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A mathematical model that combines chemotherapy and oncolytic virotherapy as an alternative treatment against a glioma

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Abstract

In this paper, we propose a mathematical model that combines chemotherapy and oncolytic virotherapy as an alternative to treatment of a glioma. The main idea is to incorporate the virotherapy after the first or second chemotherapy session using a specialist virus that attacks only tumor cells. Some simulations are presented. Based on the results, we conclude that with this combined therapy may reduce the number of chemotherapy sessions and may lead to obtain better results in the fight against gliomas.

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References

  1. N. Sanai, A. Alvarez-Buylla, M.S. Berger, Neural stem cells and the origin of gliomas. New Engl. J. Med. 353, 811–822 (2005)

    Article  CAS  Google Scholar 

  2. S.S. Stylli et al., Photodynamic therapy of high grade glioma-long term survival. J. Clin. Neurosci. 12, 389–398 (2005)

    Article  CAS  Google Scholar 

  3. S. Lonardi, A. Tosoni, A.A. Brandes, Adjuvant chemotherapy in the treatment of high grade gliomas. Cancer Treat. Rev. 31, 79–89 (2005)

    Article  CAS  Google Scholar 

  4. M. Sturrock, W. Hao, J. Schwartzbaum, G.A. Rempala, A mathematical model of pre-diagnostic glioma growth. J. Theor. Biol. 380, 299–308 (2015)

    Article  Google Scholar 

  5. E.S. Newlands et al., Temozolomide: a review of its discovery, chemical properties, pre-clinical development and clinical trials. Cancer Treat. Rev. 23, 35–61 (1997)

    Article  CAS  Google Scholar 

  6. H.S. Friedman, T. Kerby, H. Calvert, Temozolomide and treatment of malignant glioma. Clin. Cancer Res. 6, 2585–2597 (2000)

    CAS  PubMed  Google Scholar 

  7. A. Friedman et al., Glioma virotherapy: effects of innate immune suppression and increased viral replication capacity. Cancer Res. 66, 2314–2319 (2006)

    Article  CAS  Google Scholar 

  8. A. Nguyen, L. Ho, Y. Wan, Chemotherapy and oncolytic virotherapy: advanced tactics in the war against cancer. Front. Oncol. 4, 145 (2014)

    PubMed  PubMed Central  Google Scholar 

  9. G.R. Simpson, K. Relph, K. Harrington, A. Melcher, H. Pandha, Cancer immunotherapy via combining oncolytic virotherapy with chemotherapy: recent advances. Oncolytic Virother. 5, 1–13 (2016)

    CAS  PubMed  PubMed Central  Google Scholar 

  10. G. Jiang, Y. Xin, J.-N. Zheng, Y.-Q. Liu, Combining conditionally replicating adenovirus-mediated gene therapy with chemotherapy: a novel antitumor approach. Int. J. Cancer 129, 263–274 (2011)

    Article  CAS  Google Scholar 

  11. T.E. Wheldon, Mathematical Models in Cancer Research (Taylor and Francis, London, 1988)

    Google Scholar 

  12. L. Preziosi, Cancer Modelling and Simulation (Chapman and Hall/CRC, Boca Raton, 2003)

    Book  Google Scholar 

  13. W.-Y. Tan, L. Hanin, Handbook of Cancer Models with Applications (World Scientific, Singapore, 2008)

    Book  Google Scholar 

  14. H. Hatzikirou et al., Mathematical modelling of glioblastoma tumour development: a review. Math. Models Methods Appl. Sci. 15, 1779–1794 (2005)

    Article  Google Scholar 

  15. H.L.P. Harpold, E.C. Alvord, K.R. Swanson, The evolution of mathematical modeling of glioma proliferation and invasion. J. Neuropathol. Exp. Neurol. 66, 1–9 (2007)

    Article  Google Scholar 

  16. L.E. Ayala-Hernández et al., A mathematical model for the pre-diagnostic of glioma growth based on blood glucose levels. J. Math. Chem. 56, 687–699 (2018)

    Article  Google Scholar 

  17. K.C. Iarosz et al., Mathematical model of brain tumour with glia-neuron interactions and chemotherapy treatment. J. Theor. Biol. 368, 113–121 (2015)

