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Onkolitik Virüs ile Matematiksel Tümör Modeli

Year 2020, Volume: 7 Issue: 2, 609 - 620, 30.12.2020
https://doi.org/10.35193/bseufbd.595527

Abstract

Besin, sağlıklı hücreler, tümör hücreleri ve onkolitik virüs arasındaki etkileşim için verilen dört boyutlu matematiksel model [29], bu çalışmada beş boyutlu adi diferansiyel denklem sistemi şeklinde genişletilmiştir. Tümör hücreleri onkolitik virüs ile etkileşime geçtiğinden, enfekte olmuş tümör hücreleri de modele dâhil edilmiştir. Onkolitik virüsün tümörü yok etmedeki rolünü incelemek için, tümörün sistemde olmadığı durumlar için kararlılık analizi yapılmıştır. Tümör ve sağlıklı hücrelerden yoksun bir sistemin kararlılığının, sisteme verilen virüs dozunun minimum değerine bağlı olduğu tespit edilmiştir. Tümörün olmadığı ve sağlıklı hücrelerin var olduğu durumda ise, sistemin kararlılığı için elde edilen minimum virüs dozunun, bir önceki dozdan daha küçük olduğu gözlemlenmiştir. Böylece, sistemde sağlıklı hücrelerin bulunmasının, tümörün yok edilme şansını artırdığı ve gerekli ilaç dozunun azaltılmasını sağladığı sonucuna varılmıştır. Son olarak, elde edilen kararlılık analizi için nümerik sonuçlar elde edilmiş ve sistemin kararlılığı için örnekler sunulmuştur.

References

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  • Dingli, D., Cascino, M. D., Josić, K., Russell, S. J., & Bajzer, Ž. (2006). Mathematical modeling of cancer radiovirotherapy. Mathematical Biosciences, 199(1), 55-78.
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  • Okamoto, K. W., Amarasekare, P., & Petty, I. T. (2014). Modeling oncolytic virotherapy: Is complete tumor-tropism too much of a good thing?. Journal of Theoretical Biology, 358, 166-178.
  • Eftimie, R., & Eftimie, G. (2018). Tumour-associated macrophages and oncolytic virotherapies: a mathematical investigation into a complex dynamics. Letters in Biomathematics, 5(sup1), S6-S35.
  • Mahasa, K. J., Eladdadi, A., De Pillis, L., & Ouifki, R. (2017). Oncolytic potency and reduced virus tumor-specificity in oncolytic virotherapy. A mathematical modelling approach. PloS One, 12(9), e0184347.
  • Wang, Z., Guo, Z., & Peng, H. (2016). A mathematical model verifying potent oncolytic efficacy of M1 virus. Mathematical Biosciences, 276, 19-27.
  • Lin, Y., Zhang, H., Liang, J., Li, K., Zhu, W., Fu, L., et al (2014). Identification and characterization of alphavirus M1 as a selective oncolytic virus targeting ZAP-defective human cancers. Proceedings of the National Academy of Sciences, 111(42), E4504-E4512.
  • De Pillis, L. G., & Radunskaya, A. (2003). The dynamics of an optimally controlled tumor model: A case study. Mathematical and Computer Modelling, 37(11), 1221-1244.

A Mathematical Tumor Model with Oncolytic Virus

Year 2020, Volume: 7 Issue: 2, 609 - 620, 30.12.2020
https://doi.org/10.35193/bseufbd.595527

Abstract

In this study, a four-dimensional model [29] that is given for interactions between nutrient, healthy cells, tumor cells, and oncolytic virus, is extended with a five-dimensional ordinary differential equations system. Infected tumor cells are included in the model since oncolytic virus infects tumor cells. In order to investigate the role of oncolytic virus in eradication of tumor burden, stability analysis has been performed in case of no tumor cells in the system. It is determined that the stability of the system in case of no tumor cells and healthy cells is related with the minimum virus dosage injected into the host. In case of no tumor cells, but healthy cells, the minimum dosage is smaller than the previous case for stability of the equilibrium point. Therefore, this study demonstrates that existence of healthy cells in the host increases the chance of eradication of tumor cells, and it leads to a decrease in virus dosage. Finally, some numerical results have been obtained for the stability analysis and numerical findings have been presented.

