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Optimisation of time-scheduled regimenfor anti-cancer drug infusion

Published online by Cambridge University Press:  15 November 2005

Claude Basdevant ,
Jean Clairambault  and
Francis Lévi
Claude Basdevant
Affiliation:
Université Paris-Nord, Villetaneuse and École Normale Supérieure, 75005 Paris, France. [email protected]
Jean Clairambault
Affiliation:
INRIA, projet BANG, 78153 Rocquencourt, France. [email protected] (corresponding author)
Francis Lévi
Affiliation:
INSERM E 0354, Hôpital Paul-Brousse, 94800 Villejuif, France. [email protected]
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Abstract

The chronotherapy concept takes advantage of the circadian rhythm of cells physiology in maximising a treatment efficacy on its target while minimising its toxicity on healthy organs. The object of the present paper is to investigate mathematically and numerically optimal strategies in cancer chronotherapy. To this end a mathematical model describing the time evolution of efficiency and toxicity of an oxaliplatin anti-tumour treatment has been derived. We then applied an optimal control technique to search for the best drug infusion laws.The mathematical model is a set of six coupled differentialequations governing the time evolution of both the tumour cell population(cells of Glasgow osteosarcoma, a mouse tumour) and the mature jejunalenterocyte population, to be shielded from unwanted side effectsduring a treatment by oxaliplatin. Starting from known tumour and villi populations, and a time dependent freeplatinum Pt (the active drug) infusion law being given,the mathematical model allows to compute the time evolution of both tumour andvilli populations. The tumour population growth is based on Gompertz law and the Pt anti-tumour efficacy takes into account the circadian rhythm. Similarly the enterocyte population is subject to a circadian toxicityrhythm. The model has been derived using, as far as possible, experimental data.We examine two different optimisation problems. The eradication problem consists in finding the drug infusion law able to minimise the number of tumour cells while preserving a minimal level for the villi population. On the other hand, the containment problem searches for a quasi periodic treatment able to maintain the tumour population at the lowest possible level, while preserving the villi cells. The originality of these approaches is that the objective and constraint functions we use are L ∞ criteria. We are able to derive their gradients with respect to the infusion rate and then to implement efficient optimisation algorithms.

Keywords

Dynamical systemsoptimisationcircadian rhythmsdrugstherapeuticscancer.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 39 , Issue 6 , November 2005 , pp. 1069 - 1086
Copyright
© EDP Sciences, SMAI, 2005

