Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-26T07:56:19.829Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected],[email protected]
⋆ Corresponding authors. E-mails: [email protected],[email protected]
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Andrew, S., Baker, C.T.H., Bocharov, G.A.. Rival approaches to mathematical modelling in immunology. J. Comput. Appl. Math., 205 (2007), 669–686. CrossRefGoogle Scholar
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. CrossRef
Beauchemin, C., Dixit, N.M., Perelson, A.S.. Characterizing T cell movement within lymph nodes in the absence of antigen. J. Immunol., 178 (2007), 5505–5512. CrossRefGoogle Scholar
Beltman, J.B., Maree, A.F., Lynch, J.N., Miller, M.J., de Boer, R.J.. Lymph node topology dictates T cell migration behavior. J. Exp. Med., 204 (2007), 771–780. CrossRefGoogle Scholar
Bocharov, G.A., Marchuk, G.I.. Applied problems of mathematical modelling in immunology. Comput. Math. Math. Phys., 40 (2000), 1905–1920. Google Scholar
G., Bocharov. Understanding complex regulatory systems: Integrating molecular biology and systems analysis. Transf. Med. Hemoth., 32 (2005), No. 6, 304–321. Google Scholar
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.
Danilov, A.A.. Unstructured tetrahedral mesh generation technology. Comput. Math. Math. Phys., 50 (2010), 146–163. CrossRefGoogle Scholar
Danilov, A.A., Vassilevski, Yu.V.. A monotone nonlinear finite volume method for diffusion equations on conformal polyhedral meshes. Russ. J. Numer. Anal. Math. Modelling, 24 (2009), 207–227. CrossRefGoogle Scholar
Faroogi, Z., Mohler, R.R.. Distribution models of recirculating lymphocytes. IEEE Trans. Biomed. Engrg., 36 (1989), 355–362. CrossRefGoogle Scholar
Grossman, Z., Meier-Schellersheim, M., Paul, W.E., Picker, L.J.. Pathogenesis of HIV infection: what the virus spares is as important as what it destroys. Nat. Med., 12 (2006), 289–295. CrossRefGoogle ScholarPubMed
Junt, T., Scandella, E., Ludewig, B.. Form follows function: lymphoid tissues microarchitecture in antimicrobial immune defense. Nature Rev. Immunol., 8 (2008), 764–775. CrossRefGoogle Scholar
J. Keener, J. Sneyd. Mathematical physiology. Springer-Verlag, New York, 1998.
Kepler, T.B., Chan, C.. Spatiotemporal programming of a simple inflammatory process. Immunol. Reviews, 216 (2007), 153–163. CrossRefGoogle ScholarPubMed
Klauschen, F., Ishii, M., Qi, H., Bajenoff, M., Egen, J.G., Germain, R.N., Meier-Schellersheim, M.. Quantifying cellular interaction dynamics in 3D fluorescence microscopy data. Nat. Protoc., 4 (2009), 1305–1311. CrossRefGoogle ScholarPubMed
Lammermann, T., Sixt, M.. The microanatomy of T cell responses. Immunol. Reviews, 221 (2008), 26–43. CrossRefGoogle ScholarPubMed
P., Lane, R.-P., Sekaly. HIV and the architecture of immune responses. Semin. Immunol. 20 (2008), 157–158. Google Scholar
Linderman, J.J., Riggs, T., Pande, M., Miller, M., Marino, S., Kirschner, D.E.. Characterizing the dynamics of CD4+ T cell priming within a lymph node. J. Immunol., 184 (2010), 2873–2885. CrossRefGoogle Scholar
G.I. Marchuk. Mathematical modelling of immune response in infectious diseases. Kluwer Academic Publishres, Dordrecht, 1997.
G.I. Marchuk. Methods of Numerical Mathematics. Springer-Verlag, New York, 1982.
G.I., Marchuk, V., Shutyaev, G., Bocharov Adjoint equations and analysis of complex systems: application to virus infection modeling. J. Comput. Appl. Math., 184 (2005), 177–204. Google Scholar
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.
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
Mohler, R.R., Bruni, C., Gandolfi, A.. A systems approach to immunology. Proceedings of the IEEE, 68 (1980), 964–990 CrossRefGoogle Scholar
Perelson, A.S., Wiegel, F.W.. Scaling aspects of lymphocyte trafficking. J. Theor. Biol., 257 (2009), 9–16. CrossRefGoogle ScholarPubMed
Scandella, E., Bolinger, B., Lattmann, E., Miller, S., Favre, S., Littman, D.R., Finke, D., Luther, S.A., Junt, T., Ludewig, B.. Restoration of lymphoid organ integrity through the interaction of lymphoid tissue-inducer cells with stroma of the T cell zone. Nature Immunol., 9 (2008), 667–675. CrossRefGoogle ScholarPubMed
Pfeiffer, F., Kumar, V., Butz, S., Vestweber, D., Imhof, B.A., Stein, J.V., Engelhardt, B.. Distinct molecular composition of blood and lymphatic vascular endothelial cell junctions establishes specific functional barriers within the peripheral lymph node. Eur. J. Immunol., 38 (2008), 2142–2155. CrossRefGoogle ScholarPubMed
D.J., Stekel, C.E., Parker, M.A., Nowak. A model of lymphocyte recirculation. Immunol. Today, 18 (1997), No. 5, 216–21. Google Scholar
Stekel, D.J.. The simulation of density-dependent effects in the recirculation of T lymphocytes. Scand. J. Immunol., 47 (1998), 426–430. CrossRefGoogle ScholarPubMed
Stoll, S., Delon, J., Brotz, T.M., Germain, R.N.. Dynamic imaging of T cell-dendritic cell interactions in lymph nodes. Science, 296 (2002), 1873–1876.CrossRefGoogle Scholar