Cancer modelling
Free Access
Issue
Math. Model. Nat. Phenom.
Volume 15, 2020
Cancer modelling
Article Number 19
Number of page(s) 13
DOI https://doi.org/10.1051/mmnp/2019031
Published online 12 March 2020
  1. N. André, M. Carré and E. Pasquier, Metronomics: towards personalized chemotherapy? Nat. Rev. Clin. Oncol. 11 (2014) 413–431. [Google Scholar]
  2. N. Bellomo, N. Li and P.K. Maini, On the foundations of cancer modelling: selected topics, speculations, and perspectives. Math. Models Methods Appl. Sci. 18 (2008) 593–646. [Google Scholar]
  3. A. Besse, G. Clapp, S. Bernard, F. Nicolini, D. Levy and T. Lepoutre, Stability analysis of a model of interaction between the immune system and cancer cells in cml. Bull. Math. Biol. 80 (2017) 1084–1110. [Google Scholar]
  4. S. Bunimovich-Mendrazitsky, H. Byrne and L. Stone, Mathematical model of pulsed immunotherapy for superficial bladder cancer. Bull. Math. Biol. 70 (2008) 2055–2076. [Google Scholar]
  5. C. Carrère, Optimization of an in vitro chemotherapy to avoid resistant tumours. J. Theor. Biol. 413 (2017) 24–33. [CrossRef] [PubMed] [Google Scholar]
  6. L.G. De Pillis and A. Radunskaya, A mathematical tumor model with immune resistance and drug therapy: an optimal control approach. Comput. Math. Methods Med. 3 (2001) 79–100. [Google Scholar]
  7. L.G. De Pillis, W. Gu and A.E. Radunskaya, Mixed immunotherapy and chemotherapy of tumors: modeling, applications and biological interpretations. J. Theor. Biol. 238 (2006) 841–862. [CrossRef] [PubMed] [Google Scholar]
  8. V.T. DeVita and P. S. Schein, The use of drugs in combination for the treatment of cancer: rationale and results. New England J. Med. 288 (1973) 998–1006. [CrossRef] [Google Scholar]
  9. A. D’Onofrio, U. Ledzewicz and H. Schättler, On the dynamics of tumor-immune system interactions and combined chemo-and immunotherapy, in New Challenges for Cancer Systems Biomedicine. Springer, Berlin (2012) 249–266. [CrossRef] [Google Scholar]
  10. R. Eftimie, J.L. Bramson and D.J. Earn, Interactions between the immune system and cancer: a brief review of non-spatial mathematical models. Bull. Math. Biol. 73 (2011) 2–32. [Google Scholar]
  11. F. Frascoli, P.S. Kim, B.D. Hughes and K.A. Landman, A dynamical model of tumour immunotherapy. Math. Biosci. 253 (2014) 50–62. [Google Scholar]
  12. R.A. Gatenby, J. Brown and T. Vincent, Lessons from applied ecology: cancer control using an evolutionary double bind. Cancer Res. 69 (2009) 7499–7502. [Google Scholar]
  13. M. Gerlinger and C. Swanton, How darwinian models inform therapeutic failure initiated by clonal heterogeneity in cancer medicine. Br. J. Cancer 103 (2010) 1139–1143. [CrossRef] [PubMed] [Google Scholar]
  14. N. Hartung, C.T.-K. Huynh, C. Gaudy-Marqueste, A. Flavian, N. Malissen, M.-A. Richard-Lallemand, F. Hubert and J.-J. Grob, Study of metastatic kinetics in metastatic melanoma treated with b-raf inhibitors: introducing mathematical modelling of kinetics into the therapeutic decision. PloS One 12 (2017) e0176080. [CrossRef] [PubMed] [Google Scholar]
  15. N.L. Komarova, J.A. Burger and D. Wodarz. Evolution of ibrutinib resistance in chronic lymphocytic leukemia (cll). Proc. Natl. Acad. Sci. 111 (2014) 13906–13911. [CrossRef] [Google Scholar]
  16. V.A. Kuznetsov, I.A. Makalkin, M.A. Taylor and A.S. Perelson, Nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis. Bull. Math. Biol. 56 (1994) 295–321. [Google Scholar]
  17. H. Ledford, The perfect blend. Nature 532 (2016) 162–164. [Google Scholar]
  18. U. Ledzewicz and H. Schättler, Application of mathematical models to metronomic chemotherapy: What can be inferred from minimal parameterized models? Cancer Lett. 401 (2017) 74–80. [Google Scholar]
  19. U. Ledzewicz, S. Wang, H. Schättler, N. André, M.A.H. Heng and E. Pasquier, On drug resistance and metronomic chemotherapy: a mathematical modeling and optimal control approach. Math. Biosci. Eng. 14 (2017) 217–235. [CrossRef] [PubMed] [Google Scholar]
