Geodesic
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

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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.

DOI : 10.1051/m2an/2011041
Classification : 35F16, 65M25, 92C50
Keywords: anticancer therapy modelling, angiogenesis, structured population dynamics, lagrangian scheme 
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     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://geodesic.mathdoc.fr/articles/10.1051/m2an/2011041/}
}
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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

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