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Zh. Vychisl. Mat. Mat. Fiz., 2008, Volume 48, Number 6, Pages 946–966 (Mi zvmmf4571)  

This article is cited in 21 scientific papers (total in 21 papers)

Optimal control synthesis in therapy of solid tumor growth

A. S. Bratus', E. S. Chumerina

Moscow State Transport University (MIIT), ul. Obraztsova 15, Moscow, 101475, Russia

Abstract: A mathematical model of tumor growth therapy is considered. The total amount of a drug is bounded and fixed. The problem is to choose an optimal therapeutic strategy, i.e., to choose an amount of the drug permanently affecting the tumor that minimizes the number of tumor cells by a given time. The problem is solved by the dynamic programming method. Exact and approximate solutions to the corresponding Hamilton–Jacobi–Bellman equation are found. An error estimate is proved. Numerical results are presented.

Key words: optimal therapy, dynamic programming method, avascular tumor, optimal control synthesis.

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English version:
Computational Mathematics and Mathematical Physics, 2008, 48:6, 892–911

Bibliographic databases:

UDC: 519.626
Received: 27.02.2007
Revised: 14.12.2007

Citation: A. S. Bratus', E. S. Chumerina, “Optimal control synthesis in therapy of solid tumor growth”, Zh. Vychisl. Mat. Mat. Fiz., 48:6 (2008), 946–966; Comput. Math. Math. Phys., 48:6 (2008), 892–911

Citation in format AMSBIB
\by A.~S.~Bratus', E.~S.~Chumerina
\paper Optimal control synthesis in therapy of solid tumor growth
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2008
\vol 48
\issue 6
\pages 946--966
\jour Comput. Math. Math. Phys.
\yr 2008
\vol 48
\issue 6
\pages 892--911

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Antipov, A. S. Bratus', “Mathematical model of optimal chemotherapy strategy with allowance for cell population dynamics in a heterogeneous tumor”, Comput. Math. Math. Phys., 49:11 (2009), 1825–1836  mathnet  crossref  isi
    2. Chumerina E.S., “Choice of optimal strategy of tumor chemotherapy in Gompertz model”, J. Comput. Systems Sci. Internat., 48:2 (2009), 325–331  crossref  mathscinet  zmath  isi  elib  scopus
    3. Bratus' A. S., Zaichik S.Yu., “Smooth solutions of the Hamilton–Jacobi–Bellman equation in a mathematical model of optimal treatment of viral infections”, Differ. Equ., 46:11 (2010), 1571–1583  crossref  mathscinet  zmath  isi  scopus
    4. Todorov Y., Fimmel E., Bratus A.S., Semenov Y.S., Nuernberg F., “An optimal strategy for leukemia therapy: a multi-objective approach”, Russian J. Numer. Anal. Math. Modelling, 26:6 (2011), 589–604  crossref  mathscinet  zmath  isi  elib  scopus
    5. Antipov A.V., “Optimal multitherapy strategy in mathematical model of dynamics of the number of nonuniform tumor cells”, J. Comput. Syst. Sci. Int., 50:3 (2011), 499–510  crossref  mathscinet  zmath  isi  elib  elib  scopus
    6. Bratus A.S., Fimmel E., Todorov Y., Semenov Y.S., Nürnberg F., “On strategies on a mathematical model for leukemia therapy”, Nonlinear Anal. Real World Appl., 13:3 (2012), 1044–1059  crossref  mathscinet  zmath  isi  elib  scopus
    7. Bratus A. Todorov Y. Yegorov I. Yurchenko D., “Solution of the Feedback Control Problem in the Mathematical Model of Leukaemia Therapy”, J. Optim. Theory Appl., 159:3 (2013), 590–605  crossref  mathscinet  zmath  isi  elib  scopus
    8. Kovalenko S.Yu., Bratus A.S., “Zadacha vyzhivaemosti v raspredelennoi matematicheskoi modeli terapii gliomy”, Kompyuternye issledovaniya i modelirovanie, 5:4 (2013), 749–765  elib
    9. S. Yu. Kovalenko, A. S. Bratus, “Zadacha vyzhivaemosti v raspredelennoi matematicheskoi modeli terapii gliomy”, Kompyuternye issledovaniya i modelirovanie, 5:4 (2013), 749–765  mathnet  crossref
    10. S. Yu. Kovalenko, A. S. Bratus, “Otsenki kriteriya optimalnosti v zadache modelirovaniya terapii gliom”, Matem. biologiya i bioinform., 9:1 (2014), 20–32  mathnet
    11. I. E. Egorov, “Optimalnoe pozitsionnoe upravlenie v matematicheskoi modeli terapii zlokachestvennoi opukholi s uchetom reaktsii immunnoi sistemy”, Matem. biologiya i bioinform., 9:1 (2014), 257–272  mathnet
    12. Bratus A.S., Fimmel E., Kovalenko S.Yu., “On Assessing Quality of Therapy in Non-Linear Distributed Mathematical Models For Brain Tumor Growth Dynamics”, Math. Biosci., 248 (2014), 88–96  crossref  mathscinet  zmath  isi  elib  scopus
    13. Yegorov I. Todorov Y., “Synthesis of Optimal Control in a Mathematical Model of Tumour-Immune Dynamics”, Optim. Control Appl. Methods, 36:1 (2015), 93–108  crossref  mathscinet  zmath  isi  elib  scopus
    14. Bratus A.S. Kovalenko S.Yu. Fimmel E., “On Viable Therapy Strategy For a Mathematical Spatial Cancer Model Describing the Dynamics of Malignant and Healthy Cells”, Math. Biosci. Eng., 12:1 (2015), 163–183  crossref  mathscinet  zmath  isi  elib  scopus
    15. N. N. Subbotina, N. G. Novoselova, “Optimalnyi rezultat v zadache upravleniya sistemoi s kusochno monotonnoi dinamikoi”, Tr. IMM UrO RAN, 23, no. 4, 2017, 265–280  mathnet  crossref  elib
    16. Shakeri E., Latif-Shabgahi G., Abharian A.E., “Adaptive Non-Linear Control For Cancer Therapy Through a Fokker-Planck Observer”, IET Syst. Biol., 12:2 (2018), 73–82  crossref  isi  scopus
    17. Shakeri E., Latif-Shabgahi G., Abharian A.E., “Predictive Drug Dosage Control Through a Fokker-Planck Observer”, Comput. Appl. Math., 37:3 (2018), 3813–3831  crossref  mathscinet  isi  scopus
    18. Subbotina N.N., Novoselova N.G., “The Value Function in a Problem of Chemotherapy of a Malignant Tumor Growing According to the Gompertz Law”, IFAC PAPERSONLINE, 51:32 (2018), 855–860  crossref  isi
    19. N. N. Subbotina, N. G. Novoselova, “On Applications of the Hamilton–Jacobi Equations and Optimal Control Theory to Problems of Chemotherapy of Malignant Tumors”, Proc. Steklov Inst. Math., 304 (2019), 257–267  mathnet  crossref  crossref  mathscinet  isi  elib
    20. Novoselova N.G., “Numerical Constructions of Optimal Feedback in Models of Chemotherapy of a Malignant Tumor”, J. Bioinform. Comput. Biol., 17:1, SI (2019), 1940004  crossref  isi  scopus
    21. N. G. Novoselova, N. N. Subbotina, “Postroenie mnozhestva vyzhivaemosti v zadache khimioterapii zlokachestvennoi opukholi, rastuschei po zakonu Gompertsa”, Tr. IMM UrO RAN, 26, no. 1, 2020, 173–181  mathnet  crossref  elib
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