Modeling the Impact of Anticancer Agents on Metastatic Spreading

S. Benzekry; N. André; A. Benabdallah; J. Ciccolini; C. Faivre; F. Hubert; D. Barbolosi

Mathematical Modelling of Natural Phenomena (2012)

  • Volume: 7, Issue: 1, page 306-336
  • ISSN: 0973-5348

Abstract

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

How to cite

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Benzekry, S., et al. "Modeling the Impact of Anticancer Agents on Metastatic Spreading." Mathematical Modelling of Natural Phenomena 7.1 (2012): 306-336. <http://eudml.org/doc/222338>.

@article{Benzekry2012,
abstract = {Treating cancer patients with metastatic disease remains an ultimate challenge in clinical oncology. Because invasive cancer precludes or limits the use of surgery, metastatic setting is often associated with (poor) survival, rather than sustained remission, in patients with common cancers like lung, digestive or breast carcinomas. Mathematical modeling may help us better identify non detectable metastatic status to in turn optimize treatment for patients with metastatic disease. In this paper we present a family of models for the metastatic growth. They are based on four principles : to be as simple as possible, involving the least possible number of parameters, the main informations are obtained from the primary tumor and being able to recover the variety of phenomena observed by the clinicians. Several simulations of therapeutic strategies are presented illustrating possible applications of modeling to the clinic.},
author = {Benzekry, S., André, N., Benabdallah, A., Ciccolini, J., Faivre, C., Hubert, F., Barbolosi, D.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {modeling; metastases; anti-angiogenic therapy; metronomic chemotherapy},
language = {eng},
month = {1},
number = {1},
pages = {306-336},
publisher = {EDP Sciences},
title = {Modeling the Impact of Anticancer Agents on Metastatic Spreading},
url = {http://eudml.org/doc/222338},
volume = {7},
year = {2012},
}

TY - JOUR
AU - Benzekry, S.
AU - André, N.
AU - Benabdallah, A.
AU - Ciccolini, J.
AU - Faivre, C.
AU - Hubert, F.
AU - Barbolosi, D.
TI - Modeling the Impact of Anticancer Agents on Metastatic Spreading
JO - Mathematical Modelling of Natural Phenomena
DA - 2012/1//
PB - EDP Sciences
VL - 7
IS - 1
SP - 306
EP - 336
AB - Treating cancer patients with metastatic disease remains an ultimate challenge in clinical oncology. Because invasive cancer precludes or limits the use of surgery, metastatic setting is often associated with (poor) survival, rather than sustained remission, in patients with common cancers like lung, digestive or breast carcinomas. Mathematical modeling may help us better identify non detectable metastatic status to in turn optimize treatment for patients with metastatic disease. In this paper we present a family of models for the metastatic growth. They are based on four principles : to be as simple as possible, involving the least possible number of parameters, the main informations are obtained from the primary tumor and being able to recover the variety of phenomena observed by the clinicians. Several simulations of therapeutic strategies are presented illustrating possible applications of modeling to the clinic.
LA - eng
KW - modeling; metastases; anti-angiogenic therapy; metronomic chemotherapy
UR - http://eudml.org/doc/222338
ER -

