Computational modeling of solid tumor growth: the avascular stage

Didier Bresch; Thierry Colin; Emmanuel Grenier; Benjamin Ribba; Olivier Saut

inria-00148610, version 4

Computational modeling of solid tumor growth: the avascular stage

Didier Bresch^a^, 1, Thierry Colin^b^, 2, 3, Emmanuel Grenier^c^, 4, Benjamin Ribba^d^, 5, Olivier Saut ( Author to contact preferably )^a^, 2, 3

SIAM Journal on Scientific Computing 32, 4 (2010) 2321-2344

Abstract: In this paper, we present a mathematical model for avascular tumor growth and its numerical study in two and three dimensions. For this purpose, we use a multiscale model using PDEs to describe the evolution of the tumor cell densities. In our model, cell cycle regulation depends mainly on micro-environment. The cancer growth of volume induces cells motion and tumor expansion. According to biology, cells grow against a basal membrane which interacts mechanistically with the tumor. We use a level set method to describe this membrane and we compute its influence on cell movement thanks to a Stokes equation. The evolution of oxygen, diffusing from blood vessel to cancer cells and used to estimate hypoxia, is given by a stationary diffusion equation solved with a penalization method. The model has been applied to investigate the therapeutic benefit of anti-invasive agents and constitutes now the basis of a numerical platform for tumor growth simulation.

a – CNRS
b – Université Sciences et Technologies - Bordeaux I
c – Ecole Normale Supérieure de Lyon
d – Université Claude Bernard - Lyon I
1: Laboratoire de Mathématiques (LAMA)
CNRS : UMR5127 – Université de Savoie
2: Institut de Mathématiques de Bordeaux (IMB)
CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II
3: MC2 (INRIA Bordeaux - Sud-Ouest)
INRIA – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II – CNRS : UMR
4: Unité de Mathématiques Pures et Appliquées (UMPA-ENSL)
CNRS : UMR5669 – École Normale Supérieure - Lyon
5: Ciblage thérapeutique en Oncologie (EA3738)
Université Claude Bernard - Lyon I

inria-00148610, version 4
http://hal.archives-ouvertes.fr/inria-00148610
oai:hal.archives-ouvertes.fr:inria-00148610
From: Olivier Saut <>
Submitted on: Thursday, 10 December 2009 18:42:08
Updated on: Wednesday, 5 January 2011 11:17:43

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%% inria-00148610, version 4
%% http://hal.archives-ouvertes.fr/inria-00148610
@article{bresch:inria-00148610,
    hal_id = {inria-00148610},
    url = {http://hal.archives-ouvertes.fr/inria-00148610},
    title = {{Computational modeling of solid tumor growth: the avascular stage}},
    author = {Bresch, Didier and Colin, Thierry and Grenier, Emmanuel and Ribba, Benjamin and Saut, Olivier},
    abstract = {{In this paper, we present a mathematical model for avascular tumor growth and its numerical study in two and three dimensions. For this purpose, we use a multiscale model using PDEs to describe the evolution of the tumor cell densities. In our model, cell cycle regulation depends mainly on micro-environment. The cancer growth of volume induces cells motion and tumor expansion. According to biology, cells grow against a basal membrane which interacts mechanistically with the tumor. We use a level set method to describe this membrane and we compute its influence on cell movement thanks to a Stokes equation. The evolution of oxygen, diffusing from blood vessel to cancer cells and used to estimate hypoxia, is given by a stationary diffusion equation solved with a penalization method. The model has been applied to investigate the therapeutic benefit of anti-invasive agents and constitutes now the basis of a numerical platform for tumor growth simulation.}},
    keywords = {Avascular tumor growth. Multiscale models. Cell cycle modeling. Fluid dynamics. Level-set methods.},
    language = {English},
    affiliation = {Laboratoire de Math{\'e}matiques - LAMA , Institut de Math{\'e}matiques de Bordeaux - IMB , MC2 - INRIA Bordeaux - Sud-Ouest , Unit{\'e} de Math{\'e}matiques Pures et Appliqu{\'e}es - UMPA-ENSL , Ciblage th{\'e}rapeutique en Oncologie - EA3738},
    pages = {2321--2344},
    journal = {SIAM Journal on Scientific Computing},
    volume = {32},
    number = {4 },
    audience = {international },
    year = {2010},
    pdf = {http://hal.archives-ouvertes.fr/inria-00148610/PDF/modcan.pdf},
}

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