Skip to main content

Mechanics of Atherosclerotic Plaques: Effect of Heart Rate



Atherosclerotic plaques are highly heterogeneous, nonlinear materials with uncharacteristic structural behaviors. It is well known that mechanics of atherosclerotic plaques significantly depend on plaque geometry, location, composition, and loading conditions. There is no question that atherosclerotic plaques are viscoelastic. Plaques are characterized as the buildup of low-density lipoprotein cholesterol, macrophages, monocytes, and foam cells at a place of inflammation inside arterial walls. Lipid core and fibrous cap are the two major ingredients that are frequently used for the identification of main constituting quantities of atherosclerotic plaques. The lipid core contains of debris from dead cells, esterified cholesterol and cholesterol crystals. The fibrous cap contains smooth muscle cells and collagen fibers. All these materials contribute to the viscoelastic properties of atherosclerotic plaques. Computational studies have shown great potential to characterize this mechanical behavior. Different types of plaque morphologies and mechanical properties have been used in a computational platform to estimate the stability of rupture-prone plaques and detect their locations. In this study for the first time to the best of authors' knowledge, we hypothesize that heart rate is also one of the major factors that should be taken into account while mechanics of plaques is studied.


We propose a tunable viscoelastic constitutive material model for the fibrous cap tissue in order to calculate the peak cap stress in normal physiological (dynamic) conditions while heart rate changes from 60 bpm to 150 bpm in 2D plane stress models. A critical discussion on stress distribution in the fibrous cap area is made with respect to heart rate for the first time.


Results strongly suggest the viscoelastic properties of the fibrous cap tissue and heart rate together play a major role in the estimation of the pick cap stress values.


The results of current study may provide a better understanding on the mechanics of vulnerable atherosclerotic plaques and that any experimental methods assessing the viscoelasticity of plaque composition during progression are highly desirable.

This is a preview of subscription content, access via your institution.

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8


  1. 1.

    Akyildiz, A., L. Speelman, H. Nieuwstadt, H. van Brummelen, R. Virmani, A. van der Lugt, et al. The effects of plaque morphology and material properties on peak cap stress in human coronary arteries. Comput. Methods Biomech. Biomed. Eng. 2015.

    Google Scholar 

  2. 2.

    Akyildiz, A., L. Speelman, H. van Brummelen, M. Gutierrez, R. Virmani, A. van der Lugt, and F. Gijsen. Effects of intima stiffness and plaque morphology on peak cap stress. Biomed. Eng. Online 10(1):25, 2011.

    Article  Google Scholar 

  3. 3.

    Bentzon, J. F., F. Otsuka, R. Virmani, and E. Falk. Mechanisms of plaque formation and rupture. Circ. Res. 114(12):1852–1866, 2014.

    Article  Google Scholar 

  4. 4.

    Cardoso, L., A. Kelly-Arnold, N. Maldonado, D. Laudier, and S. Weinbaum. Effect of tissue properties, shape and orientation of microcalcifications on vulnerable cap stability using different hyperelastic constitutive models. J. Biomech. 47(4):870–877, 2014.

    Article  Google Scholar 

  5. 5.

    Casscells, W., M. Naghavi, and J. Willerson. Vulnerable atherosclerotic plaque—a multifocal disease. Circulation 107(16):2072–2075, 2003.

    Article  Google Scholar 

  6. 6.

    Cilla, M., E. Peña, and M. A. Martínez. 3D computational parametric analysis of eccentric atheroma plaque: Influence of axial and circumferential residual stresses. Biomech. Model. Mechanobiol. 11(7):1001–1013, 2012.

    Article  Google Scholar 

  7. 7.

    Farb, A., A. Burke, A. Tang, Y. Liang, P. Mannan, J. Smialek, et al. Coronary plaque erosion without rupture into a lipid core—A frequent cause of coronary thrombosis in sudden coronary death. Circulation 93(7):1354–1363, 1996.

    Article  Google Scholar 

  8. 8.

    Fayad, Z. Computed tomography and magnetic resonance imaging for noninvasive coronary angiography and plaque imaging: current and potential future concepts. Circulation 106(15):2026–2034, 2002.

    Article  Google Scholar 

  9. 9.

