Indirect control of drug resistant cancer populations

Drug resistance is one of the major obstacles against successful anticancer chemotherapy. Antiangiogenic therapy is one of the possible ways of overcoming this difficulty because it is directed towards the normal cells building blood vessels supplying tumor which are not mutagenic. Such therapy enables indirect control of cancer populations without the effect of drug resistance. In the paper we discuss four models of antiangiogenic therapy from control theoretic point of view. All of them consist of a model of tumor growth bounded by the capacity of a vascular network developed by the tumor in the process of angiogenesis and different models of dynamics of this network and they are based on the idea proposed by Hahnfeldt et al. Moreover we analyse optimal control problems resulted from their use to treatment protocols design and we propose a model of combined antiangiogenic and chemotherapy.