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Reaction-Diffusion Modelling of Interferon Distribution inSecondary 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 thedistribution of interferon-α (IFNα) in a lymph node(LN). The numerical treatment of the model is based on using an original unstructured meshgeneration software Ani3D and nonlinear finite volume method for diffusion equations. Thestudy results in suggestion that due to the variations in hydraulic conductivity ofvarious zones of the secondary lymphoid organs the spatial stationary distribution ofIFNα is essentially heterogeneous across the organs. Highly protecteddomains such as sinuses, conduits, co-exist with the regions in which where the stationaryconcentration of IFNα is lower by about 100-fold. This is the first studywhere the spatial distribution of soluble immune factors in secondary lymphoid organs ismodelled 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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