Skip to main content
SpringerLink
Log in

Computer Modeling of Atherosclerosis

  • Chapter
  • First Online:
Computational Medicine in Data Mining and Modeling

Abstract

Atherosclerosis is a progressive disease characterized by inflammation, monocyte-macrophage migration, and lipid accumulation in the vascular wall. The three-dimensional blood flow is governed 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 the convection-diffusion equation. LDL transport in lumen of the vessel is described by Kedem-Katchalsky equations. The inflammatory process is solved using three additional reaction–diffusion partial differential equations. We presented basic 2D axisymmetric and 3D benchmark examples. The fitting of parameters for different models is described. Computational results and comparison with animal experiments are presented. Also plaque formation and progression model was applied on the patient data clinical data. Finally, the main conclusions of the work performed are given, with connecting between modeling and experimental work. Matching of plaque location and progression in time between experimental and computer model shows a potential benefit for future prediction of this vascular decease using computer simulation.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 119.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. P. Libby, Inflammation in atherosclerosis. Nature, 2002, 868–874.

    Google Scholar 

  2. J. Loscalzo& A.I. Schafer, Thrombosis and Hemorrhage (Third edition. Lippincott Williams & Wilkins, Philadelphia, 2003).

    Google Scholar 

  3. J.M. Tarbell, Mass transport in arteries and the localization of atherosclerosis, Annual Review of Biomedical Engineering, 5, 2003, 79–118.

    Article  Google Scholar 

  4. P. Zunino, Mathematical and numerical modeling of mass transfer in the vascular system. (PhD thesis, Lausanne, Switzerland: EPFL, 2002).

    Google Scholar 

  5. A. Quarteroni, A. Veneziani, P. Zunino, Mathematical and numerical modeling of the solute dynamics in blood flow and arterial walls, SIAM Journal of Numerical Analysis, 39, 2002, 1488–1511.

    Article  MathSciNet  Google Scholar 

  6. M.R. Kaazempur-Mofrad, C.R. Ethier, Mass transport in an anatomically realistic human right coronary artery, Ann Biomed Eng 29, 2001, 121–127.

    Article  Google Scholar 

  7. S. Wada, M. Koujiya, T. Karino, Theoretical study of the effect of local flow disturbances on the concentration of low-density lipoproteins at the luminal surface of end-to-end anastomosed vessels, Med BiolEngComput 40, 2002, 576–587.

    Google Scholar 

  8. D. K. Stangeby, C.R. Ethier, Computational analysis of coupled blood-wall arterial LDL transport, J BiomechEng-T ASME 124, 2002, 1–8.

    Article  Google Scholar 

  9. N. Sun, N.B. Wood, A.D. Hughes, S.A.M. Thom, X.Y. Xu, Fluid-wall modelling of mass transfer in an axisymmetric stenosis: effects of shear dependent transport properties, Ann Biomed Eng 34, 2006, 1119–1128.

    Article  Google Scholar 

  10. L. Ai, K. Vafai, A coupling model for macromolecule transport in a stenosed arterial wall, Int J. Heat Mass Tran 49, 2006, 1568–1591.

    Article  MATH  Google Scholar 

  11. U. Olgac, V. Kurtcuoglu, V. Poulikakos, Computational modeling of coupled blood-wall mass transport of LDL: effects of local wall shear stress, Am J. Physiol Heart CircPhysiol 294, 2008, 909–919.

    Article  Google Scholar 

  12. R. Ross, Atherosclerosis: a defense mechanism gone awry, Am J Pathol., 143, 1993, 987–1002.

    Google Scholar 

  13. N. Filipovic, N. Meunier, and M. Kojic, PAK-Athero, Specialized three-dimensional PDE software for simulation of plaque formation and development inside the arteries, University of Kragujevac, 34000 Kragujevac, Serbia, 2010.

