Evaluation of Dosimetric Gain and Uncertainties in Proton Therapy Delivery with Scanned Pencil Beam in Treatment of Base-of-skull and Spinal Tumors

GPU-accelerated Monte Carlo-based online adaptive proton therapy - a feasibility study

PURPOSE

To develop an online Graphic-Processing-Unit (GPU)-accelerated Monte-Carlo-based adaptive radiation therapy (ART) workflow for pencil beam scanning (PBS) proton therapy to address inter-fraction anatomical changes in patients treated with PBS.

METHODS AND MATERIALS

A four-step workflow was developed using our in-house developed GPU-accelerated Monte-Carlo-based treatment planning system to implement online Monte-Carlo-based ART for PBS. The first step conducts diffeomorphic demon-based deformable image registration (DIR) to propagate contours on the initial planning CT (pCT) to the verification CT (vCT) to form a new structure set. The second step performs forward dose calculation of the initial plan on the vCT with the propagated contours after manual approval (possible modifications involved). The third step triggers a re-optimization of the plan depending on whether the verification dose meets the clinical requirements or not. A robust evaluation will be done for both the verification plan in the second step and the re-opotimized plan in the third step. The fourth step involves a two-stage (before and after delivery) patient specific quality assurance (PSQA) of the re-optimized plan. The before-delivery PSQA is to compare the plan dose to the dose calculated using an independent fast open-source Monte Carlo code, MCsquare. The after-delivery PSQA is to compare the plan dose to the dose re-calculated using the log file (spot MU, spot position, and spot energy) collected during the delivery. Jaccard index (JI), Dice similarity coefficients (DSCs), and Hausdorff distance (HD) were used to assess the quality of the propagated contours in the first step. A commercial plan evaluation software, ClearCheck™, was integrated into the workflow to carry out efficient plan evaluation. 3D Gamma analysis was used during the fourth step to ensure the accuracy of the plan dose from re-optimization. Three patients with three different disease sites were chosen to evaluate the feasibility of the online ART workflow for PBS.

RESULTS

For all three patients, the propagated contours were found to have good volume conformance [JI (lowest-highest: 0.833-0.983) and DSC (0.909-0.992)] but sub-optimal boundary coincidence [HD (2.37-20.76 mm)] for organs at risk (OARs). The verification dose evaluated by ClearCheck™ showed significant degradation of the target coverage due to the inter-fractional anatomical changes. Re-optimization on the vCT resulted in great improvement of the plan quality to a clinically acceptable level. 3D Gamma analyses of PSQA confirmed the accuracy of the plan dose before delivery (mean Gamma index = 98.74% with a threshold of 2%/2 mm/10%), and after delivery based on the log files (mean Gamma index = 99.05% with a threshold of 2%/2 mm/10%). The average time cost for the complete execution of the workflow was around 858 seconds, excluding the time for manual intervention.

CONCLUSION

The proposed online ART workflow for PBS was demonstrated to be efficient and effective by generating a re-optimized plan that significantly improved the plan quality. This article is protected by copyright. All rights reserved.

Intensity-modulated proton therapy (IMPT) interplay effect evaluation of asymmetric breathing with simultaneous uncertainty considerations in patients with non-small cell lung cancer

PURPOSE

Intensity-modulated proton therapy (IMPT) is sensitive to uncertainties from patient setup and proton beam range, as well as interplay effect. In addition, respiratory motion may vary from cycle to cycle, and also from day to day. These uncertainties can severely degrade the original plan quality and potentially affect patient's outcome. In this work, we developed a new tool to comprehensively consider the impact of all these uncertainties and provide plan robustness evaluation under them.

METHODS

We developed a comprehensive plan robustness evaluation tool that considered both uncertainties from patient setup and proton beam range, as well as respiratory motion simultaneously. To mimic patients' respiratory motion, the time spent in each phase was randomly sampled based on patient-specific breathing pattern parameters as acquired during the four-dimensional (4D)-computed tomography (CT) simulation. Spots were then assigned to one specific phase according to the temporal relationship between spot delivery sequence and patients' respiratory motion. Dose in each phase was calculated by summing contributions from all the spots delivered in that phase. The final 4D dynamic dose was obtained by deforming all doses in each phase to the maximum exhalation phase. Three hundred (300) scenarios (10 different breathing patterns with 30 different setup and range uncertainty scenario combinations) were calculated for each plan. The dose-volume histograms (DVHs) band method was used to assess plan robustness. Benchmarking the tool as an application's example, we compared plan robustness under both three-dimensional (3D) and 4D robustly optimized IMPT plans for 10 nonrandomly selected patients with non-small cell lung cancer.

RESULTS

The developed comprehensive plan robustness tool had been successfully applied to compare the plan robustness between 3D and 4D robustly optimized IMPT plans for 10 lung cancer patients. In the presence of interplay effect with uncertainties considered simultaneously, 4D robustly optimized plans provided significantly better CTV coverage (D_95% , P = 0.002), CTV homogeneity (D_5% -D_95% , P = 0.002) with less target hot spots (D_5% , P = 0.002), and target coverage robustness (CTV D_95% bandwidth, P = 0.004) compared to 3D robustly optimized plans. Superior dose sparing of normal lung (lung D_mean , P = 0.020) favoring 4D plans and comparable normal tissue sparing including esophagus, heart, and spinal cord for both 3D and 4D plans were observed. The calculation time for all patients included in this study was 11.4 ± 2.6 min.

CONCLUSION

A comprehensive plan robustness evaluation tool was successfully developed and benchmarked for plan robustness evaluation in the presence of interplay effect, setup and range uncertainties. The very high efficiency of this tool marks its clinical adaptation, highly practical and versatile nature, including possible real-time intra-fractional interplay effect evaluation as a potential application for future use.

