Free Access
Volume 39, Number 6, November-December 2005
Page(s) 1069 - 1086
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] [Google Scholar]
  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] [Google Scholar]
  3. J.F. Bonnans, J.C. Gilbert, C. Lemarechal and C.A. Sagastizabal, Numerical Optimization: Theoretical and Practical Aspects. Springer Universitext (2003). [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  7. L. Canaple, T. Kazikawa and V. Laudet, The days and nights of cancer cells. Cancer Research 63 (2003) 7545–7552. [PubMed] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  11. B.F. Dibrov, Resonance effect in self-renewing tissues. J. Theor. Biol. 192 (1998) 15–33. [CrossRef] [PubMed] [Google Scholar]
  12. L. Edelstein-Keshet, Mathematical Models in Biology. NY: McGraw-Hill (1988) 210–270. [Google Scholar]
  13. A.W. El-Kareh and T.W. Secomb, A mathematical model for cisplatin cellular pharmacodynamics. Neoplasia 5 (2004) 161–169. [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  17. L. Fu and C.C. Lee, The circadian clock: pacemaker and tumour suppressor. Nature Reviews 3 (2003) 351–361. [CrossRef] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  20. M. Gyllenberg and G.F. Webb, Quiescence as an explanation of gompertzian tumor growth. Growth, Development and Aging 53 (1989) 25–33. [Google Scholar]
  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] [Google Scholar]
  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. [Google Scholar]
  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. [Google Scholar]
  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. [Google Scholar]
  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 (2003). [Google Scholar]
  26. F. Lévi, G. Metzger, C. Massari and G. Milano, Oxaliplatin: Pharmacokinetics and Chronopharmacological Aspects. Clin. Pharmacokinet. 38 (2000) 1–21. [CrossRef] [PubMed] [Google Scholar]
  27. F. Lévi (Ed.), Cancer Chronotherapeutics. Special issue of Chronobiology International 19 #1 (2002). [Google Scholar]
  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. [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  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] [Google Scholar]
  32. U. Schibler, Circadian rhythms. Liver regeneration clocks on. Science 302 (5643) (2003) 234–235. [Google Scholar]
  33. G. Swan, Role of optimal control theory in cancer chemotherapy. Math. Biosci. 101 (1990) 237–284. [CrossRef] [PubMed] [Google Scholar]
  34. G.F. Webb, Resonance phenomena in cell population chemotherapy models. Rocky Mountain J. Math. 20 (1990) 1195–1216. [CrossRef] [MathSciNet] [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.

Recommended for you