    Article  Google Scholar 

  18. W. Schuette, Treatment of brain metastases from lung cancer: chemotherapy. Lung Cancer 45, 253–257 (2004)

    Article  Google Scholar 

  19. B. Ribba et al., A tumor growth inhibition model for low-grade glioma treated with chemotherapy or radiotherapy. Clin. Cancer Res. 18, 5071–5080 (2012)

    Article  CAS  Google Scholar 

  20. J.T. Wu, H.M. Byrne, D.H. Kirn, L.M. Wein, Modeling and analysis of a virus that replicates selectively in tumor cells. Bull. Math. Biol. 63, 731–768 (2001)

    Article  CAS  Google Scholar 

  21. M.A. Nowak, R.M. May, Virus Dynamics: Mathematical Principles of Immunology and Virology (Oxford University Press, Oxford, 2000)

    Google Scholar 

  22. K.W. Okamoto, P. Amarasekare, I.T.D. Petty, Modeling oncolytic virotherapy: is complete tumor-tropism too much of a good thing? J. Theor. Biol. 358, 166–178 (2014)

    Article  Google Scholar 

  23. M. Rajalakshmi, M. Ghosh, Modeling treatment of cancer using virotherapy with generalized logistic growth of tumor cells. Stoch. Anal. Appl. 36, 1068–1086 (2018)

    Article  Google Scholar 

  24. S.T.R. Pinho, F.S. Barcelar, R.F.S. Andrade, H.I. Freedman, A mathematical model for the effect of anti-angiogenic therapy in the treatment of cancer tumours by chemotherapy. Nonlinear Anal.: Real World Appl. 14, 815–828 (2013)

    Article  CAS  Google Scholar 

  25. J.S. Spratt, T.L. Spratt, Rates of growth of pulmonary metastases and host survival. Ann. Surg. 159, 161–171 (1964)

    Article  Google Scholar 

  26. F.S. Borges et al., Model for tumour growth with treatment by continuous and pulsed chemotherapy. BioSystems 116, 43–48 (2014)

    Article  CAS  Google Scholar 

  27. R. Said et al., Cyclophosphamide pharmacokinetics in mice: a comparison between retro orbital sampling versus serial tail vein bleeding. Open Pharmacol. J. 1, 30–35 (2007)

    CAS  Google Scholar 

  28. C.S. Holling, The functional response of predator to pray density and its role in mimicry and population regulation. Mem. Entomol. Soc. Can. 45, 1–60 (1965)

    Article  Google Scholar 

  29. Y. Pei, L. Chen, Q. Zhang, C. Li, Extinction and permanence of one-prey multi-predators of Holling type II function response system with impulsive biological control. J. Theor. Biol. 235, 495–503 (2005)

    Article  Google Scholar 

  30. Y. Zhu, J. Yin, Burst size distributions from measurements of single cells infected with vesicular stomatitis virus, in: AIChE Annual Meeting. American Institute of Chemical Engineers, Cincinnati, Ohio (2005) 432f

  31. D.M. Rommelfanger et al., Dynamics of melanoma tumor therapy with vesicular stomatitis virus: explaining the variability in outcomes using mathematical modeling. Gene Ther. 19, 543–549 (2012)

    Article  CAS  Google Scholar 

  32. L. Fernandez, L. Orduna, M Perez, J. M. Orduna. A new approach for the visualization of DNA methylation results. Comput. Math. Methods (2019). https://doi.org/10.1002/cmm4.1043

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Acknowledgements

This manuscript is an extended version of a paper presented in July 2019 at the XIX International Conference “Computational and Mathematical Methods is Science and Engineering”, in Rota, Spain. One of us (EUC) wishes to thank CONACYT for the financial support granted through scholarship 390634 and to the Universidad de Guadalajara for PROINPEP support.

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Correspondence to E. Urenda-Cázares.

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Urenda-Cázares, E., Gallegos, A. & Macías-Díaz, J.E. A mathematical model that combines chemotherapy and oncolytic virotherapy as an alternative treatment against a glioma. J Math Chem 58, 544–554 (2020). https://doi.org/10.1007/s10910-019-01084-3

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  • DOI: https://doi.org/10.1007/s10910-019-01084-3

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