Annals of Biomedical Engineering

, Volume 39, Issue 9, pp 2445–2455 | Cite as

Inelasticity of Human Carotid Atherosclerotic Plaque

  • Eoghan Maher
  • Arthur Creane
  • Sherif Sultan
  • Niamh Hynes
  • Caitríona Lally
  • Daniel J. Kelly


Little mechanical test data exists regarding the inelastic behavior of atherosclerotic plaques. As a result finite element (FE) models of stenting procedures commonly use hyperelastic material models to describe the soft tissue response thus limiting the accuracy of the model to the expansion stage of stent implantation and leave them unable to predict the lumen gain. In this study, cyclic mechanical tests were performed to characterize the inelastic behavior of fresh human carotid atherosclerotic plaque tissue due to radial compressive loading. Plaques were classified clinically as either mixed (M), calcified (Ca), or echolucent (E). An approximately linear increase in the plastic deformation was observed with increases in the peak applied strain for all plaque types. While calcified plaques generally appeared stiffest, it was observed that the clinical classification of plaques had no significant effect on the magnitude of permanent deformation on unloading. The test data was characterized using a constitutive model that accounts for both permanent deformation and stress softening to describe the compressive plaque behavior on unloading. Material constants are reported for individual plaques as well as mean values for each plaque classification. This data can be considered as a first step in characterizing the inelastic behavior of atherosclerotic plaques and could be used in combination with future mechanical data to improve the predictive capabilities of FE models of angioplasty and stenting procedures particularly in relation to lumen gain.


Mechanical properties Plastic deformation Permanent deformation Stress softening Plaque Constitutive model 



This material is based on works supported by the Science Foundation Ireland under Grant No. 07/RFP/ENMF660.