    Google Scholar 

  14. Goldstein J., Anderson R., Brown M., “Coated pits, coated vesicles, and receptor-mediated endocytosis.”Nature, 1979, Vol. 279, pp. 679–684.

    Article  Google Scholar 

  15. Bratzler R. L., Chisolm G.M., Colton C. K., Smith K. A., Lees R. S., “The distribution of labeled low-density lipoproteins across the rabbit thoracic aorta in vivo.” Atherosclerosis, 1977, Vol. 28, pp. 289–307.

    Article  Google Scholar 

  16. Kojic, M., Filipovic, N., Stojanovic B., Kojic N., (2008) Computer modeling in bioengineering: Theoretical Background, Examples and Software, John Wiley and Sons, Chichester, England.

    Book  Google Scholar 

  17. Brooks A.N., Hughes T.J.R., “Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier–Stokes equations.”Comput. Meths. Appl. Mech. Engrg., 1982, Vol. 32, pp. 199–259.

    Article  MathSciNet  MATH  Google Scholar 

  18. Filipovic N., Mijailovic S., Tsuda A., Kojic M. “An Implicit Algorithm Within The Arbitrary Lagrangian–Eulerian Formulation for Solving Incompressible Fluid Flow With Large Boundary Motions.” Comp. Meth. Appl. Mech. Eng., 2006, Vol. 195, pp. 6347–6361.

    Article  MATH  Google Scholar 

  19. Yuan S.W., Finkelstein A.B.., “Laminar pipe flow with injection and suction through a porous wall.” Transaction of ASME, 1956, Vol. 78, pp. 719–724.

    Google Scholar 

  20. Goh V. K., Lau C. P., Mohlenkamp S., Rumberger J. A., Achenbach A., Budoff M. J., Cardiovascular Ultrasound, 2010, 8:5.

    Google Scholar 

  21. Cheng C., Tempel D., Haperen V. R., Baan A. V. D., Grosveld F., Daemen Mat J.A.P., Krams R., Crom D.R., Atherosclerotic Lesion Size and Vulnerability Are Determined by Patterns of Fluid Shear Stress, Circulation Vol. 113, 2006, pp. 2744–2753

    Article  Google Scholar 

  22. Himburg, H., Grzybowski, D., Hazel, A., LaMack, J. Li X. and Friedman M., Spatial comparison between wall shear stress measures and porcine arterial endothelial permeability. Am J Physiol Hear Circ Pysiol 286, 1916–1922, 2004.

    Google Scholar 

  23. Birukova A.A., K. G. Birukov, K. Smurova, D. Adyshev, K. Kaibuchi, I. Alieva, J. G. Garcia and A. D. Verin. Novel role of microtubules in thrombin-induced endothelial barrier dysfunction. Faseb J. Dec 2004;18(15):1879–1890.

    Google Scholar 

  24. Tai S. C., G. B. Robb and P. A. Marsden. Endothelial nitric oxide synthase: a new paradigm for gene regulation in the injured blood vessel. ArteriosclerThrombVasc Biol. Mar 2004;24(3):405–412.

    Google Scholar 

  25. Vargas C. B., F. F. Vargas, J. G. Pribyl and P. L. Blackshear. Hydraulic conductivity of the endothelial and outer layers of the rabbit aorta. Am J Physiol. Jan 1979;236(1):H53–60.

    Google Scholar 

  26. Rappitsch G., K. Perktold, Pulsatile albumin transport in large arteries: a numerical simulation study, J. Biomech. Eng. 118 (1996) 511–519.

    Article  Google Scholar 

  27. Wada, S., Karino, T., (2000) Computational study on LDL transfer from flowing blood to arterial walls. In: Yamaguchi, T. (Ed.), Clinical Application of Computational Mechanics to the Cardiovascular System. Springer, Berlin, 157–173.

