Intensity modulated radiation therapy (IMRT) is one of radiation therapies for cancers, and it is considered to be effective for complicated shapes of tumors, since dose distributions from each irradiation can be modulated arbitrary. Fluence map optimization (FMO), which optimizes beam intensities with given beam angles, is often formulated as an optimization problem with dose volume constraints (DVCs). Romeijn et al. (2003) developed a linear programming (LP) method that approximated DVCs, and Kishimoto and Yamashita (2018) modified it to a successive LP method (SLPM) to find a feasible treatment plan in a wider region than the method of Romeijn et al. However, these two methods did not consider uncertainty, like observational errors or beam inaccuracy, in a series of treatment planning. In this paper, we propose a numerical method that enhances SLPM utilizing a robust optimization approach. We mathematically prove that the proposed method with extended LP problems holds favorable properties of SLPM, even taking uncertainty in influence matrix into consideration. In particular, when the optimal value of the LP problem is non-positive, the proposed method guarantees that the output solution can satisfy all DVCs. Through numerical experiments, we observed that the proposed method found a feasible plan that SLPM could not find. Even when the proposed method could not output a feasible solution, it was still effective to reduce the largest deviations from DVCs.
Research Report B-494, Dept. of Mathematical and Computing Science, Tokyo Institute of Technology