Investigation of intensity-modulated radiotherapy optimization with gEUD-based objectives by means of simulated annealing.

Inverse treatment planning of intensity-modulated radiation therapy (IMRT) is complicated by several sources of error, which can cause deviations of optimized plans from the true optimal solution. These errors include the systematic and convergence error, the local minima error, and the optimizer convergence error. We minimize these errors by developing an inverse IMRT treatment planning system with a Monte Carlo based dose engine and a simulated annealing search engine as well as a deterministic search engine. In addition, different generalized equivalent uniform dose (gEUD)-based and hybrid objective functions were implemented and investigated with simulated annealing. By means of a head-and-neck IMRT case we have analyzed the properties of these gEUD-based objective functions, including its search space and the existence of local optima errors. We found evidence that the use of a previously published investigation of a gEUD-based objective function results in an uncommon search space with a golf hole structure. This special search space structure leads to trapping in local minima, making it extremely difficult to identify the true global minimum, even when using stochastic search engines. Moreover, for the same IMRT case several local optima have been detected by comparing the solutions of 100 different trials using a gradient optimization algorithm with the global optimum computed by simulated annealing. We have demonstrated that the hybrid objective function, which includes dose-based objectives for the target and gEUD-based objectives for normal tissue, results in equally good sparing of the critical structures as for the pure gEUD objective function and lower target dose maxima.