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Analysis and numerical solution of stochastic phase‐field models of tumor growth
Author(s) -
Lima Ernesto A. B. F.,
Almeida Regina C.,
Oden J. Tinsley
Publication year - 2015
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21934
Subject(s) - mathematics , partial differential equation , partial derivative , stochastic partial differential equation , collocation (remote sensing) , orthogonal collocation , stochastic process , collocation method , stochastic modelling , ordinary differential equation , finite element method , field (mathematics) , mathematical optimization , differential equation , computer science , mathematical analysis , statistics , physics , machine learning , thermodynamics , pure mathematics
Carcinogenesis, as every biological process, is not purely deterministic as all systems are subject to random perturbations from the environment. In tumor growth models, the values of the parameters are subjected 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 macrocellular 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 to identify the more influential parameters. A mixed finite element method and a stochastic collocation scheme are introduced to approximate random‐variables components of the solution. The results of numerous numerical experiments are also presented and discussed. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 552–574, 2015