Direct Aperture Optimization for Intensity Modulated Radiation Therapy: Two Calibrated Metaheuristics and Liver Cancer Case Study

Integrated treatment planning for cancer patients has high importance in intensity modulated radiation therapy (IMRT). Direct aperture optimization (DAO) is one of the prominent approaches used in recent years to attain this goal. Considering a set of beam directions, DAO is an integrated approach to optimize the intensity and leaf position of apertures in each direction. In this paper, first, a mixed integer-nonlinear mathematical formulation for the DAO problem in IMRT treatment planning is presented. Regarding the complexity of the problem, two well-known metaheuristic algorithms, particle swarm optimization (PSO) and differential evolution (DE), are utilized to solve the model. The parameters of both algorithms are calibrated using the Taguchi method. The performance of two proposed algorithms is evaluated by 10 real patients with liver cancer disease. The statistical analysis of results using paired samples t-test demonstrates the outperformance of the PSO algorithm compared to differential evolution, in terms of both the treatment plan quality and the computational time. Finally, a sensitivity analysis is performed to provide more insights about the performance of algorithms and the results revealed that increasing the number of beam angles and allowable apertures improve the treatment quality with a computational cost.