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Composite waves for a cell population system modeling tumor growth and invasion

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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.

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Authors and Affiliations

  1. Department of mathematics, Institute of Natural Sciences and MOE-LSC, Shanghai Jiao Tong University, Shanghai, 200240, China

    Min Tang

  2. INRIA Paris Rocquencourt, Paris, France

    Min Tang

  3. Laboratoire Jacques-Louis Lions, UPMC Univ Paris 06 and CNRS UMR 7598, F-75005, Paris, France

    Nicolas Vauchelet, Ibrahim Cheddadi, Irene Vignon-Clementel, Dirk Drasdo & Benoît Perthame

  4. INRIA Paris Rocquencourt, Paris, France

    Nicolas Vauchelet, Ibrahim Cheddadi, Irene Vignon-Clementel, Dirk Drasdo & Benoît Perthame

Authors
  1. Min Tang
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  2. Nicolas Vauchelet
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  3. Ibrahim Cheddadi
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  4. Irene Vignon-Clementel
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  5. Dirk Drasdo
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  6. Benoît Perthame
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Correspondence to Min Tang.

Additional information

In honor of the scientific heritage of Jacques-Louis Lions

Project supported by the ANR grant PhysiCancer and the BMBF grant LungSys.

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Tang, M., Vauchelet, N., Cheddadi, I. et al. Composite waves for a cell population system modeling tumor growth and invasion. Chin. Ann. Math. Ser. B 34, 295–318 (2013). https://doi.org/10.1007/s11401-013-0761-4

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  • DOI: https://doi.org/10.1007/s11401-013-0761-4

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