    Chapter  Google Scholar 

  28. Moore J.A., C.R. Ethier, Oxygen mass transfer calculations in large arteries, J. Biomech. Eng. 119 (1997) 469–475.

    Article  Google Scholar 

  29. Stangeby D.K., C.R. Ethier, Coupled computational analysis of arterial LDL transport—effects of hypertension, Comput. Meth. Biomech. Biomed. Eng. 5 (2002) 233–241.

    Article  Google Scholar 

  30. Kedem O., Katchalsky A. (1958): Thermodynamic analysis of the permeability of biological membranes to non-electrolytes. Biochim. Biophys. Acta 27, 229–246

    Article  Google Scholar 

  31. Kedem O., Katchalsky A. (1961): A physical interpretation of the phenomenological coefficients of membrane permeability. J. Gen. Physiol. 45, 143–179

    Article  Google Scholar 

  32. 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, second print, New York.

    Google Scholar 

  33. Oberdan Parodi, Themis Exarchos, Paolo Marraccini, Federico Vozzi, Zarko Milosevic, Dalibor Nikolic, Antonis Sakellarios, Panagiotis Siogkas, Dimitris I. Fotiadis, Nenad Filipovic, 2012, Patient-specific prediction of coronary plaque growth from CTA angiography: a multiscale model for plaque formation and progression, IEEE Trans Inf Technol Biomed. 16(5):952–65.

    Article  Google Scholar 

  34. Sadat U, Teng Z, Young VE, Zhu C, Tang TY, Graves MJ, Gillard JH (2010) Impact of plaque haemorrhage and its age on structural stresses in atherosclerotic plaques of patients with carotid artery disease: an MR imaging-based finite element simulation study. Int J Cardiovasc Imaging DOI 10.1007/s10554-010-9679-z.

    Google Scholar 

  35. Yang C, Tang D and Atluri S (2010) Three-Dimensional Carotid Plaque Progression Simulation Using Meshless Generalized Finite Difference Method Based on Multi-Year MRI Patient-Tracking Data, CMES 57: 51–76

    MathSciNet  MATH  Google Scholar 

  36. Nelder J. and Mead R 1965. “A simplex method for function minimization”, Computer Journal 7 (4): 308–313.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Kragujevac, Kragujevac, Serbia

    Nenad Filipovic

  2. Bioengineering R&D Center, BioIRC, Kragujevac, Serbia

    Nenad Filipovic, Milos Radovic, Velibor Isailovic, Zarko Milosevic, Dalibor Nikolic, Igor Saveljic & Tijana Djukic

  3. University of Ioannina, Ioannina, Greece

    Exarchos Themis & Dimitris Fotiadis

  4. National Research Council, Pisa, Italy

    Oberdan Parodi

Authors
  1. Nenad Filipovic
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Milos Radovic
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Velibor Isailovic
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zarko Milosevic
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Dalibor Nikolic
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Igor Saveljic
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Tijana Djukic
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Exarchos Themis
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Dimitris Fotiadis
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Oberdan Parodi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nenad Filipovic .

Editor information

Editors and Affiliations

  1. Mathematical Institute, Serbian Academy of Science and Arts, Belgrade, Serbia

    Goran Rakocevic

  2. Faculty of Engineering, University of Kragujevac, Kragujevac, Serbia

    Tijana Djukic

  3. Faculty of Engineering, University of Kragujevac, Kragujevac, Serbia

    Nenad Filipovic

  4. School of Electrical Engineering, University of Belgrade, Belgrade, Serbia

    Veljko Milutinović

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media New York

About this chapter

Cite this chapter

Filipovic, N. et al. (2013). Computer Modeling of Atherosclerosis. In: Rakocevic, G., Djukic, T., Filipovic, N., Milutinović, V. (eds) Computational Medicine in Data Mining and Modeling. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8785-2_7

Download citation

  • DOI: https://doi.org/10.1007/978-1-4614-8785-2_7

  • Published:

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-8784-5

  • Online ISBN: 978-1-4614-8785-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation