Document Type : Full Research Paper


1 Assistant Professor, Tissue Mechanics Laboratory, Faculty of Biomedical Engineering, Sahand University of Technology, Tabriz, Iran

2 M.Sc. Student, Tissue Mechanics Laboratory, Faculty of Biomedical Engineering, Sahand University of Technology, Tabriz, Iran



Atherosclerosis, a common cardiovascular disease, is among the leading causes of death. Many of the heart attacks results from ruptured atherosclerotic lesion and emboli formation. Then, the susceptibility of the lesion is a key factor in preventing negative outcomes of the rupture. Mechanisms of plaque rupture are under debate. However, a general agreement on the bold contribution of hemodynamic factors including the blood pressure is established. In the current study, biomechanical impacts of plaque calcification procedure and the changed thickness of fibrous cap were investigated. To do so, a cross-section of the constricted coronary artery is reconstructed from the histological images and extruded in the axial direction of the artery to produce the three dimensional configuration of the coronary model. Holzapfel strain energy density function is utilized for mechanical description of the arterial tissue and the fibrous cap which enables us to adopt collagen fiber orientation into the mechanical model. Furthermore, since the constricted vessel configuration is asymmetrical, instead of simplified cylindrical coordinates for collagen orientation, a discrete coordinate system is assigned to every element and respective circumferential, axial and radial directions were assigned. With calcification, plaque is more stable and produces monotonic stress patterns in its vicinity. Also, the fibrous cap thickness plays an important role as a barrier to inhibit stress concentration from soft lipid core and disturb the mechanical loads to the neighboring regions. These two parameters, provide useful insight on mechanical load distribution around an atherosclerotic lesion and the pathway of arterial tissue toward a new homeostasis.


