Free Access
Issue
Math. Model. Nat. Phenom.
Volume 6, Number 7, 2011
Mathematical modeling in biomedical applications
Page(s) 13 - 26
DOI https://doi.org/10.1051/mmnp/20116702
Published online 15 June 2011
  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. [CrossRef] [MathSciNet]
  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. Characterizing T cell movement within lymph nodes in the absence of antigen. J. Immunol., 178 (2007), 5505–5512. [PubMed]
  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. [CrossRef] [PubMed]
  5. G.A. Bocharov, G.I. Marchuk. Applied problems of mathematical modelling in immunology. Comput. Math. Math. Phys., 40 (2000), 1905–1920. [MathSciNet]
  6. G. Bocharov. Understanding complex regulatory systems: Integrating molecular biology and systems analysis. Transf. Med. Hemoth., 32 (2005), No. 6, 304–321. [CrossRef]
  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. Unstructured tetrahedral mesh generation technology. Comput. Math. Math. Phys., 50 (2010), 146–163. [MathSciNet]
  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. [CrossRef]
  10. Z. Faroogi, R.R. Mohler. Distribution models of recirculating lymphocytes. IEEE Trans. Biomed. Engrg., 36 (1989), 355–362. [CrossRef]
  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. [CrossRef] [PubMed]
  12. T. Junt, E. Scandella, B. Ludewig. Form follows function: lymphoid tissues microarchitecture in antimicrobial immune defense. Nature Rev. Immunol., 8 (2008), 764–775. [CrossRef] [PubMed]
  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.
  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. [CrossRef] [PubMed]
  16. T. Lammermann, M. Sixt. The microanatomy of T cell responses. Immunol. Reviews, 221 (2008), 26–43. [CrossRef] [PubMed]
  17. P. Lane, R.-P. Sekaly. HIV and the architecture of immune responses. Semin. Immunol. 20 (2008), 157–158. [CrossRef]
  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. [CrossRef] [PubMed]
  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. [CrossRef] [MathSciNet]
  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. A systems approach to immunology. Proceedings of the IEEE, 68 (1980), 964–990 [CrossRef]
  25. A.S. Perelson, F.W. Wiegel. Scaling aspects of lymphocyte trafficking. J. Theor. Biol., 257 (2009), 9–16. [CrossRef] [PubMed]
  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. [CrossRef]
  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. [CrossRef] [PubMed]
  28. D.J. Stekel, C.E. Parker, M.A. Nowak. A model of lymphocyte recirculation. Immunol. Today, 18 (1997), No. 5, 216–21. [CrossRef] [PubMed]
  29. D.J. Stekel. The simulation of density-dependent effects in the recirculation of T lymphocytes. Scand. J. Immunol., 47 (1998), 426–430. [CrossRef] [PubMed]
  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. [CrossRef] [PubMed]

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