References

  • National Cancer Institute. July, 2019. What is cancer? https://www.cancer.gov/about-cancer/understanding/what-is-cancer.
  • Schreiber, R. D., Old, L. J., & Smyth, M. J. (2011). Cancer immunoediting: integrating immunity’s roles in cancer suppression and promotion. Science, 331(6024), 1565-1570.
  • Finn, O. J. (2012). Immuno-oncology: understanding the function and dysfunction of the immune system in cancer. Annals of Oncology, 23(suppl_8), viii6-viii9.
  • Dunn, G. P., Old, L. J., & Schreiber, R. D. (2004). The three Es of cancer immunoediting. Annual Reviews of Immunology, 22, 329-360.
  • Bray, F., Ferlay, J., Soerjomataram, I., Siegel, R. L., Torre, L. A., & Jemal, A. (2018). Global cancer statistics 2018: GLOBOCAN estimates of incidence and mortality worldwide for 36 cancers in 185 countries. CA: A Cancer Journal for Clinicians, 68(6), 394-424.
  • Miller, K. D., Siegel, R. L., Lin, C. C., Mariotto, A. B., Kramer, J. L., Rowland, J. H., Stein, K. D., Alteri, R. & Jemal, A. D.V.M. (2016). Cancer treatment and survivorship statistics, 2016. CA: A Cancer Journal for Clinicians, 66(4), 271-289.
  • Mamat, M., Subiyanto, K. A., & Kartono, A. (2013). Mathematical model of cancer treatments using immunotherapy, chemotherapy and biochemotherapy. Applied Mathematical Sciences, 7(5), 247-261.
  • Melief, C. J. (2008). Cancer immunotherapy by dendritic cells. Immunity, 9(3), 372-383.
  • Senkus-Konefka, E., & Jassem, J. (2006). Complications of breast-cancer radiotherapy. Clinical Oncology, 18(3), 229-235.
  • Brennan, M. F. (2005). Current status of surgery for gastric cancer: A review. Gastric Cancer, 8(2), 64-70.
  • Zhang, J., Yang, P. L., & Gray, N. S. (2009). Targeting cancer with small molecule kinase inhibitors. Nature Reviews Cancer, 9(1), 28.
  • Russell, S. J., Peng, K. W., & Bell, J. C. (2012). Oncolytic virotherapy. Nature Biotechnology, 30(7), 658.
  • Kuznetsov, V. A., Makalkin, I. A., Taylor, M. A., & Perelson, A. S. (1994). Nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis. Bulletin of Mathematical Biology, 56(2), 295-321.
  • Enderling, H., & Chaplain, M. A. J. (2014). Mathematical modeling of tumor growth and treatment. Current pharmaceutical design, 20(30), 4934-4940.
  • De Pillis, L. G., Radunskaya, A. E., & Wiseman, C. L. (2005). A validated mathematical model of cell-mediated immune response to tumor growth. Cancer Research, 65(17), 7950-7958.
  • Webb, S. D., Sherratt, J. A., & Fish, R. G. (2002). Cells behaving badly: a theoretical model for the Fas/FasL system in tumour immunology. Mathematical Biosciences, 179(2), 113-129.
  • Nazari, F., Pearson, A. T., Nör, J. E., & Jackson, T. L. (2018). A mathematical model for IL-6-mediated, stem cell driven tumor growth and targeted treatment. PLoS Computational Biology, 14(1), e1005920.
  • Wei, H. C. (2018). A mathematical model of tumour growth with Beddington–DeAngelis functional response: a case of cancer without disease. Journal of Biological Dynamics, 12(1), 194-210.
  • Robertson-Tessi, M., El-Kareh, A., & Goriely, A. (2012). A mathematical model of tumor–immune interactions. Journal of Theoretical Biology, 294, 56-73.
  • De Pillis, L. G., Gu, W., & Radunskaya, A. E. (2006). Mixed immunotherapy and chemotherapy of tumors: modeling, applications and biological interpretations. Journal of Theoretical Biology, 238(4), 841-862.
  • Ledzewicz, U., Wang, S., Schättler, H., André, N., Heng, M. A., & Pasquier, E. (2017). On drug resistance and metronomic chemotherapy: A mathematical modeling and optimal control approach. Mathematical Biosciences & Engineering, 14(1), 217-235.
  • Lawler, S. E., Speranza, M. C., Cho, C. F., & Chiocca, E. A. (2017). Oncolytic viruses in cancer treatment: A review. JAMA Oncology, 3(6), 841-849.
  • Dingli, D., Cascino, M. D., Josić, K., Russell, S. J., & Bajzer, Ž. (2006). Mathematical modeling of cancer radiovirotherapy. Mathematical Biosciences, 199(1), 55-78.
  • Bajzer, Ž., Carr, T., Josić, K., Russell, S. J., & Dingli, D. (2008). Modeling of cancer virotherapy with recombinant measles viruses. Journal of Theoretical Biology, 252(1), 109-122.
  • Wodarz, D. (2004). Computational approaches to study oncolytic virus therapy: insights and challenges. Gene Therapy and Molecular Biology, 8, 137-146.
  • Okamoto, K. W., Amarasekare, P., & Petty, I. T. (2014). Modeling oncolytic virotherapy: Is complete tumor-tropism too much of a good thing?. Journal of Theoretical Biology, 358, 166-178.
  • Eftimie, R., & Eftimie, G. (2018). Tumour-associated macrophages and oncolytic virotherapies: a mathematical investigation into a complex dynamics. Letters in Biomathematics, 5(sup1), S6-S35.
  • Mahasa, K. J., Eladdadi, A., De Pillis, L., & Ouifki, R. (2017). Oncolytic potency and reduced virus tumor-specificity in oncolytic virotherapy. A mathematical modelling approach. PloS One, 12(9), e0184347.
  • Wang, Z., Guo, Z., & Peng, H. (2016). A mathematical model verifying potent oncolytic efficacy of M1 virus. Mathematical Biosciences, 276, 19-27.
  • Lin, Y., Zhang, H., Liang, J., Li, K., Zhu, W., Fu, L., et al (2014). Identification and characterization of alphavirus M1 as a selective oncolytic virus targeting ZAP-defective human cancers. Proceedings of the National Academy of Sciences, 111(42), E4504-E4512.
  • De Pillis, L. G., & Radunskaya, A. (2003). The dynamics of an optimally controlled tumor model: A case study. Mathematical and Computer Modelling, 37(11), 1221-1244.
There are 31 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Tuğba Akman Yıldız 0000-0003-1206-2287

Publication Date December 30, 2020
Submission Date July 23, 2019
Acceptance Date November 9, 2020
Published in Issue Year 2020 Volume: 7 Issue: 2

Cite

APA Akman Yıldız, T. (2020). A Mathematical Tumor Model with Oncolytic Virus. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi, 7(2), 609-620. https://doi.org/10.35193/bseufbd.595527