Accelerated robust optimization algorithm for proton therapy treatment planning

Purpose: Robust optimization is a computational expensive process resulting in long plan computation times. This issue is especially critical for moving targets as these cases need a large number of uncertainty scenarios to robustly optimize their treatment plans. In this study, we propose a novel worst-case robust optimization algorithm, called dynamic minimax, that accelerates the conventional minimax optimization. Dynamic minimax optimization aims at speeding up the plan optimization process by decreasing the number of evaluated scenarios in the optimization.

Methods: For a given pool of scenarios (e.g., 63 = 7 setup × 3 range × 3 breathing phases), the proposed dynamic minimax algorithm only considers a reduced number of candidate-worst scenarios, selected from the full 63 scenario set. These scenarios are updated throughout the optimization by randomly sampling new scenarios according to a hidden variable P, called the "probability acceptance function," which associates with each scenario the probability of it being selected as the worst case. By doing so, the algorithm favors scenarios that are mostly "active," that is, frequently evaluated as the worst case. Additionally, unconsidered scenarios have the possibility to be re-considered, later on in the optimization, depending on the convergence towards a particular solution. The proposed algorithm was implemented in the open-source robust optimizer MIROpt and tested for six four-dimensional (4D) IMPT lung tumor patients with various tumor sizes and motions. Treatment plans were evaluated by performing comprehensive robustness tests (simulating range errors, systematic setup errors, and breathing motion) using the open-source Monte Carlo dose engine MCsquare.

Results: The dynamic minimax algorithm achieved an optimization time gain of 84%, on average. The dynamic minimax optimization results in a significantly noisier optimization process due to the fact that more scenarios are accessed in the optimization. However, the increased noise level does not harm the final quality of the plan. In fact, the plan quality is similar between dynamic and conventional minimax optimization with regard to target coverage and normal tissue sparing: on average, the difference in worst-case D95 is 0.2 Gy and the difference in mean lung dose and mean heart dose is 0.4 and 0.1 Gy, respectively (evaluated in the nominal scenario).

Conclusions: The proposed worst-case 4D robust optimization algorithm achieves a significant optimization time gain of 84%, without compromising target coverage or normal tissue sparing.