. J. Elast. Phys. Sci. Solids 61:1–48, 2000.CrossRefGoogle Scholar
  20. 20.
    Huang, C.-Y., A. Stankiewicz, G. A. Ateshian, and V. C. Mow. Anisotropy, inhomogeneity, and tension–compression nonlinearity of human glenohumeral cartilage in finite deformation. J. Biomech. 38:799–809, 2005.CrossRefPubMedPubMedCentralGoogle Scholar
  21. 21.
    Humphrey, J., D. Vawter, and R. Vito. Pseudoelasticity of excised visceral pleura. J. Biomech. Eng. 109:115–120, 1987.CrossRefPubMedGoogle Scholar
  22. 22.
    Humphrey, J. D. Cardiovascular solid mechanics: cells, tissues, and organs. Springer: New York, 2002.Google Scholar
  23. 23.
    Lagarias, J., J. Reeds, M. Wright, and P. Wright. Convergence properties of the nelder–mead simplex method in low dimensions. SIAM J. Optim. 9:112–147, 1998.CrossRefGoogle Scholar
  24. 24.
    Lawton, R. W. The thermoelastic behavior of isolated aortic strips of the dog. Circ. Res. 2:344–353, 1954.CrossRefPubMedGoogle Scholar
  25. 25.
    Misra, J., and S. Chakravarty. Study of compressibility in vascular rheology. Rheol. Acta 19:381–388, 1980.CrossRefGoogle Scholar
  26. 26.
    Nelder, J. A., and R. Mead. A simplex method for function minimization. Comput. J. 7:308–313, 1965.CrossRefGoogle Scholar
  27. 27.
    Nolan, D., and J. McGarry. On the correct interpretation of measured force and calculation of material stress in biaxial tests. J. Mech. Behav. Biomed. Mater. 2015. doi: 10.1016/j.jmbbm.2015.08.019.PubMedGoogle Scholar
  28. 28.
    Nolan, D., A. Gower, M. Destrade, R. Ogden, and J. McGarry. A robust anisotropic hyperelastic formulation for the modelling of soft tissue. J. Mech. Behav. Biomed. Mater. 39:48–60, 2014.CrossRefPubMedGoogle Scholar
  29. 29.
    Peña, E., A. P. Del Palomar, B. Calvo, M. Martínez, and M. Doblaré. Computational modelling of diarthrodial joints. physiological, pathological and pos-surgery simulations. Arch. Comput. Methods Eng. 14:47–91, 2007.Google Scholar
  30. 30.
    Raghavan, M., and D. A. Vorp. Toward a biomechanical tool to evaluate rupture potential of abdominal aortic aneurysm: identification of a finite strain constitutive model and evaluation of its applicability. J. Biomech. 33:475–482, 2000.CrossRefPubMedGoogle Scholar
  31. 31.
    Raghavan, M., S. Trivedi, A. Nagaraj, D. McPherson, and K. Chandran. Three-dimensional finite element analysis of residual stress in arteries. Ann. Biomed. Eng., 32, 257–263, 2004.CrossRefPubMedGoogle Scholar
  32. 32.
    Sacks, M. S. Biaxial mechanical evaluation of planar biological materials. J. Elast. Phys. Sci. Solids 61:199–246, 2000.Google Scholar
  33. 33.
    Schneider, C. A., W. S. Rasband, and K. W. Eliceiri. NIH image to ImageJ: 25 years of image analysis. Nat. Methods 9:671–675, 2012.CrossRefPubMedGoogle Scholar
  34. 34.
    Silver, F., D. Christiansen, and C. Buntin. Mechanical properties of the aorta: a review. Crit. Rev. Biomed. Eng. 17:323–358, 1988.Google Scholar
  35. 35.
    Silver, F. H., P. B. Snowhill, and D. J. Foran. Mechanical behavior of vessel wall: a comparative study of aorta, vena cava, and carotid artery. Ann. Biomed. Eng. 31:793–803, 2003.CrossRefPubMedGoogle Scholar
  36. 36.
    Smith, H. E., T. J. Mosher, B. J. Dardzinski, B. G. Collins, C. M. Collins, Q. X. Yang, V. J. Schmithorst, and M. B. Smith. Spatial variation in cartilage t2 of the knee. J. Magn. Reson. Imaging 14:50–55, 2001.CrossRefPubMedGoogle Scholar
  37. 37.
    Sokolis, D. P., E. M. Kefaloyannis, M. Kouloukoussa, E. Marinos, H. Boudoulas, and P. E. Karayannacos. A structural basis for the aortic stress–strain relation in uniaxial tension. J. Biomech. 39:1651–1662, 2006.CrossRefPubMedGoogle Scholar
  38. 38.
    Storåkers, B. On material representation and constitutive branching in finite compressible elasticity. J. Mech. Phys. Solids 34:125–145, 1986.CrossRefGoogle Scholar
  39. 39.
    Sun, W., and M. S. Sacks. Finite element implementation of a generalized fung-elastic constitutive model for planar soft tissues. Biomech. Model. Mechanobiol. 4:190–199, 2005.CrossRefPubMedGoogle Scholar
  40. 40.
    Takamizawa, K., and K. Hayashi. Strain energy density function and uniform strain hypothesis for arterial mechanics. J. Biomech. 20:7–17, 1987.CrossRefPubMedGoogle Scholar
  41. 41.
    Tickner, E. G., and A. H. Sacks. A theory for the static elastic behavior of blood vessels. Biorheology 4:151, 1967.PubMedGoogle Scholar
  42. 42.
    Vaishnav, R. N., and J. Vossoughi. Residual stress and strain in aortic segments. J. Biomech. 20:235–239, 1987.CrossRefPubMedGoogle Scholar
  43. 43.
    Vilarta, R., and B. D. C. Vidal. Anisotropic and biomechanical properties of tendons modified by exercise and denervation: aggregation and macromolecular order in collagen bundles. Matrix 9:55–61, 1989.CrossRefPubMedGoogle Scholar
  44. 44.
    Volokh, K. Compressibility of arterial wall in ring-cutting experiments. Mol. Cell. Biomech. 3:35, 2006.PubMedGoogle Scholar
  45. 45.
    Vorp, D. A., M. Raghavan, and M. W. Webster. Mechanical wall stress in abdominal aortic aneurysm: influence of diameter and asymmetry. J. Vasc. Surg. 27:632–639, 1998.CrossRefPubMedGoogle Scholar
  46. 46.
    Yosibash, Z., I. Manor, I. Gilad, and U. Willentz. Experimental evidence of the compressibility of arteries. J. Mech. Behav. Biomed. Mater. 39:339–354, 2014.CrossRefPubMedGoogle Scholar

Copyright information

© Biomedical Engineering Society 2015

Authors and Affiliations

  1. 1.Biomedical EngineeringNational University of IrelandGalwayIreland

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