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] [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  5. G.A. Bocharov, G.I. Marchuk. Applied problems of mathematical modelling in immunology. Comput. Math. Math. Phys., 40 (2000), 1905–1920. [MathSciNet] [Google Scholar]
  6. G. Bocharov. Understanding complex regulatory systems: Integrating molecular biology and systems analysis. Transf. Med. Hemoth., 32 (2005), No. 6, 304–321. [CrossRef] [Google Scholar]
  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. [Google Scholar]
  8. A.A. Danilov. Unstructured tetrahedral mesh generation technology. Comput. Math. Math. Phys., 50 (2010), 146–163. [MathSciNet] [Google Scholar]
  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] [Google Scholar]
  10. Z. Faroogi, R.R. Mohler. Distribution models of recirculating lymphocytes. IEEE Trans. Biomed. Engrg., 36 (1989), 355–362. [CrossRef] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  13. J. Keener, J. Sneyd. Mathematical physiology. Springer-Verlag, New York, 1998. [Google Scholar]
  14. T.B. Kepler, C. Chan. Spatiotemporal programming of a simple inflammatory process. Immunol. Reviews, 216 (2007), 153–163. [Google Scholar]
  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] [Google Scholar]
  16. T. Lammermann, M. Sixt. The microanatomy of T cell responses. Immunol. Reviews, 221 (2008), 26–43. [CrossRef] [PubMed] [Google Scholar]
  17. P. Lane, R.-P. Sekaly. HIV and the architecture of immune responses. Semin. Immunol. 20 (2008), 157–158. [CrossRef] [Google Scholar]
  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] [Google Scholar]
  19. G.I. Marchuk. Mathematical modelling of immune response in infectious diseases. Kluwer Academic Publishres, Dordrecht, 1997. [Google Scholar]
  20. G.I. Marchuk. Methods of Numerical Mathematics. Springer-Verlag, New York, 1982. [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  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 [Google Scholar]
  24. R.R. Mohler, C. Bruni, A. Gandolfi. A systems approach to immunology. Proceedings of the IEEE, 68 (1980), 964–990 [CrossRef] [Google Scholar]
  25. A.S. Perelson, F.W. Wiegel. Scaling aspects of lymphocyte trafficking. J. Theor. Biol., 257 (2009), 9–16. [CrossRef] [PubMed] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.