Robust treatment planning with conditional value at risk chance constraints in intensity-modulated proton therapy.

Intensity-modulated proton therapy (IMPT) is highly sensitive to range uncertainties and uncertainties caused by setup variation. The conventional inverse treatment planning of IMPT based on the planning target volume (PTV) is not often sufficient to ensure robustness of treatment plans. We applied a probabilistic framework (chance-constrained optimization) in IMPT planning to hedge against the influence of uncertainties. We retrospectively selected one patient with lung cancer, one patient with head and neck (H&N) cancer, and one with prostate cancer for this analysis. Using their original images and prescriptions, we created new IMPT plans using two methods: (1) a robust chance-constrained treatment planning method with the clinical target volume (CTV) as the target; (2) the margin-based method with PTV as the target, which was solved by commercial software, CPLEX, using linear programming. For the first method, we reformulated the model into a tractable mixed-integer programming problem and sped up the calculation using Benders decomposition. The dose-volume histograms (DVHs) from the nominal and perturbed dose distributions were used to assess and compare plan quality. DVHs for all uncertain scenarios along with the nominal DVH were plotted. The width of the "bands" of DVHs was used to quantify the plan sensitivity to uncertainty. The newly developed Benders decomposition method was compared with a commercial solution to demonstrate its computational efficiency. The trade-off between nominal plan quality and plan robustness was investigated. Our chance-constrained model outperformed the PTV method in terms of tumor coverage, tumor dose homogeneity, and plan robustness. Our model was shown to produce IMPT plans to meet the dose-volume constraints of organs at risk (OARs) and had better sparing of OARs than the PTV method in the three clinical cases included in this study. The chance-constrained model provided a flexible tool for users to balance between plan robustness and plan quality. In addition, our in-house developed method was found to be much faster than the commercial solution. With explicit control of plan robustness, the chance-constrained robust optimization model generated superior IMPT plans compared to the PTV-based method.

An Y ，Liang J ，Schild SE ，Bues M ，Liu W ... -  《-》

Comparison of linear and nonlinear programming approaches for "worst case dose" and "minmax" robust optimization of intensity-modulated proton therapy dose distributions.

Robust optimization of intensity-modulated proton therapy (IMPT) takes uncertainties into account during spot weight optimization and leads to dose distributions that are resilient to uncertainties. Previous studies demonstrated benefits of linear programming (LP) for IMPT in terms of delivery efficiency by considerably reducing the number of spots required for the same quality of plans. However, a reduction in the number of spots may lead to loss of robustness. The purpose of this study was to evaluate and compare the performance in terms of plan quality and robustness of two robust optimization approaches using LP and nonlinear programming (NLP) models. The so-called "worst case dose" and "minmax" robust optimization approaches and conventional planning target volume (PTV)-based optimization approach were applied to designing IMPT plans for five patients: two with prostate cancer, one with skull-based cancer, and two with head and neck cancer. For each approach, both LP and NLP models were used. Thus, for each case, six sets of IMPT plans were generated and assessed: LP-PTV-based, NLP-PTV-based, LP-worst case dose, NLP-worst case dose, LP-minmax, and NLP-minmax. The four robust optimization methods behaved differently from patient to patient, and no method emerged as superior to the others in terms of nominal plan quality and robustness against uncertainties. The plans generated using LP-based robust optimization were more robust regarding patient setup and range uncertainties than were those generated using NLP-based robust optimization for the prostate cancer patients. However, the robustness of plans generated using NLP-based methods was superior for the skull-based and head and neck cancer patients. Overall, LP-based methods were suitable for the less challenging cancer cases in which all uncertainty scenarios were able to satisfy tight dose constraints, while NLP performed better in more difficult cases in which most uncertainty scenarios were hard to meet tight dose limits. For robust optimization, the worst case dose approach was less sensitive to uncertainties than was the minmax approach for the prostate and skull-based cancer patients, whereas the minmax approach was superior for the head and neck cancer patients. The robustness of the IMPT plans was remarkably better after robust optimization than after PTV-based optimization, and the NLP-PTV-based optimization outperformed the LP-PTV-based optimization regarding robustness of clinical target volume coverage. In addition, plans generated using LP-based methods had notably fewer scanning spots than did those generated using NLP-based methods.

Zaghian M ，Cao W ，Liu W ，Kardar L ，Randeniya S ，Mohan R ，Lim G ... -  《Journal of Applied Clinical Medical Physics》

PTV-based IMPT optimization incorporating planning risk volumes vs robust optimization.