Main Subjects

  1. Wang, M. Naghavi, C. Allen, R. M. Barber, Z. A. Bhutta, A. Carter, D. C. Casey, F. J. Charlson, A. Z. Chen, et al., “Global, regional, and national life expectancy, all-cause mortality, and cause-specific mortality for 249 causes of death, 1980–2015: a systematic analysis for the Global Burden of Disease Study 2015,” Lancet 388, 1459–1544 (Elsevier, 2016).
  2. C. Thompson, A. H. Allam, G. P. Lombardi, L. S. Wann, M. L. Sutherland, J. D. Sutherland, M. A.-T. Soliman, B. Frohlich, D. T. Mininberg, et al., “Atherosclerosis across 4000 years of human history: the Horus study of four ancient populations,” Lancet 381, 1211–1222 (Elsevier, 2013).
  3. S. Berenson, S. R. Srinivasan, W. Bao, W. P. Newman, R. E. Tracy, and W. A. Wattigney, “Association between multiple cardiovascular risk factors and atherosclerosis in children and young adults,” N. Engl. J. Med. 338, 1650–1656 (Mass Medical Soc, 1998).
  4. Ahmadpour-B, A. Nooraeen, M. Tafazzoli-Shadpour, and H. Taghizadeh, “Contribution of atherosclerotic plaque location and severity to the near-wall hemodynamics of the carotid bifurcation: an experimental study and FSI modeling,” Biomech. Model. Mechanobiol. 20, 1–17 (Springer, 2021).
  5. Teng, Y. Zhang, Y. Huang, J. Feng, J. Yuan, Q. Lu, M. P. F. Sutcliffe, A. J. Brown, Z. Jing, et al., “Material properties of components in human carotid atherosclerotic plaques: A uniaxial extension study,” Acta Biomater. 10, 5055–5063 (2014).
  6. R. MAGAREY, “The pathogenesis of atherosclerosis,” Med. J. Aust. 42, 1049–1052 (Elsevier, 1955).
  7. A. Holzapfel, J. J. Mulvihill, E. M. Cunnane, and M. T. Walsh, “Computational approaches for analyzing the mechanics of atherosclerotic plaques: A review,” J. Biomech. 47, 859–869 (2014).
  8. D. Richardson, M. J. Davies, and G. V. R. R. Born, “Influence of Plaque Configuration and Stress Distribution on Fissuring of Coronary Atherosclerotic Plaques,” Lancet 334, 941–944 (Elsevier, 1989).
  9. Taghizadeh, “Mechanobiology of the arterial tissue from the aortic root to the diaphragm,” Med. Eng. Phys. 96, 64–70 (2021).
  10. G. Papaioannou, E. N. Karatzis, M. Vavuranakis, J. P. Lekakis, and C. Stefanadis, “Assessment of vascular wall shear stress and implications for atherosclerotic disease,” Int. J. Cardiol. 113, 12–18 (2006).
  11. S. Lim, T. Vos, A. D. Flaxman, G. Danaei, K. Shibuya, H. Adair-Rohani, M. A. AlMazroa, M. Amann, H. R. Anderson, et al., “A comparative risk assessment of burden of disease and injury attributable to 67 risk factors and risk factor clusters in 21 regions, 1990-2010: A systematic analysis for the Global Burden of Disease Study 2010,” Lancet 380, 2224–2260 (2012).
  12. -Y. Li, V. Taviani, T. Tang, U. Sadat, V. Young, A. Patterson, M. Graves, and J. H. Gillard, “The mechanical triggers of plaque rupture: shear stress vs pressure gradient,” Br. J. Radiol. 82, S39–S45 (The British Institute of Radiology, 2009).
  13. H. Arroyo and R. T. Lee, “Mechanisms of plaque rupture: mechanical and biologic interactions,” Cardiovasc. Res. 41, 369–375 (1999).
  14. Cardoso and S. Weinbaum, “Changing views of the biomechanics of vulnerable plaque rupture: a review,” Ann. Biomed. Eng. 42, 415–431 (Springer, 2014).
  15. C. Akyildiz, L. Speelman, B. van Velzen, R. R. F. Stevens, A. F. W. Van Der Steen, W. Huberts, and F. J. H. Gijsen, “Intima heterogeneity in stress assessment of atherosclerotic plaques,” Interface Focus 8, 20170008 (The Royal Society, 2018).
  16. C. Akyildiz, L. Speelman, H. van Brummelen, M. A. Gutiérrez, R. Virmani, A. van der Lugt, A. F. W. van der Steen, J. J. Wentzel, and F. J. H. Gijsen, “Effects of intima stiffness and plaque morphology on peak cap stress,” Biomed. Eng. Online 10, 1–13 (Springer, 2011).
  17. Tang, R. D. Kamm, C. Yang, J. Zheng, G. Canton, R. Bach, X. Huang, T. S. Hatsukami, J. Zhu, et al., “Image-based modeling for better understanding and assessment of atherosclerotic plaque progression and vulnerability: data, modeling, validation, uncertainty and predictions,” J. Biomech. 47, 834–846 (Elsevier, 2014).
  18. M. Loree, B. J. Tobias, L. J. Gibson, R. D. Kamm, D. M. Small, and R. T. Lee, “Mechanical properties of model atherosclerotic lesion lipid pools.,” Arterioscler. Thromb. a J. Vasc. Biol. 14, 230–234 (Am Heart Assoc, 1994).
  19. Taghizadeh and M. Tafazzoli-Shadpour, “Characterization of mechanical properties of lamellar structure of the aortic wall: Effect of aging,” J. Mech. Behav. Biomed. Mater. 65 (2017).
  20. R. Douglas, A. J. Brown, J. H. Gillard, M. R. Bennett, M. P. F. Sutcliffe, and Z. Teng, “Impact of Fiber Structure on the Material Stability and Rupture Mechanisms of Coronary Atherosclerotic Plaques,” Ann. Biomed. Eng. 45, 1462–1474 (Springer, 2017).
  21. Noble, K. D. Carlson, E. Neumann, B. Lewis, D. Dragomir-Daescu, A. Lerman, A. Erdemir, and M. D. Young, “Finite element analysis in clinical patients with atherosclerosis,” J. Mech. Behav. Biomed. Mater. 125, 104927 (Elsevier, 2022).
