Free access
Issue
ESAIM: M2AN
Volume 39, Number 6, November-December 2005
Page(s) 1069 - 1086
DOI http://dx.doi.org/10.1051/m2an:2005052
Published online 15 November 2005
  1. Z. Agur, R. Arnon and B. Schechter, Effect of the dosing interval on myelotoxicity and survival in mice treated by cytarabine. Eur. J. Cancer 28A (1992) 1085–1090. [CrossRef] [PubMed]
  2. L.K. Andersen and M.C. Mackey, Resonance in periodic chemotherapy: a case study of acute myelogenous leukemia. J. Theor. Biol. 209 (2001) 113–130. [CrossRef] [PubMed]
  3. J.F. Bonnans, J.C. Gilbert, C. Lemarechal and C.A. Sagastizabal, Numerical Optimization: Theoretical and Practical Aspects. Springer Universitext (2003).
  4. 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) 3362–3368. [PubMed]
  5. N.A. Boughattas, B. Hecquet, C. Fournier, B. Bruguerolle, A. Trabelsi, K. Bouzouita, B. Omrane and F. Lévi, Comparative pharmacokinetics of oxaliplatin (L-OHP) and carboplatin (CBDCA) in mice with reference to circadian dosing time. Biopharmaceutics and drug disposition 15 (1994) 761–773. [CrossRef]
  6. N.F. Britton, N.A. Wright and J.D. Murray, A mathematical model for cell population kinetics in the intestine. J. Theor. Biol. 98 (1982) 531–541. [CrossRef] [PubMed]
  7. L. Canaple, T. Kazikawa and V. Laudet, The days and nights of cancer cells. Cancer Research 63 (2003) 7545–7552. [PubMed]
  8. J. Clairambault, D. Claude, E. Filipski, T. Granda and F. Lévi, Toxicité et efficacité antitumorale de l'oxaliplatine sur l'ostéosarcome de Glasgow induit chez la souris : un modèle mathématique. Pathologie-Biologie 51 (2003) 212–215. [CrossRef] [PubMed]
  9. L. Cojocaru and Z.A. Agur, Theoretical analysis of interval drug dosing for cell-cycle-phase-specific drugs. Math. Biosci. 109 (1992) 85–97. [CrossRef] [PubMed]
  10. B.F. Dibrov, M.A. Zhabotinski, Yu.A. Neyfakh, M.P. Orlova and L.I. Churikova, Mathematical model of cancer chemotherapy. Periodic schedules of of phase-specific cytotoxic agent administration increasing the selectivity of therapy. Math. Biosci. 73 (1985) 1–34. [CrossRef] [MathSciNet]
  11. B.F. Dibrov, Resonance effect in self-renewing tissues. J. Theor. Biol. 192 (1998) 15–33. [CrossRef] [PubMed]
  12. L. Edelstein-Keshet, Mathematical Models in Biology. NY: McGraw-Hill (1988) 210–270.
  13. A.W. El-Kareh and T.W. Secomb, A mathematical model for cisplatin cellular pharmacodynamics. Neoplasia 5 (2004) 161–169.
