Journal of Mathematical Biology

, Volume 50, Issue 2, pp 189–207 | Cite as

Derivation of hyperbolic models for chemosensitive movement

  • Francis FilbetEmail author
  • Philippe Laurençot
  • Benoît Perthame


A Chapman-Enskog expansion is used to derive hyperbolic models for chemosensitive movements as a hydrodynamic limit of a velocity-jump process. On the one hand, it connects parabolic and hyperbolic chemotaxis models since the former arise as diffusion limits of a similar velocity-jump process. On the other hand, this approach provides a unified framework which includes previous models obtained by ad hoc methods or methods of moments. Numerical simulations are also performed and are motivated by recent experiments with human endothelial cells on matrigel. Their movements lead to the formation of networks that are interpreted as the beginning of a vasculature. These structures cannot be explained by parabolic models but are recovered by numerical experiments on hyperbolic models. Our kinetic model suggests that some kind of local interactions might be enough to explain them.


Endothelial Cell Numerical Experiment Kinetic Model Mathematical Biology Previous Model 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Francis Filbet
    • 1
    Email author
  • Philippe Laurençot
    • 2
  • Benoît Perthame
    • 3
  1. 1.Mathématiques et Applications, Physique Mathématique d’Orléans, CNRS UMR 6628Université d’OrléansOrléans cedex 2France
  2. 2.Mathématiques pour l’Industrie et la Physique, CNRS UMR 5640Université Paul Sabatier – Toulouse 3Toulouse cedex 4France
  3. 3.Département de Mathématiques Appliquées, CNRS UMR 8553Ecole Normale SupérieureParis cedex 05France

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