Liu W ，Frank SJ ，Li X ，Li Y ，Zhu RX ，Mohan R ... -  《-》

A novel and individualized robust optimization method using normalized dose interval volume constraints (NDIVC) for intensity-modulated proton radiotherapy.

Intensity-modulated proton therapy (IMPT) is known to be sensitive to patient setup and range uncertainty issues. Multiple robust optimization methods have been developed to mitigate the impact of these uncertainties. Here, we propose a new robust optimization method, which provides an alternative way of robust optimization in IMPT, and is clinically practical, which will enable users to control the balance between nominal plan quality and plan robustness in a user-defined fashion. We calculated nine individual dose distributions which corresponded to one nominal and eight extreme scenarios caused by patient setup and proton beam's range uncertainties. For each voxel, the normalized dose interval (NDI) is defined as the full dose range variation divided by the maximum dose in all uncertainty scenarios (NDI = [max - min dose]/max dose), which was then used to calculate the normalized dose interval volume histogram (NDIVH) curves. The areas under the NDIVH curves were used to quantify plan robustness. A normalized dose interval volume constraint (NDIVC) applied to the target was incorporated to specify the desired robustness which was user-defined. Users could then explore the trade-off between nominal plan quality and plan robustness by adjusting the position of the NDIVCs on the NDIVH curves freely. We benchmarked our method using one lung, five head and neck (H&N), and three prostate cases by comparing our results to those derived using the voxel-wise worst-case robust optimization. Using the benchmark cases, our new method achieved quality IMPT plans comparable to those derived from the voxel-wise worst-case robust optimization for both nominal plan quality and plan robustness in general; even more conformal and more homogeneous target dose distributions in some cases, if proper NDIVCs were applied. The AUC under NDIVH, as a precise quantitative index of plan robustness, was consistent with DVH bandwidths. Additionally, we demonstrated the feasibility of adjusting the position of NDIVCs in the NDIVH curves which allowed users to explore the trade-off between nominal plan quality and plan robustness. The NDIVH-based robust optimization method provided a novel and individualized way of robust optimization in IMPT, and enables users to adjust the balance between nominal plan quality and plan robustness in a user-defined fashion. This method is applicable for continued improvement and developing the next generation of IMPT planning algorithms in the future.

Shan J ，Sio TT ，Liu C ，Schild SE ，Bues M ，Liu W ... -  《-》

Robust intensity-modulated proton therapy to reduce high linear energy transfer in organs at risk.

We propose a robust treatment planning model that simultaneously considers proton range and patient setup uncertainties and reduces high linear energy transfer (LET) exposure in organs at risk (OARs) to minimize the relative biological effectiveness (RBE) dose in OARs for intensity-modulated proton therapy (IMPT). Our method could potentially reduce the unwanted damage to OARs. We retrospectively generated plans for 10 patients including two prostate, four head and neck, and four lung cancer patients. The "worst-case robust optimization" model was applied. One additional term as a "biological surrogate (BS)" of OARs due to the high LET-related biological effects was added in the objective function. The biological surrogate was defined as the sum of the physical dose and extra biological effects caused by the dose-averaged LET. We generated nine uncertainty scenarios that considered proton range and patient setup uncertainty. Corresponding to each uncertainty scenario, LET was obtained by a fast LET calculation method developed in-house and based on Monte Carlo simulations. In each optimization iteration, the model used the worst-case BS among all scenarios and then penalized overly high BS to organs. The model was solved by an efficient algorithm (limited-memory Broyden-Fletcher-Goldfarb-Shanno) in a parallel computing environment. Our new model was benchmarked with the conventional robust planning model without considering BS. Dose-volume histograms (DVHs) of the dose assuming a fixed RBE of 1.1 and BS for tumor and organs under nominal and uncertainty scenarios were compared to assess the plan quality between the two methods. For the 10 cases, our model outperformed the conventional robust model in avoidance of high LET in OARs. At the same time, our method could achieve dose distributions and plan robustness of tumors assuming a fixed RBE of 1.1 almost the same as those of the conventional robust model. Explicitly considering LET in IMPT robust treatment planning can reduce the high LET to OARs and minimize the possible toxicity of high RBE dose to OARs without sacrificing plan quality. We believe this will allow one to design and deliver safer proton therapy.

An Y ，Shan J ，Patel SH ，Wong W ，Schild SE ，Ding X ，Bues M ，Liu W ... -  《-》