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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 includes proliferating and quiescent compartments of tumor cells indexed by successively mutated cell phenotypes of increasingly proliferative aggressiveness. The model incorporates spatial dependence due to both random motility and directed movement haptotaxis. The model structures tumor cells by both cell age and cell size. The model consists of a system of nonlinear partial differential equations for the compartments of tumor cells, extracellular matrix, matrix degradative enzyme, and oxygen. The existence, uniqueness, positivity, regularity, and growth characteristics of the solutions are investigated.

Keywords

tumor growthhaptotaxisanalytic semigroupsnonlinear partial differential equations
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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