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Composite Waves for a Cell Population System Modeling Tumor Growth and Invasion

In: Partial Differential Equations: Theory, Control and Approximation

Author

Listed:
  • Min Tang

    (Shanghai Jiao Tong University, Department of Mathematics, Institute of Natural Sciences and MOE-LSC
    INRIA Paris Rocquencourt)

  • Nicolas Vauchelet

    (INRIA Paris Rocquencourt
    UPMC Univ Paris 06 and CNRS UMR 7598, Laboratoire Jacques-Louis Lions)

  • Ibrahim Cheddadi

    (INRIA Paris Rocquencourt
    UPMC Univ Paris 06 and CNRS UMR 7598, Laboratoire Jacques-Louis Lions)

  • Irene Vignon-Clementel

    (INRIA Paris Rocquencourt
    UPMC Univ Paris 06 and CNRS UMR 7598, Laboratoire Jacques-Louis Lions)

  • Dirk Drasdo

    (INRIA Paris Rocquencourt
    UPMC Univ Paris 06 and CNRS UMR 7598, Laboratoire Jacques-Louis Lions)

  • Benoît Perthame

    (INRIA Paris Rocquencourt
    UPMC Univ Paris 06 and CNRS UMR 7598, Laboratoire Jacques-Louis Lions)

Abstract

In the recent biomechanical theory of cancer growth, solid tumors are considered as liquid-like materials comprising elastic components. In this fluid mechanical view, the expansion ability of a solid tumor into a host tissue is mainly driven by either the cell diffusion constant or the cell division rate, with the latter depending on the local cell density (contact inhibition) or/and on the mechanical stress in the tumor. For the two by two degenerate parabolic/elliptic reaction-diffusion system that results from this modeling, the authors prove that there are always traveling waves above a minimal speed, and analyse their shapes. They appear to be complex with composite shapes and discontinuities. Several small parameters allow for analytical solutions, and in particular, the incompressible cells limit is very singular and related to the Hele-Shaw equation. These singular traveling waves are recovered numerically.

Suggested Citation

  • Min Tang & Nicolas Vauchelet & Ibrahim Cheddadi & Irene Vignon-Clementel & Dirk Drasdo & Benoît Perthame, 2014. "Composite Waves for a Cell Population System Modeling Tumor Growth and Invasion," Springer Books, in: Philippe G. Ciarlet & Tatsien Li & Yvon Maday (ed.), Partial Differential Equations: Theory, Control and Approximation, edition 127, pages 401-429, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-41401-5_16
    DOI: 10.1007/978-3-642-41401-5_16
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