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Inelasticity of Human Carotid Atherosclerotic Plaque

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Abstract

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.

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References

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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. 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.

    Article  Google Scholar 

  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. 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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    PubMed  CAS  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    PubMed  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  16. Hokanson, J., and S. Yazdani. A constitutive model of the artery with damage. Mech. Res. Commun. 24:151–159, 1997.

    Article  Google Scholar 

  17. Holzapfel, G. A. Nonlinear Solid Mechanics. New York: John Wiley & Sons, 2000.

    Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    PubMed  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  Google Scholar 

  25. Li, D., and A. M. Robertson. A structural multi-mechanism damage model for cerebral arterial tissue. J. Biomech. Eng. 131:101013, 2009.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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. 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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  Google Scholar 

  40. Tanaka, E., and H. Yamada. Inelastic constitutive modeling for blood vessels based on viscoplasticity. Front. Med. Biol. Eng. 2:177–180, 1990.

    PubMed  CAS  Google Scholar 

  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.

    PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  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.

    Article  PubMed  CAS  Google Scholar 

  44. Volokh, K. Y., and D. A. Vorp. A model of growth and rupture of abdominal aortic aneurysm. J. Biomech. 41:1015–1021, 2008.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

  46. Waller, B. F. The eccentric coronary atherosclerotic plaque: morphologic observations and clinical relevance. Clin. Cardiol. 12:14–20, 1989.

    Article  PubMed  CAS  Google Scholar 

  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. 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.

    Article  PubMed  Google Scholar 

  49. Wulandana, R., and A. M. Robertson. An inelastic multi-mechanism constitutive equation for cerebral arterial tissue. Biomech. Model. Mechanobiol. 4:235–248, 2005.

    Article  PubMed  CAS  Google Scholar 

  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.

    Article  PubMed  Google Scholar 

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Acknowledgments

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

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Correspondence to Daniel J. Kelly.

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Associate Editor Peter E. McHugh oversaw the review of this article.

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Maher, E., Creane, A., Sultan, S. et al. Inelasticity of Human Carotid Atherosclerotic Plaque. Ann Biomed Eng 39, 2445–2455 (2011). https://doi.org/10.1007/s10439-011-0331-4

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