Optimization of combined anticancer treatment using models with multiple control delays

Helmut Maurer; Andrzej Świerniak

doi:10.1007/978-3-319-60699-6_77

Optimization of combined anticancer treatment using models with multiple control delays

Helmut Maurer
, Andrzej Świerniak

Department of Systems Biology and Engineering (RAU/RAU1)

University of Münster
Silesian University of Technology

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

In the paper we study some control properties of a two compartmental model of response to anticancer treatment which combines antiangiogenic and cytotoxic drugs and takes into account multiple delays in control. Mode precisely we formulate sufficient local controllability conditions for semilinear systems which result from the use of Hakufeldt et al. model, endowed with two control variables representing antiangiogenic modality, combined with chemotherapy which contain delays related to PK/PD effects and some clinical recommendations e.g. normalization of vascular network. Then the optimized protocols of the combined therapy for the model, considered as solutions of an optimal control problem for dynamical systems with delays in control, are found using necessary conditions of optimality and numerical calculations. Structural sensitivity of considered control properties and optimal solutions are also discussed.

Original language	English
Title of host publication	Trends in Advanced Intelligent Control, Optimization and Automation - Proceedings of KKA 2017-The 19th Polish Control Conference, 2017
Editors	Wojciech Mitkowski, Krzysztof Oprzedkiewicz, Pawel Skruch, Janusz Kacprzyk
Publisher	Springer Verlag
Pages	799-817
Number of pages	19
ISBN (Print)	9783319606989
DOIs	https://doi.org/10.1007/978-3-319-60699-6_77
Publication status	Published - 2017
Event	19th Polish Control Conference, KKA 2017 - Krakow, Poland Duration: 18 Jun 2017 → 21 Jun 2017

Publication series

Name	Advances in Intelligent Systems and Computing
Volume	577
ISSN (Print)	2194-5357

Conference

Conference	19th Polish Control Conference, KKA 2017
Country/Territory	Poland
City	Krakow
Period	18/06/17 → 21/06/17

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 3 Good Health and Well-being

ASJC Scopus subject areas

Control and Systems Engineering
General Computer Science

Access to Document

10.1007/978-3-319-60699-6_77

Cite this

Maurer, H., & Świerniak, A. (2017). Optimization of combined anticancer treatment using models with multiple control delays. In W. Mitkowski, K. Oprzedkiewicz, P. Skruch, & J. Kacprzyk (Eds.), Trends in Advanced Intelligent Control, Optimization and Automation - Proceedings of KKA 2017-The 19th Polish Control Conference, 2017 (pp. 799-817). (Advances in Intelligent Systems and Computing; Vol. 577). Springer Verlag. https://doi.org/10.1007/978-3-319-60699-6_77

Maurer, Helmut ; Świerniak, Andrzej. / Optimization of combined anticancer treatment using models with multiple control delays. Trends in Advanced Intelligent Control, Optimization and Automation - Proceedings of KKA 2017-The 19th Polish Control Conference, 2017. editor / Wojciech Mitkowski ; Krzysztof Oprzedkiewicz ; Pawel Skruch ; Janusz Kacprzyk. Springer Verlag, 2017. pp. 799-817 (Advances in Intelligent Systems and Computing).

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title = "Optimization of combined anticancer treatment using models with multiple control delays",

abstract = "In the paper we study some control properties of a two compartmental model of response to anticancer treatment which combines antiangiogenic and cytotoxic drugs and takes into account multiple delays in control. Mode precisely we formulate sufficient local controllability conditions for semilinear systems which result from the use of Hakufeldt et al. model, endowed with two control variables representing antiangiogenic modality, combined with chemotherapy which contain delays related to PK/PD effects and some clinical recommendations e.g. normalization of vascular network. Then the optimized protocols of the combined therapy for the model, considered as solutions of an optimal control problem for dynamical systems with delays in control, are found using necessary conditions of optimality and numerical calculations. Structural sensitivity of considered control properties and optimal solutions are also discussed.",

author = "Helmut Maurer and Andrzej {\'S}wierniak",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing AG 2017.; 19th Polish Control Conference, KKA 2017 ; Conference date: 18-06-2017 Through 21-06-2017",

year = "2017",

doi = "10.1007/978-3-319-60699-6\_77",

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series = "Advances in Intelligent Systems and Computing",

