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Mathematical modelling of cancer invasion of tissue the role and effect of nonlocal interactions

Opened Access Mathematical modelling of cancer invasion of tissue the role and effect of nonlocal interactions

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Autor: Szymanska, Zuzanna
Morales Rodrigo, Cristian
Lachowicz, Miroslaw
Chaplain, Mark A.J.
Departamento: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Fecha: 2009-02
Publicado en: Mathematical Models and Methods in Applied Sciences, 19 (2), 257-281.
Tipo de documento: Artículo
Resumen: In this paper we consider a mathematical model of cancer cell invasion of tissue (extracellular matrix). Two crucial components of tissue invasion are (i) cancer cell proliferation, and (ii) over-expression and secretion of proteolytic enzymes by the cancer cells. The proteolytic enzymes are responsible for the degradation of the tissue, enabling the proliferating cancer cells to actively invade and migrate into the degraded tissue. Our model focuses on the role of nonlocal kinetic terms modelling competition for space and degradation. The model consists of a system of reaction-diffusion-taxis partial differential equations, with nonlocal (integral) terms describing the interactions between cancer cells and the host tissue. We first of all prove results concerning the local existence, uniqueness and regularity of solutions of our system of nonlinear PDEs. We then extend these results to prove global existence, uniqueness and regularity of the solutions. Using Green’s functions, we t...
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Cita: Szymanska, Z., Morales Rodrigo, C., Lachowicz, M. y Chaplain, M.A.J. (2009). Mathematical modelling of cancer invasion of tissue the role and effect of nonlocal interactions. Mathematical Models and Methods in Applied Sciences, 19 (2), 257-281.
Tamaño: 338.6Kb
Formato: PDF

URI: http://hdl.handle.net/11441/45115

DOI: 10.1142/S0218202509003425

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