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Mathematical Biosciences and Engineering

2011, Volume 8, Issue 2: 371-383. doi: 10.3934/mbe.2011.8.371
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Tumor cells proliferation and migration under the influence of their microenvironment

  • 1.
    Department of Mathematics, Ohio State University, Columbus, OH 43210
  • 2.
    Department of Mathematics & Statistics, University of Michigan, Dearborn, MI 48128
  • Received: 01 February 2010 Accepted: 29 June 2018 Published: 01 April 2011

  • MSC : Primary: 92C45, 92C50; Secondary: 92B05.

  • It is well known that tumor microenvironment affects tumor growth and metastasis: Tumor cells may proliferate at different rates and migrate in different patterns depending on the microenvironment in which they are embedded. There is a huge literature that deals with mathematical models of tumor growth and proliferation, in both the avascular and vascular phases. In particular, a review of the literature of avascular tumor growth (up to 2006) can be found in Lolas [8] (G. Lolas, Lecture Notes in Mathematics, Springer Berlin / Heidelberg, 1872, 77 (2006)). In this article we report on some of our recent work. We consider two aspects, proliferation and of migration, and describe mathematical models based on in vitro experiments. Simulations of the models are in agreement with experimental results. The models can be used to generate hypotheses regarding the development of drugs which will confine tumor growth.

    Citation: Avner Friedman, Yangjin Kim. Tumor cells proliferation and migration under the influence of their microenvironment[J]. Mathematical Biosciences and Engineering, 2011, 8(2): 371-383. doi: 10.3934/mbe.2011.8.371

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  • It is well known that tumor microenvironment affects tumor growth and metastasis: Tumor cells may proliferate at different rates and migrate in different patterns depending on the microenvironment in which they are embedded. There is a huge literature that deals with mathematical models of tumor growth and proliferation, in both the avascular and vascular phases. In particular, a review of the literature of avascular tumor growth (up to 2006) can be found in Lolas [8] (G. Lolas, Lecture Notes in Mathematics, Springer Berlin / Heidelberg, 1872, 77 (2006)). In this article we report on some of our recent work. We consider two aspects, proliferation and of migration, and describe mathematical models based on in vitro experiments. Simulations of the models are in agreement with experimental results. The models can be used to generate hypotheses regarding the development of drugs which will confine tumor growth.


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