An Integrated Beam Angle Selection and Direct Aperture Optimisation Model for the IMRT Problem

Intensity-modulated radiation therapy (IMRT) is one of the most common radiation techniques used in cancer treatment. The main goal of IMRT is to deliver the prescribed radiation dose to the tumour area while sparing surrounding healthy organs. Traditionally, the IMRT problem has been divided into three sequential sub-problems. First, the beam angles from which radiation is delivered are selected. This problem is called the beam angle optimisation (BAO) problem. Then, the optimal radiation intensity for the beam angles selected in the previous step is computed in the so-called fluence map optimisation problem (FMO). Finally, the aperture shapes and their sequencing are generated by solving a sequencing problem (MLC). One drawback of this is that each step's outcome heavily depends on the quality of the previous step. Further, the optimal intensities obtained during the FMO problem are usually impossible to deliver using the available physical devices. Thus, the treatment plan computed during the second step of the sequential approach suffers an important impairment during the aperture shape optimisation process. To address this issue, some researchers have integrated the FMO problem and the MLC into a problem called the direct aperture optimisation (DAO) problem. In the DAO problem, the idea is that, given a set of beam angles, it seeks a set of aperture shapes and their corresponding intensities. Obtaining a treatment plan is fully deliverable, unlike in the FMO problem. However, the DAO problem still depends on the quality of the beam angles selected in the BAO problem. In this study, we propose an integrated BAO + DAO that, to our knowledge, has not been previously proposed in the literature. We solve the integrated problem by using a Local Search to seek high-quality beam angle configurations and a local search to solve that DAO problem for each generated beam angle configuration.