MATHEMATICAL MODELLING OF A NON-NECROTIC TUMOR GROWTH. ONE COMPONENT SPHERICALLY SIMETRIC MODEL
Pages 108-117
D. Grecu, A. S. Carstea, A. T. Grecu, Anca Visinescu
Abstract
A spherically symmetric model, proposed several years ago by Byrne and Chaplain for a non-necrotic
vascularized tumor is reviewed. The nutrient and inhibitor are satisfying reaction-diffusion equations, while
the tumor radius is determined from a very simple integro-differential equation resulting from a balance of
cell proliferation and cell death. In principle the coefficients characterizing the model together with the
boundary and initial conditions can be space and time dependent, but explicit calculations are done when
these are constant. A special attention was given to the stationary state of the inhibitor-free model. The tumor
radius is determined graphically from a very simple implicit equation, and it depends only on one parameters
Λ. Stationary states exist if Λ ∈(Λcrit,1/3). The model was extended assuming a space dependence (two
regions, one near the surface and the rest of the tumor) for a concentration CB of the nutrient in the
vasculature. The implicit relation determining the radius is found.