An, Yu

PurposeCurrently, in clinical practice of intensity‐modulated proton therapy (IMPT), the influence of the minimum monitor unit (MU) constraint is taken into account through postprocessing after the optimization is completed. This may degrade the plan quality and plan robustness. This study aims to mitigate the impact of the minimum MU constraint directly during the plan robust optimization.Methods and materialsCao et al. have demonstrated a two‐stage method to account for the minimum MU constraint using linear programming without the impact of uncertainties considered. In this study, we took the minimum MU constraint into consideration using quadratic optimization and simultaneously had the impact of uncertainties considered using robust optimization. We evaluated our method using seven cancer patients with different machine settings.ResultThe new method achieved better plan quality than the conventional method. The D95% of the clinical target volume (CTV) normalized to the prescription dose was (mean [min–max]): (99.4% [99.2%–99.6%]) vs. (99.2% [98.6%–99.6%]). Plan robustness derived from these two methods was comparable. For all seven patients, the CTV dose–volume histogram band gap (narrower band gap means more robust plans) at D95% normalized to the prescription dose was (mean [min–max]): (1.5% [0.5%–4.3%]) vs. (1.2% [0.6%–3.8%]).ConclusionOur new method of incorporating the minimum MU constraint directly into the plan robust optimization can produce machine‐deliverable plans with better tumor coverage while maintaining high‐plan robustness.

Purpose 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. Methods 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. Results 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. Conclusions 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.

Background and purposeIntensity‐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.Material and methodsWe 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.ResultsOur 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.ConclusionWith explicit control of plan robustness, the chance‐constrained robust optimization model generated superior IMPT plans compared to the PTV‐based method.