Free Access
Issue
Math. Model. Nat. Phenom.
Volume 4, Number 3, 2009
Cancer modelling (Part 2)
Page(s) 12 - 67
DOI https://doi.org/10.1051/mmnp/20094302
Published online 05 June 2009
  1. M. Adimy, F. Crauste. Global stability of a partial differential equation with distributed delay due to cellular replication. Nonlinear Analysis, 54 (2003), No. 8,1469–1491. [Google Scholar]
  2. M. Adimy, F. Crauste, S. Ruan. A mathematical study of the hematopoiesis process with applications to chronic myelogenous leukemia. SIAM J. Appl. Math., 65 (2005), No. 4,1328–1352. [Google Scholar]
  3. M. Adimy, F. Crauste, A. El Abdllaoui. Discrete maturity-structured model of cell differentiation with applications to acute myelogenous leukemia. J. Biological Systems, 16 (2008), No. 3, 395–424. [CrossRef] [Google Scholar]
  4. B.D. Aguda. Modeling the cell division cycle. In A. Friedman (Ed.) Tutorials in Mathematical Biosciences III: Cell Cycle, Proliferation, and Cancer, pp. 1–22. Springer, New York, 2005. [Google Scholar]
  5. Z. Agur. Mathematical modelling of cancer chemotherapy: Investigation of the resonance phenomenon. In: O. Arino et al. (Ed.). Advances in mathematical population dynamics -molecules, cells and man. Papers from the 4th international conference, Rice Univ., Houston, TX, USA, May 23–27, 1995, Ser. Math. Biol. Med. 6 (1997), pp. 571–578, World Scientific, Singapore. [Google Scholar]
  6. T. Alarcón, H.M. Byrne, P.K. Maini. Towards whole-organ modelling of tumour growth. Prog. Biophys. Mol. Biol., 85 (2004), No. 2-3, 451–72. [CrossRef] [PubMed] [Google Scholar]
  7. L. Alberghina, H.W. Westerhoff (Eds.). Systems Biology. Definitions and Perspectives. Springer, Berlin, 2005. [Google Scholar]
  8. B.B. Aldridge, J.M. Burke, D.A. Lauffenburger, P.K. Sorger. Physicochemical modelling of cell signalling. Nature Rev. Mol. Cell Biol., 8 (2006), No. 11, 1195–1203. [Google Scholar]
  9. A. Altinok, F. Lévi, A. Goldbeter. Identifying mechanisms of chronotolerance and chronoefficacy for the anticancer drugs 5-fluorouracil and oxaliplatin by computational modeling. Eur. J. Pharm. Sci., 36 (2009), No. 1, 20–38. [CrossRef] [PubMed] [Google Scholar]
  10. J.C. Ameisen. La sculpture du vivant. Stock, Paris, 1999. [Google Scholar]
  11. A.R.A. Anderson, M.A. Chaplain. Chap 10 in L. Preziosi (Ed.). Cancer modelling and simulation, Chapman and Hall, London, 2003. [Google Scholar]
  12. A.R.A. Anderson, A.M. Weaver, P.T. Cummings, V. Quaranta. Tumor morphology and phenotypic evolution driven by selective pressure from the microenvironment. Cell, 127 (2006), No. 5, 905–915. [Google Scholar]
  13. A. Aouba, F. Péquignot, A. Le Toullec, E. Jougla. Les causes médicales de décès en France en 2004 et leur évolution / Medical causes of death in France in 2004 and trends 1980-2004 (English abstract). Bulletin épidémiologique hebdomadaire de l'INVS,18 septembre 2007, 35–36. Available on line from http://www.invs.sante.fr/beh/2007/35_36/ [Google Scholar]
  14. O. Arino. A survey of structured cell population dynamics. Acta Biotheor., 43 (1995), No. 1-2, 3–25. [CrossRef] [PubMed] [Google Scholar]
  15. O. Arino, M. Kimmel. Comparison of approaches to modeling of cell population dynamics. SIAM J. Appl. Math., 53 (1993), No. 5, 1480–1504. [CrossRef] [MathSciNet] [Google Scholar]
  16. O. Arino, E. Sanchez. A survey of cell population dynamics. J. Theor. Med., 1 (1997), No. 1, 35–51. [CrossRef] [Google Scholar]
  17. H. Barbason, B. Bouzahzah, C. Herens, J. Marchandise, J. Sulon, J. van Cantfort. Circadian synchronization of liver regeneration in adult rats: the role played by adrenal hormones. Cell Prolif., 22 (1989), No. 6, 451–460. [CrossRef] [Google Scholar]
  18. J. Barnes. The Presocratic philosophers. Paperback edition,1 vol., Routledge, London, 1982. [Google Scholar]
  19. M.-A. Barrat-Petit, C. Naulin-Ifi, P. Mahler, G. Milano. Dihydropyrimidine déshydrogénase (DPD) : rythme et conséquences. (in French, English summary). Pathol.-Biol., 53 (2005), No. 5, 261–264. [CrossRef] [PubMed] [Google Scholar]
  20. C. Basdevant, J. Clairambault, F. Lévi. Optimisation of time-scheduled regimen for anti-cancer drug infusion. Mathematical Modelling and Numerical Analysis, 39 (2006), No. 6, 1069–1086. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  21. B. Basse, B.C. Baguley, E.S. Marshall, W.R. Joseph, B. van Brunt, G. Wake, D.J.N. Wall. A mathematical model for analysis of the cell cycle in cell lines derived from human tumors. J. Math. Biol., 47 (2003), No. 4, 295–312. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  22. F. Bekkal Brikci, J. Clairambault, B. Perthame. Analysis of a molecular structured population model with polynomial growth for the cell cycle. Mathematical and Computer Modelling, 47 (2008), No. 7-8, 699–713. [CrossRef] [MathSciNet] [Google Scholar]
  23. F. Bekkal Brikci, J. Clairambault, B. Ribba, 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]
  24. N. Bellomo (Ed.). Selected Topics in Cancer Modeling: Genesis, Evolution, Immune Competition, and Therapy. Birkhäuser, Boston, 2008. [Google Scholar]
  25. N. Bellomo, M. Delitala. From the mathematical kinetic, and stochastic game theory to modelling mutations, onset, progression and immune competition of cancer cells. Physics of Life Reviews, 5 (2008), No. 4, 183–206. [CrossRef] [Google Scholar]
  26. Y. Ben-Neriah, G.Q. Daley, A.M. Mes-Masso, O.N. Witte, D. Baltimore. The chronic myelogenous leukemia-specific p210 protein is the product of the BCR/ABL hybrid gene. Science, 233 (1986), No. 4760 , 212–214. [Google Scholar]
  27. S. Bernard, HP. Herzel. Why do cells cycle with a 24 h period? Genome Informatics, 17 (2006), No. 1, 72–79. [Google Scholar]
  28. S. Bernard, J. Bélair, M.C. Mackey. Oscillations in cyclical neutropenia: New evidence based on mathematical modeling. J. Theor. Biol., 223 (2003), No. 3, 283–298. [CrossRef] [PubMed] [Google Scholar]
  29. N. Bessonov, A. Ducrot, V. Volpert. Modeling of leukemia development in the bone marrow. Proc. of the annual Symposium on Mathematics applied in Biology and Biophysics, Tome XLVIII (2005), vol. 2, 79–88. [Google Scholar]
  30. N. Bessonov, I. Demin, L. Pujo-Menjouet, V. Volpert. A multi-agent model describing self-renewal of differentiation effects on the blood cell population. Mathematical and computer modelling, 49 (2009), No. 11-12, 2116–2127. [CrossRef] [MathSciNet] [Google Scholar]
  31. M. Bizzarri, A. Cucina, F. Conti, F. D'Anselmi. Beyond the Oncogene Paradigm: Understanding the Complexity in Cancerogenesis. Acta Biotheor., 56 (2008), No. 3, 173–196. [CrossRef] [PubMed] [Google Scholar]
  32. G.A. Bjarnason, R.C.K. Jordan, R.C.K., R.B. Sothern. Circadian variation in the expression of cell-cycle proteins in the human oral epithelium. Am. J. Pathol., 154 (1999), No. 2, 613–622. [CrossRef] [PubMed] [Google Scholar]
  33. M.V. Blagosklonny, A. Pardee. The restriction point of the cell cycle. Cell Cycle, 1 (1974), No. 2, 103–110. [Google Scholar]
  34. J.L. Boldrini, M.I.S. Costa. Therapy burden, drug resistance, and optimal treatment regimen for cancer therapy. IMA J. Math. Appl. Med. Biology, 17 (2000), No. 1, 33–51. [CrossRef] [Google Scholar]
