Buti Gregory, Souris Kevin, Barragán Montero Ana M, Cohilis Marie, Lee John A, Sterpin Edmond
Radiotherapy and Oncology (MIRO), Institut de Recherche Expérimentale et Clinique (IREC), Center of Molecular Imaging, Université Catholique de Louvain, Brussels, Belgium.
Department of Oncology, Laboratory of Experimental Radiotherapy, Katholieke Universiteit Leuven, Leuven, Belgium.
Med Phys. 2020 Jul;47(7):2746-2754. doi: 10.1002/mp.14132. Epub 2020 Mar 31.
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.
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.
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).
The proposed worst-case 4D robust optimization algorithm achieves a significant optimization time gain of 84%, without compromising target coverage or normal tissue sparing.
稳健优化是一个计算成本高昂的过程，会导致较长的计划计算时间。这个问题对于移动目标尤为关键，因为这些病例需要大量的不确定性场景来稳健地优化其治疗计划。在本研究中，我们提出了一种新颖的最坏情况稳健优化算法，称为动态极小极大算法，它加速了传统的极小极大优化。动态极小极大优化旨在通过减少优化中评估的场景数量来加快计划优化过程。
对于给定的一组场景（例如，63 = 7 次设置×3 种范围×3 个呼吸阶段），所提出的动态极小极大算法仅考虑从完整的 63 个场景集中选择的数量减少的候选最坏情况场景。在整个优化过程中，根据一个隐藏变量 P（称为“概率接受函数”）随机采样新场景来更新这些场景，该函数将每个场景被选为最坏情况的概率与之关联。通过这样做，该算法倾向于那些大多“活跃”的场景，即经常被评估为最坏情况的场景。此外，未考虑的场景有可能在优化后期根据向特定解的收敛情况被重新考虑。所提出的算法在开源稳健优化器 MIROpt 中实现，并针对六名具有不同肿瘤大小和运动的四维（4D）IMPT 肺癌患者进行了测试。使用开源蒙特卡罗剂量引擎 MCsquare 通过执行全面的稳健性测试（模拟范围误差、系统设置误差和呼吸运动）来评估治疗计划。
动态极小极大算法平均实现了 84%的优化时间增益。由于在优化中访问了更多场景，动态极小极大优化导致优化过程明显更嘈杂。然而，增加的噪声水平不会损害计划的最终质量。事实上，在目标覆盖和正常组织保护方面，动态极小极大优化与传统极小极大优化的计划质量相似：平均而言，最坏情况 D95 的差异为 0.2 Gy，平均肺剂量和平均心脏剂量的差异分别为 0.4 和 0.1 Gy（在标称场景中评估）。
所提出的最坏情况 4D 稳健优化算法实现了 84%的显著优化时间增益，而不会损害目标覆盖或正常组织保护。