  20. K. Leon, K. Garcia, J. Carneiro and A. Lage, How regulatory cd25+cd4+t cells impinge on tumor immunobiology? On the existence of two alternative dynamical classes of tumors. J. Theor. Biol. 247 (2007) 122–137. [CrossRef] [PubMed] [Google Scholar]
  21. A. Lorz, T. Lorenzi, M.E. Hochberg, J. Clairambault and B. Perthame, Populational adaptive evolution, chemotherapeutic resistance and multiple anti-cancer therapies. ESAIM: M2AN 47 (2013) 377–399. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  22. J.D. Martin, G. Seano and R.K. Jain, Normalizing function of tumor vessels: Progress, opportunities, and challenges. Ann. Rev. Physiol. 81 (2019) 505–534. [CrossRef] [Google Scholar]
  23. F. Meng, J.W. Evans, D. Bhupathi, M. Banica, L. Lan, G. Lorente, J.-X. Duan, X. Cai, A.M. Mowday, C.P. Guise, et al., Molecular and cellular pharmacology of the hypoxia-activated prodrug th-302. Mol. Cancer Ther. 11 (2012) 740–751. [CrossRef] [PubMed] [Google Scholar]
  24. S.M. Mumenthaler, J. Foo, N.C. Choi, N. Heise, K. Leder, D.B. Agus, W. Pao, F. Michor and P. Mallick, The impact of microenvironmental heterogeneity on the evolution of drug resistance in cancer cells. Cancer Inform. 14 (2015) 19–31. [PubMed] [Google Scholar]
  25. J.D. Murray, Mathematical Biology. Springer-Verlag, Berlin (2002). [Google Scholar]
  26. E. Piretto, M. Delitala and M. Ferraro, Combination therapies and intra-tumoral competition: insights from mathematical modelling. J. Theor. Biol. 446 (2018) 149–159. [CrossRef] [PubMed] [Google Scholar]
  27. E. Piretto, M. Delitala and M. Ferraro, How combination therapies shape drug resistance in heterogeneous tumoral populations. Lett. Biomath. 5 (2018) S160–S177. [Google Scholar]
  28. C. Pouchol, J. Clairambault, A. Lorz and E. Trelat, Asymptotic analysis and optimal control of an integro-differential system modelling healthy and cancer cells exposed to chemotherapy. J. Math. Pures. Appl. 116 (2018) 268–308. [Google Scholar]
  29. R. Ramakrishnan, D. Assudani, S. Nagaraj, T. Hunter, H.-I. Cho, S. Antonia, S. Altiok, E. Celis and D.I. Gabrilovich, Chemotherapy enhances tumor cell susceptibility to ctl-mediated killing during cancer immunotherapy in mice. J. Clin. Investig. 120 (2010) 1111. [Google Scholar]
  30. N.A. Saunders, F. Simpson, E.W. Thompson, M.M. Hill, L. Endo-Munoz, G. Leggatt, R.F. Minchin and A. Guminski, Role of intratumoural heterogeneity in cancer drug resistance: molecular and clinical perspectives. EMBO Mol. Med. 4 (2012) 675–684. [CrossRef] [PubMed] [Google Scholar]
  31. R. Serre, S. Benzekry, L. Padovani, C. Meille, N. Andre, J. Ciccolini, F. Barlesi, X. Muracciole and D. Barbolosi, Mathematical modeling of cancer immunotherapy and its synergy with radiotherapy. Cancer Res. 76 (2016) 4931–4940. [Google Scholar]
  32. Y. Shaked, U. Emmenegger, G. Francia, L. Chen, C.R. Lee, S. Man, A. Paraghamian, Y. Ben-David and R.S. Kerbel, Low-dose metronomic combined with intermittent bolus-dose cyclophosphamide is an effective long-term chemotherapy treatment strategy. Cancer Res. 65 (2005) 7045–7051. [Google Scholar]
  33. S. Slovin, Chemotherapy and immunotherapy combination in advanced prostate cancer. Clin. Adv. Hematol. Oncol. 10 (2012) 90–100. [PubMed] [Google Scholar]
  34. T. Stiehl, C. Lutz and A. Marciniak-Czochra, Emergence of heterogeneity in acute leukemias. Biol. Direct 11 (2016) 51. [PubMed] [Google Scholar]
  35. D.P. Tabassum and K. Polyak, Tumorigenesis: it takes a village. Nature Rev. Cancer 15 (2015) 473–483. [CrossRef] [Google Scholar]
  36. S. Wilson and D. Levy, A mathematical model of the enhancement of tumor vaccine efficacy by immunotherapy. Bull. Math. Biol. 74 (2012) 1485–1500. [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.