  35. N.A. Boughattas, F. Lévi, et al. Circadian Rhythm in Toxicities and Tissue Uptake of 1,2-diamminocyclohexane(trans-1)oxaloplatinum(II) in Mice. Cancer Research, 49 (1989), No. 12, 3362–3368. [PubMed] [Google Scholar]
  36. K. Boushaba, H.A. Levine, M. Nilsen-Hamilton. A mathematical model for the regulation of tumor dormancy based on enzyme kinetics. Bull. Math. Biol., 68 (2006), No. 7, 1495–1526. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  37. L. Bourgey. Observation et expérience chez Aristote. Vrin, coll. Bibliothèque d'Histoire de la Philosophie, Paris, 1955. [Google Scholar]
  38. M. Breccia, G. Alimena. Resistance to imatinib in chronic myeloid leukemia and therapeutic approaches to circumvent the problem. Cardiovasc. Hematol. Disord. Drug Targets, 9 (2009), No. 1, 21–28. [CrossRef] [PubMed] [Google Scholar]
  39. N.F. Britton. Reaction-diffusion equations and their applications to biology. Academic Press, London, 1986 [Google Scholar]
  40. M.P. Brynildsen, J.J. Collins. Systems biology makes it personal. Mol. Cell, 34 (2009), No. 1, 137–138. [CrossRef] [PubMed] [Google Scholar]
  41. F.J. Burns, I.F. Tannock. On the existence of a G0 phase in the cell cycle. Cell Tissue Kinet., 19 (1970), No. 4, 321–334. [Google Scholar]
  42. H.M. Byrne, D. Drasdo. Individual-based and continuum models of growing cell populations: a comparison. J. Math. Biol., 58 (2009), No. 4-5, 657–87. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  43. L. Calzone, S. Soliman. Coupling the cell cycle and the circadian cycle. INRIA internal research report #5835 (2006). Available online from http://hal.inria.fr/INRIA-RRRT. [Google Scholar]
  44. A. Cappuccio, M.A. Herrero, L. Nunez. Biological optimization of tumor radiosurgery. Med Phys., 36 (2009), No. 1, 98–104. [CrossRef] [PubMed] [Google Scholar]
  45. N. Champagnat, R. Ferrière, S. Méléard. Unifying evolutionary dynamics: From individual stochastic processes to macroscopic models. Theoretical Population Biology, 69 (2006), No. 3, 297–321. [CrossRef] [PubMed] [Google Scholar]
  46. S.G. Chaney, S.L. Campbell, E. Bassett, Y.B. Wu. Recognition and processing of cisplatin- and oxaliplatin-DNA adducts. Clin. Rev. Oncol. Hematol., 53 (2003), No. 1, 3–11. [CrossRef] [Google Scholar]
  47. J.T. Chang, C. Carvalho, S. Mori S, A.H. Bild, M.L. Gatza, Q. Wang Q, J.E. Lucas JE, A. Potti, P.G. Febbo, M. West, J.R. Nevins. A genomic strategy to elucidate modules of oncogenic pathway signaling networks. Mol. Cell, 34 (2009), No.1, 104–14. [CrossRef] [PubMed] [Google Scholar]
  48. G. Chiorino, J.A.J. Metz, D. Tomasoni, P. Ubezio. Desynchronization rate in cell populations: mathematical modeling and experimental data. J. Theor. Biol., 208 (2001), No.2, 185–199. [CrossRef] [PubMed] [Google Scholar]
  49. A. Ciliberto, M.J. Petrus, J.J. Tyson, J.C. Sible. A kinetic model of the cyclin E/Cdk2 developmental timer in Xenopus laevis embryos. Biophys. Chem., 104 (2003), No. 3, 573–89. [CrossRef] [PubMed] [Google Scholar]
  50. A. Ciliberto, B. Novak, J.J. Tyson. Steady states and oscillations in the p53/Mdm2 network. Cell Cycle, 4 (2005), No. 3, 488–493. [CrossRef] [PubMed] [Google Scholar]
  51. J. Clairambault. A step toward optimization of cancer therapeutics. Physiologically based modelling of circadian control on cell proliferation. IEEE-EMB Magazine, 27 (2008), No.1, 20–24. [CrossRef] [Google Scholar]
  52. J. Clairambault, S. Gaubert, B. Perthame. An inequality for the Perron and Floquet eigenvalues of monotone differential systems and age structured equations. C. R. Acad. Sci. (Paris) Ser. I Mathématique, 345 (2007), No. 10, 549-554. [Google Scholar]
  53. J. Clairambault. Modelling oxaliplatin drug delivery to circadian rhythm in drug metabolism and host tolerance. Advanced Drug Delivery Reviews (ADDR), 59 (2007), No. 9-10, 1054–1068. [CrossRef] [PubMed] [Google Scholar]
  54. J. Clairambault, P. Michel, B. Perthame. A model of the cell cycle and its circadian control. In: Mathematical Modeling of Biological Systems, Volume I: Cellular Biophysics, Regulatory Networks, Development, Biomedicine, and Data Analysis, Deutsch, A., Brusch, L., Byrne, H., de Vries, G., Herzel, H. (Eds.), Birkhäuser, Boston, pp. 239-251, 2007. [Google Scholar]
  55. J. Clairambault, P. Michel, B. Perthame. Circadian rhythm and tumour growth. C. R. Acad. Sci. (Paris) Mathématique (Équations aux dérivées partielles), 342 (2006), No. 1, 17–22. [Google Scholar]
  56. L. Cojocaru, Z. Agur. A theoretical analysis of interval drug dosing for cell-cycle-phase-specific drugs. Math. BioSci., 109 (1992), No 1, 85–97. [Google Scholar]
  57. C. Colijn, M.C. Mackey. A mathematical model of hematopoiesis: I. Periodic chronic myelogenous leukemia. J. Theor. Biol., 237 (2005), No. 2, 117–132. [CrossRef] [PubMed] [Google Scholar]
  58. M.I.S Costa, J.L. Boldrini. Chemotherapeutic treatments: a study of the interplay among drug resistance, toxicity and recuperation from side effects. Bull. Math. Biol., 59 (1997), No. 2, 205–232. [CrossRef] [PubMed] [Google Scholar]
  59. M.I.S. Costa, J.L. Boldrini. Conflicting objectives in chemotherapy with drug resistance. Bull. Math. Biol., 59 (1997), No. 4, 707–724. [CrossRef] [PubMed] [Google Scholar]
  60. C. Csajka, D. Verotta. Pharmacokinetic-pharmacodynamic modelling: history and perspectives. J. Pharmacokinet. Pharmacodyn., 33 (2006), No. 3, 227–79. [CrossRef] [PubMed] [Google Scholar]
  61. A. Csikasz Nagy, D. Battogtokh, K.C. Chen, B. Novak, J.J. Tyson. Analysis of a generic model of eukaryotic cell-cycle regulation. Biophys J., 90 (2006), No. 12, 4361–79. [CrossRef] [PubMed] [Google Scholar]
  62. R. Dautray, J.-L. Lions. Mathematical analysis and numerical methods for sciences and technology. Ch. VIII, 187–199, Springer, Berlin,1990. [Google Scholar]
  63. T. David-Pfeuty. The flexible evolutionary anchorage-dependent Pardee's restriction point of mammalian cells: how its deregulation may lead to cancer. Biochim Biophys Acta., 1765 (2006), No. 1, 38–66. [PubMed] [Google Scholar]
  64. B.F. Dibrov, A.M. Zhabotinsky, Yu.A. Neyfakh, M.P. Orlova, L.I. Churikova. Optimal scheduling for cell synchronization by cycle-phase-specific blockers. Math. BioSci., 66 (1983), No. 2, 167–185. [CrossRef] [Google Scholar]
  65. B.F. Dibrov, A.M. Zhabotinsky, Yu.A. Neyfakh, M.P. Orlova, L.I. Churikova. Mathematical model of cancer chemotherapy. Periodic schedules of phase-specific cytotoxic-agent administration increasing the selectivity of therapy. Math. BioSci., 73 (1985), No. 1, 1–31. [CrossRef] [MathSciNet] [Google Scholar]
  66. O. Diekmann, P.E. Jabin, S. Mischler, B. Perthame. The dynamics of adaptation: an illuminating example and a Hamilton-Jacobi approach. Theoretical Population Biology, 67 (2005), No. 4, 257–271. [CrossRef] [PubMed] [Google Scholar]
  67. L. Dimitrio. Irinotecan: Modelling intracellular pharmacokinetics and pharmacodynamics, M2 master thesis (in French, English summary). University Pierre-et-Marie-Curie and INRIA internal report, June 2007. [Google Scholar]
