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Mathematical and numerical analysis of a modelfor anti-angiogenic therapy in metastatic cancers

Published online by Cambridge University Press:  05 October 2011

Sébastien Benzekry
Sébastien Benzekry*
Affiliation:
LATP, UMR 6632. Université de Provence, Technopole Château-Gombert, 39 rue F. Joliot Curie, 13453 Marseille Cedex 13, France. Laboratoire de Toxicocinétique et Pharmacocinétique UMR-MD3, 27 boulevard Jean Moulin, 13005 Marseille, France. [email protected]
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Abstract

We introduce a phenomenological model for anti-angiogenic therapy in the treatment of metastatic cancers. It is a structured transport equation with a nonlocal boundary condition describing the evolution of the density of metastases that we analyze first at the continuous level. We present the numerical analysis of a lagrangian scheme based on the characteristics whose convergence establishes existence of solutions. Then we prove an error estimate and use the model to perform interesting simulations in view of clinical applications.

Keywords

Anticancer therapy modellingangiogenesisstructured population dynamicslagrangian scheme
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 46 , Issue 2 , March 2012 , pp. 207 - 237
Copyright
© EDP Sciences, SMAI, 2011

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