Multi-Input Optimal Control Problems for Combined Tumor Anti-Angiogenic and Radiotherapy Treatments1

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