  68. D. Dingli, A. Traulsen, J.M. Pacheco. Stochastic dynamics of hematopoietic tumor stem cells. Cell Cycle, 6 (2007), No. 4, 461–466. [CrossRef] [PubMed] [Google Scholar]
  69. D. Dingli, A. Traulsen, F. Michor. (A)symmetric stem cell replication and cancer. PLoS Comput. Biol., 2007, Mar 16;3(3):e53. [doi:10.1371/journal.pcbi.0030053]. [Google Scholar]
  70. D. Dingli, A. Traulsen, J.M. Pacheco. Compartmental architecture and dynamics of hematopoiesis. PLoS One, 2007, Apr. 4, 2(4): e345. [doi:10.1371/journal.pone.0000345]. [Google Scholar]
  71. D. Dingli, J.M. Pacheco. Some dynamic aspects of hematopoietic stem cells. Stem Cell Rev., 4 (2008), No. 1, 57–64. [CrossRef] [PubMed] [Google Scholar]
  72. D. Dingli, T. Antal, A. Traulsen, J.M. Pacheco. Progenitor self-renewal and cyclical neutropenia. Cell Prolif., 42 (2009), No. 3, 330–338. [CrossRef] [PubMed] [Google Scholar]
  73. M. Doumic-Jauffret. Analysis of a population model structured by the cells molecular content. Mathematical Modelling of Natural Phenomena, 2 (2007), No. 3, 121–15. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  74. D. Drasdo, S. Höhme, M. Block. On the Role of Physics in the Growth and Pattern Formation of Multi-Cellular Systems: What can we Learn from Individual-Cell Based Models? J. Stat. Phys.,128 (2007), No. 1-2, 287–345. [Google Scholar]
  75. B.J. Druker, et al. Effects of a selective inhibitor of the Abl tyrosine kinase activity on the growth of BCR-ABL positive cells. Nature Med., 2 (1996), No. 5, 561–566. [CrossRef] [Google Scholar]
  76. B.J. Druker, et al. Efficacy and safety of a specific inhibitor of the BCR-ABL tyrosine kinase in chronic myeloid leukemia. N. Engl. J. Med., 344 (2001), No. 14, 1031–1037. [CrossRef] [PubMed] [Google Scholar]
  77. A. Ducrot, V. Volpert. On a model of leukemia development with a spatial cell distribution. Mathematical Modelling of Natural Phenomena, 2 (2007), No. 3, 101–120. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  78. M. Eisen. Mathematical models in cell biology and cancer chemotherapy. Lectures Notes in Biomathematics 30, Springer, Berlin, 1979. [Google Scholar]
  79. M. Elshaikh, M. Ljungman, R. Ten Haken, A.S. Lichter. Advances in Radiation Oncology. Annu. Rev. Med., 57 (2006),19–31. [Google Scholar]
  80. S. Faivre, D. Chan, R. Salinas, B. Woynarowska, J.M. Woynarowski. DNA strand breaks and apoptosis induced by oxaliplatin in cancer cells. Biochemical pharmacology, 66 (2003), No. 2, 225–237. [CrossRef] [PubMed] [Google Scholar]
  81. E. Fearon, B. Vogelstein. A genetic model for colorectal tumorigenesis. Cell, 61 (1990), No. 5, 759–67. [CrossRef] [PubMed] [Google Scholar]
  82. J.E. Ferrell Jr. Tripping the switch fantastic: how a protein kinase cascade can convert graded inputs into switch-like outputs. Trends Biochem. Sci., 21 (1996), No. 12, 460–466. [CrossRef] [PubMed] [Google Scholar]
  83. J.E. Ferrell Jr. How responses get more switch-like as you move down a protein kinase cascade. Trends Biochem. Sci., 22 (1997), No. 8, 288–289. [Google Scholar]
  84. E. Filipski, V.M. King, X.M. Li, T.G. Granda, F. Lévi. Host circadian clock as a control point in tumor progression. J. Natl. Cancer Inst., 94 (2002), No. 9, 690–697. [CrossRef] [PubMed] [Google Scholar]
  85. E. Filipski, P.F. Innominato, M.W. Wu, X.M. Li, S. Iacobelli, L.J. Xian, F. Lévi. Effect of light and food schedules on liver and tumor molecular clocks in mice. J. Natl. Cancer Inst., 97 (2005), No. 7, 507–517. [CrossRef] [PubMed] [Google Scholar]
  86. G. Finak, N. Bertos, F. Pepin, S. Sadekova, M. Souleimanova, H. Zhao, H. Chen, G. Omeroglu, S. Meterissian, A. Omeroglu, M. Hallett, M. Park. Stromal gene expression predicts clinical outcome in breast cancer. Nature Med., 14 (2008), No. 5, 518–527. [CrossRef] [PubMed] [Google Scholar]
  87. B. Finkenstädt, E.A. Heron, M. Komorowski, K. Edwards, S. Tang, C.V. Harper CV, J.R. Davis, M.R. White, A.J. Millar, D.A. Rand. Reconstruction of transcriptional dynamics from gene reporter data using differential equations. Bioinformatics, 24 (2008), No. 24, 2901–2907. [CrossRef] [PubMed] [Google Scholar]
  88. K.R. Fister, J.C. Panetta. Optimal control applied to cell-cycle-specific cancer chemotherapy. SIAM J. Appl. Math., 60 (2000), No. 3, 1059–1072. [Google Scholar]
  89. C. Foley, S. Bernard, M.C. Mackey. Cost-effective G-CSF therapy strategies for cyclical neutropenia: Mathematical modelling based hypotheses. J. Theor. Biol., 238 (2006), No. 4, 754–763. [CrossRef] [PubMed] [Google Scholar]
  90. C. Foley, M.C. Mackey. Dynamic hematological disease: a review. J. Math. Biol., 58 (2009), No. 1-2, 285-322. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  91. C. Foley, M.C. Mackey. Mathematical model for G-CSF administration after chemotherapy. J. Theor. Biol., 257 (2009), No. 1, 27–44. [CrossRef] [PubMed] [Google Scholar]
  92. D.B. Forger, M.E. Jewett, R.E. Kronauer. A simpler model of the human circadian pacemaker. J. Biol .Rhythms, 14 (1999), No. 6, 532–7. [Google Scholar]
  93. D.B. Forger, R.E. Kronauer. Reconciling mathematical models of biological clocks by averaging on approximate manifolds. SIAM J. Appl. Math., 62 (2002), No. 4, 1281–1296. [CrossRef] [MathSciNet] [Google Scholar]
  94. D.B. Forger, C.S. Peskin. A detailed predictive model of the mammalian circadian clock. Proc. Natl. Acad. Sci. USA, 100 (2003), No. 25, 14806–14811. [CrossRef] [Google Scholar]
  95. D.B. Forger, D.A. Dean 2nd, K. Gurdziel, J.-C. Leloup, C. Lee, C. Von Gall, J.P. Etchegaray, R.E. Kronauer, A. Goldbeter, C.S. Peskin, M.E. Jewett, D.R. Weaver. Development and validation of computational models for mammalian circadian oscillators. OMICS, 7 (2003), No. 4, 387–400. [CrossRef] [PubMed] [Google Scholar]
  96. S. A. Frank. Dynamics of Cancer. Incidence, Inheritance and evolution. Princeton university Press, Princeton, 2007. [Google Scholar]
  97. A. Friedman (Ed.). Cell Cycle, Proliferation, and Cancer. Tutorials in Mathematical Biosciences III, Lecture Notes in Mathematics 1872 / Mathematical Biosciences Subseries, Springer, New York, 2006. [Google Scholar]
  98. L. Fu, H. Pelicano, J. Liu, P. Huang, C.C. Lee. The circadian gene Per2 plays an important role in tumor suppression and DNA damage response in vivo. Cell, 111 (2002), No. 1, 41–50. [CrossRef] [PubMed] [Google Scholar]
  99. L. Fu, L., C.C. Lee. The circadian clock: pacemaker and tumor suppressor. Nature Rev. Cancer, 3 (2003), No. 5, 350–361. [CrossRef] [PubMed] [Google Scholar]
  100. J. Galle, G. Aust, G. Schaller, T. Beyer, D. Drasdo. Individual cell-based models of the spatio-temporal organisation of multicellular systems - achievements and limitations. Cytometry A, 69A (2006), No. 7, 704–710. [CrossRef] [Google Scholar]
  101. R.A. Gatenby, E.T. Gawlinski. A reaction-diffusion model of cancer invasion. Cancer Res., 56 (1996), No. 24, 745–53. [PubMed] [Google Scholar]
  102. R.A. Gatenby, E.T. Gawlinski. The glycolytic phenotype in carcinogenesis and tumor invasion: insights through mathematical models. Cancer Res., 63 (2003), No. 14, 3847–54. [PubMed] [Google Scholar]
  103. R.A. Gatenby, R.J. Gillies. A microenvironmental model of carcinogenesis. Nature Rev. Cancer, 8 (2008), No. 1, 56–61. [CrossRef] [Google Scholar]
