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Mathematical Medicine and Biology Advance Access originally published online on October 3, 2005
Mathematical Medicine and Biology 2005 22(4):291-303; doi:10.1093/imammb/dqi009
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© The author 2005. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Multistep navigation of leukocytes: a stochastic model with memory effects

Dietmar Oelz1, Christian Schmeiser2 and Alexander Soreff3,**

1 Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstrasse, 8-10, A-1040 Wien, Austria, 2 Faculty of Mathematics, University of Vienna, Nordbergstrasse 15, 1090 Wien, Austria and Johann Radon Institute for Computational and Applied Mathematics (RICAM), Linz, 3 Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstrasse, 8-10, A-1040 Wien, Austria

** Email: soreff{at}aurora.anum.tuwien.ac.at

We present a model for the chemotactically directed migration of neutrophil leukocytes. It reproduces the multistep navigation by memory effects investigated experimentally by E. F. Foxman, J. J. Campbell and E. C. Butcher in 1997. The model consists of a system of stochastic differential equations. The long time behaviour of the corresponding deterministic system is analysed and two approaches for the numerical solution of the full stochastic system are compared. One of them consists in performing direct simulations, the other one is based on a moment approximation of the Fokker–Planck equation and numerical methods for convection-dominated partial differential equations.

Keywords: chemotaxis; leukocytes

Received on 22 November 2004. revised on 9 May 2005.


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