The goal of radiation therapy (RT) is to eliminate cancerous cells by directing radiation beams to the hit the cancer target while sparing the surrounding healthy tissue. In breast cancer, the proximity of the heart to the radiation beams often results in the delivery of excessive dose to the heart, leading to a high risk of cardiac complications after the treatment. The heart moves in and out of the radiation beams due to breathing motion which is often irregular and unpredictable. The challenge is to remain within the clinical limits on the volume of the heart receiving a high dose in the presence of breathing motion uncertainty.

This thesis investigates robust optimization (RO) methods to minimize the radiation dose to the heart in breast cancer RT. %under breathing motion uncertainty. First, we present a new optimization framework that combines robust optimization, to take into account breathing motion uncertainty, with a conditional value-at-risk (CVaR) representation of clinical dose-volume criteria. This framework is general and applicable to any problem with an underlying loss/return distribution that changes over time based on the state of some system.

We then explore a range of constraint generation solution strategies to solve the resulting large-scale RO problems and compare the computational efficiency of the proposed approach with that of traditional solution methods. Our computational experiments show that the proposed constraint generation strategies can reduce the solution time by an order of magnitude.

Next, we apply our robust method to real data of several breast cancer patients and dosimetrically compare the results with those of the current clinical treatment planning methods. Our results demonstrate that the robust approach can substantially reduce the radiation to the heart and is less sensitive to breathing motion compared to the conventional clinical method.

Finally, we apply the concept of Pareto robust optimization (PRO) to breast cancer RT. Using clinical patient datasets, we show that RO and PRO solutions are very close for all patients. We find PRO solutions that have a potentially lower heart dose than RO solutions under non-worst-case breathing scenarios while maintaining the worst-case performance of RO solutions.