  104. S. Génieys, V. Volpert, P. Auger. Adaptive dynamics: modelling Darwin's divergence principle. C. R. Acad. Sci. Paris Biologie, 329 (2006), No. 11, 876–879. [Google Scholar]
  105. S. Génieys, N. Bessonov, V. Volpert. Mathematical model of evolutionary branching. Mathematical and Computer Modelling, 49 (2009), No. 11-12, 2109–2115. [CrossRef] [MathSciNet] [Google Scholar]
  106. A. Gerisch, M.A. Chaplain. Mathematical modelling of cancer cell invasion of tissue: local and non-local models and the effect of adhesion. J. Theor. Biol., 250 (2008), No. 4, 684–704. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  107. N. Geva-Zatorsky, N. Rosenfeld, S. Itzkovitz, R. Milo, A. Sigal, E. Dekel, T. Yarnitzky, Y. Liron, P. Polak, G. Lahav, U. Alon. Oscillations and variability in the p53 system. Mol. Syst. Biol., 2 (2006), 2:2006.0033. Epub 2006 Jun 13. [doi:10.1038/msb4100068]. [Google Scholar]
  108. D. Gholam, S. Giacchetti, C. Brézault-Bonnet, M. Bouchahda, D. Hauteville, R. Adam, B. Ducot, O. Ghémard, F. Kustlinger, C. Jasmin, F. Lévi. Chronomodulated irinotecan, oxaliplatin, and leucovorin-modulated 5-Fluorouracil as ambulatory salvage therapy in patients with irinotecan- and oxaliplatin-resistant metastatic colorectal cancer. Oncologist, 11 (2006), No. 10, 1072–80. [CrossRef] [PubMed] [Google Scholar]
  109. A. Goldbeter, D.E. Koshland Jr. An amplified sensitivity arising from covalent modification in biological systems. Proc. Natl. Acad. Sci. USA, 78 (1981), No. 11, 6840–4. [CrossRef] [Google Scholar]
  110. A. Goldbeter. A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase. Proc. Natl. Acad. Sci. USA, 88 (1991), No. 20, 9107–11. [CrossRef] [Google Scholar]
  111. A. Goldbeter. A model for circadian oscillations in the Drosophila period protein (PER). Proc Roy. Soc. B (Biol. Sci.) 261 (1995), No. 1362, 319–324. [Google Scholar]
  112. A. Goldbeter. Biochemical oscillations and cellular rhythms. Cambridge University Press, 1996. [Google Scholar]
  113. J.H. Goldie, A.J. Coldman. A mathematical model for relating the drug sensitivity of tumors to their spontaneous mutation rate. Canc. Treat. Rep., 63 (1979), No. 11-12, 1727–1733. [Google Scholar]
  114. J.H. Goldie, A.J. Coldman. Drug Resistance in Cancer: Mechanisms and Models. Cambridge University Press,1998. [Google Scholar]
  115. B.C. Goodwin. Temporal organization in cells: a dynamic theory of cellular control processes. Academic Press, New York, 1963. [Google Scholar]
  116. B.C. Goodwin. Oscillatory behavior in enzymatic control processes. In: Advances in enzyme regulation, vol. 3 (G. Weber, Ed.), pp. 425–438, Pergamon Press, Oxford, 1965. [Google Scholar]
  117. M.M. Gottesmann, T. Fojo, S.E. Bates. Multidrug resistance in cancer: Role of ABC transporters. Nature Rev. Cancer, 2 (2002), No. 1, 48–58. [CrossRef] [PubMed] [Google Scholar]
  118. T. Granda, X.H. Liu, R. Smaaland, N. Cermakian, E. Filipski, P. Sassone-Corsi, F. Lévi. Circadian regulation of cell cycle and apoptosis in mouse bone marrow and tumor. FASEB J., 19 (2005), No. 2, 304–306. [PubMed] [Google Scholar]
  119. M. Gyllenberg, G. Webb. Quiescence as an explanation of Gompertzian tumor growth. Growth Dev. Aging, 153 (1989), No. 1-2, 25–33. [Google Scholar]
  120. M. Gyllenberg, G. Webb. A nonlinear structured population model of tumor growth with quiescence. J. Math. Biol., 28 (1990), No. 6, 671–94. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  121. T. Haferlach. Molecular genetic pathways as therapeutic targets in AML. In: Educational book, ASH 2008 meeting, pp. 400–411, 2008. [Google Scholar]
  122. D. Hanahan, R.A. Weinberg. The hallmarks of cancer. Cell, 100 (2000), No. 1, 57–70. [CrossRef] [PubMed] [Google Scholar]
  123. J.C. Harrison, J.E. Haber. Surviving the breakup; the DNA damage checkpoint. Annu. Rev. Genet., 40 (2006), 209–235. [Google Scholar]
  124. C. Haurie, D.C. Dale, M.C. Mackey. Cyclical neutropenia and other periodic hematological diseases: A review of mechanisms and mathematical models. Blood, 92 (1998), No. 8, 2629–2640. [PubMed] [Google Scholar]
  125. R. Heinrich, S. Schuster. The regulation of cellular systems. Chapman and Hall, New York, 1996. [Google Scholar]
  126. E.A. Heron, B. Finkenstädt, D.A. Rand. Bayesian inference for dynamic transcriptional regulation; the Hes1 system as a case study. Bioinformatics, 23 (2007), No. 19, 2596–603. [Google Scholar]
  127. P. Hinow, S.E. Wang, C.L. Arteaga, G.F. Webb. A mathematical model separates quantitatively the cytostatic and cytotoxic effects of a HER2 tyrosine kinase inhibitor. Theor. Biol. Med. Modelling, (2007). [doi:10.1186/1742-4682-4-14.] [Google Scholar]
  128. M. Hollstein, D. Sidransky, B. Vogelstein, C.C. Harris. p53 mutations in human cancers. Science, 253 (1991), No. 5015, 49–53. [CrossRef] [PubMed] [Google Scholar]
  129. P.J. Houghton, G.S. Germain, F.C. Harwood, J.D. Schuetz, C.F. Stewart, E. Buchdunger, P. Traxler. Imatinib mesylate is a potent inhibitor of the ABCG2 (BCRP) transporter and reverses resistance to Topotecan and SN-38 in vitro. Canc. Res., 64 (2004), No. 7, 2333–2337. [CrossRef] [Google Scholar]
  130. A. Iliadis, D. Barbolosi. Optimizing drug regimens in cancer chemotherapy by an efficacy-toxicity mathematical model. Computers Biomed. Res., 33 (2000), No. 3, 211–226. [CrossRef] [PubMed] [Google Scholar]
  131. A. Iliadis, D. Barbolosi. Optimising drug regimens in cancer chemotherapy: a simulation study using a PK-PD model. Computers Biol. Med., 31 (2001), No. 3, 157–172. [CrossRef] [PubMed] [Google Scholar]
  132. F. Innocenti, D.L. Kroetz, E. Schuetz, M.E. Dolan, J. Ramirez, M. Relling, P.X. Chen, S. Das, G.L. Rosner, M.J. Ratain. Comprehensive pharmacogenetic analysis of Irinotecan neutropenia and pharmacokinetics. J. Clin. Oncol., (2009), Apr. 6 [Epub ahead of print]. [doi: 10.1200/JCO.2008.20.6300]. [Google Scholar]
  133. T.L. Jackson, H.M. Byrne. A mathematical model to study the effects of drug resistance and vasculature on the response of solid tumors to chemotherapy. Math. Biosci., 164 (2000), No. 1, 17–38. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  134. A. Jemal, R. Siegel, E. Ward, T. Murray, J.Q. Xu, M.J. Thun. Cancer Statistics, 2007. CA Cancer J. Clin., 57 (2007), No. 1, 43–66. [CrossRef] [PubMed] [Google Scholar]
  135. B. Kang, Y.Y. Li, X. Chang, L. Liu, Y.X. Li. Modeling the effects of cell cycle M-phase transcriptional inhibition on circadian oscillation. PLoS Comput. Biol., (2008). [doi: 10.1371/journal.pcbi.1000019]. [Google Scholar]
  136. M.B. Kastan, J. Bartek. Cell-cycle checkpoints and cancer. Nature, 432 (2004), No. 7015, 316–323. [CrossRef] [PubMed] [Google Scholar]
  137. J.P. Keener, J. Sneyd. Mathematical physiology. Springer, New York, 1998. [Google Scholar]
  138. Yu. Kheifetz, Yu. Kogan, Z. Agur. Long-range predictability in models of cell populations subjected to phase-specific drugs: Growth-rate approximation using properties of positive compact operators. Math. Models Meth. Appl. Sci., 16 (2006), No. 7, 1–18. [CrossRef] [Google Scholar]
