Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-22T19:28:35.477Z Has data issue: false hasContentIssue false
  • English
  • Français

Modeling the Impact of Anticancer Agents on MetastaticSpreading

Published online by Cambridge University Press:  25 January 2012

S. Benzekry ,
N. André ,
A. Benabdallah ,
J. Ciccolini ,
C. Faivre ,
F. Hubert  and
D. Barbolosi
S. Benzekry
Affiliation:
CMI-LATP, UMR 6632, Université de Provence, Technopôle Château-Gombert 39, rue F. Joliot-Curie, 13453 Marseille cedex 13, France Laboratoire de Toxicocinétique et Pharmacocinétique UMR INSERM 911, CRO2 27, boulevard Jean Moulin, 13005 Marseille, France
N. André
Affiliation:
Service d’Hématologie et Oncologie Pédiatrique, Hôpital pour enfants de La Timone Marseille, France Metronomics Global Health Initiative
A. Benabdallah
Affiliation:
CMI-LATP, UMR 6632, Université de Provence, Technopôle Château-Gombert 39, rue F. Joliot-Curie, 13453 Marseille cedex 13, France
J. Ciccolini
Affiliation:
Laboratoire de Toxicocinétique et Pharmacocinétique UMR INSERM 911, CRO2 27, boulevard Jean Moulin, 13005 Marseille, France
C. Faivre
Affiliation:
Laboratoire de Toxicocinétique et Pharmacocinétique UMR INSERM 911, CRO2 27, boulevard Jean Moulin, 13005 Marseille, France
F. Hubert
Affiliation:
CMI-LATP, UMR 6632, Université de Provence, Technopôle Château-Gombert 39, rue F. Joliot-Curie, 13453 Marseille cedex 13, France
D. Barbolosi*
Affiliation:
Laboratoire de Toxicocinétique et Pharmacocinétique UMR INSERM 911, CRO2 27, boulevard Jean Moulin, 13005 Marseille, France
*
⋆Corresponding author. E-mail: [email protected]
Get access

Abstract

Treating cancer patients with metastatic disease remains an ultimate challenge inclinical oncology. Because invasive cancer precludes or limits the use of surgery,metastatic setting is often associated with (poor) survival, rather than sustainedremission, in patients with common cancers like lung, digestive or breast carcinomas.Mathematical modeling may help us better identify non detectable metastatic status to inturn optimize treatment for patients with metastatic disease. In this paper we present afamily of models for the metastatic growth. They are based on four principles : to be assimple as possible, involving the least possible number of parameters, the maininformations are obtained from the primary tumor and being able to recover the variety ofphenomena observed by the clinicians. Several simulations of therapeutic strategies arepresented illustrating possible applications of modeling to the clinic.

Keywords

modelingmetastasesanti-angiogenic therapymetronomic chemotherapy
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 7 , Issue 1: Cancer modeling , 2012 , pp. 306 - 336
Copyright
© EDP Sciences, 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Références

