Modeling of the migration of endothelial cells on bioactive  micropatterned polymers

Thierry Colin; Marie-Christine Durrieu; Julie Joie; Yifeng Lei; Youcef Mammeri; Clair Poignard; Olivier Saut

doi:10.3934/mbe.2013.10.997

Article Contents

2013, Volume 10, Issue 4: 997-1015. Doi: 10.3934/mbe.2013.10.997

This issue Previous Article Stability and Hopf bifurcation in a diffusive predator-prey system incorporating a prey refuge Next Article Darwinian dynamics of a juvenile-adult model

Modeling of the migration of endothelial cells on bioactive micropatterned polymers

1.
Univ. Bordeaux, IMB, UMR 5251, F-33400 Talence
2.
INSERM, IECB, UMR 5248, F-33607 Pessac
3.
Univ. Bordeaux, IECB, UMR 5248, F-33607 Pessac
4.
INRIA, F-33400 Talence
5.
CNRS, IMB, UMR 5251, F-33400 Talence

Received: May 31, 2012

Revised: March 31, 2013

Published: May 2013

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Abstract

In this paper, a macroscopic model describing endothelial cell migration on bioactive micropatterned polymers is presented. It is based on a system of partial differential equations of Patlak-Keller-Segel type that describes the evolution of the cell densities. The model is studied mathematically and numerically. We prove existence and uniqueness results of the solution to the differential system. We also show that fundamental physical properties such as mass conservation, positivity and boundedness of the solution are satisfied. The numerical study allows us to show that the modeling results are in good agreement with the experiments.

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Mathematics Subject Classification: Primary: 92B05, 92C17.

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