A One Dimensional Model for Blood Flow: Application to Vascular Prosthesis

  • Luca Formaggia
  • Fabio Nobile
  • Alfio Quarteroni
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 19)


We investigate a one dimensional model of blood flow in human arteries. In particular we consider the case when an abrupt variation of the mechanical characteristic of an artery is caused by the presence of a vascular prosthesis (e.g. a stent). The derivation of the model and the numerical scheme adopted for its solution are detailed. Numerical experiments show the effectiveness of the model for the problem at hand.


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  1. 1.
    R. Botnar, G. Rappitsch, M.B. Scheidegger, D. Liepsch, K. Perktold, and P. Boesiger. Hemodynamics in the carotid artery bifurcation: A comparison between numerical simulations and in-vitro measurements. J. of Biomech., 33:137–144, 2000.CrossRefGoogle Scholar
  2. 2.
    S. Canic. On the shock formation in pulsaltile blood flow through a ”stented” aorta modeled by a system of hyperbolic conservation laws with discontinuous coefficients. (In Preparation), 2000.Google Scholar
  3. 3.
    L. Formaggia, J.-F. Gerbeau, F. Nobile, and A.Quarteroni. On the coupling of 3D and ID Navier-Stokes equations for flow problems in compliant vessels. Technical Report 3862, INRIA, 2000. to appear in Comp. Methods in Appl. Mech. Engng.Google Scholar
  4. 4.
    E. Godlewski and P.-A. Raviart. Numerical approximation of hyperbolic systems of conservation laws, volume 118 of Applied Mathematical Sciences. Springer, New York, 1996.Google Scholar
  5. 5.
    K. Hayashi, K. Handa, S. Nagasawa, and A. Okumura. Stiffness and elastic behaviour of human intracranial and extracranial arteries. J. Biomech., 13:175–184, 1980.CrossRefGoogle Scholar
  6. 6.
    T.H. Hughes, C. Taylor, and C. Zarins. Finite element modeling of blood flow in arteries. Comp. Meth. Appl. Mech. Eng., 158:155–196, 1998.MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    G.L. Langewouters, K.H. Wesseling, and W.J.A. Goedhard. The elastic properties of 45 human thoracic and 20 abdominal aortas in vitro and the parameters of a new model. J. Biomech., 17:425–435, 1984.CrossRefGoogle Scholar
  8. 8.
    L.Formaggia, F. Nobile, A. Quarteroni, and A. Veneziani. Multiscale modelling of the circulatory system: a preliminary analysis. Computing and Visualisation in Science, 2:75–83, 1999.MATHCrossRefGoogle Scholar
  9. 9.
    F. Phythoud, N. Stergiopulos, and J.-J. Meister. Forward and backward waves in the arterial system: nonlinear separation using Riemann invariants. Technology and Health Care, 3:201–207, 1995.Google Scholar
  10. 10.
    A. Quarteroni, M. Tuveri, and A. Veneziani. Computational vascular fluid dynamics: Problems, models and methods. Computing and Visualisation in Science, 2:163–197, 2000.MATHCrossRefGoogle Scholar
  11. 11.
    A. Quarteroni and A. Valli. Domain decomposition methods for partial differential equations. Oxford University Press, Oxford, 1999.MATHGoogle Scholar
  12. 12.
    A. Tozeren. Elastic properties of arteries and their influence on the cardiovascular system. ASME J. Biomech. Eng., 106:182–185, 1984.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Luca Formaggia
    • 2
  • Fabio Nobile
    • 2
  • Alfio Quarteroni
    • 1
    • 2
  1. 1.Mathematics DepartmentPolitecnico di MilanoMilanoItaly
  2. 2.Mathematics DepartmentEPFLLausanneSwitzerland

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