André, N., Rome, A., Coze, C., Padovani, L., Pasquier, E., Camoin, L., and Gentet, J.-C.. Metronomic etoposide/cyclophosphamide/celecoxib regimen to children and adolescents with refractory cancer : a preliminary monocentric study. Clin. Therapeutics, 30 (2008), No. 7, 1336–1340. CrossRefGoogle ScholarPubMed
Barbolosi, D., Benabdallah, A., Hubert, F., and Verga, F.. Mathematical and numerical analysis for a model of growing metastatic tumors. Math. Biosci., 218 (2009), No. 1, 1–14. CrossRefGoogle ScholarPubMed
Barbolosi, D., Freyer, G., Ciccolini, J., and Iliadis, A.. Optimisation de la posologie et des modalités d’administration des agents cytotoxiques à l’aide d’un modèle mathématique. Bulletin du Cancer, 90 (2003), No. 2, 167–175. Google Scholar
Barbolosi, D. and Iliadis, A.. Optimizing drug regimens in cancer chemotherapy : a simulation study using a pk–pd model. Comput. Biol. Med., 31 (2001), 157–172. CrossRefGoogle ScholarPubMed
Barbolosi, D., Verga, F., Benabdallah, A., Hubert, F., Mercier, C., Ciccolini, J., and Faivre, C.. Modélisation du rique d’évolution métastatique chez les patients supposés avoir une maladie localisée. Oncologie, 13 (2011), No. 8, 528–533. CrossRefGoogle Scholar
Baruchel, S., Diezi, M., Hargrave, D., Stempak, D., Gammon, J., Moghrabi, A., Coppes, MJ., Fernandez, C.V., and Bouffet, E.. Safety and pharmacokinetics of temozolomide using a dose-escalation, metronomic schedule in recurrent paediatric brain tumours. Eur. J. Cancer, 42 (2006), 2335–2342. CrossRefGoogle ScholarPubMed
Benzekry, S.. Mathematical analysis of a two-dimensional population model of metastatic growth including angiogenesis. J. Evol. Equ., 11 (2011), No. 1, 187. Google Scholar
Benzekry, S.. Mathematical and numerical analysis of a model for anti-angiogenic therapy in metastatic cancers. M2AN, 46 (2012), No. 2, 207–237. CrossRefGoogle Scholar
S. Benzekry. Passing to the limit 2D-1D in a model for metastatic growth. To appear in J. Biol. Dyn., (2011), http://hal.archives-ouvertes.fr/hal-00521968/fr/.
S. Benzekry and A. Benabdallah. An optimal control problem for anti-cancer therapies in a model for metastatic evolution. In preparation (2011), http://hal.archives-ouvertes.fr/hal-00521968/fr/.
S. Benzekry, G. Chapuisat, J. Ciccolini, A. Erlinger, and Hubert F., A new mathematical model for optimizing the combination between anti-angiogenic and cytotoxic drugs in oncology. In preparation (2011), http://hal.archives-ouvertes.fr/hal-00641476/fr/.
Browder, T., Butterfield, C. E., Kraling, B. M., Shi, B., Marshall, B., O’Reilly, M. S., and Folkman, J.. Antiangiogenic scheduling of chemotherapy improves efficacy against experimental drug-resistant cancer. Cancer Res., 60 (2000), 1878–1886. Google ScholarPubMed
Bruno, R., Vivier, N., Vergniol, J. C., De Phillips, S. L., Montay, G., and Sheiner, L. B.. A population pharmacokinetic model for docetaxel (Taxotere) : model building and validation. J. Pharmacokinet Biopharm., 24 (1996), 153–172. CrossRefGoogle Scholar
Casanova, M., Ferrari, A., Bisogno, G., Merks, J. H., De Salvo, G. L., Meazza, C., Tettoni, K., Provenzi, M., Mazzarino, I., and Carli, M.. Vinorelbine and low-dose cyclophosphamide in the treatment of pediatric sarcomas : pilot study for the upcoming European Rhabdomyosarcoma Protocol. Cancer, 101 (2004), 1664–1671. CrossRefGoogle ScholarPubMed
Chefrour, M., Fischel, J. L., Formento, P., Giacometti, S., Ferri-Dessens, R. M., Marouani, H., Francoual, M., Renee, N., Mercier, C., Milano, G., and Ciccolini, J.. Erlotinib in combination with capecitabine (5’dFUR) in resistant pancreatic cancer cell lines. J. Chemother., 22 (2010), 129–133. CrossRefGoogle Scholar
Choi, L. M., Rood, B., Kamani, N., La Fond, D., Packer, R. J., Santi, M. R., and Macdonald, T. J.. Feasibility of metronomic maintenance chemotherapy following high-dose chemotherapy for malignant central nervous system tumors. Pediatr. Blood Cancer, 50 (2008), 970–975. CrossRefGoogle ScholarPubMed
