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Modeling tumor cell migration: from microscopic to macroscopic
Deroulers C., Aubert M., Badoual M., Grammaticos B.
Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 79, 3 (2009) 031917 - http://hal.archives-ouvertes.fr/hal-00348694
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Sciences du Vivant/Biologie cellulaire/Interactions cellulaires
Modeling tumor cell migration: from microscopic to macroscopic
Christophe Deroulers ()1, Marine Aubert ()1, Mathilde Badoual ()1, Basil Grammaticos ()1
1 :  IMNC - Imagerie et Modélisation en Neurobiologie et Cancérologie
CNRS : UMR8165 – IN2P3 – Université Paris XI - Paris Sud – Université Paris VII - Paris Diderot
BATIMENT 104 15 Rue Georges Clémenceau 91406 ORSAY CEDEX
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.

Physical Review E: Statistical, Nonlinear, and Soft Matter Physics
Articles dans des revues avec comité de lecture

Cell migration – gap junctions – contact interactions – tumor modeling – hydrodynamic limit – cellular automaton – lattice gas – kinetically constrained model – spheroid
PACS : 87.18.Gh, 87.10.Ed, 05.10.-a, 87.10.Hk, 87.19.xj, 87.19.lk
Final published version; 14 pages, 7 figures

Comité de financement des théoriciens de l'IN2P3
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comp_exp_th.eps(31.5 KB)
comparaison_courant_stationnaire_2d.eps(13.7 KB)
comparaison_densite_stationnaire_2d.eps(95.3 KB)
comparaison_densite_stationnaire_2d_etf.eps(90.7 KB)
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explication_correlations_pres_reservoir_vide.eps(297.5 KB)
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english.bbl(34.2 KB)
english.tex(82.6 KB)
english.pdf(1003.6 KB)
english.ps(2.8 MB)