  139. P.S. Kim, P.P. Lee, D. Levy. Modeling Imatinib-treated chronic myelogenous leukemia: reducing the complexity of agent-based models. Bull. Math. Biol. 70 (2008), No. 3, 728–744. [Google Scholar]
  140. P.S. Kim, P.P. Lee, D. Levy. A PDE model for Imatinib-treated chronic myelogenous leukemia. Bull. Math. Biol. 70 (2008), No. 7, 1994–2016. [Google Scholar]
  141. M. Kimmel, A. Swierniak. Control theory approach to cancer chemotherapy: Benefiting from phase dependence and overcoming drug resistance. In: Cell cycle, proliferation, and cancer (A. Friedman, Ed.), Springer LN 1872, pp. 185–216, Springer, New York, 2006. [Google Scholar]
  142. H. Kitano (Ed.). Foundations of Systems Biology. MIT Press, Cambridge (MA), 2001. [Google Scholar]
  143. H. Kitano. Computational systems biology. Nature, 420 (2002), No. 6912, 206–210. [CrossRef] [PubMed] [Google Scholar]
  144. H. Kitano. Cancer as a robust system: Implications for anticancer therapy. Nature Rev. Cancer, 4 ( 2004), No. 3, 227–235. [Google Scholar]
  145. H. Kitano. A robustness-based approach to systems-oriented drug design. Nature Rev. Drug Discovery, 6 (2007), No. 3, 202–210. [CrossRef] [Google Scholar]
  146. M. Kivisaar. Stationary phase mutagenesis: mechanisms that accelerate adaptation of microbial populations under environmental stress. Environm. Microbiol., 5 (2003), No. 10, 814–827. [CrossRef] [PubMed] [Google Scholar]
  147. M. von Kleist, W. Huisinga. Physiologically based pharmacokinetic modelling: a sub-compartmentalized model of tissue distribution. J Pharmacokinet Pharmacodyn., 34 (2007), No. 6, 789–806. [CrossRef] [PubMed] [Google Scholar]
  148. A.G. Knudson. Two genetic hits (more or less) to cancer. Nature Rev. Cancer, 1 (2001), No. 2, 157–162. [CrossRef] [PubMed] [Google Scholar]
  149. K. Kohn. Molecular interaction map of the mammalian cell cycle control and DNA repair systems. Mol. Biol. Cell, 10 (1999), No. 8, 2703–34. [CrossRef] [PubMed] [Google Scholar]
  150. K.W. Kohn, M.I. Aladjem, S. Kim, J.N. Weinstein, Y. Pommier. Depicting combinatorial complexity with the molecular interaction map notation. Mol. Sys. Biol., 51 (2006), 1–12. [doi:10.1038/msb4100088]. [Google Scholar]
  151. K.W. Kohn, M.I. Aladjem, J.N. Weinstein, Y. Pommier. Molecular interaction maps of bioregulatory networks: a general rubric for systems biology. Mol. Biol. Cell, 17 (2006), No. 1, 1–13. [Google Scholar]
  152. F. Kozusko, P.H. Chen, S.G. Grant, B.W. Day, J.C. Panetta. A mathematical model of in vitro cancer cell growth and treatment with the antimitotic agent curacin A. Math. Biosci., 170 (2001), No. 1, 1–16. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  153. F. Kozusko, Z. Bajzer. Combining Gompertzian growth and cell population dynamics. Math. Biosci., 185 (2003), No. 2, 153–67. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  154. A. Kramer, F.C. Yang, P. Snodgrass, X. Li, T.E. Scammell. Regulation of daily locomotor activity and sleep by hypothalamic EGF receptor signaling. Science, 294 (2001), No. 5551, 2511–15. [CrossRef] [PubMed] [Google Scholar]
  155. J.-J. Kupiec. A Darwinian theory for the origin of cellular differentiation. Molecular and General Genetics, 255 (1997), No. 2, 201–208. [CrossRef] [PubMed] [Google Scholar]
  156. J.-J. Kupiec, P. Sonigo. Ni Dieu ni gène. Pour une autre théorie de l'hérédité. Seuil, Paris, 2000. [Google Scholar]
  157. J.-J. Kupiec. L'origine des individus. Fayard, Paris, 2008. [Google Scholar]
  158. D.M. Kweekel, H. Gelderblom, H.-J. Guchelaar. Pharmacology of oxaliplatin and the use of pharmacogenomics to individualize therapy. Canc. Treat. Rev., 31 (2005), No.2, 90–105. [CrossRef] [Google Scholar]
  159. D.M. Kweekel, H. Gelderblom, H.-J. Guchelaar. Clinical and pharmacogenetic factors associated with irinotecan toxicity. Canc. Treat. Rev., 34 (2008), No. 7, 655–669. [Google Scholar]
  160. E. Laconi. The evolving concept of tumor microenvironments. Bioessays, 29 (2007), No. 8, 738–44. [CrossRef] [PubMed] [Google Scholar]
  161. G. Lahav, N. Rosenfeld, A. Sigal, N. Geva-Zatorsky, A.J. Levine, M.B. Elowitz, U. Alon. Dynamics of the p53-Mdm2 feedback loop in individual cells. Nature Genet., 36 (2004), No. 2, 147–150. [CrossRef] [PubMed] [Google Scholar]
  162. L.G. Lajtha. On DNA labeling in the study of the dynamics of bone marrow cell populations. In: Stohlman, Jr., F. (Ed), The Kinetics of Cellular Proliferation, pp. 173-182, Grune and Stratton, New York, 1959. [Google Scholar]
  163. J.L. Lebowitz, S.I. Rubinow. A theory for the age and generation time distribution of a microbial population. J. Math. Biol., 1 (1974), No. 1, 17–36. [CrossRef] [MathSciNet] [Google Scholar]
  164. U. Ledzewicz, H. Schättler. Structure of optimal controls for a cancer chemotherapy model with PK/PD. In: Proceedings of the 43rd Conference on Decision and Control, Atlantis, Bahamas islands, pp. 1376–1381, IEEE Publishing, 2004. [Google Scholar]
  165. J.-C. Leloup, D. Gonze, A. Goldbeter. Limit cycle models for circadian rhythms based on transcriptional regulation in Drosophila and Neurospora. J. Biol. Rhythms, 14 (1999), No. 6, 433–448. [CrossRef] [PubMed] [Google Scholar]
  166. J.-C. Leloup, A. Goldbeter. Towards a detailed computational model for the mammalian circadian clock. Proc. Natl. Acad. Sci. USA, 100 (2003), No. 12, 7051–7056. [CrossRef] [Google Scholar]
  167. F. Lévi (Ed.). Cancer chronotherapeutics. Special issue of Chronobiology International, Vol. 19 (2002), No. 1. [Google Scholar]
  168. F. Lévi. Chronotherapeutics: the relevance of timing in cancer therapy. Cancer Causes Control, 17 (2006), No. 4, 611–621. [CrossRef] [PubMed] [Google Scholar]
  169. F. Lévi, G. Metzger, C. Massari, G. Milano. Oxaliplatin: Pharmacokinetics and Chronopharmacological Aspects. Clin. Pharmacokinet., 38 (2000), No. 1, 1–21. [CrossRef] [PubMed] [Google Scholar]
  170. F. Lévi , U. Schibler. Circadian Rhythms: Mechanisms and Therapeutic Implications. Ann. Rev. Pharmacol. Toxicol., 47 (2007), 493–528. [Google Scholar]
  171. F. Lévi, A. Altinok, J. Clairambault, A. Goldbeter. Implications of circadian clocks for the rhythmic delivery of cancer therapeutics. Phil. Trans. Roy. Soc. A, 366 (2008), No. 1880, 3575–3598. [Google Scholar]
  172. A.J. Levine, J. Momand, C.A. Finlay. The p53 tumor suppressor gene. Nature, 351 (1991), No. 6326, 453–456. [CrossRef] [PubMed] [Google Scholar]
  173. M. Loeffler, I. Roeder. Tissue stem cells: definition, plasticity, heterogeneity, self-organization and models - A conceptual approach. Cells Tissues Organs, 171 (2002), No. 1, 8–26. [CrossRef] [PubMed] [Google Scholar]
  174. X.M. Li, G. Metzger, E. Filipski, N. Boughattas, G. Lemaigre, B. Hecquet., E. Filipski, F. Lévi. Pharmacologic modulation of reduced glutathione circadian rhythms with buthionine sulfoximine: relationship with cisplatin toxicity in mice. Tox. Appl. Pharmacol., 143 (1997), No. 2, 281–290. [CrossRef] [Google Scholar]
  175. X.M. Li, G. Metzger, E. Filipski, G. Lemaigre, F. Lévi. Modulation of nonprotein sulphydryl compounds rhythm with buthionine sulphoximine: relationship with oxaliplatin toxicity in mice. Arch.Toxicol., 72 (1998), No. 9, 574–579. [CrossRef] [PubMed] [Google Scholar]
