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

U. Ledzewicz () and H. Schättler ()
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U. Ledzewicz: Southern Illinois University Edwardsville
H. Schättler: Washington University

Journal of Optimization Theory and Applications, 2012, vol. 153, issue 1, No 12, 195-224

Abstract: 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.

Keywords: Optimal control; Totally singular controls; Combination therapy; Anti-angiogenic treatments; Radiotherapy; 49K15; 92C50 (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-011-9954-8

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