Optimal Scheduling of Radiotherapy and Angiogenic Inhibitors : A Mathematical Approach to the Antiangiogenic Hypothesis

We incorporate a previously validated mathematical model of a vascularized tumor into an optimal control problem to determine the temporal scheduling of radiotherapy and angiogenic inhibitors that maximizes the control of a primary tumor. Our results reveal that optimal antiangiogenic monotherapy gives a large initial injection to attain a 20:1 ratio of tumor cell volume to endothelial cell volume. It thereafter maintains this 20:1 ratio via a continuous dose rate that is intensified over time. In our optimal combination regimen, the antiangiogenic treatment again maintains a constant tumor-to-endothelial cell ratio, but is administered in a dose-intensified manner only during the latter portion of the radiation fractionation schedule