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Reaction-Diffusion Modelling of Interferon Distribution in Secondary Lymphoid Organs

Published online by Cambridge University Press:  15 June 2011

G. Bocharov ,
A. Danilov ,
Yu. Vassilevski ,
G.I. Marchuk ,
V.A. Chereshnev  and
B. Ludewig
G. Bocharov*
Affiliation:
Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russia
A. Danilov*
Affiliation:
Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russia
Yu. Vassilevski
Affiliation:
Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russia
G.I. Marchuk
Affiliation:
Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russia
V.A. Chereshnev
Affiliation:
Institute of Immunology and Physiology, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia
B. Ludewig
Affiliation:
Institute of Immunobiology, Cantonal Hospital of St. Gallen, St. Gallen, Switzerland
*
⋆ Corresponding authors. E-mails: bocharov@inm.ras.ru, a.a.danilov@gmail.com
⋆ Corresponding authors. E-mails: bocharov@inm.ras.ru, a.a.danilov@gmail.com
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Abstract

This paper proposes a quantitative model of the reaction-diffusion type to examine the distribution of interferon-α (IFNα) in a lymph node (LN). The numerical treatment of the model is based on using an original unstructured mesh generation software Ani3D and nonlinear finite volume method for diffusion equations. The study results in suggestion that due to the variations in hydraulic conductivity of various zones of the secondary lymphoid organs the spatial stationary distribution of IFNα is essentially heterogeneous across the organs. Highly protected domains such as sinuses, conduits, co-exist with the regions in which where the stationary concentration of IFNα is lower by about 100-fold. This is the first study where the spatial distribution of soluble immune factors in secondary lymphoid organs is modelled for a realistic three-dimensional geometry.

Keywords

mathematical modelimmune responsereaction-diffusion equation3D distribution of interferon-α
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 6 , Issue 7: Mathematical modeling in biomedical applications , 2011 , pp. 13 - 26
Copyright
© EDP Sciences, 2011

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