Stochastic models for tumor growth in (1+1) dimension

Strong experimental evidences and scaling analysis have shown that tumors growth belongs to the molecular beam epitaxy (MBE) universality class. This type of growth is described by three characteristics: 1) linear growth rate 2) the constraint of cell proliferation to the tumor border 3) surface diffusion of cells at the growing edge. All of these features have been experimentally seen. Stochastic partial differential equations with correct geometrical symmetries are reproduced some of the fundamental mechanisms of the tumor growth as a statistical approach. In the present article we presented a more general model in (1+1) dimension by adding 1 r term to the deterministic term . By solving this equation، we understand that with this approximation tumor reach faster to radially symmetric solution and its growth will become more favorable.