Modelos de reação difusão para o crescimento de tumores

Abstract

In this doctoral thesis, we present a new approach for the simulation of tumor growth. This approach consists in associate stochastic microscopic rules, which describe the cell dynamics, with macroscopic reaction-diffusion equations, describing the concentration of several chemicals (nutrients, growth factors, drugs, etc.) in the tissue. We applied this method for simulate the dynamics and, mainly, the morphology of tumors in situ. Specifically, we use effective kinetic models in order to simulate cell division, death, and motility depending on the above-cited concentrations. Firstly, a model in which the interactions among cancer cells are mediated by growth factors and controls the cell actions was studied. This model exhibits a wide morphology diversity for tumors, which evolve in time as Gompertz laws. Secondly, a new model, in which the nutrient competition determines the cell actions, was studied in order to generate the ramified and papillary morphologies commonly observed in real tumors, but not obtained in the model that just considers the growth factors. Finally, the effects of distinct chemotherapeutic strategies, using cytotoxic or antimitotic drugs, in the nutrient limited model were studied. Several interesting results emerge from these models such as wide pattern diversity, morphology transitions, scaling and growth laws, qualitative reproduction of tumor behaviors and morphologies, suggestions for new experiments in order to determine possible behaviors not yet observed in real tumors, etc. In order to complement the thesis, we studied, through simulations and analytical methods, a stochastic model that is a generalization of the classical model for the growth of tumors proposed by Williams & Bjerknes.