    Fuster, V., P. Moreno, Z. Fayad, R. Corti, and J. Badimon. Atherothrombosis and high-risk plaque part I: Evolving concepts. J. Am. Coll. Cardiol. 46(6):937–954, 2005.

    Article  Google Scholar 

  10. 10.

    Heiland, V. M., C. Forsell, J. Roy, U. Hedin, and T. C. Gasser. Identification of carotid plaque tissue properties using an experimental-numerical approach. J. Mech. Behav. Biomed. Mater. 27:226–238, 2013.

    Article  Google Scholar 

  11. 11.

    Huang, X., C. Yang, J. Zheng, R. Bach, D. Muccigrosso, P. Woodard, and D. Tang. Higher critical plaque wall stress in patients who died of coronary artery disease compared with those who died of other causes: A 3D FSI study based on ex vivo MRI of coronary plaques. J. Biomech. 47(2):432–437, 2014.

    Article  Google Scholar 

  12. 12.

    Hurst, J. In Hurst’s the heart (13th ed.). New York: McGraw-Hill Medical, 2011.

    Google Scholar 

  13. 13.

    Kiousis, D., S. Rubinigg, M. Auer, G. Holzapfel, and Hållfasthetslära (Inst.), Skolan för teknikvetenskap (SCI). Biomekanik. A methodology to analyze changes in lipid core and calcification onto fibrous cap vulnerability: the human atherosclerotic carotid bifurcation as an illustratory example. J. Biomech. Eng.-Trans. ASME 131(12):121002, 2009.

    Article  Google Scholar 

  14. 14.

    Mohammadi, H., and K. Mequanint. An inverse numerical approach for modeling aortic heart valve leaflet tissue oxygenation. J. Cardiovasc. Eng. Technol. 3(1):73–79, 2012.

    Article  Google Scholar 

  15. 15.

    Mohammadi, H., and K. Mequanint. Effect of stress intensity factor in evaluation of instability of atherosclerotic plaque. J. Mech. Med. Biol. 2014.

    Google Scholar 

  16. 16.

    Ohayon, J., G. Finet, A. M. Gharib, D. A. Herzka, P. Tracqui, J. Heroux, and R. I. Pettigrew. Necrotic core thickness and positive arterial remodeling index: Emergent biomechanical factors for evaluating the risk of plaque rupture. Am. J. Physiol. Heart Circ. Physiol. 295(2):717–727, 2008.

    Article  Google Scholar 

  17. 17.

    Ohayon, I., G. Finet, F. Treyve, G. Rioufol, and O. Dubreuil. A three-dimensional finite element analysis of stress distribution in a coronary atherosclerotic plaque: in vivo prediction of plaque rupture location. In: Biomechanics applied to computer assisted surgery, edited by Y. Payan. Trivandrum: Research Signpost, 2005, pp. 225–241.

    Google Scholar 

  18. 18.

    Veress, A. I., J. F. Cornhill, K. A. Powell, E. E. Herderick, and J. D. Thomas. Finite element modeling of atherosclerotic plaque. In Paper presented at the Proceedings of computers in cardiology conference, pp. 791–794. 1993.

  19. 19.

    Zareh, M., G. Fradet, G. Naser, and H. Mohammadi. Are two-dimensional images sufficient to assess the atherosclerotic plaque vulnerability: a viscoelastic and anisotropic finite element model. Cardio. Vasc. Syst. 3(1):3, 2015.

    Article  Google Scholar 

Download references


The authors acknowledge the University of British Columbia and NSERC (Discovery Grant) for financial support.

Conflict of interest

The authors declare that they have no conflict of interest.


NSERC/Discovery Grant and University of British Columbia.

Author information



Corresponding author

Correspondence to Hadi Mohammadi.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Associate Editor Ajit P. Yoganathan oversaw the review of this article.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zareh, M., Katul, R. & Mohammadi, H. Mechanics of Atherosclerotic Plaques: Effect of Heart Rate. Cardiovasc Eng Tech 10, 344–353 (2019).

Download citation


  • Atherosclerotic plaque
  • Plaque vulnerability
  • Plaque instability
  • Pulsatile flow
  • Finite element method
  • Viscoelasticity
  • Heart rate