References

top
  1. N. André, A. Rome, C. Coze, L. Padovani, E. Pasquier, L. Camoin, and J.-C. Gentet. Metronomic etoposide/cyclophosphamide/celecoxib regimen to children and adolescents with refractory cancer : a preliminary monocentric study. Clin. Therapeutics, 30 (2008), No. 7, 1336–1340.  
  2. D. Barbolosi, A. Benabdallah, F. Hubert, and F. Verga. Mathematical and numerical analysis for a model of growing metastatic tumors. Math. Biosci., 218 (2009), No. 1, 1–14.  
  3. D. Barbolosi, G. Freyer, J. Ciccolini, and A. Iliadis. 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.  
  4. D. Barbolosi and A. Iliadis. Optimizing drug regimens in cancer chemotherapy : a simulation study using a pk–pd model. Comput. Biol. Med., 31 (2001), 157–172.  
  5. D. Barbolosi, F. Verga, A. Benabdallah, F. Hubert, C. Mercier, J. Ciccolini, and C. Faivre. Modélisation du rique d’évolution métastatique chez les patients supposés avoir une maladie localisée. Oncologie, 13 (2011), No. 8, 528–533.  
  6. S. Baruchel, M. Diezi, D. Hargrave, D. Stempak, J. Gammon, A. Moghrabi, MJ. Coppes, C.V. Fernandez, and E. Bouffet. Safety and pharmacokinetics of temozolomide using a dose-escalation, metronomic schedule in recurrent paediatric brain tumours. Eur. J. Cancer, 42 (2006), 2335–2342.  
  7. S. Benzekry. Mathematical analysis of a two-dimensional population model of metastatic growth including angiogenesis. J. Evol. Equ., 11 (2011), No. 1, 187.  
  8. S. Benzekry. Mathematical and numerical analysis of a model for anti-angiogenic therapy in metastatic cancers. M2AN, 46 (2012), No. 2, 207–237.  
  9. S. Benzekry. Passing to the limit 2D-1D in a model for metastatic growth. To appear in J. Biol. Dyn., (2011), .  URIhttp://hal.archives-ouvertes.fr/hal-00521968/fr/
  10. S. Benzekry and A. Benabdallah. An optimal control problem for anti-cancer therapies in a model for metastatic evolution. In preparation (2011), .  URIhttp://hal.archives-ouvertes.fr/hal-00521968/fr/
  11. 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), .  URIhttp://hal.archives-ouvertes.fr/hal-00641476/fr/
  12. T. Browder, C. E. Butterfield, B. M. Kraling, B. Shi, B. Marshall, M. S. O’Reilly, and J. Folkman. Antiangiogenic scheduling of chemotherapy improves efficacy against experimental drug-resistant cancer. Cancer Res., 60 (2000), 1878–1886.  
  13. R. Bruno, N. Vivier, J. C. Vergniol, S. L. De Phillips, G. Montay, and L. B. Sheiner. A population pharmacokinetic model for docetaxel (Taxotere) : model building and validation. J. Pharmacokinet Biopharm., 24 (1996), 153–172.  
  14. M. Casanova, A. Ferrari, G. Bisogno, J. H. Merks, G. L. De Salvo, C. Meazza, K. Tettoni, M. Provenzi, I. Mazzarino, and M. Carli. Vinorelbine and low-dose cyclophosphamide in the treatment of pediatric sarcomas : pilot study for the upcoming European Rhabdomyosarcoma Protocol. Cancer, 101 (2004), 1664–1671.  
  15. M. Chefrour, J. L. Fischel, P. Formento, S. Giacometti, R. M. Ferri-Dessens, H. Marouani, M. Francoual, N. Renee, C. Mercier, G. Milano, and J. Ciccolini. Erlotinib in combination with capecitabine (5’dFUR) in resistant pancreatic cancer cell lines. J. Chemother., 22 (2010), 129–133.  
  16. L. M. Choi, B. Rood, N. Kamani, D. La Fond, R. J. Packer, M. R. Santi, and T. J. Macdonald. Feasibility of metronomic maintenance chemotherapy following high-dose chemotherapy for malignant central nervous system tumors. Pediatr. Blood Cancer, 50 (2008), 970–975.  
  17. E. Comen, L. Norton, and J. Massague. Clinical implications of cancer self-seeding. Nat. Rev. Clin. Oncol., 8 (2011), 369–377.  
  18. A. Devys, T. Goudon, and P. Laffitte. A model describing the growth and the size distribution of multiple metastatic tumors. Discret. and contin. dyn. syst. series B, 12 (2009), No. 4.  
  19. A. d’Onofrio, A. Gandolfi, and A. Rocca. The dynamics of tumour-vasculature interaction suggests low-dose, time-dense anti-angiogenic schedulings. Cell Prolif., 42 (2009), 317–329.  
  20. J. M.L. Ebos, C. R. Lee, W. Crus-Munoz, G. A. Bjarnason, and J. G. Christensen. Accelerated metastasis after short-term treatment with a potent inhibitor of tumor angiogenesis. Cancer Cell, 15 (2009), 232–239.  
  21. J. Folkman. Antiangiogenesis : new concept for therapy of solid tumors, Ann. Surg., 175 (1972), 409–416.  
  22. A. Fontana, A. Falcone, L. Derosa, T. Di Desidero, R. Danesi, and G. Bocci. Metronomic chemotherapy for metastatic prostate cancer : a ’young’ concept for old patients ?. Drugs Aging, 27 (2010), 689–696.  
  23. A. B. Francesconi, S. Dupre, M. Matos, D. Martin, B. G. Hughes, D. K. Wyld, and J. D. Lickliter. Carboplatin and etoposide combined with bevacizumab for the treatment of recurrent glioblastoma multiforme. J. Clin. Neurosci., 17 (2010), 970–974.  
