Model hierarchies for cell aggregation by chemotaxis

Fabio Chalub*, Yasmin Dolak-Struss, Peter Markowich, Dietmar Oelz, Christian Schmeiser, Alexander Soreff

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

73 Scopus citations

Abstract

We present partial differential equation (PDE) model hierarchies for the chemotactically driven motion of biological cells. Starting from stochastic differential models, we derive a kinetic formulation of cell motion coupled to diffusion equations for the chemoattractants. We also derive a fluid dynamic (macroscopic) Keller-Segel type chemotaxis model by scaling limit procedures. We review rigorous convergence results and discuss finitetime blow-up of Keller-Segel type systems. Finally, recently developed PDE-models for the motion of leukocytes in the presence of multiple chemoattractants and of the slime mold Dictyostelium Discoideum are reviewed.

Original languageEnglish (US)
Pages (from-to)1173-1197
Number of pages25
JournalMathematical Models and Methods in Applied Sciences
Volume16
Issue numberSUPPL. 1
DOIs
StatePublished - Jul 2006
Externally publishedYes

Keywords

  • Chemotaxis
  • Keller-Segel model
  • Macroscopic limit
  • Moment expansion

ASJC Scopus subject areas

  • Modeling and Simulation
  • Applied Mathematics

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