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Governing Equations of Blood Flow and Respective Numerical Methods

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Computational Cardiovascular Mechanics

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Abstract

Coronary heart disease which is a major cause of heart failure in the United States has a focal nature which is due to local hemodynamic disturbances. The computational fluid dynamics (CFD) method has become a powerful approach to understand blood flows in the cardiovascular system and its local features. This chapter outlines the field equations for blood flow and some of the approaches for numerical solutions. Specifically, the text focuses on the finite difference (FD) and finite element (FE) methods with applications to blood flow dynamics in coronary arteries.

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References

  1. Fung YC. Biomechanics: circulation, 4th Ed. New York: Springer-Verlag, 1996.

    Google Scholar 

  2. Perktold K, Resch M, Florian H. Pulsatile non-Newtonian flow characteristics in a three-dimensional human carotid bifurcation model. ASME J Biomech Eng. 1991;113:464–75.

    Article  Google Scholar 

  3. Buchanan JR Jr, Kleinstreuer C, Truskey GA, Lei M. Relation between non-uniform hemodynamics and sites of altered permeability and lesion growth at the rabbit aorto-celiac junction. Atherosclerosis. 1999;143:27–40.

    Article  Google Scholar 

  4. Kleinstreuer C, Hyun S, Buchanan JR Jr, Longest PW, Archie JP Jr, Truskey GA. Hemodynamic parameters and early intimal thickening in branching blood vessels. Crit Rev Biomed Eng. 2001;29:1–64.

    Article  Google Scholar 

  5. Berger SA, Jou LD. Flows in stenotic vessels. Annu Rev Fluid Mech. 2002;32:347–82.

    Article  MathSciNet  Google Scholar 

  6. He X, Ku DN. Pulsatile flow in the human left coronary artery bifurcation: average conditions. ASME J Biomech Eng. 1996;118:74–82.

    Article  Google Scholar 

  7. Ku DN. Blood flow in arteries. Annu Rev Fluid Mech. 1997;29:399–434.

    Article  MathSciNet  Google Scholar 

  8. Ramaswamy SD, Vigmostad SC, Wahle A, Lia YG., Olszewski M.E, Braddy KC, Brennan TMH., Rossen JD, Sonka M., Chandran KB. Fluid dynamics in a human left anterior descending coronary artery with arterial motion. Ann Biomed Eng. 2004;32:1628–41.

    Article  Google Scholar 

  9. Bird RB, Stewart WE, Lightfoot EN. Transport phenomena. New York: John Willey & Sons, 1962.

    Google Scholar 

  10. Panton RL. Incompressible flow. New York: John Willey & Sons, 1984.

    MATH  Google Scholar 

  11. Acheson DJ. Elementary Fluid Dynamics. Oxford applied mathematics and computing science series. 1990.

    Google Scholar 

  12. Li BQ. Discontinuous finite elements in fluid dynamics and heat transfer. London: Springer-Verlag, 2006.

    MATH  Google Scholar 

  13. Nichols WW. O’Rourke MF. McDonald’s blood flow in arteries: theoretical, experimental and clinical principles, 4th Ed. New York: Oxford University Press, 1998.

    Google Scholar 

  14. Patankar SV. Numerical heat transfer and fluid flow, Hemisphere, 1980.

    Google Scholar 

  15. Fletcher CAJ. Computational techniques for fluid dynamics, Volume I. Berlin: Springer-Verlag, 1991a.

    Book  Google Scholar 

  16. Fletcher CAJ. Computational techniques for fluid dynamics, Volume II. Berlin: Springer-Verlag, 1991b.

    Book  Google Scholar 

  17. Ferziger JH, Peric M. Computational methods for fluid dynamics. New York: Springer-Verlag, 2002.

    Book  MATH  Google Scholar 

  18. Huo Y, Kassab GS. A hybrid one-dimensional/Womersley model of pulsatile blood flow in the entire coronary arterial tree. Am J Physiol Heart Circ Physiol. 2007;292:H2623–33.

    Article  Google Scholar 

  19. Guo X, Kassab GS. Distribution of stress and strain along the porcine aorta and coronary arterial tree. Am J Physiol Heart Circ Physiol. 2004;286:H2361–8.

    Article  Google Scholar 

  20. Huo Y, Kassab GS. Pulsatile blood flow in the entire coronary arterial tree: theory and experiment. Am J Physiol Heart Circ Physiol. 2006;291:H1074–87.

    Article  Google Scholar 

  21. Huo Y, Kassab GS. A scaling law of vascular volume. Biophys J. 2009b;96:347–53.

    Article  Google Scholar 

  22. Kassab GS, Rider CA, Tang NJ, Fung YC. Morphometry of pig coronary arterial trees. Am J Physiol Heart Circ Physiol. 1993;265:H350–65.

    Google Scholar 

  23. Huo Y, Wischgoll T, Kassab GS. Flow patterns in three-dimensional porcine epicardial coronary arterial tree. Am J Physiol Heart Circ Physiol. 2007;293:H2959–70.

    Article  Google Scholar 

  24. Huo Y, Kassab GS. The scaling of blood flow resistance: from a single vessel to the entire distal tree. Biophys J. 2009a;96:339–46.

    Article  Google Scholar 

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Acknowledgments

These studies were supported in part by the National Institute of Health–National Heart, Lung, and Blood Institute Grants 2 R01 HL055554-11, HL084529, and HL087235 (Kassab, G. S.) and the American Heart Association Scientist Development Grant 0830181 N (Huo, Y.).

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Authors and Affiliations

  1. Department of Biomedical Engineering, Surgery, and Cellular and Integrative Physiology, IUPUI, 46202, Indianapolis, IN, USA

    Yunlong Huo

  2. Weldon School of Biomedical Engineering, Purdue University, 47906, West Lafayette, IN, USA

    Ghassan S. Kassab

  3. Department of Biomedical Engineering Department of Surgery Department of Cellular and Integrative Physiology Indiana Center for Vascular Biology and Medicine, IUPUI, 46202, Indianapolis, IN, USA

    Ghassan S. Kassab

Authors
  1. Yunlong Huo
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  2. Ghassan S. Kassab
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Corresponding author

Correspondence to Yunlong Huo .

Editor information

Editors and Affiliations

  1. Veterans Affairs Medical Center, University of California, San Francisco, Clement St. 4150, San Francisco, 94121, U.S.A.

    Julius M. Guccione

  2. Purdue University Indianapolis, Indiana University, Barnhill Drive 635, Indianapolis, 46202, U.S.A.

    Ghassan S. Kassab

  3. Veterans Affairs Medical Center, University of California, San Francisco, Clement St. 4150, San Francisco, 94121, U.S.A.

    Mark B. Ratcliffe

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Huo, Y., Kassab, G.S. (2010). Governing Equations of Blood Flow and Respective Numerical Methods. In: Guccione, J., Kassab, G., Ratcliffe, M. (eds) Computational Cardiovascular Mechanics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-0730-1_8

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  • DOI: https://doi.org/10.1007/978-1-4419-0730-1_8

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  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-0729-5

  • Online ISBN: 978-1-4419-0730-1

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