  1. 1.
    Auer, M., R. Stollberger, P. Regitnig, F. Ebner, and G. A. Holzapfel. In vitro angioplasty of atherosclerotic human femoral arteries: analysis of the geometrical changes in the individual tissues using MRI and image processing. Ann. Biomed. Eng. 38:1276–1287, 2010.PubMedCrossRefGoogle Scholar
  2. 2.
    Balzani, D., J. Schroder, and D. Gross. Simulation of discontinuous damage incorporating residual stresses in circumferentially overstretched atherosclerotic arteries. Acta Biomater. 2:609–618, 2006.PubMedCrossRefGoogle Scholar
  3. 3.
    Barrett, S. R., M. P. Sutcliffe, S. Howarth, Z. Y. Li, and J. H. Gillard. Experimental measurement of the mechanical properties of carotid atherothrombotic plaque fibrous cap. J. Biomech. 41(9):1995–2002, 2009.Google Scholar
  4. 4.
    Calvo, B., E. Pena, M. A. Martinez, and M. Doblare. An uncoupled directional damage model for fibred biological soft tissues. Formulation and computational aspects. Int. J. Numer. Methods Eng. 69:2037–2057, 2007.CrossRefGoogle Scholar
  5. 5.
    Chua, S. N. D., B. J. MacDonald, and M. S. J. Hashmi. Finite element simulation of slotted tube (stent) with the presence of plaque and artery by balloon expansion. J. Mater. Process. Technol. 155–156:1772–1779, 2004.Google Scholar
  6. 6.
    Delfino, A., N. Stergiopulos, J. E. Moore, Jr., and J. J. Meister. Residual strain effects on the stress field in a thick wall finite element model of the human carotid bifurcation. J. Biomech. 30:777–786, 1997.PubMedCrossRefGoogle Scholar
  7. 7.
    Diani, J., M. Brieu, and J. M. Vacherand. A damage directional constitutive model for Mullins effect with permanent set and induced anisotropy. Eur. J. Mech. A Solids 25:483–496, 2006.CrossRefGoogle Scholar
  8. 8.
    Dorfmann, A., and R. W. Ogden. A constitutive model for the Mullins effect with permanent set in particle-reinforced rubber. Int. J. Solids Struct. 41:1855–1878, 2004.CrossRefGoogle Scholar
  9. 9.
    Early, M., and D. J. Kelly. The role of vessel geometry and material properties on the mechanics of stenting in the coronary and peripheral arteries. Proc. Inst. Mech. Eng. H 224:465–476, 2010.PubMedGoogle Scholar
  10. 10.
    Early, M., C. Lally, P. J. Prendergast, and D. J. Kelly. Stresses in peripheral arteries following stent placement: a finite element analysis. Comput. Methods Biomech. Biomed. Eng. 12:25–33, 2009.CrossRefGoogle Scholar
  11. 11.
    Ebenstein, D. M., D. Coughlin, J. Chapman, C. Li, and L. A. Pruitt. Nanomechanical properties of calcification, fibrous tissue, and hematoma from atherosclerotic plaques. J. Biomed. Mater. Res. A 91:1028–1037, 2009.PubMedGoogle Scholar
  12. 12.
    Emery, J. L., J. H. Omens, and A. D. McCulloch. Strain softening in rat left ventricular myocardium. J. Biomech. Eng. 119:6–12, 1997.PubMedCrossRefGoogle Scholar
  13. 13.
    Gasser, T. C., and G. A. Holzapfel. A rate-independent elastoplastic model for biological fiber-reinforced composites at finite strains: continuum basis, algorithmic formulation and finite element implementation. Comput. Mech. 29:340–360, 2002.CrossRefGoogle Scholar
  14. 14.
    Gasser, T. C., and G. A. Holzapfel. Finite element modeling of balloon angioplasty by considering overstretch of remnant non-diseased tissues in lesions. Comput. Mech. 40:47–60, 2007.CrossRefGoogle Scholar
  15. 15.
    Gil, R., C. Di Mario, F. Prati, C. von Birgelen, P. Ruygrok, J. R. Roelandt, and P. W. Serruys. Influence of plaque composition on mechanisms of percutaneous transluminal coronary balloon angioplasty assessed by ultrasound imaging. Am. Heart J. 131:591–597, 1996.PubMedCrossRefGoogle Scholar
  16. 16.
    Hokanson, J., and S. Yazdani. A constitutive model of the artery with damage. Mech. Res. Commun. 24:151–159, 1997.CrossRefGoogle Scholar
  17. 17.
    Holzapfel, G. A. Nonlinear Solid Mechanics. New York: John Wiley & Sons, 2000.Google Scholar
  18. 18.
