Analysis and Numerical Solution of Stochastic Phase-Field Models of Tumor Growth

Carcinogenesis, as every biological process, is not purely deterministic since all systems are subject to random perturbations from the environment. In tumor growth models, the values of the parameters are subject to many uncertainties that can arise from experimental variations or due to patient-specific data. The present work is devoted to the development and analysis of numerical methods for the solution of a system of stochastic partial differential equations governing a six-species tumor growth model. The model system simulates the stochastic behavior of cellular and macro cellular events affecting the evolution of avascular cancerous tissue. It is a continuous phase-field model that incorporates several key features in tumor dynamics. A sensitivity analysis is performed in order to identify the more influential parameters. A mixed finite element method and a stochastic collocation scheme are introduced to approximate randomvariables components of the solution. The results of numerous numerical experiments are also presented and discussed.