Modeling of the migration of endothelial cells on bioactive micropatterned polymers
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 nu...
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| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2013-05-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.997 |
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| author | Thierry Colin Marie-Christine Durrieu Julie Joie Yifeng Lei Youcef Mammeri Clair Poignard Olivier Saut |
| author_facet | Thierry Colin Marie-Christine Durrieu Julie Joie Yifeng Lei Youcef Mammeri Clair Poignard Olivier Saut |
| author_sort | Thierry Colin |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-003fe406981d46fbb033179139bf5735 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2013-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-003fe406981d46fbb033179139bf57352025-01-24T02:26:20ZengAIMS PressMathematical Biosciences and Engineering1551-00182013-05-01104997101510.3934/mbe.2013.10.997Modeling of the migration of endothelial cells on bioactive micropatterned polymersThierry Colin0Marie-Christine Durrieu1Julie Joie2Yifeng Lei3Youcef Mammeri4Clair Poignard5Olivier Saut6Univ. Bordeaux, IMB, UMR 5251, F-33400 TalenceUniv. Bordeaux, IMB, UMR 5251, F-33400 TalenceUniv. Bordeaux, IMB, UMR 5251, F-33400 TalenceUniv. Bordeaux, IMB, UMR 5251, F-33400 TalenceUniv. Bordeaux, IMB, UMR 5251, F-33400 TalenceUniv. Bordeaux, IMB, UMR 5251, F-33400 TalenceUniv. Bordeaux, IMB, UMR 5251, F-33400 TalenceIn 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.https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.997keller-segel type modelendothelial cells migration.tissue engineering |
| spellingShingle | 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 Mathematical Biosciences and Engineering keller-segel type model endothelial cells migration. tissue engineering |
| title | Modeling of the migration of endothelial cells on bioactive micropatterned polymers |
| title_full | Modeling of the migration of endothelial cells on bioactive micropatterned polymers |
| title_fullStr | Modeling of the migration of endothelial cells on bioactive micropatterned polymers |
| title_full_unstemmed | Modeling of the migration of endothelial cells on bioactive micropatterned polymers |
| title_short | Modeling of the migration of endothelial cells on bioactive micropatterned polymers |
| title_sort | modeling of the migration of endothelial cells on bioactive micropatterned polymers |
| topic | keller-segel type model endothelial cells migration. tissue engineering |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.997 |
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