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A Spatial Model of Tumor Growth with Cell Age,Cell Size, and Mutation of Cell Phenotypes

Published online by Cambridge University Press:  15 June 2008

J. Dyson ,
R. Villella-Bressan  and
G. Webb
J. Dyson
Affiliation:
Mansfield College, University of Oxford, Oxford, England
R. Villella-Bressan
Affiliation:
Dipartimento di Matematica Pura e Applicata, Universita di Padova, Padova, Italy
G. Webb*
Affiliation:
Department of Mathematics, Vanderbilt University, Nashville, Tennessee, USA
*
glenn.f.webb@vanderbilt.edu
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Abstract

A model of tumor growth in a spatial environment is analyzed. The model includesproliferating and quiescent compartments of tumor cells indexed by successively mutated cell phenotypesof increasingly proliferative aggressiveness. The model incorporates spatial dependencedue to both random motility and directed movement haptotaxis. The model structures tumor cellsby both cell age and cell size. The model consists of a system of nonlinear partial differentialequations for the compartments of tumor cells, extracellular matrix, matrix degradative enzyme,and oxygen. The existence, uniqueness, positivity, regularity, and growth characteristics of thesolutions are investigated.

Keywords

tumor growthhaptotaxisanalytic semigroupsnonlinear partial differential equations

Information

Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 2 , Issue 3: Cancer modelling , 2007 , pp. 69 - 100
Copyright
© EDP Sciences, 2007

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