doi: 10.17586/2226-1494-2021-21-4-599-605


Mathematical modeling of an optimal oncotherapy for malignant tumors.

I. A. Narkevich, E. V. Milovanovich, O. V. Slita, V. Y. Tertychny-Dauri


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Narkevich I.A., Milovanovich E.V., Slita O.V., Tertychny-Dauri V.Yu. Mathematical modeling of an optimal oncotherapy for malignant tumors. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2021, vol. 21, no. 4, pp. 599–605 (in Russian). doi: 10.17586/2226-1494-2021-21-4-599-605



Abstract
The paper presents a mathematical model of the optimal treatment for malignant neoplasms. The neoplasm is considered as a distributed parameter object. The scheme for an optimal oncotherapy using a system of partial differential equations of parabolic type is analyzed. The authors propose a solution to the problem using Bellman optimization and the method of adjustable parameters. The optimal control law of the oncotherapy mode is derived. The main results include a scheme for the formation of the Bellman optimal strategy for regulation of control parameters and dynamic parameters, under which the target conditions are guaranteed over time. The work describes an optimization criterion that reflects the total costs of the control system for the oncological treatment. Simulation results demonstrate the efficiency of the optimal control of treatment process. The results of this work can be used in modern clinical practice at the stage of predictive selection of the most effective treatment strategy.

Keywords: optimal control, distributed-parameters plant, oncotherapy, diffusion process, quality functional

References
  1. Kovalenko S.Yu., Bratus' A.S. Up and down estimate of therapy quality in non-linear distributed mathematical glioma model. Mathematical Biology and Bioinformatics, 2014, vol. 9, no. 1, pp. 20–32. (in Russian). https://doi.org/10.17537/2014.9.20
  2. Murray J.D. Mathematical Biology II. Spatial Models and Biomedical Applications. NY: Springer-Verlag, 2003. 814 p.
  3. Shilbergeld D.L., Chicoine M.R. Isolation and characterization of human malignant glioma cells from histologically normal brain. Journal of Neurosurgery, 1997, vol. 86, no. 3, pp. 525–531. https://doi.org/10.3171/jns.1997.86.3.0525
  4. Swanson K.R., Alvord E.C., Murray J.D. Virtual resection of gliomas: effect of extent of resection on recurrence. Mathematical and Computer Modelling, 2003, vol. 37, no. 11, pp. 1177–1190. https://doi.org/10.1016/S0895-7177(03)00129-8
  5. ButkovskiiA.G., PustylnikovL.M. Theory of Mobile Control for Systems with Distributed Parameters. Moscow, Nauka Publ., 1980, 384 p. (in Russian)
  6. Tolstykh V.K. Application of the gradient method to problems of optimizing systems with distributed parameters. USSR Computational Mathematics and Mathematical Physics, 1986, vol. 26, no. 1, pp. 86–88. https://doi.org/10.1016/0041-5553(86)90186-2
  7. Lions J.-L. Contrôle optimal de systémes gouvernés par des équations aux dérivées partielles. Dunod, 1968, 426 p.
  8. ButkovskiiA.G. MethodsofControlforSystemswithDistributedParameters. Moscow, Nauka Publ., 1975, 568 p. (in Russian)
  9. Sirazetdinov T.K. Optimization of Systems with Distributed Parameters. Moscow, Nauka Publ., 1977, 479 p. (in Russian)
  10. Degtyarev G.L. Optimal control of distributed processes with a moving boundary. Automation and Remote Control, 1972, vol. 33, no. 10, pp. 1600–1605.
  11. Osipov Iu.S., Kriazhimskii A.V., Okhezin S.P. Control problems in systems with distributed parameters. Dynamics of Control Systems, Novosibirsk, Nauka Publ., 1979, pp. 199–208. (in Russian)
  12. Tertychnyi-Dauri V.Yu. Optimal stabilization of adaptive dynamical systems with distributed parameters: I. Differential Equations, 2001, vol. 37, no. 8, pp. 1148–1159. https://doi.org/10.1023/A:1012475603732
  13. Tertychnyi-Dauri V.Yu. Optimal stabilization of adaptive dynamical systems with distributed parameters: II. Differential Equations, 2001, vol. 37, no. 11, pp. 1618–1626. https://doi.org/10.1023/A:1017925001127
  14. Tertychnyi-Dauri V.Yu. Conditional variational problems of control for distributed-parameter systems. Automation and Remote Control, 2008, vol. 69, no. 11, pp. 1873–1891. https://doi.org/10.1134/S0005117908110040
  15. Tertychny-Dauri V.Yu. Galamech. Vol. 1. Adaptive Mechanics. Moscow, Fizmatlit Publ., 2019, 544 p. (in Russian)
  16. Tertychny-Dauri V.Yu. Galamech. Vol. 6. Mathematical Mechanics. Moscow, Fizmatlit Publ., 2019, 592 p. (in Russian)


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