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Optimal Combined Radio- and Anti-Angiogenic Cancer Therapy

Author

Listed:
  • Urszula Ledzewicz

    (Southern Illinois University Edwardsville
    Lodz University of Technology)

  • Helmut Maurer

    (Westfälische Wilhelms Universität Münster)

  • Heinz Schättler

    (Washington University)

Abstract

A mathematical model for combination of radio- and anti-angiogenic therapy is considered as optimal control problem with the objective of minimizing the tumor volume subject to isoperimetric constraints that limit the total radiation dose and the overall amount of anti-angiogenic agents to be given. The dynamics combines a model for tumor development under angiogenic inhibitors with the linear-quadratic model for the damage done by radiation ionization. The system has been investigated analytically as an optimal control problem and explicit expressions for possible singular controls were derived before. In this paper, for varying total radiation doses, examples of numerically computed optimal controls are given that verify and confirm these analytical structures: optimal schedules for the anti-angiogenic agents typically start with a brief full-dose segment, and then use up all inhibitors along a time-varying singular control while optimal radiotherapy schedules intensify the dosing and, after a brief period when the control is singular, end with a maximum dose segment. Singular controls occur for both the anti-angiogenic and radiotherapy dose rates. A discussion of the difficulties in proving the strong local optimality of corresponding trajectories is included.

Suggested Citation

  • Urszula Ledzewicz & Helmut Maurer & Heinz Schättler, 2019. "Optimal Combined Radio- and Anti-Angiogenic Cancer Therapy," Journal of Optimization Theory and Applications, Springer, vol. 180(1), pages 321-340, January.
    • Handle: RePEc:spr:joptap:v:180:y:2019:i:1:d:10.1007_s10957-018-1426-y
    DOI: 10.1007/s10957-018-1426-y
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    References listed on IDEAS

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    1. U. Ledzewicz & H. Schättler, 2012. "Multi-input Optimal Control Problems for Combined Tumor Anti-angiogenic and Radiotherapy Treatments," Journal of Optimization Theory and Applications, Springer, vol. 153(1), pages 195-224, April.
    2. U. Felgenhauer, 2012. "Structural Stability Investigation of Bang-Singular-Bang Optimal Controls," Journal of Optimization Theory and Applications, Springer, vol. 152(3), pages 605-631, March.
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    Cited by:

    1. Urszula Ledzewicz & Heinz Schättler, 2020. "On the Role of the Objective in the Optimization of Compartmental Models for Biomedical Therapies," Journal of Optimization Theory and Applications, Springer, vol. 187(2), pages 305-335, November.

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