Robust fractionation in cancer radiotherapy

Abstract

In cancer radiotherapy, the standard formulation of the optimal fractionation problem based on the linear-quadratic dose-response model is a non-convex quadratically constrained quadratic program (QCQP). An optimal solution for this QCQP can be derived by solving a two-variable linear program. Feasibility of this solution, however, crucially depends on the so-called alphaover-beta ratios for the organs-at-risk, whose true values are unknown. Consequently, the dosing schedule presumed optimal, in fact, may not even be feasible in practice. We address this by proposing a robust counterpart of the nominal formulation. We show that a robust solution can be derived by solving a small number of two-variable linear programs, each with a small number of constraints. We quantify the price of robustness, and compare the incidence and extent of infeasibility of the nominal and robust solutions via numerical experiments.