  176. D.B. Longley, D.P. Harkin, P.G. Johnston. 5-Fluorouracil: mechanisms of action and clinical strategies. Nature Rev. Cancer, 3 (2003), No. 5, 330–338. [CrossRef] [PubMed] [Google Scholar]
  177. R.A. Lockshin, Z. Zakeri, J.L. Tilly (Eds.). When cells die. Wiley, New York, 1998. [Google Scholar]
  178. R.A. Lockshin, Z. Zakeri (Eds.). When cells die II. Wiley, New York, 2004. [Google Scholar]
  179. H. Lodish. Ed. Molecular Cell Biology. Freeman, New York, 2003. [Google Scholar]
  180. T.G. Lugo, A.M. Pendergast, A.J. Muller, O.N. Witte. Tyrosine kinase activity and transformation potency of BCR-ABL oncogene products. Science, 247 (1990), No. 4946, 1079–1082. [CrossRef] [PubMed] [Google Scholar]
  181. A.G. McKendrick. Applications of mathematics to medical problems. Proc. Edinburgh Math. Soc., 54 (1926), 98–130. [Google Scholar]
  182. M.C. Mackey. Unified Hypothesis for the Origin of Aplastic Anemia and Periodic Hematopoiesis. Blood, 51 (1978), No. 5, 941–956. [PubMed] [Google Scholar]
  183. M.C. Mackey. Dynamic hematological disorders of stem cell origin. In: G. Vassileva-Popova and E.V. Jensen (Eds). Biophysical and Biochemical Information Transfer in Recognition, pp. 373-409, Plenum Press, New York, 1979. [Google Scholar]
  184. M.C. Mackey, R. Rudnicki. Global stability in a delayed partial differential equation describing cellular replication. J. Math. Biol., 33 (1994), No. 1, 89–109. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  185. M.C. Mackey, R. Rudnicki.. A new criterion for the global stability of simultaneous cell replication and maturation process. J. Math. Biol., 38 (1999),195–219. [Google Scholar]
  186. M.C. Mackey. Cell kinetic status of haematopoietic stem cells. Cell Prolif., 34 (2001), No. 2, 71–83. [CrossRef] [PubMed] [Google Scholar]
  187. P. Macklin, S. McDougall, A.R.A Anderson, M.A. Chaplain, V. Cristini, J. Lowengrub. Multiscale modelling and nonlinear simulation of vascular tumour growth. J. Math. Biol., 58 (2009), No. 4-5, 765–98. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  188. M.V. Maffini, J.M. Calabro, A.M. Soto, C. Sonnenschein. Stromal regulation of neoplastic development. Age-dependent normalization of neoplastic mammary cells by mammary stroma. Am. J. Pathol., 167 (2005), No. 5, 1405–1410. [CrossRef] [PubMed] [Google Scholar]
  189. P. Magal, S.G. Ruan (Eds.). Structured population models in biology and epidemiology. Springer LN in Mathematics 1936, Springer, New York, 2008. [Google Scholar]
  190. P. Magni, M. Simeoni, I. Poggesi, M. Rocchetti. A mathematical model to study the effects of drugs administration on tumor growth dynamics. Math. Biosci., 200 (2006), No. 2, 127–51. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  191. M. Malumbres, M. Barbacid. To cycle or not to cycle: a critical decision in cancer. Nature Rev. Cancer, 1 (2001), No. 3, 222–231. [Google Scholar]
  192. A. Marciniak-Czochra, T. Stiehl, A.D. Ho, W. Jäger, W. Wagner. Modeling of asymmetric cell division in hematopoietic stem cells - Regulation of self-renewal is essential for efficient repopulation. Stem Cells Dev., 18 (2009), No. 3, 57–66. [CrossRef] [PubMed] [Google Scholar]
  193. J. Massagué. G1 cell-cycle control and cancer. Nature, 432 (2004), No. 7015, 298–306. [CrossRef] [PubMed] [Google Scholar]
  194. T. Matsuo, S. Yamaguchi, S. Mitsui, A. Emi, F. Shimoda, H. Okamura. Control mechanism of the circadian clock for timing of cell division in vivo. Science, 302 (2003), No. 5643, 255–259. [CrossRef] [PubMed] [Google Scholar]
  195. L. Mazelin, A. Bernet, C. Bonod-Bidaud, L. Pays, S. Arnaud, C. Gespach, D.E. Bredesen, J.-Y. Scoazec, P. Mehlen. Netrin-1 controls colorectal tumorigenesis by regulating apoptosis. Nature, 431 (2004), No. 7004, 80–4. [CrossRef] [PubMed] [Google Scholar]
  196. P. Mehlen, C. Thibert. Dependence receptors: between life and death. Cell Mol Life Sci., 61 (2004), No. 15, 1854–66. [PubMed] [Google Scholar]
  197. S. Méléard, V.C. Tran. Trait substitution sequence processes and canonical equation for age-structured populations. J. Math. Biol., 58 (2009), No. 6, 881–921. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  198. J. Mendelsohn, J. Baselga. Status of Epidermal Growth Factor Receptor Antagonists in the Biology and Treatment of Cancer. J. Clin. Oncol., 21 (2003), No. 14, 2787–2799. [CrossRef] [PubMed] [Google Scholar]
  199. J.A.J. Metz, O. Diekmann. The dynamics of physiologically structured populations. LN in biomathematics 68, Springer, New York, 1986. [Google Scholar]
  200. P. Michel, S. Mischler, B. Perthame. The entropy structure of models of structured population dynamics. General relative entropy inequality: an illustration on growth models. J. Math. Pures et Appl., 84 (2005), No. 9, 1235–1260. [Google Scholar]
  201. G. Milano, J. Robert. Pharmaco génétique - pharmacogénomie, quelle est la différence ? Oncologie, 7 (2005), No. 1, 4–5. [Google Scholar]
  202. S. Mischler, B. Perthame, L. Ryzhik. Stability in a Nonlinear Population Maturation Model. Mathematical Models and Methods in Applied Sciences (M3AS), 12 (2002), No. 12, 1751–1772. [CrossRef] [Google Scholar]
  203. M. Mishima, G. Samimi, A. Kondo, X. Lin, S.B. Howell, The cellular pharmacology of oxaliplatin resistance. Eur. J. Cancer, 38 (2002), No. 10, 1405–1412. [Google Scholar]
  204. D. Morgan. The Cell Cycle: Principles of Control. Primers in Biology series, Oxford University Press, 2006. [Google Scholar]
  205. M.-C. Mormont, F. Lévi. Cancer chronotherapy: principles, applications and perspectives. Cancer, 97 (2003), No. 1,155–169. [Google Scholar]
  206. J.D. Murray. Mathematical biology, 2 vol., 3rd edition, Springer, New York, 2002, 2003. [Google Scholar]
  207. J.M. Murray. Optimal drug regimens in cancer chemotherapy for single drugs that block progression through the cell cycle. Math. BioSci., 123 (1994), No. 2, 183–193. [CrossRef] [PubMed] [Google Scholar]
  208. I.A. Nestorov, L.J. Aarons, P.A. Arundel, M. Rowland. Lumping of whole-body physiologically based pharmacokinetic models. J Pharmacokinet Biopharm., 26 (1998), No.1, 21–46. [PubMed] [Google Scholar]
  209. B. Novak, Z. Pataki, A. Ciliberto, J.J. Tyson. Mathematical model of the cell division cycle of fission yeast. Chaos, 11 (2001), No. 1, 277–286. [CrossRef] [PubMed] [Google Scholar]
  210. B. Novak, J.J. Tyson. A model for restriction point control of the cell cycle. J. Theor. Biol., 230 (2004), No. 4, 563–579. [CrossRef] [PubMed] [Google Scholar]
  211. B. Novak, J.J. Tyson. Design principles of biochemical oscillators. Nature Rev. Mol. Cell Biol., 9 (2008), No. 12, 981–991. [CrossRef] [PubMed] [Google Scholar]
  212. T. Oguri, T. Isobe, K. Fujitaka, N. Ishikawa, N. Kohno. Association between expression of the MRP3 gene and exposure to platinum drugs in lung cancer. Int. J. Canc., 93 (2001), No. 4, 584–589. [CrossRef] [Google Scholar]
