Free Access
Math. Model. Nat. Phenom.
Volume 4, Number 3, 2009
Cancer modelling (Part 2)
Page(s) 183 - 209
Published online 05 June 2009
  1. O. Arino. A survey of structured cell population dynamics. Acta Biotheor., 43 (1995), 3–25. [CrossRef] [PubMed] [Google Scholar]
  2. O. Arino and M. Kimmel. Comparison of approaches to modeling of cell population dynamics. SIAM J. Appl. Math., 53(1993), No. 5, 1480–1504. [Google Scholar]
  3. O. Arino and E. Sanchez. A survey of cell population dynamics. J. Theor. Med., 1 (1997), No. 1, 35–51. [CrossRef] [Google Scholar]
  4. S. Bernard and H. Herzel. Why do cells cycle with a 24 hour period? Genome Inform., 17, (2006), No. 1, 72–79. [Google Scholar]
  5. F. Bekkal Brikci, J. Clairambault, and B. Perthame. Analysis of a molecular structured population model with possible polynomial growth for the cell division cycle. Math. Comput. Modelling, 47 (2008), No. 7-8, 699–713. [Google Scholar]
  6. F. Bekkal Brikci, J. Clairambault, B. Ribba, and B. Perthame. An age-and-cyclin-structured cell population model for healthy and tumoral tissues. J. Math. Biol., 57 (2008), No. 1, 91–110. [Google Scholar]
  7. J. Clairambault, S. Gaubert, and B. Perthame. An inequality for the Perron and Floquet eigenvalues of monotone differential systems and age structured equations. C. R. Math. Acad. Sci. Paris, 345 (2007), No. 10, 549–554. [Google Scholar]
  8. J. Clairambault, P. Michel, and B. Perthame. Circadian rhythm and tumour growth. C. R. Acad. Sci., 342 (2006), No. 1, 17–22. [Google Scholar]
  9. J. Clairambault, P. Michel, and B. Perthame. (2007) A mathematical model of the cell cycle and its circadian control, to appear in Mathematical modeling of Biological Systems, Volume I. A. Deutsch and L. Brusch and H. Byrne and G. de Vries and H.-P. Herzel (eds), Birkhäuser, pp 247–259 proceedings of ECMTB conference, Dresden 2005). [Google Scholar]
  10. R. Dautray and J.L. Lions. Mathematical Analysis and Numerical Methods for Science and Technology. Springer, 1988. [Google Scholar]
  11. M. Doumic. Analysis of a population model structured by the cells molecular content. Mathematical Modelling of Natural Phenomena, 2 (2007), No. 3, 121–152. [Google Scholar]
  12. E. Filipski, P.F. Innominato., M. Wu, X.M. Liand S. Iacobelli, L.J. Xian, and F. Levi. Effects of light and food schedules on liver and tumor molecular clocks in mice. Journal of the National Cancer Institute, 97 (April 2005), No. 7, 507–517, . [Google Scholar]
  13. E. Filipski, Verdun M King, X.M. Li, T. G. Granda, M. Mormont, XuHui Liu, B. Claustrat, M. H. Hastings, and F. Levi. Host circadian clock as a control point in tumor progression. J Natl Cancer Inst, 94( May 2002), No 9, 690–697,. [Google Scholar]
  14. A. Goldbeter. A minimal cascade for the mitotic oscillator involving cyclin and cdc2 kinase. Proc. Nat. Acad. Sci. USA, 88 (October 1991), 9107–9111. [Google Scholar]
  15. R. A. Horn and C. R. Johnson. Matrix analysis. Cambridge University Press, New York, NY, USA, 1986. [Google Scholar]
  16. J. Keener and J. Sneyd. Mathematical Physiology, volume 8. Springer, 1998. [Google Scholar]
  17. F. Levi, A. Altinok, J. Clairambault, and A. Goldbeter. Implications of circadian clocks for the rhythmic delivery of cancer therapeutics. Phil. Trans. R. Soc. A, 366 (2008), 3575–3598. [Google Scholar]
  18. F. Levi and U. Schibler. Circadian rhythms: mechanisms and therapeutic implications. Annu. Rev. Pharmacol. Toxicol., 47 (2007), 593–628. [Google Scholar]
  19. J.A.J. Metz and O. Diekmann. The dynamics of physiologically structured populations, volume 68 of L.N. in biomathematics. Springer, 1986. [Google Scholar]
  20. P. Michel, S. Mischler, and B. Perthame. General relative entropy inequality: an illustration on growth models. J. Math. Pures et Appl., 84 (May 2005), No. 9, 1235–1260. [Google Scholar]
  21. D. O Morgan. The Cell Cycle. Primers in Biology. Oxford University Press, 2007. [Google Scholar]
  22. J.D. Murray. Mathematical Biology, volume 1. Springer, 3rd edition, 2002. [Google Scholar]
  23. B. Novak. Modeling the cell division cycle. Lund(Sweden), April 15-18 1999. Bioinformatics'99. Available online at: [Google Scholar]
  24. B. Perthame. Transport equations in biology. Birkhäuser, 2007. [Google Scholar]
  25. E. Seijo Solis. A report on the discretization of a one-phase model of the cell cycle. Inria internship report, INRIA, 2006. [Google Scholar]
  26. J.J. Tyson, K. Chen, and B. Novak. Network dynamics and cell physiology. Nat. Rev. Mol. Cell Biol., 2 (2001), 908–916. [Google Scholar]

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