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Mathematical Biosciences and Engineering

2013, Volume 10, Issue 4: 997-1015. doi: 10.3934/mbe.2013.10.997
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Modeling of the migration of endothelial cells on bioactive micropatterned polymers

  • 1.
    Univ. Bordeaux, IMB, UMR 5251, F-33400 Talence
  • 2.
    INSERM, IECB, UMR 5248, F-33607 Pessac
  • 3.
    Univ. Bordeaux, IECB, UMR 5248, F-33607 Pessac
  • 4.
    INRIA, F-33400 Talence
  • 5.
    CNRS, IMB, UMR 5251, F-33400 Talence
  • Published: 01 June 2013

  • MSC : Primary: 92B05, 92C17.

  • In this paper, a macroscopic model describing endothelial cellmigration on bioactive micropatterned polymers is presented. It isbased on a system of partial differential equations ofPatlak-Keller-Segel type that describes theevolution of the cell densities. The model is studiedmathematically and numerically. We prove existence and uniquenessresults of the solution to the differential system. We also show thatfundamental physical properties such as mass conservation, positivityand boundedness of the solution are satisfied. The numerical study allows us to show that the modeling results are in good agreement with the experiments.

    Citation: Thierry Colin, Marie-Christine Durrieu, Julie Joie, Yifeng Lei, Youcef Mammeri, Clair Poignard, Olivier Saut. Modeling of the migration of endothelial cells on bioactive micropatterned polymers[J]. Mathematical Biosciences and Engineering, 2013, 10(4): 997-1015. doi: 10.3934/mbe.2013.10.997

    Related Papers:

  • In this paper, a macroscopic model describing endothelial cellmigration on bioactive micropatterned polymers is presented. It isbased on a system of partial differential equations ofPatlak-Keller-Segel type that describes theevolution of the cell densities. The model is studiedmathematically and numerically. We prove existence and uniquenessresults of the solution to the differential system. We also show thatfundamental physical properties such as mass conservation, positivityand boundedness of the solution are satisfied. The numerical study allows us to show that the modeling results are in good agreement with the experiments.


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  • © 2013 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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