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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

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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Keywords Keller-Segel type model; endothelial cells migration.; Tissue engineering

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. Mathematical Biosciences and Engineering, 2013, 10(4): 997-1015. doi: 10.3934/mbe.2013.10.997

References

  • 1. Bulletin of Mathematical Biology, 60 (1998), 857-899.
  • 2. Acta Biomaterialia, 6 (2010), 3824-3846.
  • 3. I. Colloq. Math., 66 (1993), 319-334.
  • 4. Electron. J. Differential Equations, 2006, No. 44, 32 pp. (electronic).
  • 5. Nature, 436 (2005), 193-200.
  • 6. Science, 276 (1997), 1425-1428.
  • 7. in Vitro Cell. Dev. Biol., 35 (1999), 441-448.
  • 8. C. R. Math. Acad. Sci. Paris, 339 (2004), 611-616.
  • 9. Handbook of Numerical Analysis, (eds. P. G Ciarlet and J. L Lions), 2007.
  • 10. Annu. Rev. Biomed. Eng., 2 (2000), 227-256.
  • 11. Nature, 288 (1980), 551-556.
  • 12. Math. Nachr., 195 (1998), 77-114.
  • 13. J. Math. Biol., 58 (2008), 183-217.
  • 14. Nonlinear Differ. Equ. Appl., 8 (2001), 399-423.
  • 15. Springer Series in Comput. Math., 33, Springer, 2003.
  • 16. Biomaterials, 20 (1999), 2333-2342.
  • 17. Nat. Med., 9 (2003), 685-593.
  • 18. Nat Biotechnol, 23 (2005), 821-823.
  • 19. J. of Computational Physics, 126 (1996), 202-228.
  • 20. in vivo, Nature, 442 (2006), 453-456.
  • 21. Journal of Theo. Biol., 30 (1971), 235-248.
  • 22. Small, In Revision.
  • 23. PLoS ONE, 7 (2012), e41163.
  • 24. Journal of Computational Physics, 115 (1994), 200-212.
  • 25. Cell, 112 (2003), 19-28.
  • 26. Tissue Eng., 12 (2006), 1143-50.
  • 27. Biosens. Bioelectron, 14 (1999), 317-325.
  • 28. Blood Cells Mol. Dis., 39 (2007), 212-220.
  • 29. London Math. Soc. Monographs Series, Princeton University Press. 31, 2005.
  • 30. Bull. Math. Biophys., 15 (1953), 311-338.
  • 31. Curr. Opin. Biotechnol, 21 (2010), 704-709.
  • 32. Macromol Biosci., 10 (2010), 12-27.
  • 33. Adv. Differential Equations, 6 (2001), 21-50.
  • 34. Arch. Rational Mech. Anal., 153 (2000), 91-151.
  • 35. To Appear in AMS. Proc., 141 (2013), 1067-1081. (Avalaible on http://arxiv.org/abs/1009.1965v2).

 

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