Liu, Wei

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.

AbstractMonte Carlo (MC) simulation has been used to generate commissioning data for the beam modeling of treatment planning system (TPS). We have developed a method called radial projection (RP) for postprocessing of MC‐simulation‐generated data. We used the RP method to reduce the statistical uncertainty of the lateral profile of proton pencil beams with axial symmetry. The RP method takes advantage of the axial symmetry of dose distribution to use the mean value of multiple independent scores as the representative score. Using the mean as the representative value rather than any individual score results in substantial reduction in statistical uncertainty. Herein, we present the concept and step‐by‐step implementation of the RP method, as well as show the advantage of the RP method over conventional measurement methods for generating lateral profile. Lateral profiles generated by both methods were compared to demonstrate the uncertainty reduction qualitatively, and standard error comparison was performed to demonstrate the reduction quantitatively. The comparisons showed that statistical uncertainty was reduced substantially by the RP method. Using the RP method to postprocess MC data, the corresponding MC simulation time was reduced by a factor of 10 without quality reduction in the generated result from the MC data. We concluded that the RP method is an effective technique to increase MC simulation efficiency for generating lateral profiles for axially symmetric pencil beams.

AbstractBackgroundIn treatment planning for intensity‐modulated proton therapy (IMPT), we aim to deliver the prescribed dose to the target yet minimize the dose to adjacent healthy tissue. Mixed‐integer programming (MIP) has been applied in radiation therapy to generate treatment plans. However, MIP has not been used effectively for IMPT treatment planning with dose‐volume constraints. In this study, we incorporated dose‐volume constraints in an MIP model to generate treatment plans for IMPT.MethodsWe created a new MIP model for IMPT with dose volume constraints. Two groups of IMPT treatment plans were generated for each of three patients by using MIP models for a total of six plans: one plan was derived with the Limited‐memory Broyden–Fletcher–Goldfarb–Shanno (L‐BFGS) method while the other plan was derived with our MIP model with dose‐volume constraints. We then compared these two plans by dose‐volume histogram (DVH) indices to evaluate the performance of the new MIP model with dose‐volume constraints. In addition, we developed a model to more efficiently find the best balance between tumor coverage and normal tissue protection.ResultsThe MIP model with dose‐volume constraints generates IMPT treatment plans with comparable target dose coverage, target dose homogeneity, and the maximum dose to organs at risk (OARs) compared to treatment plans from the conventional quadratic programming method without any tedious trial‐and‐error process. Some notable reduction in the mean doses of OARs is observed.ConclusionsThe treatment plans from our MIP model with dose‐volume constraints can meet all dose‐volume constraints for OARs and targets without any tedious trial‐and‐error process. This model has the potential to automatically generate IMPT plans with consistent plan quality among different treatment planners and across institutions and better protection for important parallel OARs in an effective way.

PurposeTo implement and evaluate a novel and fast method for proton range verification by using a planar scintillator and step wedge.MethodsA homogenous proton pencil beam plan with 35 energies was designed and delivered to a 2D flat scintillator with a step wedge. The measurement was repeated 15 times (3 different days, 5 times per day). The scintillator image was smoothed, the Bragg peak and distal fall off regions were fitted by an analytical equation, and the proton range was calculated using simple trigonometry. The accuracy of this method was verified by comparing the measured ranges to those obtained using an ionization chamber and a scanning water tank, the gold standard. The reproducibility was evaluated by comparing the ranges over 15 repeated measurements. The sensitivity was evaluated by delivering to same beam to the system with a film inserted under the wedge.ResultsThe range accuracy of all 35 proton energies measured over 3 days was within 0.2 mm. The reproducibility in 15 repeated measurements for all 35 proton ranges was ±0.045 mm. The sensitivity to range variation is 0.1 mm for the worst case. This efficient procedure permits measurement of 35 proton ranges in less than 3 min. The automated data processing produces results immediately. The setup of this system took less than 5 min. The time saving by this new method is about two orders of magnitude when compared with the time for water tank range measurements.ConclusionsA novel method using a scintillator with a step wedge to measure the proton range was implemented and evaluated. This novel method is fast and sensitive, and the proton range measured by this method was accurate and highly reproducible.