Comen, E., Norton, L., and Massague, J.. Clinical implications of cancer self-seeding. Nat. Rev. Clin. Oncol., 8 (2011), 369–377. Google ScholarPubMed
Devys, A., Goudon, T., and Laffitte, P.. A model describing the growth and the size distribution of multiple metastatic tumors. Discret. and contin. dyn. syst. series B, 12 (2009), No. 4. Google Scholar
d’Onofrio, A., Gandolfi, A., and Rocca, A.. The dynamics of tumour-vasculature interaction suggests low-dose, time-dense anti-angiogenic schedulings. Cell Prolif., 42 (2009), 317–329. CrossRefGoogle ScholarPubMed
Ebos, J. M.L., Lee, C. R., Crus-Munoz, W., Bjarnason, G. A., and Christensen, J. G.. Accelerated metastasis after short-term treatment with a potent inhibitor of tumor angiogenesis. Cancer Cell, 15 (2009), 232–239. CrossRefGoogle ScholarPubMed
Folkman, J.. Antiangiogenesis : new concept for therapy of solid tumors, Ann. Surg., 175 (1972), 409–416. CrossRefGoogle Scholar
Fontana, A., Falcone, A., Derosa, L., Di Desidero, T., Danesi, R., and Bocci, G.. Metronomic chemotherapy for metastatic prostate cancer : a ’young’ concept for old patients ?. Drugs Aging, 27 (2010), 689–696. CrossRefGoogle ScholarPubMed
Francesconi, A. B., Dupre, S., Matos, M., Martin, D., Hughes, B. G., Wyld, D. K., and Lickliter, J. D.. Carboplatin and etoposide combined with bevacizumab for the treatment of recurrent glioblastoma multiforme. J. Clin. Neurosci., 17 (2010), 970–974. CrossRefGoogle ScholarPubMed
Gasparini, G., Longo, R., Fanelli, M., and Teicher, B. A.. Combination of antiangiogenic therapy with other anticancer therapies : Results, challenges, and open questions. Journal of Clinical Oncology, 23 (2005), No. 6 1295–1311. CrossRefGoogle ScholarPubMed
Hahnfeldt, P., Folkman, J., and Hlatky, L.. Minimizing long-term tumor burden : the logic for metronomic chemotherapeutic dosing and its antiangiogenic basis. J. Theor. Biol., 220 (2003), 545–554. CrossRefGoogle ScholarPubMed
Hahnfeldt, P., Panigraphy, D., Folkman, J., and Hlatky, L.. Tumor development under angiogenic signaling : a dynamical theory of tumor growth, treatment, response and postvascular dormancy. Cancer Research, 59 (1999), 4770–4775. Google ScholarPubMed
Iliadis, A. and Barbolosi, D.. Optimizing drug regimens in cancer chemotherapy by an efficacy-toxicity mathematical model. Comput. Biomed. Res., 33 (2000), 211–226. CrossRefGoogle ScholarPubMed
Iwata, K., Kawasaki, K., and N, Shigesada. A dynamical model for the growth and size distribution of multiple metastatic tumors. J. Theor. Biol., 203 (2000), 177–186. CrossRefGoogle ScholarPubMed
Jain, R. K.. Normalizing tumor vasculature with anti-angiogenic therapy : A new paradigm for combination therapy. Nature Medicine, 7 (2001), 987–989. CrossRefGoogle ScholarPubMed
Jordan, K., Wolf, H. H., Voigt, W., Kegel, T., Mueller, L. P., Behlendorf, T., Sippel, C., Arnold, D., and Schmoll, H. J.. Bevacizumab in combination with sequential high-dose chemotherapy in solid cancer, a feasibility study. Bone Marrow Transplant., 45 (2010), 1704–1709. CrossRefGoogle ScholarPubMed
Kerbel, R.S. and Kamen, B.A.. The anti-angiogenic basis of metronomic chemotherapy. Nature Reviews Cancer, 4 (2004), 423–436. CrossRefGoogle ScholarPubMed
Kieran, M. W., Turner, C. D., Rubin, J. B., Chi, S.N., Zimmerman, M.A., Chordas, C., Klement, G., Laforme, A., Gordon, A., Thomas, A., Neuber, D., Browder, T., and Folkman, J.. A feasibility trial of antiangiogenic (metronomic) chemotherapy in pediatric patients with recurrent or progressive cancer. J. Pediatr. Hematol. Oncol., 27 (2005), No. 11, 573–581. CrossRefGoogle ScholarPubMed
