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Numerical Simulation of a Contractivity Based Multiscale Cancer Invasion Model

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Multiscale Models in Mechano and Tumor Biology

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 122))

Abstract

We present a problem-suited numerical method for a particularly challenging cancer invasion model. This model is a multiscale haptotaxis advection-reaction-diffusion system that describes the macroscopic dynamics of two types of cancer cells coupled with microscopic dynamics of the cells adhesion on the extracellular matrix. The difficulties to overcome arise from the non-constant advection and diffusion coefficients, a time delay term, as well as stiff reaction terms.

Our numerical method is a second order finite volume implicit-explicit scheme adjusted to include (a) non-constant diffusion coefficients in the implicit part, (b) an interpolation technique for the time delay, and (c) a restriction on the time increment for the stiff reaction terms.

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Author information

Authors and Affiliations

  1. Institute of Mathematics, Johannes Gutenberg-University, Staudingerweg 9, 55128, Mainz, Germany

    Niklas Kolbe, Mária Lukáčová-Medvid’ová & Bettina Wiebe

  2. Institute of Applied Mathematics, Heidelberg University, Im Neuenheimer Feld 205, 69120, Heidelberg, Germany

    Nikolaos Sfakianakis

Authors
  1. Niklas Kolbe
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  2. Mária Lukáčová-Medvid’ová
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  3. Nikolaos Sfakianakis
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  4. Bettina Wiebe
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Corresponding author

Correspondence to Nikolaos Sfakianakis .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Numerical Analysis and Scientific Computing Group, Technische Universität Darmstadt, Darmstadt, Germany

    Alf Gerisch

  2. School of Mathematics and Statistics, University of Glasgow, Glasgow, United Kingdom

    Raimondo Penta

  3. Department of Mathematics, Numerical Analysis and Scientific Computing Group, Technische Universität Darmstadt, Darmstadt, Germany

    Jens Lang

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Kolbe, N., Lukáčová-Medvid’ová, M., Sfakianakis, N., Wiebe, B. (2017). Numerical Simulation of a Contractivity Based Multiscale Cancer Invasion Model. In: Gerisch, A., Penta, R., Lang, J. (eds) Multiscale Models in Mechano and Tumor Biology . Lecture Notes in Computational Science and Engineering, vol 122. Springer, Cham. https://doi.org/10.1007/978-3-319-73371-5_4

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