Performance of a linear controller in the nonlinear model of drug and virus delivery in cancer chemovirotherapy: A comparison between continuous and discrete approaches

Document Type : Research Note

Authors

School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran

Abstract

Best cancer treatment is the one which reduces the tumor’s density in minimum time with less side effects, considering the input limitations. In this paper, a tracking controller was designed to achieve the mentioned objectives, simultaneously. An ordinary differential equations (ODEs)-based mathematical model of a human’s body under chemovirotherapy was selected, which includes the uninfected and infected tumor cells, free viruses, immune cells, and a chemotherapeutic drug. Stability analysis was used to determine the sensible equilibrium points. For tracking purposes, a servo controller based on the entire eigenstructure assignment (EESA) approach was applied to the model, continuously and discretely. By regulating the command input properties, optimal treatment duration with limited drug dosage and virus dosage was determined. The results indicate that the discrete controller performs smoother than the continuous controller. In the discrete controller, optimum time interval for the injection of drugs and viruses was determined to propose an optimal treatment schedule.

Keywords

References

References:
1. Cause, G.D. and Age, S., By Country and by Region, 2000-2019, World Health Organization (2020).
2. Head, B., Harris, L., Kayser, K., et al. "Coping with the financial consequences of cancer", Supportive Care in Cancer, 26(3), pp. 975-987 (2018).
3. Organization, W.H., Global Tuberculosis Report 2013, World Health Organization (2013).
4. Andre, T., Colin, P., Louvet, C., et al. "Semimonthly versus monthly regimen of  fluorouracil and leucovorin administered for 24 or 36 weeks as adjuvant therapy in stage II and III colon cancer: results of a randomized trial", Journal of Clinical Oncology, 21(15), pp. 2896- 2903 (2003).
5. Ungerechts, G., Engeland, C.E., Buchholz, C.J., et al. "Virotherapy research in Germany: from engineering to translation", Human Gene Therapy, 28(10), pp. 800-819 (2017).
6. Nguyen, A., Ho, L., and Wan, Y. "Chemotherapy and oncolytic virotherapy: advanced tactics in the war against cancer", Frontiers in Oncology, 4, p. 145 (2014).
7. Binz, E. and Lauer, U.M. "Chemovirotherapy: Combining chemotherapeutic treatment with oncolytic virotherapy", Oncolytic Virotherapy, 4, p. 39 (2015).
8. Bartee, E. "Potential of oncolytic viruses in the treatment of multiple myeloma", Oncolytic Virotherapy, 7, p. 1 (2017).
9. Biotech, O. "Inc. announces additional data from REO 018 randomized study of REOLYSIN® in head and neck cancers 2014" (2019).
10. Biotech, O. "Oncolytics Biotech Inc. announces additional data from REO 018 randomized study of REOLYSIN in head and neck cancers [press release]", Oncolytics Biotech (2014).
11. Malinzi, J. "Mathematical analysis of a mathematical model of chemovirotherapy: effect of drug infusion method", Computational and Mathematical Methods in Medicine, 86, pp. 97-100 (2019).
12. Magi, S., Iwamoto, K., and Okada-Hatakeyama, M. "Current status of mathematical modeling of cancer - from the viewpoint of cancer hallmarks", Current Opinion in Systems Biology, 2, pp. 39-48 (2017).
13. Eftimie, R., Bramson, J.L., and Earn, D.J.D. "Interactions between the immune system and cancer: A brief review of non-spatial mathematical models", Bulletin of Mathematical Biology, 73(1), pp. 2-32 (2011).
14. Martin, R.B., Fisher, M.E., Minchin, R.F., et al. "A mathematical model of cancer chemotherapy with an optimal selection of parameters", Mathematical Biosciences, 99(2), pp. 205-230 (1990).
15. Panetta, J.C. and Adam, J. "A mathematical model of cycle-specific chemotherapy", Mathematical and Computer Modelling, 22(2), pp. 67-82 (1995).
16. Pontryagin, L.S., Mathematical Theory of Optimal Processes, Routledge (2018).
17. Zietz, S. and Nicolini, C. "Mathematical approaches to optimization of cancer chemotherapy", Bulletin of Mathematical Biology, 41(3), pp. 305-324 (1979).
18. Wang, P., Liu, R., Jiang, Z., et al. "The optimization of combination chemotherapy schedules in the presence of drug resistance", IEEE Transactions on Automation Science and Engineering, 16(1), pp. 165-179 (2018).
19. de Pillis, L., Renee Fister, K., Gu, W., et al. "Mathematical model creation for cancer chemoimmunotherapy", Computational and Mathematical Methods in Medicine, 10(3), pp. 165-184 (2009).
20. Liu, W. and Freedman, H. "A mathematical model of vascular tumor treatment by chemotherapy", Mathematical and Computer Modelling, 42(9-10), pp. 1089- 1112 (2005).
21. Pinho, S.T.R.d., Freedman, H., and Nani, F. "A chemotherapy model for the treatment of cancer with metastasis", Mathematical and Computer Modelling, 36(7-8), pp. 773-803 (2002).
