Reaction-diffusion modelling of interferon distribution in secondary lymphoid organs

Mathematical Modelling of Natural Phenomena

Volumn 6, Issue 7, 2011, Pages 13-26

  Bocharov, G ^a   Danilov, A ^a   Vassilevski, Yu ^a   Marchuk, G I ^a   Chereshnev, V A ^b   Ludewig, B ^c  

^a INSTITUTE OF NUMERICAL MATHEMATICS   (Russian Federation)

^b INSTITUTE OF IMMUNOLOGY AND PHYSIOLOGY   (Russian Federation)

^c CANTONAL HOSPITAL ST GALLEN   (Switzerland)

Author keywords

3D distribution of interferon ; Immune response; Mathematical model; Reaction diffusion equation

Indexed keywords

DIFFUSION EQUATIONS; IMMUNE FACTOR; IMMUNE RESPONSE; LYMPH NODE; LYMPHOID ORGANS; NUMERICAL TREATMENTS; QUANTITATIVE MODELS; REACTION DIFFUSION; REACTION DIFFUSION EQUATIONS; STATIONARY CONCENTRATIONS; STATIONARY DISTRIBUTION; THREE DIMENSIONAL GEOMETRY; UNSTRUCTURED MESH GENERATION;

ANTIBIOTICS; DIFFUSION IN LIQUIDS; FINITE VOLUME METHOD; GLYCOPROTEINS; LINEAR EQUATIONS; MATHEMATICAL MODELS; MEDICAL APPLICATIONS; MESH GENERATION; NONLINEAR EQUATIONS; NUMERICAL METHODS; PARTIAL DIFFERENTIAL EQUATIONS; THREE DIMENSIONAL COMPUTER GRAPHICS;

THREE DIMENSIONAL;

EID: 79960934740     PISSN: 09735348     EISSN: 17606101     Source Type: Journal    
DOI: 10.1051/mmnp/20116702     Document Type: Article

References (30)

1. S. Andrew, C.T.H. Baker, G.A. Bocharov. Rival approaches to mathematical modelling in immunology. J. Comput. Appl. Math., 205 (2007), 669-686. (Pubitemid 46719712)
2. V. Baldazzi, P. Paci, M. Bernaschi, F. Castiglione. Modeling lymphocyte homing and encounters in lymph nodes. BMC Bioinform., 10 (2009), doi:http://dx.doi.org/10.1186/1471-2105-10-387" 10.1186/1471-2105-10-387.
3. C. Beauchemin, N.M. Dixit, A.S. Perelson. Characterizing T cell movement within lymph nodes in the absence of antigen. J. Immunol., 178 (2007), 5505-5512. (Pubitemid 46674345)
4. J.B. Beltman, A.F. Maree, J.N. Lynch, M.J. Miller, R.J. de Boer. Lymph node topology dictates T cell migration behavior. J. Exp. Med., 204 (2007), 771-780. (Pubitemid 46631607)
5. G.A. Bocharov, G.I. Marchuk. Applied problems of mathematical modelling in immunology. Comput. Math. Math. Phys., 40 (2000), 1905-1920.
6. G. Bocharov . Understanding complex regulatory systems: Integrating molecular biology and systems analysis. Transf. Med. Hemoth., 32 (2005), No. 6, 304-321. (Pubitemid 41803448)
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:http://dx.doi.org/10.1371/journal. ppat.1001017, 1-14" 10.1371/journal.ppat.1001017, 1-14.
8. A.A. Danilov. Unstructured tetrahedral mesh generation technology. Comput. Math. Math. Phys., 50 (2010), 146-163.
9. A.A. Danilov, Yu.V. Vassilevski. A monotone nonlinear finite volume method for diffusion equations on conformal polyhedral meshes. Russ. J. Numer. Anal. Math. Modelling, 24 (2009), 207-227.
10. Z. Faroogi, R.R. Mohler. Distribution models of recirculating lymphocytes. IEEE Trans. Biomed. Engrg., 36 (1989), 355-362. (Pubitemid 19102157)
11. Z. Grossman, M. Meier-Schellersheim, W.E. Paul, L.J. Picker. Pathogenesis of HIV infection: what the virus spares is as important as what it destroys. Nat. Med., 12 (2006), 289-295. (Pubitemid 43355074)
12. T. Junt, E. Scandella, B. Ludewig. Form follows function: lymphoid tissues microarchitecture in antimicrobial immune defense. Nature Rev. Immunol., 8 (2008), 764-775.
13. J. Keener, J. Sneyd. Mathematical physiology. Springer-Verlag, New York, 1998.
14. T.B. Kepler, C. Chan. Spatiotemporal programming of a simple inflammatory process. Immunol. Reviews, 216 (2007), 153-163. (Pubitemid 46426520)
15. F. Klauschen, M. Ishii, H. Qi, M. Bajenoff, J.G. Egen, R.N. Germain, M. Meier-Schellersheim. Quantifying cellular interaction dynamics in 3D fluorescence microscopy data. Nat. Protoc., 4 (2009), 1305-1311.
16. T. Lammermann, M. Sixt. The microanatomy of T cell responses. Immunol. Reviews, 221 (2008), 26-43.
17. P. Lane, R.-P. Sekaly . HIV and the architecture of immune responses. Semin. Immunol. 20 (2008), 157-158.
18. J.J. Linderman, T. Riggs, M. Pande, M. Miller, S. Marino, D.E. Kirschner. Characterizing the dynamics of CD4+ T cell priming within a lymph node. J. Immunol., 184 (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. 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. (Pubitemid 41100719)
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:http://dx.doi.org/10.1371/journal. pone.0000458" 10.1371/journal.pone.0000458
24. R.R. Mohler, C. Bruni, A. Gandolfi. A systems approach to immunology. Proceedings of the IEEE, 68 (1980), 964-990 (Pubitemid 10030042)
25. A.S. Perelson, F.W. Wiegel. Scaling aspects of lymphocyte trafficking. J. Theor. Biol., 257 (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. 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. (Pubitemid 351712637)
27. F. Pfeiffer, V. Kumar, S. Butz, D. Vestweber, B.A. Imhof, J.V. Stein, B. Engelhardt. 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.
28. D.J. Stekel, C.E. Parker, M.A. Nowak . A model of lymphocyte recirculation. Immunol. Today, 18 (1997), No. 5, 216-21. (Pubitemid 27219615)
29. D.J. Stekel. The simulation of density-dependent effects in the recirculation of T lymphocytes. Scand. J. Immunol., 47 (1998), 426-430. (Pubitemid 28231420)
30. S. Stoll, J. Delon, T.M. Brotz, R.N. Germain. Dynamic imaging of T cell-dendritic cell interactions in lymph nodes. Science, 296 (2002), 1873-1876. (Pubitemid 34596274)