Effects of Pharmacokinetics and DNA Repair on the Structure of Optimal Controls in a Simple Model of Radio-chemotherapy

In this talk two models of radiochemotherapy are considered. A reference simple model adopts a classical log-kill hypothesis for chemotherapy and a linear-quadratic response for radiotherapy. The model is represented by first order nonlinear differential equations with two control variables which can be transformed into a linear differential equations with a nonlinear control action. The multi-input optimal control problem formulated for this model is solved analytically. It is shown that optimal treatment suggests delaying both therapies as soon as possible. While this result is not clinically realistic, a modification to the original model is considered. The second model takes into account the effects of drug metabolism (pharmacokinetics) and DNA repair of adjacent strand breaks. By obtaining full analytical results for chemotherapy control and partial results for radiotherapy it is shown that an introduction of these additional processes alters the structure of optimal control, which sometimes leads to opposite conclusions. However, numerical examples are provided which suggests that in practice the differences may not be as critical as the purely theoretical results would suggest.