Dynamic Optimization in Radiotherapy

The goal in external beam radiotherapy for cancer is to maximize tumor-damage while limiting toxic eects of radiation on nearby healthy anatomies. This is achieved through spatial localization and temporal dispersion of radiation dose. Once a radi- ation intensity prole that achieves the maximum possible spatial localization is designed at the beginning of a multi-week treatment-course, the total planned dose is split into a series of predetermined equal-dosage fractions delivered daily so that healthy cells can recover between sessions. Thus, existing mathematical methods for treatment planning employ static-deterministic optimization techniques, and hence, cannot adapt to a tumor's uncertain biological response over time. In this tutorial, we review a recently proposed stochastic control framework, where the ultimate objective is to design individualized treatment strategies that dynamically adapt to tumor- response, to deliver the right dose to the right location at the right time.