AbstractThis work is to show which is more relevant to cause local failures (LFs) due to patient setup uncertainty between the planning target volume (PTV) underdosage and the potential target underdosage subject to patient setup uncertainties in head and neck (H&N) cancer treated with volumetric‐modulated arc therapy (VMAT). Thirteen LFs in 10 H&N patients treated by VMAT were analyzed. Measures have been taken to minimize the chances of insufficient target delineation for these patients and the patients were clinically determined to have LF based on the PET/CT scan results by an experienced radiologist and then reviewed by a second experienced radiation oncologist. Two methods were used to identify the possible locations of LF due to underdosage: (a) examining the standard VMAT plan, in which the underdosed volume in the nominal dose distribution (UVN) was generated by subtracting the volumes receiving the prescription doses from PTVs, and (b) plan robustness analysis, in which in addition to the nominal dose distribution, six perturbed dose distributions were created by translating the CT iso‐center in three cardinal directions by the PTV margin. The coldest dose distribution was represented by the minimum of the seven doses in each voxel. The underdosed volume in the coldest dose distribution (UVC) was generated by subtracting the volumes receiving the prescription doses in the coldest dose distribution from the volumes receiving the prescription doses in the nominal dose distribution. UVN and UVC were subsequently examined for spatial association with the locations of LF. The association was tested using the binominal distribution and the Fisher's exact test of independence. We found that of 13 LFs, 11 were associated with UVCs (P = 0.011), while three were associated with UVNs (P = 0.99). We concluded that the possible target underdosage due to patient setup uncertainties appeared to be a more relevant factor associated with LF in VMAT for H&N cancer than the compromised PTV coverage at least for the patients included in this study.

AbstractRobust 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.

Respiratory motion is traditionally assessed using tumor motion magnitude. In proton therapy, respiratory motion causes density variations along the beam path that result in uncertainties of proton range. This work has investigated the use of water‐equivalent thickness (WET) to quantitatively assess the effects of respiratory motion on calculated dose in passively scattered proton therapy (PSPT). A cohort of 29 locally advanced non‐small cell lung cancer patients treated with 87 PSPT treatment fields were selected for analysis. The variation in WET (ΔWET) along each field was calculated between exhale and inhale phases of the simulation four‐dimensional computed tomography. The change in calculated dose (ΔDose) between full‐inhale and full‐exhale phase was quantified for each field using dose differences, 3D gamma analysis, and differential area under the curve (ΔAUC) analysis. Pearson correlation coefficients were calculated between ΔDose and ΔWET. Three PSPT plans were redesigned using field angles to minimize variations in ΔWET and compared to the original plans. The median ΔWET over 87 treatment fields ranged from 1‐9 mm, while the ΔWET 95th percentile value ranged up to 42 mm. The ΔWET was significantly correlated to the ΔDose for all metrics analyzed. The patient plans that were redesigned using ΔWET analysis to select field angles were more robust to the effects of respiratory motion, as ΔAUC values were reduced by more than 60% in all three cases. The tumor motion magnitude alone does not capture the potential dosimetric error due to respiratory motion because the proton range is sensitive to the motion of all patient anatomy. The use of ΔWET has been demonstrated to identify situations where respiratory motion can impact the calculated dose. Angular analysis of ΔWET may be capable of designing radiotherapy plans that are more robust to the effects of respiratory motion.PACS number(s): 87.55.‐x

The objective of this study was to evaluate and understand the systematic error between the planned three‐dimensional (3D) dose and the delivered dose to patient in scanning beam proton therapy for lung tumors. Single‐field and multifield optimized scanning beam proton therapy plans were generated for ten patients with stage II‐III lung cancer with a mix of tumor motion and size. 3D doses in CT datasets for different respiratory phases and the time‐weighted average CT, as well as the four‐dimensional (4D) doses were computed for both plans. The 3D and 4D dose differences for the targets and different organs at risk were compared using dose‐volume histogram (DVH) and voxel‐based techniques, and correlated with the extent of tumor motion. The gross tumor volume (GTV) dose was maintained in all 3D and 4D doses, using the internal GTV override technique. The DVH and voxel‐based techniques are highly correlated. The mean dose error and the standard deviation of dose error for all target volumes were both less than 1.5% for all but one patient. However, the point dose difference between the 3D and 4D doses was up to 6% for the GTV and greater than 10% for the clinical and planning target volumes. Changes in the 4D and 3D doses were not correlated with tumor motion. The planning technique (single‐field or multifield optimized) did not affect the observed systematic error. In conclusion, the dose error in 3D dose calculation varies from patient to patient and does not correlate with lung tumor motion. Therefore, patient‐specific evaluation of the 4D dose is important for scanning beam proton therapy for lung tumors.PACS number: 87.55.D

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.