Maximum tolerated dose versus metronomic scheduling in the treatment of metastatic cancers

Journal of Theoretical Biology

Volumn 335, Issue , 2013, Pages 235-244

  Benzekry, Sébastien ^a   Hahnfeldt, Philip ^a  

^a TUFTS UNIVERSITY SCHOOL OF MEDICINE   (United States)

Author keywords

Cancer modeling; Metastasis; Metronomics; Scheduling optimization

Indexed keywords

ANGIOGENESIS INHIBITOR; CYTOTOXIC AGENT;

CANCER; DISEASE TREATMENT; MODELING; OPTIMIZATION; TUMOR;

ARTICLE; CANCER COMBINATION CHEMOTHERAPY; CANCER CONTROL; CANCER SIZE; CLINICAL PROTOCOL; COMPUTER ANALYSIS; COMPUTER SIMULATION; CONTINUOUS INFUSION; LOW DRUG DOSE; MAXIMUM TOLERATED DOSE; METASTASIS; METASTASIS INHIBITION; METRONOMIC DRUG ADMINISTRATION; MONOTHERAPY; PRIORITY JOURNAL; THEORETICAL STUDY;

CANCER MODELING; METASTASIS; METRONOMICS; SCHEDULING OPTIMIZATION;

ADMINISTRATION, METRONOMIC; ANGIOGENESIS INHIBITORS; ANTINEOPLASTIC COMBINED CHEMOTHERAPY PROTOCOLS; CYTOTOXINS; HUMANS; MAXIMUM TOLERATED DOSE; MODELS, BIOLOGICAL; NEOPLASM METASTASIS; NEOPLASMS;

EID: 84881237231     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2013.06.036     Document Type: Article

References (56)

