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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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

[1] S. Andrew, C.T.H. Baker, G.A. Bocharov J. Comput. Appl. Math. 2007 669 686

[2] V. Baldazzi, P. Paci, M. Bernaschi, F. Castiglione. Modeling lymphocyte homing and encounters in lymph nodes. BMC Bioinform., 10 (2009), doi:10.1186/1471-2105-10-387.

[3] C. Beauchemin, N.M. Dixit, A.S. Perelson J. Immunol. 2007 5505 5512

[4] J.B. Beltman, A.F. Maree, J.N. Lynch, M.J. Miller, R.J. De Boer J. Exp. Med. 2007 771 780

[5] G.A. Bocharov, G.I. Marchuk Comput. Math. Math. Phys. 2000 1905 1920

[6] Bocharov G. Transf. Med. Hemoth. 2005 304 321

[7] G. Bocharov, R. Zust, L. Cervantes-Barragan, T. Luzyanina, E. Chiglintcev, V.A. Chereshnev, V. Thiel, B. Ludewig. A systems immunology approach to plasmacytoid dendritic cell function in cytopathic virus infections. PLoS Pathogens, 6(7) (2010), e1001017.doi:10.1371/journal.ppat.1001017, 1–14.

[8] A.A. Danilov Comput. Math. Math. Phys. 2010 146 163

[9] A.A. Danilov, Yu.V. Vassilevski Russ. J. Numer. Anal. Math. Modelling 2009 207 227

[10] Z. Faroogi, R.R. Mohler IEEE Trans. Biomed. Engrg. 1989 355 362

[11] Z. Grossman, M. Meier-Schellersheim, W.E. Paul, L.J. Picker Nat. Med. 2006 289 295

[12] T. Junt, E. Scandella, B. Ludewig Nature Rev. Immunol. 2008 764 775

[13] J. Keener, J. Sneyd. Mathematical physiology. Springer-Verlag, New York, 1998.

[14] T.B. Kepler, C. Chan Immunol. Reviews 2007 153 163

[15] F. Klauschen, M. Ishii, H. Qi, M. Bajenoff, J.G. Egen, R.N. Germain, M. Meier-Schellersheim Nat. Protoc. 2009 1305 1311

[16] T. Lammermann, M. Sixt Immunol. Reviews 2008 26 43

[17] Lane P., Sekaly R.-P. Semin. Immunol. 2008 157 158

[18] J.J. Linderman, T. Riggs, M. Pande, M. Miller, S. Marino, D.E. Kirschner J. Immunol. 2010 2873 2885

[19] G.I. Marchuk. Mathematical modelling of immune response in infectious diseases. Kluwer Academic Publishres, Dordrecht, 1997.

[20] G.I. Marchuk. Methods of Numerical Mathematics. Springer-Verlag, New York, 1982.

[21] Marchuk G.I., Shutyaev V., Bocharov G. J. Comput. Appl. Math. 2005 177 204

[22] R.R. Mohler, Z. Faroogi, T. Heilig. Lymphocyte distribution and lymphatic dynamics. In: Vistas in Applied Mathematics: Numerical Analysis, Atmospheric Sciences, Immunology. (Eds. A.V. Balakrishnan, A.A. Dorodnitsyn, and J.-L. Lions) 1986, 317–333.

[23] J.H. Meyers, J.S. Justement, C.W. Hallahan, E.T. Blair, Y.A. Sun, M.A. O’Shea, G. Roby, S. Kottilil, S. Moir, C.M. Kovacs, T.W. Chun, A.S. Fauci. Impact of HIV on cell survival and antiviral activity of plasmacytoid dendritic cells. PLoS ONE, 2 (2008), No. 5, e458. doi:10.1371/journal.pone.0000458

[24] R.R. Mohler, C. Bruni, A. Gandolfi Proceedings of the IEEE 1980 964 990

[25] A.S. Perelson, F.W. Wiegel J. Theor. Biol. 2009 9 16

[26] E. Scandella, B. Bolinger, E. Lattmann, S. Miller, S. Favre, D.R. Littman, D. Finke, S.A. Luther, T. Junt, B. Ludewig Nature Immunol. 2008 667 675

[27] F. Pfeiffer, V. Kumar, S. Butz, D. Vestweber, B.A. Imhof, J.V. Stein, B. Engelhardt Eur. J. Immunol. 2008 2142 2155

[28] Stekel D.J., Parker C.E., Nowak M.A. Immunol. Today 1997 216 21

[29] D.J. Stekel Scand. J. Immunol. 1998 426 430

[30] S. Stoll, J. Delon, T.M. Brotz, R.N. Germain Science 2002 1873 1876

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