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

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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.

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Correspondence to U. Ledzewicz.

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Communicated by Alberto d’Onofrio.

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Ledzewicz, U., Schättler, H. Multi-input Optimal Control Problems for Combined Tumor Anti-angiogenic and Radiotherapy Treatments. J Optim Theory Appl 153, 195–224 (2012). https://doi.org/10.1007/s10957-011-9954-8

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