Advanced Search
Article Contents
Article Contents

Effect of residual stress on peak cap stress in arteries

Abstract Related Papers Cited by
  • Vulnerable plaques are a subset of atherosclerotic plaques that are prone to rupture when high stresses occur in the cap. The roles of residual stress, plaque morphology, and cap stiffness on the cap stress are not completely understood. Here, arteries are modeled within the framework of nonlinear elasticity as incompressible cylindrical structures that are residually stressed through differential growth. These structures are assumed to have a nonlinear, anisotropic, hyperelastic response to stresses in the media and adventitia layers and an isotropic response in the intima and necrotic layers. The effect of differential growth on the peak stress is explored in a simple, concentric geometry and it is shown that axial differential growth decreases the peak stress in the inner layer. Furthermore, morphological risk factors are explored. The peak stress in residually stressed cylinders is not greatly affected by changing the thickness of the intima. The thickness of the necrotic layer is shown to be the most important morphological feature that affects the peak stress in a residually stressed vessel.
    Mathematics Subject Classification: Primary: 92C10; Secondary: 74A10.


    \begin{equation} \\ \end{equation}
  • [1]

    A. Akyildiz, L. Speelman, H. Nieuwstadt, S. J. W. Van Der and F. Gijsen, Influence of plaque geometry on peak cap stress, Proceedings of the ASME 2011 Summer Bioegnineering ConferenceArtery Research, 5 (2011), 159-160.doi: 10.1016/j.artres.2011.10.047.


    A. Akyildiz, L. Speelman, H. van Brummelen, M. Gutiérrez, R. Virmani, A. van der Lugt, A. Van Der Steen, J. Wentzel and F. Gijsen, Effects of intima stiffness and plaque morphology on peak cap stress, Biomedical Engineering Online, 10 (2011), 1-13.doi: 10.1186/1475-925X-10-25.


    R. Baldewsing, C. De Korte, J. Schaar, F. Mastik and Van Der Steen, Finite element modeling and intravascular ultrasound elastography of vulnerable plaques: Parameter variation, Ultrasonics, 42 (2004), 723-729.doi: 10.1016/j.ultras.2003.11.017.


    S. Barrett, M. Sutcliffe, S. Howarth, Z. Li and J. Gillard, Experimental measurement of the mechanical properties of carotid atherothrombotic plaque fibrous cap, Journal of Biomechanics, 42 (2009), 1650-1655.doi: 10.1016/j.jbiomech.2009.04.025.


    E. Falk, K. S. Prediman and F. Valenin, Coronary Plaque Disruption, Circulation, 92 (1995), 657-671.doi: 10.1161/01.CIR.92.3.657.


    G. Finet, J. Ohayon and G. Rioufol, Biomechanical interaction between cap thickness, lipid core composition and blood pressure in vulnerable coronary plaque: Impact on stability or instability, Coronary artery disease, 15 (2004), 13-20.doi: 10.1097/00019501-200402000-00003.


    A. Goriely and R. Vandiver, On the mechanical stability of growing arteries, IMA Journal of Applied Mathematics, 75 (2010), 549-570.doi: 10.1093/imamat/hxq021.


    G. Holzapfel, Nonlinear Solid Mechanics: A Continuum Approach for Engineering, John Wiley & Sons Ltd. 2000.


    G. Holzapfel, T. Gasser and R. Ogden, Comparison of a multi-layer structural model for arterial walls with a Fung-type model, and issues of material stability, Journal of Biomechanical Engineering, 126 (2004), 264-275.doi: 10.1115/1.1695572.


    G. Holzapfel, G. Sommer, M. Auer, P. Regitnig and R. Ogden, Layer-specific 3D residual deformations of human aortas with non-atherosclerotic intimal thickening, Annals of Biomedical Engineering, 35 (2007), 530-545.doi: 10.1007/s10439-006-9252-z.


    G. Holzapfel, G. Sommer, C. Gasser and P. Regitnig, Determination of layer-specific mechanical properties of human coronary arteries with nonatherosclerotic intimal thickening and related constitutive modeling, American Journal of Physiology-Heart and Circulatory Physiology, 289 (2005), H2048-H2058.doi: 10.1152/ajpheart.00934.2004.


    P. Kalita and R. Schaefer, Mechanical models of artery walls, Archives of Computational Methods in Engineering, 15 (2008), 1-36.doi: 10.1007/s11831-007-9015-5.


    E. Lee, Elastic-plastic deformation at finite strains, J. Appl. Mech., 36 (1968), 1-6.doi: 10.1115/1.3564580.


    R. Lee, A. Grodzinsky, E. Frank, R. Kamm and F. Schoen, Structure-dependent dynamic mechanical behavior of fibrous caps from human atherosclerotic plaques, Circulation, 83 (1991), 1764-1770.doi: 10.1161/01.CIR.83.5.1764.


    R. Lee, S. Richardson, H. Loree, A. Grodzinsky, S. Gharib, F. Schoen and N. Pandian, Prediction of mechanical properties of human atherosclerotic tissue by high-frequency intravascular ultrasound imaging. An in vitro study, Arteriosclerosis, Thrombosis, and Vascular Biology, 12 (1992), 1-5.doi: 10.1161/01.ATV.12.1.1.


    M. Li, J. Beech-Brandt, L. John, P. Hoskins and W. Easson, Numerical analysis of pulsatile blood flow and vessel wall mechanics in different degrees of stenoses, Journal of Biomechanics, 40 (2007), 3715-3724.doi: 10.1016/j.jbiomech.2007.06.023.


    A. Li, S. Howarth and R. Trivedi, Stress analysis of carotid plaque rupture based on in vivo high resolution MRI, Journal of Biomechanics, 39 (2006), 2611-2622.doi: 10.1016/j.jbiomech.2005.08.022.