  14. S. Faivre, D. Chan, R. Salinas, B. Woynarowska and J.M. Woynarowski, DNA Single Strand Breaks and apoptosis induced by oxaliplatin in cancer cells. Biochemical Pharmacology 66 (2003) 225–237. [CrossRef] [PubMed]
  15. K.R. Fister and J.C. Panetta, Optimal control applied to cell-cycle-specific cancer chemotherapy. SIAM J. Appl. Math. 60 (2000) 1059–1072. [CrossRef] [MathSciNet]
  16. L. Fu, H. Pellicano, J. Liu, P. Huang and C.C. Lee, The Circadian Gene Period2 Plays an Important Role in Tumor Suppression and DNA Damage Response In Vivo. Cell 111 (2002) 41–50. [CrossRef] [PubMed]
  17. L. Fu and C.C. Lee, The circadian clock: pacemaker and tumour suppressor. Nature Reviews 3 (2003) 351–361. [CrossRef]
  18. T.G. Granda, R.-M. D'Attino, E. Filipski, et al., Circadian optimisation of irinotecan and oxaliplatin efficacy in mice with Glasgow osteosarcoma. Brit. J. Cancer 86 (2002) 999–1005. [CrossRef]
  19. T.G. Granda, X.H. Liu, R. Smaaland, N. Cermakian, E. Filipski, P. Sassone-Corsi and F. Levi, Circadian regulation of cell cycle and apoptosis proteins in mouse bone marrow and tumor. FASEB J. 19 (2005) 304. [PubMed]
  20. M. Gyllenberg and G.F. Webb, Quiescence as an explanation of gompertzian tumor growth. Growth, Development and Aging 53 (1989) 25–33.
  21. M. Gyllenberg and G.F. Webb, A nonlinear structured population model of tumor growth with quiescence. J. Math. Biol. 28 (1990) 671–694. [CrossRef] [MathSciNet] [PubMed]
  22. M.H. Hastings, A.B. Reddy and E.S. Maywood, A clockwork web: circadian timing in brain and periphery, in health and disease. Nat. Rev. Neurosci. 4 (2003) 649–661. [CrossRef] [PubMed]
  23. A. Iliadis and D. Barbolosi, Optimising drug regimens in cancer chemotherapy by an efficacy-toxicity mathematical model. Computers Biomed. Res. 33 (2000) 211–226. [CrossRef] [PubMed]
  24. A. Iliadis and D. Barbolosi, Optimising drug regimens in cancer chemotherapy: a simulation study using a PK-PD model. Computers Biol. Med. 31 (2001) 157–172. [CrossRef] [PubMed]
  25. M. Kimmel and A. Swierniak, Using control theory to make cancer chemotherapy beneficial from phase dependence and resistant to drug resistance. Technical report #7, Ohio State University, Nov. 2003, available on line at http://mbi.osu.edu/publications/techreport7.pdf (2003).
  26. F. Lévi, G. Metzger, C. Massari and G. Milano, Oxaliplatin: Pharmacokinetics and Chronopharmacological Aspects. Clin. Pharmacokinet. 38 (2000) 1–21. [CrossRef] [PubMed]
  27. F. Lévi (Ed.), Cancer Chronotherapeutics. Special issue of Chronobiology International 19 #1 (2002).
  28. T. Matsuo, S. Yamaguchi, S. Mitsui, A. Emi, F. Shimoda and H. Okamura, Control mechanism of the circadian clock for timing of cell division in vivo. Science 302 (5643) (2003) 255–259.
  29. M.C. McKeage, T. Hsu, G. Haddad and B.C. Baguley, Nucleolar damage correlates with neurotoxicity induced by different platinum drugs. Br. J. Cancer 85 (2001) 1219–1225. [CrossRef] [PubMed]
  30. M. Mishima, G. Samimi, A. Kondo, X. Lin and S.B. Howell, The cellular pharmacology of oxaliplatin resistance. Eur. J. Cancer 38 (2002) 1405–1412. [CrossRef] [PubMed]
  31. C.S. Potten and M. Loeffler, Stem cells: attributes, cycles, spirals, pitfalls and uncertainties. Lessons for and from the crypt. Development 110 (1990) 1001–1020. [PubMed]
  32. U. Schibler, Circadian rhythms. Liver regeneration clocks on. Science 302 (5643) (2003) 234–235.
  33. G. Swan, Role of optimal control theory in cancer chemotherapy. Math. Biosci. 101 (1990) 237–284. [CrossRef] [PubMed]
  34. G.F. Webb, Resonance phenomena in cell population chemotherapy models. Rocky Mountain J. Math. 20 (1990) 1195–1216. [CrossRef] [MathSciNet]

Recommended for you