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 language | English (US) |
|---|---|
| Pages (from-to) | 1173-1197 |
| Number of pages | 25 |
| Journal | Mathematical Models and Methods in Applied Sciences |
| Volume | 16 |
| Issue number | SUPPL. 1 |
| DOIs | |
| State | Published - Jul 2006 |
| Externally published | Yes |
Bibliographical note
Funding Information:This work has been supported by the Austrian Science Fund (FWF) through the WITTGENSTEIN AWARD 2000 of Peter Markowich, through the Wissenschafts-kolleg “Differential Equations” (project No. W8), and through FWF-Project no. P17139-N04 “Cubature on Wiener Space”. FACCC has been supported by the project POCTI/ISFL/209 (FCT/Portugal) and by the Wolfgang Pauli Institute. Y.D.S. has been supported by the Johann Radon Institute (Austrain Academy of Sciences).
Keywords
- Chemotaxis
- Keller-Segel model
- Macroscopic limit
- Moment expansion
ASJC Scopus subject areas
- Modeling and Simulation
- Applied Mathematics