Open AccessAn age and spatially structured model of tumor invasion with haptotaxis
Author(s) -
Janet Dyson,
Esteban Morcillo Sánchez,
Rosanna Villella-Bressan,
Glenn Webb
Publication year - 2007
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2007.8.45
Subject(s) - extracellular matrix , extracellular , tumor cells , cell , matrix (chemical analysis) , chemistry , biology , mathematics , microbiology and biotechnology , cancer research , biochemistry , chromatography
A model of tumor growth into surrounding tissue is analyzed. The model consists of a system of nonlinear partial differential equations for the populations of tumor cells, extracellular matrix macromolecules, oxygen concentration, and extracellular matrix degradative enzyme concentration. The spatial growth of the tumor involves the directed movement of tumor cells toward the extracellular matrix through haptotaxis. Cell age is used to track progression of cells through the cell cycle. The existence of unique global solutions is proved using the theory of fractional powers of analytic semigroup generators