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Multi-input Optimal Control Problems for Combined Tumor Anti-angiogenic and Radiotherapy Treatments

Author

Listed:
  • U. Ledzewicz

    (Southern Illinois University Edwardsville)

  • H. Schättler

    (Washington University)

Abstract

A cell-population-based model for tumor growth under anti-angiogenic treatment, with the tumor volume and its variable carrying capacity as variables, is combined with the linear-quadratic model for damage done by radiation ionization. The resulting multi-input system is analyzed as an optimal control problem with the objective of minimizing the tumor volume subject to isoperimetric constraints that limit the overall amounts of anti-angiogenic agents, respectively, the damage done to healthy tissue by radiotherapy. For various model formulations, explicit expressions for singular controls are derived for both the dosage of the anti-angiogenic therapeutic agent and the radiation dose schedule. Their role in the structure of optimal protocols is discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:153:y:2012:i:1:d:10.1007_s10957-011-9954-8
    DOI: 10.1007/s10957-011-9954-8
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    References listed on IDEAS

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    1. Thomas Boehm & Judah Folkman & Timothy Browder & Michael S. O'Reilly, 1997. "Antiangiogenic therapy of experimental cancer does not induce acquired drug resistance," Nature, Nature, vol. 390(6658), pages 404-407, November.
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    Cited by:

    1. 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.
    2. Elzbieta Ratajczyk & Urszula Ledzewicz & Heinz Schättler, 2018. "Optimal Control for a Mathematical Model of Glioma Treatment with Oncolytic Therapy and TNF- $$\alpha $$ α Inhibitors," Journal of Optimization Theory and Applications, Springer, vol. 176(2), pages 456-477, February.

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