Koscielny, S., Tubiana, M., Le, M. G., Valleron, A. J., Mouriesse, H., Contesso, G., and Sarrazin, D.. Breast cancer : relationship between the size of the primary tumour and the probability of metastatic dissemination. Br. J. Cancer, 49 (1984), 709–715. CrossRefGoogle ScholarPubMed
Lu, J. F., Bruno, R., Eppler, S., Novotny, W., Lum, B., and Gaudreault, J.. Clinical pharmacokinetics of bevacizumab in patients with solid tumors. Cancer Chemother. Pharmacol., 62 (2008), 779–786. CrossRefGoogle ScholarPubMed
Meille, C., Gentet, J. C., Barbolosi, D., Andre, N., Doz, F., and Iliadis, A.. New adaptive method for phase I trials in oncology. Clin. Pharmacol. Ther., 83 (2008), 873–881. CrossRefGoogle Scholar
Meille, C., Iliadis, A., Barbolosi, D., Frances, N., and Freyer, G.. An interface model for dosage adjustment connects hematotoxicity to pharmacokinetics. J. Pharmacokinet. Pharmacodyn., 35 (2008), 619–633. CrossRefGoogle ScholarPubMed
Paez-Ribes, M., Allen, E., Hudock, J., Takeda, T., Okuyama, H., Vinals, F., Inoue, M., Bergers, G., Hanahan, D., and Casanovas, O.. Antiangiogenic therapy elicits malignant progression of tumors to increased local invasion and distant metastasis. Cancer Cell, 15 (2009), 220–231. CrossRefGoogle ScholarPubMed
Pasquier, E., Kavallaris, M., and Andre, N.. Metronomic chemotherapy : new rationale for new directions. Nat. Rev. Clin. Oncol., 7 (2010), 455–465. CrossRefGoogle ScholarPubMed
Reardon, D. A., Desjardins, A., Peters, K., Gururangan, S., Sampson, J., Rich, J. N., McLendon, R., Herndon, J. E., Marcello, J., Threatt, S., Friedman, A. H., Vredenburgh, J. J., and Friedman, H. S.. Phase II study of metronomic chemotherapy with bevacizumab for recurrent glioblastoma after progression on bevacizumab therapy. J. Neurooncol., 103 (2011), 371–379. CrossRefGoogle ScholarPubMed
Reynolds, A. R.. Potential relevance of bell-shaped and u-shaped dose-responses for the therapeutic targeting of angiogenesis in cancer. Dose-Response, 8 (2010), 253–284. CrossRefGoogle Scholar
Riely, G. J., Rizvi, N. A., Kris, M. G., Milton, D. T., Solit, D. B., Rosen, N., Senturk, E., Azzoli, C. G., Brahmer, J. R., Sirotnak, F. M., Seshan, V. E., Fogle, M., Ginsberg, M., A., Miller V., and Rudin, C. M.. Randomized phase ii study of pulse erlotinib before or after carboplatin and paclitaxel in current or former smokers with advanced non-small-cell lung cancer. J. Clin. Oncol., 27 (2009), No. 2, 264–270. CrossRefGoogle Scholar
Spigel, D. R., Townley, P. M., Waterhouse, D. M., Fang, L., Adiguzel, I., Huang, J. E., Karlin, D. A., Faoro, L., Scappaticci, F. A., and Socinski, M. A.. Randomized Phase II Study of Bevacizumab in Combination With Chemotherapy in Previously Untreated Extensive-Stage Small-Cell Lung Cancer : Results From the SALUTE Trial. J. Clin. Oncol., 29 (2011), 2215–2222. CrossRefGoogle ScholarPubMed
Stempak, D., Gammon, J., Halton, J., Moghrabi, A., Koren, G., and Baruchel, S.. A pilot pharmacokinetic and antiangiogenic biomarker study of celecoxib and low-dose metronomic vinblastine or cyclophosphamide in pediatric recurrent solid tumors. J. Pediatr. Hematol. Oncol., 28 (2006), 720–728. CrossRefGoogle ScholarPubMed
Sterba, J., Valik, D., Mudry, P., Kepak, T., Pavelka, Z., Bajciova, V., Zitterbart, K., Kadlecova, V., and Mazanek, P.. Combined biodifferentiating and antiangiogenic oral metronomic therapy is feasible and effective in relapsed solid tumors in children : single-center pilot study. Onkologie, 29 (2006), 308–313. Google ScholarPubMed
F. Verga. Modélisation mathématique de processus métastatiques. Ph.D. thesis, Université de Provence, 2010.
Viens, P., Roche, H., Kerbrat, P., Fumoleau, P., Guastalla, J. P., and Delozier, T.. Epirubicin–docetaxel combination in first-line chemotherapy for patients with metastatic breast cancer : final results of a dose-finding and efficacy study. Am. J. Clin. Oncol., 24 (2001), 328–335. CrossRefGoogle ScholarPubMed