The Structure of Optimal Protocols for a Mathematical Model of Chemotherapy with Antiangiogenic Effects

Abstract

We analyze a mathematical model for cancer chemotherapy which includes antiangiogenic effects of the cytotoxic agent. Assuming that the total amount of agents to be given has been determined a priori based on a medical assessment of its side effects, we consider the problem how to best administer this amount. The model assumes a homogenous tumor and if the aim is to minimize the tumor volume, then optimal controls administer the total dose in a single maximum dose session. As, however, angiogenic effects of the agent are taken into account, this no longer is optimal. Lower dose strategies determined by an optimal singular arc with significantly reduced dose rates give a better response over time. In this paper, for the medically realistic domain of the mathematical model, the concatenation structure of optimal controlled trajectories as segments of bang and singular arcs is determined. This leads to simple numerical minimization procedures for the computation of globally optimal controls.