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pages = "799--817",

editor = "Wojciech Mitkowski and Krzysztof Oprzedkiewicz and Pawel Skruch and Janusz Kacprzyk",

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Maurer, H & Świerniak, A 2017, Optimization of combined anticancer treatment using models with multiple control delays. in W Mitkowski, K Oprzedkiewicz, P Skruch & J Kacprzyk (eds), Trends in Advanced Intelligent Control, Optimization and Automation - Proceedings of KKA 2017-The 19th Polish Control Conference, 2017. Advances in Intelligent Systems and Computing, vol. 577, Springer Verlag, pp. 799-817, 19th Polish Control Conference, KKA 2017, Krakow, Poland, 18/06/17. https://doi.org/10.1007/978-3-319-60699-6_77

Optimization of combined anticancer treatment using models with multiple control delays. / Maurer, Helmut; Świerniak, Andrzej.
Trends in Advanced Intelligent Control, Optimization and Automation - Proceedings of KKA 2017-The 19th Polish Control Conference, 2017. ed. / Wojciech Mitkowski; Krzysztof Oprzedkiewicz; Pawel Skruch; Janusz Kacprzyk. Springer Verlag, 2017. p. 799-817 (Advances in Intelligent Systems and Computing; Vol. 577).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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T1 - Optimization of combined anticancer treatment using models with multiple control delays

AU - Maurer, Helmut

AU - Świerniak, Andrzej

N1 - Publisher Copyright: © Springer International Publishing AG 2017.

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N2 - In the paper we study some control properties of a two compartmental model of response to anticancer treatment which combines antiangiogenic and cytotoxic drugs and takes into account multiple delays in control. Mode precisely we formulate sufficient local controllability conditions for semilinear systems which result from the use of Hakufeldt et al. model, endowed with two control variables representing antiangiogenic modality, combined with chemotherapy which contain delays related to PK/PD effects and some clinical recommendations e.g. normalization of vascular network. Then the optimized protocols of the combined therapy for the model, considered as solutions of an optimal control problem for dynamical systems with delays in control, are found using necessary conditions of optimality and numerical calculations. Structural sensitivity of considered control properties and optimal solutions are also discussed.

AB - In the paper we study some control properties of a two compartmental model of response to anticancer treatment which combines antiangiogenic and cytotoxic drugs and takes into account multiple delays in control. Mode precisely we formulate sufficient local controllability conditions for semilinear systems which result from the use of Hakufeldt et al. model, endowed with two control variables representing antiangiogenic modality, combined with chemotherapy which contain delays related to PK/PD effects and some clinical recommendations e.g. normalization of vascular network. Then the optimized protocols of the combined therapy for the model, considered as solutions of an optimal control problem for dynamical systems with delays in control, are found using necessary conditions of optimality and numerical calculations. Structural sensitivity of considered control properties and optimal solutions are also discussed.

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T3 - Advances in Intelligent Systems and Computing

SP - 799

EP - 817

BT - Trends in Advanced Intelligent Control, Optimization and Automation - Proceedings of KKA 2017-The 19th Polish Control Conference, 2017

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A2 - Oprzedkiewicz, Krzysztof

A2 - Skruch, Pawel

A2 - Kacprzyk, Janusz

PB - Springer Verlag

T2 - 19th Polish Control Conference, KKA 2017

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Maurer H, Świerniak A. Optimization of combined anticancer treatment using models with multiple control delays. In Mitkowski W, Oprzedkiewicz K, Skruch P, Kacprzyk J, editors, Trends in Advanced Intelligent Control, Optimization and Automation - Proceedings of KKA 2017-The 19th Polish Control Conference, 2017. Springer Verlag. 2017. p. 799-817. (Advances in Intelligent Systems and Computing). doi: 10.1007/978-3-319-60699-6_77

Optimization of combined anticancer treatment using models with multiple control delays

Abstract

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Conference

UN SDGs

ASJC Scopus subject areas

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