A single-cell approach in modeling the dynamics of tumor microregions. (English) Zbl 1079.92046

Rejniak, Katarzyna A.

Math. Biosci. Eng. 2, No. 3, 643-655 (2005).

Summary: 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.

MSC:

92C50	Medical applications (general)
92C37	Cell biology
76D05	Navier-Stokes equations for incompressible viscous fluids
76M20	Finite difference methods applied to problems in fluid mechanics

Keywords:

avascular tumor growth; , tumor microregions development; immersed boundary method