Computational Modeling of Solid Tumor Growth: The Avascular Stage

Authors:
Didier Bresch;Thierry Colin;Emmanuel Grenier;Benjamin Ribba;Olivier Saut
Affiliations:
Didier.Bresch@univ-savoie.fr;Thierry.Colin@math.u-bordeaux1.fr and Olivier.Saut@math.u-bordeaux1.fr;Emmanuel.Grenier@umpa.ens-lyon.fr;Benjamin.Ribba@recherche.univ-lyon1.fr;-
Venue:
SIAM Journal on Scientific Computing
Year:
2010

Citing 7
Cited 0

A numerical method for solving incompressible viscous flow problems

Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
Total variation diminishing Runge-Kutta schemes

Mathematics of Computation
Simplified discretization of systems of hyperbolic conservation laws containing advection equations

Journal of Computational Physics
Weighted ENO Schemes for Hamilton--Jacobi Equations

SIAM Journal on Scientific Computing
Evolving interfaces via gradients of geometry-dependent interior Poisson problems: application to tumor growth

Journal of Computational Physics
A level-set method for interfacial flows with surfactant

Journal of Computational Physics
Mathematical Models of Avascular Tumor Growth

SIAM Review

Quantified Score

Hi-index	0.00

Visualization

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 microenvironment. The cancer growth of volume induces cell motion and tumor expansion. According to biology, cells grow against a basal membrane which interacts mechanically 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 vessels to cancer cells and used to estimate hypoxia, is given by a stationary diffusion equation solved with a penalty 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 simulations.