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References

Agur, Z., Arnon, R. and Schechter, B., Effect of the dosing interval on myelotoxicity and survival in mice treated by cytarabine. Eur. J. Cancer 28A (1992) 1085–1090. CrossRef
Andersen, L.K. and Mackey, M.C., Resonance in periodic chemotherapy: a case study of acute myelogenous leukemia. J. Theor. Biol. 209 (2001) 113–130. CrossRef
J.F. Bonnans, J.C. Gilbert, C. Lemarechal and C.A. Sagastizabal, Numerical Optimization: Theoretical and Practical Aspects. Springer Universitext (2003).
Boughattas, N.A., Lévi, F., 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.
Boughattas, N.A., Hecquet, B., Fournier, C., Bruguerolle, B., Trabelsi, A., Bouzouita, K., Omrane, B. and Lévi, F., 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
Britton, N.F., Wright, N.A. and Murray, J.D., A mathematical model for cell population kinetics in the intestine. J. Theor. Biol. 98 (1982) 531–541. CrossRef
Canaple, L., Kazikawa, T. and Laudet, V., The days and nights of cancer cells. Cancer Research 63 (2003) 7545–7552.
Clairambault, J., Claude, D., Filipski, E., Granda, T. and Lévi, F., 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
Cojocaru, L. and Agur, Z.A., Theoretical analysis of interval drug dosing for cell-cycle-phase-specific drugs. Math. Biosci. 109 (1992) 85–97. CrossRef
Dibrov, B.F., Zhabotinski, M.A., Neyfakh, Yu.A., Orlova, M.P. and Churikova, L.I., 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
Dibrov, B.F., Resonance effect in self-renewing tissues. J. Theor. Biol. 192 (1998) 15–33. CrossRef
L. Edelstein-Keshet, Mathematical Models in Biology. NY: McGraw-Hill (1988) 210–270.
El-Kareh, A.W. and Secomb, T.W., A mathematical model for cisplatin cellular pharmacodynamics. Neoplasia 5 (2004) 161–169. CrossRef
Faivre, S., Chan, D., Salinas, R., Woynarowska, B. and Woynarowski, J.M., Single St, DNArand Breaks and apoptosis induced by oxaliplatin in cancer cells. Biochemical Pharmacology 66 (2003) 225–237. CrossRef
Fister, K.R. and Panetta, J.C., Optimal control applied to cell-cycle-specific cancer chemotherapy. SIAM J. Appl. Math. 60 (2000) 1059–1072.
Fu, L., Pellicano, H., Liu, J., Huang, P. and Lee, C.C., The Circadian Gene Period2 Plays an Important Role in Tumor Suppression and DNA Damage Response In Vivo. Cell 111 (2002) 41–50. CrossRefPubMed
Fu, L. and Lee, C.C., The circadian clock: pacemaker and tumour suppressor. Nature Reviews 3 (2003) 351–361.
Granda, T.G., D'Attino, R.-M., Filipski, E., et al., Circadian optimisation of irinotecan and oxaliplatin efficacy in mice with Glasgow osteosarcoma. Brit. J. Cancer 86 (2002) 999–1005. CrossRef
Granda, T.G., Liu, X.H., Smaaland, R., Cermakian, N., Filipski, E., Sassone-Corsi, P. and Levi, F., Circadian regulation of cell cycle and apoptosis proteins in mouse bone marrow and tumor. FASEB J. 19 (2005) 304.
M. Gyllenberg and G.F. Webb, Quiescence as an explanation of gompertzian tumor growth. Growth, Development and Aging 53 (1989) 25–33.
Gyllenberg, M. and Webb, G.F., A nonlinear structured population model of tumor growth with quiescence. J. Math. Biol. 28 (1990) 671–694. CrossRef
Hastings, M.H., Reddy, A.B. and Maywood, E.S., A clockwork web: circadian timing in brain and periphery, in health and disease. Nat. Rev. Neurosci. 4 (2003) 649–661. CrossRef
Iliadis, A. and Barbolosi, D., Optimising drug regimens in cancer chemotherapy by an efficacy-toxicity mathematical model. Computers Biomed. Res. 33 (2000) 211–226. CrossRef
Iliadis, A. and Barbolosi, D., Optimising drug regimens in cancer chemotherapy: a simulation study using a PK-PD model. Computers Biol. Med. 31 (2001) 157–172.
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).
Lévi, F., Metzger, G., Massari, C. and Milano, G., Oxaliplatin: Pharmacokinetics and Chronopharmacological Aspects. Clin. Pharmacokinet. 38 (2000) 1–21.
F. Lévi (Ed.), Cancer Chronotherapeutics. Special issue of Chronobiology International 19 #1 (2002).
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.
McKeage, M.C., Hsu, T., Haddad, G. and Baguley, B.C., Nucleolar damage correlates with neurotoxicity induced by different platinum drugs. Br. J. Cancer 85 (2001) 1219–1225. CrossRef
Mishima, M., Samimi, G., Kondo, A., Lin, X. and Howell, S.B., The cellular pharmacology of oxaliplatin resistance. Eur. J. Cancer 38 (2002) 1405–1412. CrossRef
Potten, C.S. and Loeffler, M., Stem cells: attributes, cycles, spirals, pitfalls and uncertainties. Lessons for and from the crypt. Development 110 (1990) 1001–1020.
U. Schibler, Circadian rhythms. Liver regeneration clocks on. Science 302 (5643) (2003) 234–235.
Swan, G., Role of optimal control theory in cancer chemotherapy. Math. Biosci. 101 (1990) 237–284. CrossRef
Webb, G.F., Resonance phenomena in cell population chemotherapy models. Rocky Mountain J. Math. 20 (1990) 1195–1216. CrossRef