Geodesic
Reaction-Diffusion Modelling of Interferon Distribution in Secondary Lymphoid Organs
G. Bocharov1 ; A. Danilov1 ; Yu. Vassilevski1 ; G.I. Marchuk1 ; V.A. Chereshnev2 ; B. Ludewig3
1 Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russia
2 Institute of Immunology and Physiology, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia
3 Institute of Immunobiology, Cantonal Hospital of St. Gallen, St. Gallen, Switzerland
Mathematical modelling of natural phenomena, Tome 6 (2011) no. 7 Supplement, pp. 13-26.

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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.
DOI : 10.1051/mmnp/20116702

G. Bocharov 1 ; A. Danilov 1 ; Yu. Vassilevski 1 ; G.I. Marchuk 1 ; V.A. Chereshnev 2 ; B. Ludewig 3

1 Institute of Numerical Mathematics, Russian Academy of Sciences, Moscow, Russia
2 Institute of Immunology and Physiology, Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia
3 Institute of Immunobiology, Cantonal Hospital of St. Gallen, St. Gallen, Switzerland 
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     title = {Reaction-Diffusion {Modelling} of {Interferon} {Distribution} in {Secondary} {Lymphoid} {Organs}},
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G. Bocharov; A. Danilov; Yu. Vassilevski; G.I. Marchuk; V.A. Chereshnev; B. Ludewig. Reaction-Diffusion Modelling of Interferon Distribution in Secondary Lymphoid Organs. Mathematical modelling of natural phenomena, Tome 6 (2011) no. 7 Supplement, pp. 13-26. doi : 10.1051/mmnp/20116702. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20116702/

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