Multi-input Optimal Control Problems for Combined Tumor Anti-angiogenic and Radiotherapy Treatments |
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Authors: | Email author" target="_blank">U?LedzewiczEmail author H?Sch?ttler |
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Institution: | 1.Department of Mathematics and Statistics,Southern Illinois University Edwardsville,Edwardsville,USA;2.Department of Electrical and Systems Engineering,Washington University,St. Louis,USA |
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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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Keywords: | |
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