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

Sébastien Benzekry

ESAIM: Mathematical Modelling and Numerical Analysis (2011)

  • Volume: 46, Issue: 2, page 207-237
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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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 46.2 (2011): 207-237. <http://eudml.org/doc/222159>.

@article{Benzekry2011,
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},
keywords = {Anticancer therapy modelling; angiogenesis; structured population dynamics; lagrangian scheme; anticancer therapy modelling; Lagrangian scheme},
language = {eng},
month = {10},
number = {2},
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/222159},
volume = {46},
year = {2011},
}

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
DA - 2011/10//
PB - EDP Sciences
VL - 46
IS - 2
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; anticancer therapy modelling; Lagrangian scheme
UR - http://eudml.org/doc/222159
ER -

References

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