| Contents |
| We shall consider and solve numerically a model of tumor growth
based on cancer stem cells (CSC) hypothesis which was proposed and
studied mathematically in [2]. The model consists of four
hyperbolic equations of first order to describe the evolution of
different subpopulations of cells and a fifth equation to model
the evolution of the moving boundary. The rates at which reactions
occurs are represented by parameters, containing some of them
non-local integral terms in their definition. A formulation in
terms of total derivatives is posed in order to integrate the four
hyperbolic equations. The discretization of these total
derivatives leads to computing the corresponding ODE for the
characteristics. To integrate the model equations in space a
finite element discretization is applied. We present some
numerical simulations and compare our results with the ones
obtained in [1] where a model, also based on CSC,
consisting of ODEs for the evolution of the densities of the
different subpopulations of cells is considered. Finally, some
conclusions are drawn.
[1] R. Molina-Pe\~na and M. M. Alvarez {\it A simple mathematical model based on cancer stem cell hypothesis
suggests kinetic commonalities in solid tumor growth}. PLoS ONE,
7 (2) (2012) e26233.
[2] J. I. Tello, {\it On a mathematical model of tumor
growth based on cancer stem cells}, Mathematical Biosciences and
Engineering, 10 (1) (2013), 263-278. |
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