D. GRECU, A. S. CÂRSTEA, A.T. GRECU, ANCA VIŞINESCU
Department of Theoretical Physics, „Horia Hulubei” National Institute of Physics and Nuclear Engineering, Bucharest-Măgurele
Abstract. A spherically symmetric model for a non-necrotic vascularized tumor, proposed several years ago by Byrne and Chaplain (1995) [9], was reviewed and extended. The nutrient and inhibitor concentrations are satisfying reaction-diffusion equations, and the tumor radius is determined from a very simple integro-differential equation obtained from the balance of cell proliferation and cell death. The free inhibitor model is extended assuming a space dependence for the nutrient concentration in the vasculature (two distinct regions are considered, one near the surface with a higher concentration, and the rest of the tumor). It is a very simple generalization, which is taking into account a higher tumor angiogenesis factor near the tumor surface. The stationary state of this improved model is carefully investigated.
Key words: nonlinear equations, tumor growth, carcinogenesis.