### Mathematical Biosciences and Engineering

2013, Issue 4: 997-1015. doi: 10.3934/mbe.2013.10.997

# Modeling of the migration of endothelial cells on bioactive micropatterned polymers

• Received: 01 June 2012 Accepted: 29 June 2018 Published: 01 June 2013
• MSC : Primary: 92B05, 92C17.

• In this paper, a macroscopic model describing endothelial cellmigration on bioactive micropatterned polymers is presented. It isbased on a system of partial differential equations ofPatlak-Keller-Segel type that describes theevolution of the cell densities. The model is studiedmathematically and numerically. We prove existence and uniquenessresults of the solution to the differential system. We also show thatfundamental physical properties such as mass conservation, positivityand boundedness of the solution are satisfied. The numerical study allows us to show that the modeling results are in good agreement with the experiments.

Citation: Thierry Colin, Marie-Christine Durrieu, Julie Joie, Yifeng Lei, Youcef Mammeri, Clair Poignard, Olivier Saut. Modeling of the migration of endothelial cells on bioactive micropatterned polymers[J]. Mathematical Biosciences and Engineering, 2013, 10(4): 997-1015. doi: 10.3934/mbe.2013.10.997

### Related Papers:

• In this paper, a macroscopic model describing endothelial cellmigration on bioactive micropatterned polymers is presented. It isbased on a system of partial differential equations ofPatlak-Keller-Segel type that describes theevolution of the cell densities. The model is studiedmathematically and numerically. We prove existence and uniquenessresults of the solution to the differential system. We also show thatfundamental physical properties such as mass conservation, positivityand 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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###### 通讯作者: 陈斌, bchen63@163.com
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沈阳化工大学材料科学与工程学院 沈阳 110142

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