    Holzapfel, G. A., G. Sommer, and P. Regitnig. Anisotropic mechanical properties of tissue components in human atherosclerotic plaques. J. Biomech. Eng. 126:657–665, 2004.PubMedCrossRefGoogle Scholar
  19. 19.
    Honye, J., D. J. Mahon, A. Jain, C. J. White, S. R. Ramee, J. B. Wallis, A. al-Zarka, and J. M. Tobis. Morphological effects of coronary balloon angioplasty in vivo assessed by intravascular ultrasound imaging. Circulation 85:1012–1025, 1992.PubMedGoogle Scholar
  20. 20.
    Kiousis, D. E., T. C. Gasser, and G. A. Holzapfel. A numerical model to study the interaction of vascular stents with human atherosclerotic lesions. Ann. Biomed. Eng. 35:1857–1869, 2007.PubMedCrossRefGoogle Scholar
  21. 21.
    Lally, C., F. Dolan, and P. J. Prendergast. Cardiovascular stent design and vessel stresses: a finite element analysis. J. Biomech. 38:1574–1581, 2005.PubMedCrossRefGoogle Scholar
  22. 22.
    Lee, R. T., A. J. Grodinsky, and E. H. Frank. Structure-dependent dynamic mechanical behavior of fibrous caps from human atherosclerotic plaques. Circulation 83:1764–1770, 1991.PubMedGoogle Scholar
  23. 23.
    Lee, R. T., S. G. Richardson, H. M. Loree, A. J. Grodinsky, S. A. Gharib, F. J. Schoen, and N. Pandian. Prediction of mechanical properties of human atherosclerotic tissue by high-frequency intravascular ultrasound imaging. An in vitro study. Arterioscl. Thromb. Vasc. Biol. 12:1–5, 1992.CrossRefGoogle Scholar
  24. 24.
    Li, J., D. Mayau, and V. Lagarrigue. A constitutive model dealing with damage due to cavity growth and the Mullins effect in rubber-like materials under triaxial loading. J. Mech. Phys. Solids 56:933–973, 2008.CrossRefGoogle Scholar
  25. 25.
    Li, D., and A. M. Robertson. A structural multi-mechanism damage model for cerebral arterial tissue. J. Biomech. Eng. 131:101013, 2009.PubMedCrossRefGoogle Scholar
  26. 26.
    Liang, D. K., D. Z. Yang, M. Qi, and W. Q. Wang. Finite element analysis of the implantation of a balloon-expandable stent in a stenosed artery. Int. J. Cardiol. 104:314–318, 2005.PubMedCrossRefGoogle Scholar
  27. 27.
    Loree, H. M., A. J. Grodinsky, S. Y. Park, L. J. Gibson, and R. T. Lee. Static circumferential tangential modulus of human atherosclerotic tissue. J. Biomech. 27:195–204, 1994.PubMedCrossRefGoogle Scholar
  28. 28.
    Maher, E., A. Creane, S. Sultan, N. Hynes, C. Lally, and D. J. Kelly. Tensile and compressive properties of fresh human carotid atherosclerotic plaques. J. Biomech. 42:2760–2767, 2009.PubMedCrossRefGoogle Scholar
  29. 29.
    Miehe, C. Discontinuous and continuous damage evolution in Ogden-type large-strain elastic materials. Eur. J. Mech. A Solids 14:697–720, 1995.Google Scholar
  30. 30.
    Migliavacca, F., L. Petrini, P. Massarotti, S. Schievano, F. Auricchio, and G. Dubini. Stainless and shape memory alloy coronary stents: a computational study on the interaction with the vascular wall. Biomech. Model. Mechanobiol. 2:205–217, 2004.PubMedCrossRefGoogle Scholar
  31. 31.
    Mortier, P., G. A. Holzapfel, M. De Beule, D. Van Loo, Y. Taeymans, P. Segers, P. Verdonck, and B. Verhegghe. A novel simulation strategy for stent insertion and deployment in curved coronary bifurcations: comparison of three drug-eluting stents. Ann. Biomed. Eng. 38:88–99, 2010.PubMedCrossRefGoogle Scholar
  32. 32.
    Naghdi, P. M., and J. A. Tarpp. The significance of formulating plasticity theory with reference to loading surfaces in strain space. Int. J. Eng. Sci. 13:785–797, 1975.CrossRefGoogle Scholar
  33. 33.
    Nicolaides, A. N., S. K. Kakkos, M. Griffin, G. Geroulakos, and E. Bashardi. Ultrasound plaque characterisation, genetic markers and risks. Pathophysiol. Haemost. Thromb. 32:371–377, 2002.PubMedCrossRefGoogle Scholar
  34. 34.
    Ogden, R. W., and D. G. Roxburgh. A pseudo-elastic model for the Mullins effect in filled rubber. Proc. R. Soc. Lond. A 455:2861–2877, 1999.CrossRefGoogle Scholar
  35. 35.
    Pena, E., B. Calvo, M. A. Martinez, and M. Doblare. On finite-strain damage of viscoelastic-fibred materials. Applications to soft biological tissues. Int. J. Numer. Methods Eng. 74:1198–1218, 2008.CrossRefGoogle Scholar
