ArticleJournal of mathematical biology2005
Derivation of hyperbolic models for chemosensitive movement.
Article in Journal of mathematical biology, 2005. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 11 papers.
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Who cites it
11 citing papers in PubMed.
- Multi-Cue Kinetic Model with Non-Local Sensing for Cell Migration on a Fiber Network with Chemotaxis.Bulletin of mathematical biology · 2022Article
- Self-organization in brain tumors: How cell morphology and cell density influence glioma pattern formation.PLoS computational biology · 2020Article
- Kinetic models with non-local sensing determining cell polarization and speed according to independent cues.Journal of mathematical biology · 2020Article
- Symmetries and pattern formation in hyperbolic versus parabolic models of self-organised aggregation.Journal of mathematical biology · 2015Article
- Glioma follow white matter tracts: a multiscale DTI-based model.Journal of mathematical biology · 2015Article
- Article
- Trail formation based on directed pheromone deposition.Journal of mathematical biology · 2013Article
- Hyperbolic and kinetic models for self-organized biological aggregations and movement: a brief review.Journal of mathematical biology · 2012Review
- Mathematical description of bacterial traveling pulses.PLoS computational biology · 2010Article
- Kinetic models for chemotaxis: hydrodynamic limits and spatio-temporal mechanisms.Journal of mathematical biology · 2005Article
- Derivation of hyperbolic models for chemosensitive movement.Journal of mathematical biology · 2005Article
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Authors and funding
3 authors.
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Abstract
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.
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