1. André N., Rome A., Coze C., Padovani L., Pasquier E., Camoin L., et al. Metronomic etoposide/cyclophosphamide/celecoxib regimen to children and adolescents with refractory cancer: a preliminary monocentric study. Clin. Ther. 2008, 30(7):1336-1340.
2. Araujo R.P., McElwain D.L.S. A history of the study of solid tumour growth: the contribution of mathematical modelling. Bull. Math. Biol. 2004, 66(5):1039-1091.
3. Ballesta A., Dulong S., Abbara C., Cohen B., Okyar A., Clairambault J., Levi F. A combined experimental and mathematical approach for molecular-based optimization of irinotecan circadian delivery. PLoS Comput. Biol. 2011, 7(9):e1002143.
4. Ballesta A., Clairambault J., Dulong S., Lévi F. Theoretical optimization of irinotecan-based anticancer strategies in case of drug-induced efflux. Appl. Math. Lett. 2011, 24(7):1251-1256.
5. Ballesta, A., Clairambault, J., Dulong, S., Lévi, F. A systems biomedicine approach for chronotherapeutics optimization: focus on the anticancer drug irinotecan. In: D'Onofrio, Alberto, Cerrai, Paola, Gandolfi, Alberto (Eds.), New Challenges for Cancer Systems Biomedicine, Part V, SIMAI Lecture Notes, Springer, New York, 2012, pp. 301-327.
6. Barbolosi D., Iliadis A. Optimizing drug regimens in cancer chemotherapy: a simulation study using a PK-PD model. Comput. Biol. Med. 2001, 31(3):157-172.
7. Barbolosi D., Freyer G., Ciccolini J., Iliadis A. Optimisation de la posologie et des modalités d'administration des agents cytotoxiques à l'aide d'un modèle mathématique. Bull. Cancer 2003, 90(2):167-175.
8. Barbolosi D., Benabdallah A., Hubert F., Verga F. Mathematical and numerical analysis for a model of growing metastatic tumors. Math. Biosci. 2009, 218(1 (March)):1-14.
9. Bekkal Brikci F., Clairambault J., Ribba B., Perthame B. An age-and-cyclin-structured cell population model for healthy and tumor tissues. J. Math. Biol. 2008, 57(1):91-110.
10. Benzekry S. Mathematical analysis of a two-dimensional population model of metastatic growth including angiogenesis. J. Evol. Equations 2011, 11(1 (December 23)):187-213.
11. Benzekry S. Mathematical and numerical analysis of a model for anti-angiogenic therapy in metastatic cancers. ESAIM: Math. Modell. Numer. Anal. 2011, 46(2 (October 5)):207-237.
12. Benzekry S., Chapuisat G., Ciccolini J., Erlinger A., Hubert F. A new mathematical model for optimizing the combination between antiangiogenic and cytotoxic drugs in oncology. CRAS Math. 2012, 350(1-2):23-28.
13. Benzekry S., André N., Benabdallah A., Ciccolini J., Faivre C., Hubert F., et al. Modelling the impact of anticancer agents on metastatic spreading. Math. Model. Nat. Phenom. 2012, 7(1):306-336.
14. Billy, F., Clairambault, J., Fercoq. O., 2013. Optimisation of cancer drug treatments using cell population dynamics. In: A. Friedman, E. Kashdan, U. Ledzewicz, H. Schättler (Eds.), Mathematical Methods and Models in Biomedicine, Springer. http://dx.doi.org/10.1007/978-1-4614-4178-6.
15. Billy, F., Clairambault, J., Fercoq, O., Gaubert, S., Lepoutre, T., Ouillon, T., Saito, S., Synchronisation and control of proliferation in cycling cell population models with age structure Math. Comput. Simul., , in press. http://dx.doi.org/10.1016/j.matcom.2012.03.005.
16. Browder T., Butterfield C.E., Kräling B.M., Kra B.M., Shi B., Marshall B., et al. Antiangiogenic scheduling of chemotherapy improves efficacy against experimental drug-resistant cancer. Cancer Res. 2000, 1878-1886.
17. Clairambault J., Gaubert S., Lepoutre T. Circadian rhythm and cell population growth. Math. Comput. Modell. 2011, 53:1558-1567.
18. Coldman A.J., Goldie J.H. A model for the resistance of tumor cells to cancer chemotherapeutic agents. Math. Biosci. 1983, 65:291-307.
19. d'Onofrio A., Gandolfi A. Tumour eradication by antiangiogenic therapy: analysis and extensions of the model by Hahnfeldt et al. (1999). Math. Biosci. 2004, 191(2):159-184.
20. d'Onofrio A., Gandolfi A. Chemotherapy of vascularised tumours: role of vessel density and the effect of vascular "pruning". J. Theor. Biol. 2010, 264:253-265.
21. D'Onofrio A., Ledzewicz U., Maurer H., Schättler H. On optimal delivery of combination therapy for tumors. Math. Biosci. 2009, 222(1 (November)):13-26.
22. D'Onofrio a., Gandolfi A., Rocca A. The dynamics of tumour-vasculature interaction suggests low-dose, time-dense anti-angiogenic schedulings. Cell Prolif. 2009, 42(3 (June)):317-329.
23. Devys A., Goudon T., Lafitte P. A model describing the growth and the size distribution of multiple metastatic tumors. Discrete Continuous Dyn. Syst. Ser. B 2009, 12(4 (August)):731-767.
24. Eder J.P., Supko J.G., Clark J.W., Puchalski T.A., Garcia-Carbonero R., Ryan D.P., et al. Phase I clinical trial of recombinant human endostatin administered as a short intravenous infusion repeated daily. J. Clin. Oncol. 2002, 20(18 (September)):3772-3784.
25. Eikesdal H.P., Kalluri R. Drug resistance associated with antiangiogenesis therapy. Semin. Cancer Biol. 2009, 19:310-317.
26. Ergun A., Camphausen K., Wein L.M. Optimal scheduling of radiotherapy and angiogenic inhibitors. Bull. Math. Biol. 2003, 65(3 (May)):407-424.
