| Issue |
ESAIM: M2AN
Volume 46, Number 2, November-December 2012
|
|
|---|---|---|
| Page(s) | 207 - 237 | |
| DOI | https://doi.org/10.1051/m2an/2011041 | |
| Published online | 05 October 2011 | |
Mathematical and numerical analysis of a model for anti-angiogenic therapy in metastatic cancers
1
LATP, UMR 6632. Université de Provence, Technopole Château-Gombert, 39 rue F. Joliot Curie, 13453 Marseille Cedex 13, France.
2
Laboratoire de Toxicocinétique et Pharmacocinétique UMR-MD3, 27 boulevard Jean Moulin, 13005 Marseille, France. benzekry@phare.normalesup.org
Received:
15
September
2010
Revised:
3
May
2011
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.
Mathematics Subject Classification: 35F16 / 65M25 / 92C50
Key words: Anticancer therapy modelling / angiogenesis / structured population dynamics / lagrangian scheme
© EDP Sciences, SMAI, 2011
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