A congestion model for cell migration

Abstract : This paper deals with a class of macroscopic models for cell migration in a saturated medium for two-species mixtures. Those species tend to achieve some motion according to a desired velocity, and congestion forces them to adapt their velocity. This adaptation is modelled by a correction velocity which is chosen minimal in a least-square sense. We are especially interested in two situations: a single active species moves in a passive matrix (cell migration) with a given desired velocity, and a closed-loop Keller-Segel type model, where the desired velocity is the gradient of a self-emitted chemoattractant. We propose a theoretical framework for the open-loop model (desired velocities are defined as gradients of given functions) based on a formulation in the form of a gradient flow in the Wasserstein space. We propose a numerical strategy to discretize the model, and illustrate its behaviour in the case of a prescribed velocity, and for the saturated Keller-Segel model.
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Article dans une revue
Communications on Pure and Applied Mathematics, Wiley, 2012, 11 (1), pp.243-260
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https://hal.archives-ouvertes.fr/hal-00625868
Contributeur : Nicolas Meunier <>
Soumis le : jeudi 22 septembre 2011 - 17:40:57
Dernière modification le : mercredi 4 janvier 2017 - 16:22:45

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  • HAL Id : hal-00625868, version 1
  • ARXIV : 1102.0147

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Julien Dambrine, Nicolas Meunier, Bertrand Maury, Aude Roudneff-Chupin. A congestion model for cell migration. Communications on Pure and Applied Mathematics, Wiley, 2012, 11 (1), pp.243-260. <hal-00625868>

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