27. Fidler I.J., Paget S. The pathogenesis of cancer metastasis: the "seed and soil" hypothesis revisited. Nat. Rev. Cancer 2003, 3(6):453-458.
28. Folkman J. Antiangiogenesis: new concept for therapy of solid tumors. Ann. Surg. 1972, 175(3 (March)):409-416.
29. Folkman J. Angiogenesis inhibitors generated by tumors. Mol. Med. 1995, 1(2 (January)):120-122.
30. Hahnfeldt P., Panigraphy D., Folkman J., Hlatky L. Tumor development under angiogenic signaling: a dynamical theory of tumor growth, treatment, response and postvascular dormancy. Cancer Res. 1999, 59(19 (October 1)):4770-4775.
31. Hahnfeldt P., Folkman J., Hlatky L. Minimizing long-term tumor burden: the logic for metronomic chemotherapeutic dosing and its antiangiogenic basis. J. Theor. Biol. 2003, 220:545-554.
32. Hansma a.H.G., Broxterman H.J., van der H.o.r.s.t., Yuana Y., Boven E., Giaccone G., et al. Recombinant human endostatin administered as a 28-day continuous intravenous infusion, followed by daily subcutaneous injections: a phase I and pharmacokinetic study in patients with advanced cancer. Ann. Oncol. 2005, 16(10 (October)):1695-1701.
33. Iliadis A., Barbolosi D. Dosage regimen calculations with optimal control theory. Int. J. Biomed. Comput. 1994, 36:87-93.
34. Iliadis A., Barbolosi D. Optimizing drug regimens in cancer chemotherapy by an efficacy-toxicity mathematical model. Comput. Biomed. Res. 2000, 33:211-226.
35. Iwata K., Kawasaki K., Shigesada N. A dynamical model for the growth and size distribution of multiple metastatic tumors. J. Theor. Biol. 2000, 203(2 (March 21)):177-186.
36. Jain R.K. Normalizing tumor vasculature with anti-angiogenic therapy: a new paradigm for combination therapy. Nat. Med. 2001, 7:987-989.
37. Kerbel R.S. A cancer therapy resistant to resistance. Nature 1997, 390:335-340.
38. Kerbel R.S., Kamen B.A. The anti-angiogenic basis of metronomic chemotherapy. Nat. Rev. Cancer 2004, 4(6 (June):423-436.
39. Kisker O., Becker C.M., Prox D., Fannon M., D'Amato R., Flynn E., et al. Continuous administration of endostatin by intraperitoneally implanted osmotic pump improves the efficacy and potency of therapy in a mouse xenograft tumor model. Cancer Res. 2001, 61 (October):7669-7674.
40. Klement G., Baruchel S., Rak J., Man S., Clark K., Hicklin D.J., et al. Continuous low-dose therapy with vinblastine and VEGF receptor-2 antibody induces sustained tumor regression without overt toxicity. J. Clin. Invest. 2000, 105(8 (April)):15-24.
41. Ledzewicz U., Schättler H. The influence of PK/PD on the structure of optimal controls in cancer chemotherapy models. Math. Biosci. Eng. 2005, 2(3):561-578.
42. Ledzewicz U., Schättler H. Drug resistance in cancer chemotherapy as an optimal control problem. Discrete Contin. Dyn. Syst. Ser. B. 2006, 6(1):129-150.
43. Ledzewicz U., Schättler H. Antiangiogenic therapy in cancer treatment as an optimal control problem. SIAM J. Control Optim. 2007, 46(3):1052-1079.
44. Ledzewicz U, Liu Y, Schättler H, Schattler H., 2009a. The effect of pharmacokinetics on optimal protocols for a mathematical model of tumor anti-angiogenic therapy. In: Proceedings of the 2009 Conference on American Control Conference, Piscataway, NJ, USA, IEEE Press, pp. 1060-1065.
45. Ledzewicz U., Munden J., Schättler H. Scheduling of angiogenic inhibitors for Gompertzian and logistic tumor growth models. Discrete Contin. Dyn. Syst. Ser. B. 2009, 12(2):415-438.
46. Ledzewicz U., Marriott J., Maurer H., Schättler H. Realizable protocols for optimal administration of drugs in mathematical models for anti-angiogenic treatment. Math. Med. Biol. 2010, 27(2 (June)):157-179.
47. Meille C., Gentet J.C., Barbolosi D., Andre N., Doz F. Iliadis a, et al. New adaptive method for phase I trials in oncology. Clin. Pharmacol. Ther. 2008, 83(6 (June)):873-881.
48. Meille C., Iliadis A., Barbolosi D., Frances N., Freyer G. An interface model for dosage adjustment connects hematotoxicity to pharmacokinetics. J. Pharmacokinet. Pharmacodyn. 2008, 35(6 (December)):619-633.
49. Pasquier E, Kavallaris M, Andre N. Metronomic chemotherapy: new rationale for new directions. Nat. Rev. Clin. Oncol. 2010, 7:455-465.
50. Reynolds A.R. Potential relevance of bell-shaped and U-shaped dose-responses for the therapeutic targeting of angiogenesis in cancer. Dose-Response 2010, 8(3 (January)):253-284.
51. Sterba J., Valik D., Mudry P., Kepak T., Pavelka Z., Bajciova V., et al. Combined biodifferentiating and antiangiogenic oral metronomic therapy is feasible and effective in relapsed solid tumors in children: single-center pilot study. Onkologie 2006, 29(7 (July)):308-313.
52. Swan G.W. General applications of optimal control theory in cancer chemotherapy. IMA J. Math. Appl. Med. Biol. 1988, 5(4):303-316.
53. Swan G.W. Role of optimal control theory in cancer chemotherapy. Math. Biosci. 1990, 101(2 (October)):237-284.
54. Swierniak A. Direct and indirect control of cancer populations. Bull. Pol. Acad. Sci. Tech. Sci. 2008, 56:367-378.
55. Swierniak A., Kimmel M., Smieja J. Mathematical modeling as a tool for planning anticancer therapy. Eur. J. Pharmacol. 2009, 625:108-121.
56. Tomasetti C., Levy D. An elementary approach to modeling drug resistance in cancer. Math. Biosci. Eng. 2010, 7(4):905-918.