Composite Waves for a Cell Population System Modeling Tumor Growth and Invasion

作     者：Min TANG Nicolas VAUCHELET Ibrahim CHEDDAD Irene VIGNON-CLEMENTEL Dirk DRASDO Benoit PERTHAME 

作者机构：Department of mathematicsInstitute of Natural Sciences and MOE-LSCShanghai Jiao Tong University INRIA Paris RocquencourtParisFrance Laboratoire Jacques-Louis LionsUPMC Univ Paris 06 and CNRS UMR 7598F-75005ParisFrance 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2013年第34卷第2期

页      面：295-318页

核心收录：

学科分类：1002[医学-临床医学] 100214[医学-肿瘤学] 10[医学] 

基　　金：Project supported by the ANR grant PhysiCancer and the BMBF grant LungSys 

主　　题：Traveling waves Reaction-diffusion Tumor growth Elastic material 

摘      要：In the recent biomechanical theory of cancer growth,solid tumors are considered as liquid-like materials comprising elastic *** this fluid mechanical view,the expansion ability of a solid tumor into a host tissue is mainly driven by either the cell diffusion constant or the cell division rate,with the latter depending on the local cell density(contact inhibition) or/and on the mechanical stress in the *** the two by two degenerate parabolic/elliptic reaction-diffusion system that results from this modeling,the authors prove that there are always traveling waves above a minimal speed,and analyse their *** appear to be complex with composite shapes and *** small parameters allow for analytical solutions,and in particular,the incompressible cells limit is very singular and related to the Hele-Shaw *** singular traveling waves are recovered numerically.