    S. Liu and Y. Fung, Zero-stress states of arteries, Journal of Biomechanical Engineering, 110 (1988), 82-84.doi: 10.1115/1.3108410.


    H. Loree, R. Kamm, R. Stringfellow and R. Lee, Effects of fibrous cap thickness on peak circumferential stress in model atherosclerotic vessels, Circulation research, 71 (1992), 850-858.doi: 10.1161/01.RES.71.4.850.


    H. Loree, B. Tobias, L. Gibson, R. Kamm, D. Small and R. Lee, Mechanical properties of model atherosclerotic lesion lipid pools, Arteriosclerosis, Thrombosis, and Vascular Biology, 14 (1994), 230-234.doi: 10.1161/01.ATV.14.2.230.


    M. Naghavi, P. Libby, E. Falk, S. Casscells, S. Litovsky, J. Rumberger, J. Badimon, C. Stefanadis, P. Moreno and P. Pasterkamp, From vulnerable plaque to vulnerable patient a call for new definitions and risk assessment strategies: Part I, Circulation, 108 (2003), 1664-1672.doi: 10.1161/01.CIR.0000087480.94275.97.


    J. Ohayon, N. Mesnler, A. Brolsat, J. Toczek, L. Rlou and Pl Tracqui, Elucidating atherosclerotic vulnerable plaque rupture by modeling cross substitution of ApoE mouse and human plaque components stiffnesses, Biomech. Model. Mechanobiol., 11 (2011), 801-813.doi: 10.1007/s10237-011-0353-8.


    J. Ohayon, O. Dubreuil, P. Tracqui, S. Le Floc'h, G. Rioufol, L. Chalabreysse, F. Thivolet, R. Pettigrew and G. Finet, Influence of residual stress/strain on the biomechanical stability of vulnerable coronary plaques: Potential impact for evaluating the risk of plaque rupture, American Journal of Physiology-Heart and Circulatory Physiology, 293 (2007), H1987-H1996.doi: 10.1152/ajpheart.00018.2007.


    J. Ohayon, G. Finet, A. Gharib, D. Herzka, P. Tracqui, J. Heroux, G. Rioufol, M. Kotys, A. Elagha and R. Pettigrew, Necrotic core thickness and positive arterial remodeling index: Emergent biomechanical factors for evaluating the risk of plaque rupture, American Journal of Physiology-Heart and Circulatory Physiology, 295 (2008), H717-H727.doi: 10.1152/ajpheart.00005.2008.


    A. Rachev, Theoretical study of the effect of stress-dependent remodeling on arterial geometry under hypertensive conditions, Journal of Biomechanics, 30 (1997), 819-827.doi: 10.1016/S0021-9290(97)00032-8.


    E. Rodriguez, A. Hoger and A. McCulloch, Stress-dependent finite growth in soft elastic tissues, Journal of Biomechanics, 27 (1994), 455-467.doi: 10.1016/0021-9290(94)90021-3.


    U. Sadat, Z. Teng and J. Gillard, Biomechanical structural stresses of atherosclerotic plaques, Expert Review of Cardiovascular Therapy, 8 (2010), 1469-1481.doi: 10.1586/erc.10.130.


    L. Taber, Biomechanical growth laws for muscle tissue, Journal of Theoretical Biology, 193 (1998), 201-213.doi: 10.1006/jtbi.1997.0618.


    L. Taber, A model for aortic growth based on fluid shear and fiber stresses, Journal of Biomechanical Engineering, 120 (1998), 348-354.doi: 10.1115/1.2798001.


    L. Taber and D. Eggers, Theoretical study of stress-modulated growth in the aorta, Journal of Theoretical Biology, 180 (1996), 343-357.doi: 10.1006/jtbi.1996.0107.


    L. Taber and J. Humphrey, Stress-modulated growth, residual stress, and vascular heterogeneity, Journal of Biomechanical Engineering, 123 (2001), 528-535.doi: 10.1115/1.1412451.


    D. Tang, Z. Teng, G. Canton, C. Yang, M. Ferguson, X. Huang, J. Zheng, P. Woodard and C. Yuan, Sites of rupture in human atherosclerotic carotid plaques are associated with high structural stresses, Stroke, 40 (2009), 3258-3263.


    D. Tang, C. Yang, J. Zheng, P. Woodard, G. Sicard, J. Saffitz and C. Yuan, 3D MRI-based multicomponent FSI models for atherosclerotic plaques, Annals of Biomedical Engineering, 32 (2004), 947-960.


    Z. Teng, G. Canton, C. Yuan, M. Ferguson, C. Yang, X. Huang, J. Zheng, P. Woodard and D. Tang, 3D critical plaque wall stress is a better predictor of carotid plaque rupture sites than flow shear stress: An in vivo MRI-based 3D FSI study, Journal of Biomechanical Engineering, 132 (2010), 031007.


    R. Vaishnav and J. Vossoughi, Residual stress and strain in aortic segments, Journal of Biomechanics, 20 (1987), 235-237.doi: 10.1016/0021-9290(87)90290-9.


    J. Valenta, J. Svoboda, D. Valerianova and K. Vitek, Residual strain in human atherosclerotic coronary arteries and age related geometrical changes, Biomedical Materials and Engineering, 9 (1999), 311-318.


    Y. Vengrenyuk, S. Carlier, S. Xanthos, L. Cardos, P. Ganatos, R. Virmani, S. Einav, L. Gilchrist and S. Weinbaum, A hypothesis for vulnerable plaque rupture due to stress-induced debonding around cellular microcalcifications in thin fibrous caps, PNAS, 103 (2006), 14678-14683.doi: 10.1073/pnas.0606310103.

  • 加载中

Article Metrics

HTML views() PDF downloads(33) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint