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

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 phe-notypes 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. Key words: tumor growth, haptotaxis, analytic semigroups, nonlinear partial differential equation