A new optimization based approach to experimental combination chemotherapy.

A new approach towards the design of optimal multiple drug experimental cancer chemotherapy is presented. Once an adequate model is specified, an optimization procedure is used in order to achieve an optimal compromise between after treatment tumor size and toxic effects on healthy tissues. In our approach we consider a model including cancer cell population growth and pharmacokinetic dynamics. These elements of the model are essential in order to allow less empirical relationships between multiple drug delivery policies, and their effects on cancer and normal cells. The desired multiple drug dosage schedule is computed by minimizing a customizable cost function subject to dynamic constraints expressed by the model. However, this additional dynamic wealth increases the complexity of the problem which, in general, cannot be solved in a closed form. Therefore, we propose an iterative optimization algorithm of the projected gradient type where the Maximum Principle of Pontryagin is used to select the optimal control policy