# Mathematical and numerical analysis of a model for anti-angiogenic therapy in metastatic cancers

- Volume: 46, Issue: 1, page 207-237
- ISSN: 0764-583X

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topBenzekry, Sébastien. "Mathematical and numerical analysis of a model for anti-angiogenic therapy in metastatic cancers." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 46.1 (2012): 207-237. <http://eudml.org/doc/273248>.

@article{Benzekry2012,

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.},

author = {Benzekry, Sébastien},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {anticancer therapy modelling; angiogenesis; structured population dynamics; lagrangian scheme; Lagrangian scheme},

language = {eng},

number = {1},

pages = {207-237},

publisher = {EDP-Sciences},

title = {Mathematical and numerical analysis of a model for anti-angiogenic therapy in metastatic cancers},

url = {http://eudml.org/doc/273248},

volume = {46},

year = {2012},

}

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 - Modélisation Mathématique et Analyse Numérique

PY - 2012

PB - EDP-Sciences

VL - 46

IS - 1

SP - 207

EP - 237

AB - 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.

LA - eng

KW - anticancer therapy modelling; angiogenesis; structured population dynamics; lagrangian scheme; Lagrangian scheme

UR - http://eudml.org/doc/273248

ER -

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