Stochastic models for tumoral growth

Abstract

Strong experimental evidence has indicated that tumor growth belongs to the molecular beam epitaxy universality class. This type of growth is characterized by the constraint of cell proliferation to the tumor border, and surface diffusion of cells at the growing edge. Tumor growth is thus conceived as a competition for space between the tumor and the host, and cell diffusion at the tumor border is an optimal strategy adopted for minimizing the pressure and helping tumor development. Two stochastic partial differential equations are introduced in this work in order to correctly model the physical properties of tumoral growth in (1+1) and (2+1) dimensions. The advantages of these models is that they reproduce the correct geometry of the tumor and are defined in terms of polar variables. Analysis of these models allow us to quantitatively estimate the response of the tumor to an unfavorable perturbation during the growth.