  36. 36.
    Pena, E., and M. Doblare. An anisotropic pseudo-elastic approach for modelling Mullins effect in fibrous biological materials. Mech. Res. Commun. 36:784–790, 2009.CrossRefGoogle Scholar
  37. 37.
    Pericevic, I., C. Lally, D. Toner, and D. J. Kelly. The influence of plaque composition on underlying arterial wall stress during stent expansion: the case for lesion-specific stents. Med. Eng. Phys. 31:428–433, 2009.PubMedCrossRefGoogle Scholar
  38. 38.
    Robertson, S. W., C. P. Cheng, and M. K. Razavi. Biomechanical response of stented carotid arteries to swallowing and neck motion. J. Endovasc. Ther. 15:663–671, 2008.PubMedCrossRefGoogle Scholar
  39. 39.
    Simo, J. C., and J. W. Ju. Strain- and stress-based continuum damage models—II. Computational aspects. Int. J. Solids Struct. 7:841–869, 1987.CrossRefGoogle Scholar
  40. 40.
    Tanaka, E., and H. Yamada. Inelastic constitutive modeling for blood vessels based on viscoplasticity. Front. Med. Biol. Eng. 2:177–180, 1990.PubMedGoogle Scholar
  41. 41.
    Tegos, T. J., K. J. Alomiris, M. M. Sabetai, E. Kalodiki, and A. N. Nicolaides. Significance of sonographic tissue and surface characteristics of carotid plaques. Am. J. Neuroradiol. 22:1605–1612, 2001.PubMedGoogle Scholar
  42. 42.
    Topoleski, L. D., and N. V. Salunke. Mechanical behavior of calcified plaques: a summary of compression and stress-relaxation experiments. Z. Kardiol. 89(Suppl 2):85–91, 2000.PubMedCrossRefGoogle Scholar
  43. 43.
    Topoleski, L. D. T., N. V. Salunke, and W. J. Mergner. Composition- and history-dependent radial compressive behavior of human atherosclerotic plaque. J. Biomed. Mater. Res. 35:117–127, 1997.PubMedCrossRefGoogle Scholar
  44. 44.
    Volokh, K. Y., and D. A. Vorp. A model of growth and rupture of abdominal aortic aneurysm. J. Biomech. 41:1015–1021, 2008.PubMedCrossRefGoogle Scholar
  45. 45.
    Vos, A. W., M. A. Linsen, J. T. Marcus, J. C. van den Berg, J. A. Vos, J. A. Rauwerda, and W. Wisselink. Carotid artery dynamics during head movements: a reason for concern with regard to carotid stenting? J. Endovasc. Ther. 10:862–869, 2003.PubMedCrossRefGoogle Scholar
  46. 46.
    Waller, B. F. The eccentric coronary atherosclerotic plaque: morphologic observations and clinical relevance. Clin. Cardiol. 12:14–20, 1989.PubMedCrossRefGoogle Scholar
  47. 47.
    Woo, C., W. Kinm, and J. Kwon. A study on the material properties and fatigue life prediction of natural rubber component. Mater. Sci. Eng. A 483–484:376–381, 2008.Google Scholar
  48. 48.
    Wu, W., M. Qi, X. P. Liu, D. Z. Yang, and W. Q. Wang. Delivery and release of nitinol stent in carotid artery and their interactions: a finite element analysis. J. Biomech. 40:3034–3040, 2007.PubMedCrossRefGoogle Scholar
  49. 49.
    Wulandana, R., and A. M. Robertson. An inelastic multi-mechanism constitutive equation for cerebral arterial tissue. Biomech. Model. Mechanobiol. 4:235–248, 2005.PubMedCrossRefGoogle Scholar
  50. 50.
    Zahedmanesh, H., D. John Kelly, and C. Lally. Simulation of a balloon expandable stent in a realistic coronary artery—determination of the optimum modelling strategy. J. Biomech. 43:2126–2132, 2010.PubMedCrossRefGoogle Scholar

Copyright information

© Biomedical Engineering Society 2011

Authors and Affiliations

  • Eoghan Maher
    • 1
  • Arthur Creane
    • 2
  • Sherif Sultan
    • 3
    • 4
  • Niamh Hynes
    • 3
    • 4
  • Caitríona Lally
    • 2
  • Daniel J. Kelly
    • 1
  1. 1.Trinity Centre for Bioengineering, School of EngineeringTrinity CollegeDublinIreland
  2. 2.School of Mechanical and Manufacturing EngineeringDublin City UniversityDublin 9Ireland
  3. 3.Western Vascular Institute, Department of Vascular & Endovascular SurgeryUniversity College Hospital GalwayGalwayIreland
  4. 4.Department of Vascular & Endovascular SurgeryGalway ClinicGalwayIreland

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