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Mathematical Biosciences and Engineering

2005, Volume 2, Issue 3: 643-655. doi: 10.3934/mbe.2005.2.643
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A Single-Cell Approach in Modeling the Dynamics of Tumor Microregions

  • 1.
    Mathematical Biosciences Institute, Ohio State University, 231 West 18th Avenue, Columbus, OH 43210
  • Received: 01 January 2005 Accepted: 29 June 2018 Published: 01 August 2005

  • MSC : 92C10, 92C37, 92C50, 76D05, 76M20.

  • Interactions between tumor cells and their environment lead to the formation of microregions containing nonhomogeneous subpopulations of cells and steep gradients in oxygen, glucose, and other metabolites. To address the formation of tumor microregions on the level of single cells, I propose a new two-dimensional time-dependent mathematical model taking explicitly into account the individually regulated biomechanical processes of tumor cells and the effect of oxygen consumption on their metabolism. Numerical simulations of the self-organized formation of tumor microregions are presented and the dynamics of such a process is discussed.

    Citation: Katarzyna A. Rejniak. A Single-Cell Approach in Modeling the Dynamics of Tumor Microregions[J]. Mathematical Biosciences and Engineering, 2005, 2(3): 643-655. doi: 10.3934/mbe.2005.2.643

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  • Interactions between tumor cells and their environment lead to the formation of microregions containing nonhomogeneous subpopulations of cells and steep gradients in oxygen, glucose, and other metabolites. To address the formation of tumor microregions on the level of single cells, I propose a new two-dimensional time-dependent mathematical model taking explicitly into account the individually regulated biomechanical processes of tumor cells and the effect of oxygen consumption on their metabolism. Numerical simulations of the self-organized formation of tumor microregions are presented and the dynamics of such a process is discussed.


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    3. Yunshyong Chow, Sophia R.-J. Jang, Coexistence in a discrete competition model with dispersal, 2013, 19, 1023-6198, 615, 10.1080/10236198.2012.663361
    4. 雨青 陈, Dynamic Properties of a Class of Discrete Population Model, 2019, 08, 2324-7991, 1463, 10.12677/AAM.2019.88171
    5. Chunqing Wu, Shengming Fan, Patricia J. Y. Wong, Theoretical Studies on the Effects of Dispersal Corridors on the Permanence of Discrete Predator-Prey Models in Patchy Environment, 2014, 2014, 1085-3375, 1, 10.1155/2014/140902
    6. Flávia Tereza Giordani, Fermín S. V. Bazán, Luciano Bedin, Coupling and Parameter Estimation for a Discrete Single-Species Metapopulation Model, 2025, 11, 2349-5103, 10.1007/s40819-025-01903-z
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  • © 2005 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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