American Institute of Mathematical Sciences

Advanced
2005, 2(3): 643-655. doi: 10.3934/mbe.2005.2.643

A Single-Cell Approach in Modeling the Dynamics of Tumor Microregions

Katarzyna A. Rejniak 1,

1. 

Mathematical Biosciences Institute, Ohio State University, 231 West 18th Avenue, Columbus, OH 43210, United States

Received  January 2005 Revised  June 2005 Published  August 2005

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.
Keywords: avascular tumor growth, mathe- matical modeling, tumor microregions development, immersed boundary method..
Mathematics Subject Classification: 92C10, 92C37, 92C50, 76D05, 76M2.
Citation: Katarzyna A. Rejniak. A Single-Cell Approach in Modeling the Dynamics of Tumor Microregions. Mathematical Biosciences & Engineering, 2005, 2 (3) : 643-655. doi: 10.3934/mbe.2005.2.643
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