Modeling tumor cell migration: from microscopic to macroscopic

Abstract : It has been shown experimentally that contact interactions may influence the migration of cancer cells. Previous works have modelized this thanks to stochastic, discrete models (cellular automata) at the cell level. However, for the study of the growth of real-size tumors with several millions of cells, it is best to use a macroscopic model having the form of a partial differential equation (PDE) for the density of cells. The difficulty is to predict the effect, at the macroscopic scale, of contact interactions that take place at the microscopic scale. To address this we use a multiscale approach: starting from a very simple, yet experimentally validated, microscopic model of migration with contact interactions, we derive a macroscopic model. We show that a diffusion equation arises, as is often postulated in the field of glioma modeling, but it is nonlinear because of the interactions. We give the explicit dependence of diffusivity on the cell density and on a parameter governing cell-cell interactions. We discuss in details the conditions of validity of the approximations used in the derivation and we compare analytic results from our PDE to numerical simulations and to some in vitro experiments. We notice that the family of microscopic models we started from includes as special cases some kinetically constrained models that were introduced for the study of the physics of glasses, supercooled liquids and jamming systems.
Document type :
Journal articles
Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2009, 79 (3), pp.031917. <10.1103/PhysRevE.79.031917>


https://hal.archives-ouvertes.fr/hal-00348694
Contributor : Christophe Deroulers <>
Submitted on : Thursday, March 26, 2009 - 3:11:32 PM
Last modification on : Thursday, March 26, 2009 - 4:50:44 PM

Files

english.pdf
fileSource_public_author

Identifiers

Collections

Citation

Christophe Deroulers, Marine Aubert, Mathilde Badoual, Basil Grammaticos. Modeling tumor cell migration: from microscopic to macroscopic. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, American Physical Society, 2009, 79 (3), pp.031917. <10.1103/PhysRevE.79.031917>. <hal-00348694v2>

Export

Share

Metrics

Consultation de
la notice

99

Téléchargement du document

20