4 - Robust Fractionation

Summary

The previous chapter demonstrated that an optimal dosing plan for the fractionation problem depends on the values of the LQ dose-response parameters for the tumor and the organs-at-risk. Unfortunately, these parameter values are unknown and difficult to estimate accurately. The literature often instead reports estimated interval ranges for these values. This chapter therefore pursues a robust optimization approach to the fractionation problem. The goal is to find a dosing plan that would not violate toxicity limits for the organs-at-risk as long as the “true” values of the unknown parameters belong to estimated interval ranges. These ranges are called uncertainty intervals. In fact, among all such robust plans, the treatment planner is interested in finding one that maximizes tumor-kill. The chapter provides a formulation for this problem, which is inevitably infinite-dimensional. Structural insights from the previous two chapters are utilized to reformulate this problem such that it can be instead tackled by solving a finite set of linear programs with two variables. The effect of the size of the uncertainty interval on the dosing plans is studied via numerical experiments.