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.
Mots clés : anticancer therapy modelling, angiogenesis, structured population dynamics, lagrangian scheme
@article{M2AN_2012__46_2_207_0, author = {Benzekry, S\'ebastien}, title = {Mathematical and numerical analysis of a model for anti-angiogenic therapy in metastatic cancers}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {207--237}, publisher = {EDP-Sciences}, volume = {46}, number = {2}, year = {2012}, doi = {10.1051/m2an/2011041}, mrnumber = {2855641}, zbl = {1273.92025}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2011041/} }
TY - JOUR AU - Benzekry, Sébastien TI - Mathematical and numerical analysis of a model for anti-angiogenic therapy in metastatic cancers JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2012 SP - 207 EP - 237 VL - 46 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2011041/ DO - 10.1051/m2an/2011041 LA - en ID - M2AN_2012__46_2_207_0 ER -
%0 Journal Article %A Benzekry, Sébastien %T Mathematical and numerical analysis of a model for anti-angiogenic therapy in metastatic cancers %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2012 %P 207-237 %V 46 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2011041/ %R 10.1051/m2an/2011041 %G en %F M2AN_2012__46_2_207_0
Benzekry, Sébastien. Mathematical and numerical analysis of a model for anti-angiogenic therapy in metastatic cancers. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 46 (2012) no. 2, pp. 207-237. doi : 10.1051/m2an/2011041. http://www.numdam.org/articles/10.1051/m2an/2011041/
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