A Bistable FieldModel of Cancer Dynamics

作     者：C.Cherubini A.Gizzi M.Bertolaso V.Tambone S.Filippi 

作者机构：Nonlinear Physics and Mathematical Modeling LabUniversity Campus Bio-MedicoI-00128Via A.del Portillo 21RomeItaly International Center for Relativistic Astrophysics-I.C.R.A.University of Rome“La Sapienza”I-00185 RomeItaly Alberto Sordi Foundation-Research Institute on AgingI-00128 RomeItaly Institute of Philosophy of Scientific and Technological ActivityUniversity Campus Bio-MedicoI-00128Via A.del Portillo 21RomeItaly 

出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)

年 卷 期：2012年第11卷第1期

页      面：1-18页

核心收录：

学科分类：1002[医学-临床医学] 100214[医学-肿瘤学] 0704[理学-天文学] 10[医学] 0702[理学-物理学] 

基　　金：ICRANet 

主　　题：Reaction-diffusion equations cancer modeling finite elements method 

摘      要：Cancer spread is a dynamical process occurring not only in time but also in space which,for solid tumors at least,can be modeled quantitatively by reaction and diffusion equations with a bistable behavior:tumor cell colonization happens in a portion of tissue and propagates,but in some cases the process is stopped.Such a cancer proliferation/extintion dynamics is obtained in many mathematical models as a limit of complicated interacting biological fields.In this article we present a very basic model of cancer proliferation adopting the bistable equation for a single tumor cell dynamics.The reaction-diffusion theory is numerically and analytically studied and then extended in order to take into account dispersal effects in cancer progression in analogy with ecological models based on the porous medium equation.Possible implications of this approach for explanation and prediction of tumor development on the lines of existing studies on brain cancer progression are discussed.The potential role of continuum models in connecting the two predominant interpretative theories about cancer,once formalized in appropriatemathematical terms,is discussed。