22. Dehingia, K., Sarmah, H.K., and Jeelani, M.B. "A brief review on cancer research and its treatment through mathematical modelling", Ann Cancer Res Ther, 29, pp. 34-40 (2021).
23. Malinzi, J., Eladdadi, A., and Sibanda, P. "Modelling the spatiotemporal dynamics of chemovirotherapy cancer treatment", Journal of Biological Dynamics, 11(1), pp. 244-274 (2017).
24. Swan, G.W. and Vincent, T.L. "Optimal control analysis in the chemotherapy of IgG multiple myeloma", Bulletin of Mathematical Biology, 39(3), pp. 317-337 (1977).
25. Shi, J., Alagoz, O., Erenay, F.S. et al. "A survey of optimization models on cancer chemotherapy treatment planning", Annals of Operations Research, 221(1), pp. 331-356 (2014).
26. Coldman, A.J. and Murray, J. "Optimal control for a stochastic model of cancer chemotherapy", Mathematical Biosciences, 168(2), pp. 187-200 (2000).
27. Malinzi, J., Ouifki, R., Eladdadi, A., et al. "Enhancement of chemotherapy using oncolytic virotherapy: mathematical and optimal control analysis", arXiv preprint arXiv:1807.04329 (2018).
28. Wodarz, D. and Komarova, N. "Towards predictive computational models of oncolytic virus therapy: basis for experimental validation and model selection", PloS One, 4(1), p. e4271 (2009).
29. Tian, J.P. "The replicability of oncolytic virus: defining conditions in tumor virotherapy", Mathematical Biosciences and Engineering, 8(3), pp. 841-860 (2011).
30. Kuznetsov, V.A., Makalkin, I.A., Taylor, M.A., et al. "Nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis", Bulletin of Mathematical Biology, 56(2), pp. 295-321 (1994).
31. Pinho, S.T.R., Rodrigues, D.S., and Mancera, P.F.D.A. "A mathematical model of chemotherapy response to tumour growth", Canadian Applied Mathematics Quarterly, 19(4), pp. 369-828 (2011).
32. d'Azzo, J.J. and Houpis, C.D., Linear Control System Analysis and Design: Conventional and Modern, McGraw-Hill Higher Education (1995).
33. Ogata, K., Discrete-Time Control Systems, Prentice Hall Englewood Cliffs, 2nd Edn. (1995).
34. Kautsky, J., Nichols, N.K., and Van Dooren, P. "Robust pole assignment in linear state feedback", International Journal of Control, 41(5), pp. 1129-1155 (1985).
35. Kourelis, K., Tsue, T., Girod, D., et al. "Negative prognostic factors for head and neck cancer in the young", 21, pp. 459-464 (2013).
36. Li, Y., Chu, Y., Song, R., et al. "Thalidomide combined with chemotherapy in treating elderly patients with advanced gastric cancer", Aging Clinical and Experimental Research, 30(5), pp. 499-505 (2018).
37. Guntinas-Lichius, O., Wendt, T., Buentzel, J., et al. "Head and neck cancer in Germany: a site-specific analysis of survival of the Thuringian cancer registration database", Journal of Cancer Research and Clinical Oncology, 136(1), pp. 55-63 (2010).
38. Lauer, U. and Binz, E. "Chemovirotherapy: combining chemotherapeutic treatment with oncolytic virotherapy", Oncolytic Virotherapy, 4(1), pp. 39-48 (2015).
39. Ruf, B. and Lauer, U.M. "Assessment of current virotherapeutic application schemes: "hit hard and early" versus "killing softly"?", Molecular Therapy- Oncolytics, 2, p. 15018 (2015).
40. Mobaraki, M. and Moradi, H. "Design of robust control strategy in drug and virus scheduling in nonlinear process of chemovirotherapy", Computers & Chemical Engineering, 150, 107318 (2021).
41. Bajzer, Z., Carr, T., Josic, K., et al. "Modeling of cancer virotherapy with recombinant measles viruses", Journal of Theoretical Biology, 252(1), pp. 109-122 (2008).
42. Kirschner, D. and Panetta, J.C. "Modeling immunotherapy of the tumor-immune interaction", Journal of Mathematical Biology, 37(3), pp. 235-252 (1998).
43. Brock, T.D. "The emergence of bacterial genetics", Cold Spring Harbor Laboratory Press Cold Spring Harbor, NY (1990).
44. Bollard, C.M. and Heslop, H.E. "T cells for viral infections after allogeneic hematopoietic stem cell transplant", Blood, 127(26), pp. 3331-3340 (2016).
45. Gajewski, T.F., Schreiber, H., and Fu, Y.-X. "Innate and adaptive immune cells in the tumor microenvironment", Nature Immunology, 14(10), p. 1014 (2013).
46. Le, D., Miller, J.D., and Ganusov, V.V. "Mathematical modeling provides kinetic details of the human immune response to vaccination", Frontiers in Cellular and Infection Microbiology, 4, p. 177 (2015).
47. Rein, D.T., Volkmer, A., Bauerschmitz, G., et al. "Combination of a MDR1-targeted replicative adenovirus and chemotherapy for the therapy of pretreated ovarian cancer", Journal of Cancer Research and Clinical Oncology, 138(4), pp. 603-610 (2012).
48. Weiland, T., Lampe, J., Essmann, F., et al. "Enhanced killing of therapy-induced senescent tumor cells by oncolytic measles vaccine viruses", International Journal of Cancer, 134(1), pp. 235-243 (2014).
Scientia Iranica
Volume 30, Issue 3
Transactions on Mechanical Engineering (B)
May and June 2023
Pages 969-982

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