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Numerical Modeling of Fluid Flow in Liver Lobule Using Double Porosity Model

  • M. Yu. Antonov
  • A. V. GrigorevEmail author
  • A. E. Kolesov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10187)

Abstract

Earlier in the paper of Bonfiglio et al. [2] numerical simulation of blood circulation in the liver lobule was carried out using single porosity model. Electron microscopy reveals structure of the liver lobule, which has some of the properties of fractured porous media. In this work we consider double porosity model for modeling of blood filtration in the liver lobule. A numerical algorithm based on the spatial finite element approximation and finite difference approximation in time direction using explicit-implicit computational scheme is proposed.

Keywords

Portal Vein Hepatic Artery Central Vein Liver Lobule Portal Tract 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Barenblatt, G., Zheltov, I.P., Kochina, I.: Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks [strata]. J. Appl. Math. Mech. 24(5), 1286–1303 (1960)CrossRefzbMATHGoogle Scholar
  2. 2.
    Bonfiglio, A., Leungchavaphongse, K., Repetto, R., Siggers, J.H.: Mathematical modeling of the circulation in the liver lobule. J. Biomech. Eng. 132(11), 11–21 (2010)CrossRefGoogle Scholar
  3. 3.
    Brenner, S.C., Scott, L.R.: The Mathematical Theory of Finite Element Methods. Springer, Heidelberg (2008)CrossRefzbMATHGoogle Scholar
  4. 4.
    Dupont, T., Hoffman, J., Johnson, C., Kirby, R., Larson, M., Logg, A., Scott, L.: The FEniCS project. Chalmers University of Technology, Chalmers Finite Element Centre (2003)Google Scholar
  5. 5.
    Gaspar, F.H., Grigoriev, A.V., Vabishchevich, P.N.: Explicit-implicit splitting schemes for some systems of evolutionary equations. Int. J. Numer. Anal. Model. 11, 346–357 (2014)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Giuseppe, G., Maddern, G.: Liver failure after major hepatic resection. J. Hepatobiliary Pancreat. Surg. 16(2), 145–155 (2009)CrossRefGoogle Scholar
  7. 7.
    Kiernan, F.: The anatomy and physiology of the liver. Philos. Trans. R. Soc. Lond. 123, 711–770 (1833)CrossRefGoogle Scholar
  8. 8.
    Langtangen, H.P.: A fenics tutorial. In: Logg, A., Mardal, K.-A., Wells, G. (eds.) Automated Solution of Differential Equations by the Finite Element Method, pp. 1–73. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  9. 9.
    Quarteroni, A., Valli, A.: Numerical Approximation of Partial Differential Equations. Springer, Heidelberg (2008)zbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • M. Yu. Antonov
    • 1
  • A. V. Grigorev
    • 1
    • 2
    Email author
  • A. E. Kolesov
    • 1
  1. 1.M.K.Ammosov North-Eastern Federal UniversityYakutskRussia
  2. 2.Institute of Computational Mathematics and Mathematical Geophysics SB RASNovosibirskRussia

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