Applying mixed-integer linear programming to the non-coplanar beam angle optimization of intensity-modulated radiotherapy for liver cancer.

Background: Currently, intensity-modulated radiation therapy (IMRT) is commonly used in radiotherapy clinics. However, designing a treatment plan with multiple beam angles depends on the experience of human planners, and is mostly achieved using a trial-and-error approach. It is preferrable but challenging to solve this issue automatically and mathematically using an optimization approach. The goal of this study is to develop a mixed-integer linear programming (MILP) approach for the beam angle optimization (BAO) of non-coplanar IMRT for liver cancer.

Methods: MILP models for the BAO of both coplanar and non-coplanar IMRT treatment plans were developed. The beam angles of the IMRT plans were first selected by the MILP model built using mathematical optimization software. Next, the IMRT plans with the selected beam angles was created in a commercial treatment planning system. Finally, the fluence map and dose distribution of the IMRT plans were generated under pre-defined dose-volume constraints. The IMRT plans of 10 liver cancer patients previously treated at our institute were used to assessed the proposed MILP models. For each patient, both coplanar and non-coplanar IMRT plans with beam angles optimized by the MILP models were compared with the IMRT plan clinically approved by physicians.

Results: The MILP model-guided IMRT plans showed reduced doses for most of the organs at risk (OARs). Compared with the IMRT plans clinically approved by physicians, the doses for the spinal cord (28.5 vs. 36.1, P=0.001<0.05) and liver (27.6 vs. 29.1, P=0.005<0.05) decreased significantly in the IMRT plans with non-coplanar beams selected by the MILP models.

Conclusions: The MILP model is an effective tool for the BAO in coplanar and non-coplanar IMRT treatment planning. It facilitates the automation of IMRT treatment planning for current high-precision radiotherapy.