  24. G. Gasparini, R. Longo, M. Fanelli, and B. A. Teicher. Combination of antiangiogenic therapy with other anticancer therapies : Results, challenges, and open questions. Journal of Clinical Oncology, 23 (2005), No. 61295–1311.  
  25. P. Hahnfeldt, J. Folkman, and L. Hlatky. Minimizing long-term tumor burden : the logic for metronomic chemotherapeutic dosing and its antiangiogenic basis. J. Theor. Biol., 220 (2003), 545–554.  
  26. P. Hahnfeldt, D. Panigraphy, J. Folkman, and L. Hlatky. Tumor development under angiogenic signaling : a dynamical theory of tumor growth, treatment, response and postvascular dormancy. Cancer Research, 59 (1999), 4770–4775.  
  27. A. Iliadis and D. Barbolosi. Optimizing drug regimens in cancer chemotherapy by an efficacy-toxicity mathematical model. Comput. Biomed. Res., 33 (2000), 211–226.  
  28. K. Iwata, K. Kawasaki, and Shigesada N. A dynamical model for the growth and size distribution of multiple metastatic tumors. J. Theor. Biol., 203 (2000), 177–186.  
  29. R. K. Jain. Normalizing tumor vasculature with anti-angiogenic therapy : A new paradigm for combination therapy. Nature Medicine, 7 (2001), 987–989.  
  30. K. Jordan, H. H. Wolf, W. Voigt, T. Kegel, L. P. Mueller, T. Behlendorf, C. Sippel, D. Arnold, and H. J. Schmoll. Bevacizumab in combination with sequential high-dose chemotherapy in solid cancer, a feasibility study. Bone Marrow Transplant., 45 (2010), 1704–1709.  
  31. R.S. Kerbel and B.A. Kamen. The anti-angiogenic basis of metronomic chemotherapy. Nature Reviews Cancer, 4 (2004), 423–436.  
  32. M. W. Kieran, C. D. Turner, J. B. Rubin, S.N. Chi, M.A. Zimmerman, C. Chordas, G. Klement, A. Laforme, A. Gordon, A. Thomas, D. Neuber, T. Browder, and J. Folkman. 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.  
  33. S. Koscielny, M. Tubiana, M. G. Le, A. J. Valleron, H. Mouriesse, G. Contesso, and D. Sarrazin. Breast cancer : relationship between the size of the primary tumour and the probability of metastatic dissemination. Br. J. Cancer, 49 (1984), 709–715.  
  34. J. F. Lu, R. Bruno, S. Eppler, W. Novotny, B. Lum, and J. Gaudreault. Clinical pharmacokinetics of bevacizumab in patients with solid tumors. Cancer Chemother. Pharmacol., 62 (2008), 779–786.  
  35. C. Meille, J. C. Gentet, D. Barbolosi, N. Andre, F. Doz, and A. Iliadis. New adaptive method for phase I trials in oncology. Clin. Pharmacol. Ther., 83 (2008), 873–881.  
  36. C. Meille, A. Iliadis, D. Barbolosi, N. Frances, and G. Freyer. An interface model for dosage adjustment connects hematotoxicity to pharmacokinetics. J. Pharmacokinet. Pharmacodyn., 35 (2008), 619–633.  
  37. M. Paez-Ribes, E. Allen, J. Hudock, T. Takeda, H. Okuyama, F. Vinals, M. Inoue, G. Bergers, D. Hanahan, and O. Casanovas. Antiangiogenic therapy elicits malignant progression of tumors to increased local invasion and distant metastasis. Cancer Cell, 15 (2009), 220–231.  
  38. E. Pasquier, M. Kavallaris, and N. Andre. Metronomic chemotherapy : new rationale for new directions. Nat. Rev. Clin. Oncol., 7 (2010), 455–465.  
  39. D. A. Reardon, A. Desjardins, K. Peters, S. Gururangan, J. Sampson, J. N. Rich, R. McLendon, J. E. Herndon, J. Marcello, S. Threatt, A. H. Friedman, J. J. Vredenburgh, and H. S. Friedman. Phase II study of metronomic chemotherapy with bevacizumab for recurrent glioblastoma after progression on bevacizumab therapy. J. Neurooncol., 103 (2011), 371–379.  
  40. A. R. Reynolds. Potential relevance of bell-shaped and u-shaped dose-responses for the therapeutic targeting of angiogenesis in cancer. Dose-Response, 8 (2010), 253–284.  
  41. G. J. Riely, N. A. Rizvi, M. G. Kris, D. T. Milton, D. B. Solit, N. Rosen, E. Senturk, C. G. Azzoli, J. R. Brahmer, F. M. Sirotnak, V. E. Seshan, M. Fogle, M. Ginsberg, Miller V. A., and C. M. Rudin. 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.  
  42. D. R. Spigel, P. M. Townley, D. M. Waterhouse, L. Fang, I. Adiguzel, J. E. Huang, D. A. Karlin, L. Faoro, F. A. Scappaticci, and M. A. Socinski. 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.  
  43. D. Stempak, J. Gammon, J. Halton, A. Moghrabi, G. Koren, and S. Baruchel. 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.  
  44. J. Sterba, D. Valik, P. Mudry, T. Kepak, Z. Pavelka, V. Bajciova, K. Zitterbart, V. Kadlecova, and P. Mazanek. 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.  
  45. F. Verga. Modélisation mathématique de processus métastatiques. Ph.D. thesis, Université de Provence, 2010.  
  46. P. Viens, H. Roche, P. Kerbrat, P. Fumoleau, J. P. Guastalla, and T. Delozier. 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.  

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