Optimal CAR T-cell Immunotherapy Strategies for a Leukemia Treatment Model

Evgenii Khailov, Ellina Grigorieva and Anna Klimenkova
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Evgenii Khailov: Department of Optimal Control, Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119992 Moscow, Russia
Ellina Grigorieva: Department of Mathematics and Computer Science, Texas Woman’s University, Denton, TX 76204, USA
Anna Klimenkova: Department of Optimal Control, Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119992 Moscow, Russia

Games, 2020, vol. 11, issue 4, 1-26

Abstract: CAR T-cell immunotherapy is a new development in the treatment of leukemia, promising a new era in oncology. Although so far, this procedure only helps 50–90% of patients and, like other cancer treatments, has serious side effects. In this work, we have proposed a controlled model for leukemia treatment to explore possible ways to improve immunotherapy methodology. Our model is described by four nonlinear differential equations with two bounded controls, which are responsible for the rate of injection of chimeric cells, as well as for the dosage of the drug that suppresses the so-called “cytokine storm”. The optimal control problem of minimizing the cancer cells and the activity of the cytokine is stated and solved using the Pontryagin maximum principle. The five possible optimal control scenarios are predicted analytically using investigation of the behavior of the switching functions. The optimal solutions, obtained numerically using BOCOP-2.2.0, confirmed our analytical findings. Interesting results, explaining, why therapies with rest intervals (for example, stopping injections in the middle of the treatment interval) are more effective (within the model), rather than with continuous injections, are presented. Possible improvements to the mathematical model and method of immunotherapy are discussed.

Keywords: leukemia; nonlinear control system; optimal control; Pontryagin maximum principle; switching function; Generalized Rolle’s Theorem (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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