  213. T. Oguri, Y. Bessho, H. Achiwa, H. Ozasa, K. Maeno, H. Maeda, S. Sato, R. Ueda. MRP8/ABCC11 directly confers resistance to 5-fluorouracil. Mol. Canc. Therap., 6 (2007), No. 1, 122–127. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  214. H. Okamura. Suprachiasmatic nucleus clock time in the mammalian circadian system. Cold Spring Harbor Symposia on quantitative biology, Vol. LXXII (2007), 551–556. [Google Scholar]
  215. J.M. Pacheco, A. Traulsen, D. Dingli. The allometry of chronic myeloid leukemia. J. Theor. Biol., (2009). [doi:10.1016/j.jtbi.2009.04.003]. [Google Scholar]
  216. J.C. Panetta. A mechanistic model of temozolomide myelosuppression in children with high-grade gliomas. Math. Biosci., 186 (2003), No. 1, 29–41. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  217. B. Perthame. Transport equations in biology. Birkhäuser, Boston, 2007. [Google Scholar]
  218. B. Perthame, S. Génieys. Concentration in the nonlocal Fisher equation: the Hamilton-Jacobi limit. Mathematical Modelling of Natural Phenomena, 2 (2007), No.4, 135–151. [Google Scholar]
  219. V.K. Piotrovsky. Population pharmacodynamic and pharmacokinetic modeling via mixed effects. Curr. Op. Drug Discov. Devel., 3 (2000), No. 3, 314–319. [Google Scholar]
  220. Y. Pommier. Topoisomerase I inhibitors: camptothecins and beyond. Nature Rev. Cancer, 6 (2006), No. 10, 789–802. [CrossRef] [Google Scholar]
  221. C.S. Potten, M. Loeffler. Stem cells: attributes, cycles, spirals, pitfalls and uncertainties. Lessons for and from the crypt. Development ,110 (1990), No. 4, 1001–1020. [Google Scholar]
  222. C.S. Potten, C. Booth, D.M. Pritchard. The intestinal epithelial stem cell: the mucosal governor. Int. J. Exp. Path., 78 (1997), No. 4, 219–243. [CrossRef] [Google Scholar]
  223. L. Preziosi (Ed.). Cancer modelling and simulation. Chapman and Hall / CRC, New York, 2003. [Google Scholar]
  224. A. Quintas-Cardama, H.M. Kantardjian, J.E. Cortes. Mechanisms of primary and secondary resistance to imatinib in chronic myeloid leukemia. Cancer Control,16 (2009), No. 2, 122–31. [Google Scholar]
  225. D.A. Rand. Mapping global sensitivity of cellular network dynamics: sensitivity heat maps and a global summation law. J. Roy. Soc. Interface, 5 (2008), Suppl. 1, S59–69. [Google Scholar]
  226. A. Rafii, et al. Oncologic trogocytosis of an original stromal cell induces chemoresistance of ovarian tumours. PLoS One, 3 (2008), No. 12, e3894, Dec. 2008. [doi:10.1371/journal.pone.0003894]. [Google Scholar]
  227. F.I. Raynaud, et al. In vitro et in vivo pharmacokinetic-pharmacodynamic relationships for the trisubstituted aminopurine cyclin-dependent kinase inhibitors Olomoucine, Bohemine and CYC202. Clin. Canc. Res., 11 (2005), No. 113, 4875–4888. [CrossRef] [Google Scholar]
  228. D.C. Rees, E. Johnson, O. Lewinson. ABC transporters: the power to change. Nature Rev. Mol. Cell Biol., 10 (2009), No. 3, 218–227. [CrossRef] [PubMed] [Google Scholar]
  229. S.M. Reppert, D.R. Weaver. Coordination of circadian timing in mammals. Nature, 418 (2002), No. 6901, 935–941. [CrossRef] [PubMed] [Google Scholar]
  230. B. Ribba, O. Saut, T. Colin, D. Bresch, E. Grenier, J.-P. Boissel. A multiscale mathematical model of avascular tumor growth to investigate the therapeutic benefit of anti-invasive agents. J. Theor. Biol., 243 (2006), No. 4, 532–541. [CrossRef] [PubMed] [Google Scholar]
  231. T. Rich, P.F. Innominato, J. Boerner, M.-C. Mormont, S. Iacobelli, B. Baron, C. Jasmin, F. Lévi. Elevated serum cytokines correlated with altered behavior, serum cortisol rhythm, and dampened 24-hour rest-activity patterns in patients with metastatic colorectal cancer. Clin. Cancer Res., 11 (2005), No. 5, 1757–64. [CrossRef] [PubMed] [Google Scholar]
  232. N.R. Rodrigues, A. Rowan, M.E. Smith, I.B. Kerr, W.F. Bodmer, J.V. Gannon, D.P. Lane. p53 mutations in colorectal cancer. Proc. Natl. Acad. Sci. USA, 87 (1990), No. 19, 7555–7559. [CrossRef] [Google Scholar]
  233. I. Roeder, M. Loeffler. A novel dynamic model of hematopoietic stem cell organization based on the concept of within-tissue plasticicity. Exp. Hematol., 30 (2002), No. 8, 853–861. [CrossRef] [PubMed] [Google Scholar]
  234. M. Rotenberg. Transport theory for growing cell populations. J. Theor. Biol., 103 (1983), No. 2, 181–199. [CrossRef] [PubMed] [Google Scholar]
  235. P. Ruoff, S. Mohsenzadeh, L. Rensing. Circadian rhythms and protein turnover: the effect of temperature on the period lengths of clock mutants simulated by the Goodwin oscillator. Naturwissenschaften, 83 (1996), No. 11, 514–7. [CrossRef] [PubMed] [Google Scholar]
  236. P. Ruoff, M. Vinsjevik, C. Monnerjahn, L. Rensing. The Goodwin model: simulating the effect of light pulses on the circadian sporulation rhythm of Neurospora crassa. J. Theor. Biol., 209 (2001), No. 1, 29–42. [CrossRef] [PubMed] [Google Scholar]
  237. A. Sakaue-Sawano, H. Kurokawa, T. Morimura, A. Hanyu, H. Hama, H. Osawa, S. Kashiwagi, K. Fukami, T. Miyata, H. Miyoshi, T. Imamura, M. Ogawa, H. Masai, A. Miyawaki. Visualizing spatiotemporal dynamics of multicellular cell-cycle progression. Cell, 32 (2008), No. 3, 487–98. [CrossRef] [PubMed] [Google Scholar]
  238. A. Sakaue-Sawano, K. Ohtawa, H. Hama, M. Kawano, M. Ogawa, A. Miyawaki. Tracing the silhouette of individual cells in S/G2/M phases with fluorescence. Chem Biol., 15 (2008), No. 12, 1243–8. [CrossRef] [PubMed] [Google Scholar]
  239. U. Schibler. Liver regeneration clocks on. Science, 302 (2003), No. 5642, 234–235. [CrossRef] [PubMed] [Google Scholar]
  240. D. Schiffer. Radiotherapy by particle beams (hadrontherapy) of intracranial tumours: a survey on pathology. Neurol. Sci., 26 (2005), No. 1, 5–12. [CrossRef] [PubMed] [Google Scholar]
  241. R.L. Schilsky, G.M. Milano, M.J. Ratain (Eds.). Principles of Antineoplastic Drug Development and Pharmacology. Marcel Dekker, New York, 1996. [Google Scholar]
  242. L.B. Sheiner, J.-L. Steimer. Pharmacokinetic/pharmacodynamic modeling in drug development. Annu. Rev. Pharmacol. Toxicol., 40 (2000), 67–95. [CrossRef] [PubMed] [Google Scholar]
  243. J.A. Sherratt, M.A. Chaplain. A new mathematical model for avascular tumour growth. J. Math. Biol., 43 (2001), No. 4, 291–312. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  244. Y. Shiloh. ATM and related kinases: Safeguarding genome integrity. Nature Rev. Cancer, 3 (2003), No. 3,155-168, 2003. [Google Scholar]
  245. M. Simeoni, P. Magni P, C. Cammia, G. De Nicolao, V. Croci, E. Pesenti, M. Germani, I. Poggesi, M. Rocchetti. Predictive pharmacokinetic-pharmacodynamic modeling of tumor growth kinetics in xenograft models after administration of anticancer agents. Cancer Res., 64 (2004), No. 3, 1094–1101. [CrossRef] [PubMed] [Google Scholar]
  246. R. Smaaland, O.D. Laerum, K. Lote, O. Sletvold, R.B. Sothern, R. Bjerknes. DNA Synthesis in Human Bone Marrow is Circadian Stage Dependent. Blood, 77 (1991), No. 12, 2603–2611. [PubMed] [Google Scholar]
  247. C. Sonnenschein, A.M. Soto. Carcinogenesis and metastasis now in the third dimension - What's in it for pathologists? Am. J. Pathol., 168 (2006), No. 2, 363–366. [Google Scholar]
  248. C. Sonnenschein, A.M. Soto. Theories of carcinogenesis: an emerging perspective. Seminars in cancer biology, 18 (2008), No. 5, 372–377. [CrossRef] [PubMed] [Google Scholar]
