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Tumor Growth and Invasion

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Cellular Automaton Modeling of Biological Pattern Formation

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Abstract

In this chapter, we introduce LGCA models of tumor growth and invasion . All these models are related to in vitro experiments with cancer cell lines. Besides the suggestion of cellular automaton models for particular aspects of cancer complexity the intention of this chapter is to show how combinations of interaction modules introduced in the previous chapters can be arranged for specific tumor-related applications. Development of further combinations with respect to other tumor-related problems as well as the mathematical analysis of the automaton models is open for future research (see also sec. 12.4 on “future research projects”).

Clinical oncologists and tumour biologists possess virtually no comprehensive model to serve as a framework for understanding, organizing and applying their data.

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Notes

  1. 1.

    Gatenby and Maini (2003).

  2. 2.

    Edward Abbey.

  3. 3.

    Parts of this section have been published in (Dormann and Deutsch 2002).

  4. 4.

    Mostly, \(\bar{p}_{m} +\bar{ p}_{d} +\bar{ p}_{n} \leq 1\); if this is not the case, the parameters are normalized.

  5. 5.

    The initial number of tumor cells is always 44.

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Authors and Affiliations

  1. Centre for Information Services and High Performance Computing, Technische Universität Dresden, Dresden, Germany

    Andreas Deutsch

  2. FB Mathematik/Informatik, Universität Osnabrück, Osnabrück, Germany

    Sabine Dormann

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Deutsch, A., Dormann, S. (2017). Tumor Growth and Invasion. In: Cellular Automaton Modeling of Biological Pattern Formation. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4899-7980-3_12

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