Three-Dimensional Numerical Simulation of Plaque Formation in Arteries

  • N. Filipovic
  • N. Meunier
  • D. Fotiadis
  • O. Parodi
  • M. KojicEmail author


Atherosclerosis develops from oxidized low-density lipoprotein (LDL) molecules. When oxidized LDL evolves in plaque formation within an artery wall, a series of reactions occur to repair the damage to the artery wall caused by oxidized LDL. The body’s immune system responds to damage to the artery wall caused by oxidized LDL by sending specialized white blood cells-macrophages (Mphs) to absorb the oxidized-LDL and form specialized foam cells. Macrophages accumulate inside arterial intima. Also smooth muscle cells accumulate in the atherosclerotic arterial intima, where they proliferate and secrete extracellular matrix to generate a fibrous cap.

In this study, a model of plaque formation on the pig left anterior descending (LAD) coronary artery is simulated numerically using a specific animal data obtained from IVUS and histological recordings. The 3D bloodflow is described by the Navier–Stokes equations, together with the continuity equation. Mass transfer within the blood lumen and through the arterial wall is coupled with the blood flow and is modeled by a convection-diffusion equation. The LDL transports in lumen of the vessel and through the vessel tissue (which has a mass consumption term) are coupled by Kedem–Katchalsky equations. The inflammatory process is modeled using three additional reaction-diffusion partial differential equations. A full three-dimensional model was created which includes blood flow and LDL concentration, as well as plaque formation. Matching of IVUS and histological animal data is performed using a 3D histological image reconstruction and 3D deformation of elastic body. Computed concentration of macrophages indicates that there is a newly formed matter in the intima, especially in the LAD 15 mm region from bifurcation. Understanding and prediction of the evolution of atherosclerotic plaques either into vulnerable or stable plaques are major tasks for the medical community.


Atherosclerosis Plaque formation Computer modeling IVUS Histology 



This study was funded by a grant from FP7-ICT-2007 project (grant agreement 224297, ARTreat) and BioIRC – The Methodist Hospital Research Institute, Houston.


  1. 1.
    Libby P (2002) Inflammation in atherosclerosis. Nature 420(6917):868--874Google Scholar
  2. 2.
    Osterud B, Bjorklid E (2003) Role of monocytes in atherogenesis. Physiol Rev 83(4):1069--112Google Scholar
  3. 3.
    Quarteroni A, Veneziani A, Zunino P (2002) Mathematical and numerical modeling of the solute dynamics in blood flow and arterial walls. SIAM J Numer Anal 39:1488–1511MathSciNetCrossRefGoogle Scholar
  4. 4.
    Tarbell JM (2003) Mass transport in arteries and the localization of atherosclerosis. Annu Rev Biomed Eng 5:79–118CrossRefGoogle Scholar
  5. 5.
    Zunino P (2002) Mathematical and numerical modeling of mass transfer in the vascular system. PhD Thesis, Lausanne, EPFLGoogle Scholar
  6. 6.
    Ross R (2003) Atherosclerosis: a defense mechanism gone away. Am J Pathol 143:987--1002Google Scholar
  7. 7.
    Kedem O, Katchalsky A (1961) A physical interpretation of the phenomenological coefficients of membrane permeability. J Gen Physiol 45:143–179CrossRefGoogle Scholar
  8. 8.
    Kedem O, Katchalsky A (1961) A physical interpretation of the phenomenological coefficients of membrane permeability. J Gen Physiol 45:143–179CrossRefGoogle Scholar
  9. 9.
    Kojic M, Filipovic N, Stojanovic B, Kojic N (2008) Computer modeling in bioengineering: thеoretical background, examples and software. Wiley, ChichesterCrossRefGoogle Scholar
  10. 10.
    Boynard M, Calvez V, Hamraoui A, Meunier N, Raoult A (2009) Mathematical modelling of earliest stage of atherosclerosis. In: COMPDYN 2009 – SEECCM 2009, RhodesGoogle Scholar
  11. 11.
    Calvez V, Ebde A, Meunier N, Raoult A (2008) Mathematical modelling of the atherosclerotic plaque formation. ESAIM Proc 28:1–12MathSciNetCrossRefGoogle Scholar
  12. 12.
    Filipovic N, Meunier N, Boynard M, Kojic M, Fotiadis D (2010) A 3D computer simulation of plaque formation and development in coronary artery. In: Proceedings of the ASME 2010 First Global Congress on nano engineering for medicine and biology (NEMB), Houston, 7–10 February 2010Google Scholar
  13. 13.
    Filipovic N, Mijailovic S, Tsuda A, Kojic M (2006) An implicit algorithm within the arbitrary Lagrangian–Eulerian formulation for solving incompressible fluid flow with large boundary motions. Comput Methods Appl Mech Eng 195:6347–6361CrossRefzbMATHGoogle Scholar
  14. 14.
    ARTreat FP7-224297 EU project 2008–2011. Multi-level patient-specific artery and atherogenesis model for outcome prediction, decision support treatment, and virtual hand-on training,,
  15. 15.
    Chavent G (2010) Nonlinear least squares for inverse problems, nonlinear least squares for inverse problems theoretical foundations and step-by-step guide for applications. Springer, New York (second print)Google Scholar

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© Springer New York 2014

Authors and Affiliations

  • N. Filipovic
    • 1
    • 2
  • N. Meunier
    • 3
  • D. Fotiadis
    • 4
  • O. Parodi
    • 5
  • M. Kojic
    • 6
    • 7
    Email author
  1. 1.University of KragujevacKragujevacSerbia
  2. 2.R&D Center for BioengineeringKragujevacSerbia
  3. 3.University Paris DescartesParisFrance
  4. 4.University of IoanninaIoanninaGreece
  5. 5.CNRPisaItaly
  6. 6.The Department of NanomedicineThe Methodist Hospital Research InstituteHoustonUSA
  7. 7.BioIRC Bioengineering Research and Development CenterKragujevacSerbia

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