  249. A.M. Soto, C. Sonnenschein. The somatic mutation theory of cancer: growing problems with the paradigm? BioEssays, 26 (2004), No. 10, 1097–1107. [Google Scholar]
  250. A.M. Soto, C. Sonnenschein, P.A. Miquel. On physicalism and downward causation in developmental and cancer biology. Acta biotheor., 56 (2008), No. 4, 257–74. [CrossRef] [PubMed] [Google Scholar]
  251. F.X. Su, X.Q. Hu, W.J. Jia, C. Gong, E.W. Song, P. Hamar. Glutathion S Transferase π indicates chemotherapy resistance in breast cancer. J. Surg. Res., 113 (2003), No. 1, 102–108. [CrossRef] [PubMed] [Google Scholar]
  252. G.W. Swan, T.L. Vincent. Optimal control analysis in the chemotherapy of IgG multiple myeloma. Bull. Math. Biol., 39 (1977), No. 3, 317–337. [PubMed] [Google Scholar]
  253. G.W. Swan. Applications of optimal control theory in biomedicine. Marcel Dekker, New York, 1984. [Google Scholar]
  254. K.R. Swanson, E.C. Alvord Jr, J.D. Murray. A quantitative model for differential motility of gliomas in grey and white matter. Cell Prolif., 33 (2000), No. 5, 317–29. [CrossRef] [PubMed] [Google Scholar]
  255. K.R. Swanson, C. Bridge, J.D. Murray, E.C. Alvord Jr. Virtual and real brain tumors: using mathematical modeling to quantify glioma growth and invasion. J Neurol. Sci., 16 (2003), No. 1, 1–10. [CrossRef] [Google Scholar]
  256. R. Tang, A.M. Faussat, J.-Y. Perrot, Z. Marjanovic, S. Cohen, T. Storme, H. Morjani, O. Legrand, J.-P. Marie. Zosuquidar restores drug sensitivity in P-glycoprotein expressing acute myeloid leukemia (AML). BMC Cancer, 8 (2008), 51. [doi:10.1186/1471-2407-8-51]. [CrossRef] [PubMed] [Google Scholar]
  257. T.N. Tozer, M. Rowland. Introduction to Pharmacokinetics and Pharmacodynamics: The Quantitative Basis of Drug Therapy. Lippincott, Philadelphia, 2006. [Google Scholar]
  258. Y. Tsukamoto, Y. Kato, M. Ura, I. Horii, T. Ishikawa, H. Ishitsuka, Y. Sugiyama. Investigation of 5-FU disposition after oral administration of capecitabine, a triple-prodrug of 5-FU, using a physiologically based pharmacokinetic model in a human cancer xenograft model: comparison of the simulated 5-FU exposures in the tumour tissue between human and xenograft model. Biopharm Drug Dispos., 22 (2001), No. 1, 1–14. [CrossRef] [PubMed] [Google Scholar]
  259. J.J. Tyson, C.I. Hong, C.D. Thron, B. Novak. A simple model of circadian rhythms based on dimerization and proteolysis of PER and TIM. Biophys J.,77 (1999), No. 5, 2411–7. [Google Scholar]
  260. J.J. Tyson, K. Chen, B. Novak. Network dynamics and cell physiology. Nature Rev. Mol. Cell Biol., 2 (2001), No. 12, 908–916. [CrossRef] [PubMed] [Google Scholar]
  261. P. Ubezio. Unraveling the complexity of cell cycle effects of anticancer drugs in cell populations. Disc. Cont. Dyn. Syst. B, 4 (2004), No. 1, 323–335. [CrossRef] [Google Scholar]
  262. K. Vanselow, J.T. Vanselow, P.O. Westermark, S. Reischl, B. Maier, T. Korte, A. Herrmann, H. Herzel, A. Schlosser, A. Kramer. Differential effects of PER2 phosphorylation: molecular basis for the human familial advanced sleep phase syndrome (FASPS). Genes Dev., 20 (2006), No. 19, 2660–2672. [CrossRef] [PubMed] [Google Scholar]
  263. J. Viguier, et al. ERCC1 codon 118 polymorphism is a predictive factor for the tumor response to oxaliplatin/5-fluorouracil combination chemotherapy in patients with advanced colorectal cancer. Clin Cancer Res., 11 (2005), No. 17, 6212–7. [CrossRef] [PubMed] [Google Scholar]
  264. B. Vogelstein, D. Lane, A.J. Levine. Surfing the p53 network. Nature, 408 (2010), No. 6810, 307–310. [CrossRef] [PubMed] [Google Scholar]
  265. H.M. Warenius, L. Seabra, L. Kyritsi, R. White, R. Dormer, S. Anandappa, C. Thomas, A. Howarth. Theranostic proteomic profiling of cyclins, cyclin dependent kinases and Ras in human cancer cell lines is dependent on p53 mutational status. Int. J. Oncol., 32 (2008), No. 4, 895–907. [PubMed] [Google Scholar]
  266. F.M. Watt, B.L. Hogan. Out of Eden: stem cells and their niches. Science, 287 (2000), No. 5457, 1427–1430. [CrossRef] [PubMed] [Google Scholar]
  267. G.F. Webb. Resonance phenomena in cell population chemotherapy models. Rocky Mountain J. Math., 20 (1990), No. 4, 1195–1216. [CrossRef] [MathSciNet] [Google Scholar]
  268. R.A. Weinberg. One renegade cell: how cancer begins. Basic Books, New York, 1998. [Google Scholar]
  269. H.V. Westerhoff, B.O. Palsson. The evolution of molecular biology into systems biology. Nature Biotechnol., 22 (2004), No. 10, 1249–1252. [CrossRef] [PubMed] [Google Scholar]
  270. H.V. Westerhoff. Mathematical and theoretical biology for systems biology, and then...vice versa. J. Math. Biol., 54 (2007), No. 1, 147–150. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  271. World Health Organisation (WHO). Preventing chronic diseases: a vital investment. (20055), Source: http://www.who.int/chp/chronic_disease_report/full_report.pdf 2005 [Google Scholar]
  272. D. Wodarz, D. Killer Cell Dynamics. Springer, New York, 2007. [Google Scholar]
  273. M.W. Wu, L.J. Xian, X.M. Li, P. Innominato, F. Lévi. Circadian expression of dihydropyrimidine dehydrogenase, thymidylate synthase, c-myc and p53 mRNA in mouse liver tissue. Ai Zheng (Chinese Journal of Cancer), 23 (2004), No. 3, 235–242. [Google Scholar]
  274. C. Wyman, R. Kanaar. DNA double-strand break repair: All's well that ends well. Annu. Rev. Genet., 40 (2006), 363–383. [CrossRef] [PubMed] [Google Scholar]
  275. J.H. Xing, J. Chen. The Goldbeter-Koshland switch in the first-order region and its response to dynamic disorder. PLoS ONE, 2008 May 14;3(5):e2140. [doi:10.1371/journal.pone.0002140]. [Google Scholar]
  276. S. Yamaguchi, H. Isejima, T. Matsuo, R. Okura, K. Yagita, M. Kobayashi, H. Okamura. Synchronization of cellular clocks in the`suprachiasmatic nucleus. Science, 302 (2003), No. 5649, 1408–12. [CrossRef] [PubMed] [Google Scholar]
  277. S. You, P.A. Wood, Y. Xiong, M. Kobayashi, J. Du Quiton, W.J.M. Hrushesky. Daily coordination of cancer growth and circadian clock gene expression. Breast Canc. Res. Treatment, 91 (2005), No. 1, 47–60. [CrossRef] [Google Scholar]
  278. J. Zamborsky, C.I. Hong, A. Csikasz-Nagy. Computational analysis of mammalian cell division gated by a circadian clock: quantized cell cycles and cell size control. J. Biol. Rhythms, 22 (2007), 542–553. [CrossRef] [PubMed] [Google Scholar]
  279. A. Zetterberg, O. Larsson, K.G. Wiman. What is the restriction point? Curr. Opin. Cell Biol., 7 (1995), No. 6, 835–42. [Google Scholar]
  280. L. Zitvogel, A. Tesniere, G. Kroemer. Cancer despite immunosurveillance: immunoselection and immunosubversion. Nature Rev. Immunol., 6 (2006), No. 10, 715–727. [CrossRef] [PubMed] [Google Scholar]
  281. L. Zitvogel, L. Apetoh, F. Ghiringhelli, G. Kroemer. Immunological aspects of cancer chemotherapy. Nature Rev. Immunol., 8 (2008), No. 1, 59–73. [CrossRef] [PubMed] [Google Scholar]
  282. L. Zitvogel, L. Apetoh, F. Ghiringhelli, F. André, A. Tesniere, G. Kroemer. The anticancer immune response: indispensable for therapeutic success? J. Clin. Invest., 118 (2008), No. 6, 1991–2001. [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.