  22. Helou, A. Bel‐Brunon, C. Dupont, W. Ye, C. Silvestro, M. Rochette, A. Lucas, A. Kaladji, and P. Haigron, “Influence of balloon design, plaque material composition, and balloon sizing on acute post angioplasty outcomes: an implicit Finite Element Analysis,” Int. j. numer. method. biomed. eng. (Wiley Online Library, 2021).
  23. Tian, Z. Wang, Y. Liu, J. C. Eickhoff, K. W. Eliceiri, and N. C. Chesler, “Validation of an arterial constitutive model accounting for collagen content and crosslinking,” Acta Biomater. 31, 276–287 (Elsevier, 2016).
  24. Cacho, P. J. Elbischger, J. F. Rodríguez, M. Doblaré, and G. A. Holzapfel, “A constitutive model for fibrous tissues considering collagen fiber crimp,” Int. J. Non. Linear. Mech. 42, 391–402 (Elsevier, 2007).
  25. S. Sacks, “Incorporation of experimentally-derived fiber orientation into a structural constitutive model for planar collagenous tissues,” J. Biomech. Eng. 125, 280–287 (2003).
  26. C. Gasser, R. W. Ogden, and G. A. Holzapfel, “Hyperelastic modelling of arterial layers with distributed collagen fibre orientations,” J. R. Soc. interface 3, 15–35 (2005).
  27. Weisbecker, C. Viertler, D. M. Pierce, and G. A. Holzapfel, “The role of elastin and collagen in the softening behavior of the human thoracic aortic media.,” J. Biomech. 46, 1859–1865 (United States, United States, 2013).
  28. Taghizadeh, M. Tafazzoli-Shadpour, M. B. Shadmehr, and N. Fatouraee, “Evaluation of biaxial mechanical properties of aortic media based on the lamellar microstructure,” Materials (Basel). 8, 302–316 (2015).
  29. C. Akyildiz, H. H. G. Hansen, H. A. Nieuwstadt, L. Speelman, C. L. De Korte, A. F. W. van der Steen, and F. J. H. Gijsen, “A framework for local mechanical characterization of atherosclerotic plaques: combination of ultrasound displacement imaging and inverse finite element analysis,” Ann. Biomed. Eng. 44, 968–979 (Springer, 2016).
  30. Madani, A. Bakhaty, J. Kim, Y. Mubarak, and M. R. K. Mofrad, “Bridging finite element and machine learning modeling: stress prediction of arterial walls in atherosclerosis,” J. Biomech. Eng. 141 (American Society of Mechanical Engineers Digital Collection, 2019).
  31. -K. K. Chai, A. C. Akyildiz, L. Speelman, F. J. H. H. Gijsen, C. W. J. J. Oomens, M. R. H. M. H. M. van Sambeek, A. van der Lugt, F. P. T. T. Baaijens, A. van der Lugt, et al., “Local anisotropic mechanical properties of human carotid atherosclerotic plaques - Characterisation by micro-indentation and inverse finite element analysis,” J. Mech. Behav. Biomed. Mater. 43, 59–68 (2015).
  32. Karimi, M. Navidbakhsh, S. Faghihi, A. Shojaei, and K. Hassani, “A finite element investigation on plaque vulnerability in realistic healthy and atherosclerotic human coronary arteries,” Proc. Inst. Mech. Eng. Part H J. Eng. Med. 227, 148–161 (IMECHE, 2012).
  33. Versluis, A. J. Bank, and W. H. Douglas, “Fatigue and plaque rupture in myocardial infarction,” J. Biomech. 39, 339–347 (Elsevier, 2006).
  34. -Y. Li, S. Howarth, R. A. Trivedi, J. M. U-King-Im, M. J. Graves, A. Brown, L. Wang, and J. H. Gillard, “Stress analysis of carotid plaque rupture based on in vivo high resolution MRI,” J. Biomech. 39, 2611–2622 (2006).
  35. Taghizadeh, M. Tafazzoli-Shadpour, and M. B. Shadmehr, “Analysis of arterial wall remodeling in hypertension based on lamellar modeling,” J. Am. Soc. Hypertens. 9, 735–744 (2015).
  36. Maehara, G. S. Mintz, J. M. Ahmed, S. Fuchs, M. T. Castagna, A. D. Pichard, L. F. Satler, R. Waksman, W. O. Suddath, et al., “An intravascular ultrasound classification of angiographic coronary artery aneurysms,” Am. J. Cardiol. 88, 365–370 (Elsevier, 2001).
  37. Ohayon, 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,” Biomech. Appl. to Comput. Assist. Surg. 37, 225–241 (Research Signpost, 2005).
  38. Sadat, Z.-Y. Li, V. E. Young, M. J. Graves, J. R. Boyle, E. A. Warburton, K. Varty, E. O’Brien, and J. H. Gillard, “Finite element analysis of vulnerable atherosclerotic plaques: a comparison of mechanical stresses within carotid plaques of acute and recently symptomatic patients with carotid artery disease,” J. Neurol. Neurosurg. Psychiatry 81, 286–289 (BMJ Publishing Group Ltd, 2010).
  39. Shi, J. Gao, Q. Lv, H. Cai, F. Wang, R. Ye, and X. Liu, “Calcification in Atherosclerotic Plaque Vulnerability: Friend or Foe?,” in Front. Physiol. 11 (2020).
  40. Matsumoto and K. Hayashi, “Stress and strain distribution in hypertensive and normotensive rat aorta considering residual strain,” J. Biomech. Eng. 118, 62–73 (United States, United States, 1996).
  41. Huang, R. Virmani, H. Younis, A. P. Burke, R. D. Kamm, and R. T. Lee, “The impact of calcification on the biomechanical stability of atherosclerotic plaques,” Circulation 103, 1051–1056 (Am Heart Assoc, 2001).
  42. Zareh, 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,” Cardiovasc. Syst. 3 (Citeseer, 2015).