Robust optimization to reduce the impact of biological effect variation from physical uncertainties in intensity-modulated proton therapy

Robust optimization (RO) methods are applied to intensity-modulated proton therapy (IMPT) treatment plans to ensure their robustness in the face of treatment delivery uncertainties, such as proton range and patient setup errors. However, the impact of those uncertainties on the biological effect of protons has not been specifically considered. In this study, we added biological effect-based objectives into a conventional RO cost function for IMPT optimization to minimize the variation in biological effect. One brain tumor case, one prostate tumor case and one head & neck tumor case were selected for this study. Three plans were generated for each case using three different optimization approaches: planning target volume (PTV)-based optimization, conventional RO, and RO incorporating biological effect (BioRO). In BioRO, the variation in biological effect caused by IMPT delivery uncertainties was minimized for voxels in both target volumes and critical structures, in addition to a conventional voxel-based worst-case RO objective function. The biological effect was approximated by the product of dose-averaged linear energy transfer (LET) and physical dose. All plans were normalized to give the same target dose coverage, assuming a constant relative biological effectiveness (RBE) of 1.1. Dose, biological effect, and their uncertainties were evaluated and compared among the three optimization approaches for each patient case. Compared with PTV-based plans, RO plans achieved more robust target dose coverage and reduced biological effect hot spots in critical structures near the target. Moreover, with their sustained robust dose distributions, BioRO plans not only reduced variations in biological effect in target and normal tissues but also further reduced biological effect hot spots in critical structures compared with RO plans. Our findings indicate that IMPT could benefit from the use of conventional RO, which would reduce the biological effect in normal tissues and produce more robust dose distributions than those of PTV-based optimization. More importantly, this study provides a proof of concept that incorporating biological effect uncertainty gap into conventional RO would not only control the IMPT plan robustness in terms of physical dose and biological effect but also achieve further reduction of biological effect in normal tissues.

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

PURPOSE

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.

METHOD

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.

RESULTS

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.

CONCLUSIONS

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.

Impact of Spot Size and Spacing on the Quality of Robustly Optimized Intensity Modulated Proton Therapy Plans for Lung Cancer

PURPOSE

To investigate how spot size and spacing affect plan quality, robustness, and interplay effects of robustly optimized intensity modulated proton therapy (IMPT) for lung cancer.

METHODS AND MATERIALS

Two robustly optimized IMPT plans were created for 10 lung cancer patients: first by a large-spot machine with in-air energy-dependent large spot size at isocenter (σ: 6-15 mm) and spacing (1.3 σ), and second by a small-spot machine with in-air energy-dependent small spot size (σ: 2-6 mm) and spacing (5 mm). Both plans were generated by optimizing radiation dose to internal target volume on averaged 4-dimensional computed tomography scans using an in-house-developed IMPT planning system. The dose-volume histograms band method was used to evaluate plan robustness. Dose evaluation software was developed to model time-dependent spot delivery to incorporate interplay effects with randomized starting phases for each field per fraction. Patient anatomy voxels were mapped phase-to-phase via deformable image registration, and doses were scored using in-house-developed software. Dose-volume histogram indices, including internal target volume dose coverage, homogeneity, and organs at risk (OARs) sparing, were compared using the Wilcoxon signed-rank test.

RESULTS

Compared with the large-spot machine, the small-spot machine resulted in significantly lower heart and esophagus mean doses, with comparable target dose coverage, homogeneity, and protection of other OARs. Plan robustness was comparable for targets and most OARs. With interplay effects considered, significantly lower heart and esophagus mean doses with comparable target dose coverage and homogeneity were observed using smaller spots.

CONCLUSIONS

Robust optimization with a small spot-machine significantly improves heart and esophagus sparing, with comparable plan robustness and interplay effects compared with robust optimization with a large-spot machine. A small-spot machine uses a larger number of spots to cover the same tumors compared with a large-spot machine, which gives the planning system more freedom to compensate for the higher sensitivity to uncertainties and interplay effects for lung cancer treatments.

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.

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

BACKGROUND AND PURPOSE

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.

MATERIAL AND METHODS

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.

RESULTS

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.

CONCLUSION

With explicit control of plan robustness, the chance-constrained robust optimization model generated superior IMPT plans compared to the PTV-based method.

Robustness quantification methods comparison in volumetric modulated arc therapy to treat head and neck cancer

BACKGROUND

To compare plan robustness of volumetric modulated arc therapy (VMAT) with intensity modulated radiation therapy (IMRT) and to compare the effectiveness of 3 plan robustness quantification methods.

METHODS AND MATERIALS

The VMAT and IMRT plans were created for 9 head and neck cancer patients. For each plan, 6 new perturbed dose distributions were computed using ±3 mm setup deviations along each of the 3 orientations. Worst-case analysis (WCA), dose-volume histogram (DVH) band (DVHB), and root-mean-square dose-volume histogram (RVH) were used to quantify plan robustness. In WCA, a shaded area in the DVH plot bounded by the DVHs from the lowest and highest dose per voxel was displayed. In DVHB, we displayed the envelope of all DVHs in band graphs of all the 7 dose distributions. The RVH represents the relative volume on the vertical axis and the root-mean-square-dose on the horizontal axis. The width from the first 2 methods at different target DVH indices (such as D95% and D5%) and the area under the RVH curve for the target were used to indicate plan robustness. Results were compared using Wilcoxon signed-rank test.

RESULTS

The DVHB showed that the width at D95% of IMRT was larger than that of VMAT (unit Gy) (1.59 vs 1.18) and the width at D5% of IMRT was comparable to that of VMAT (0.59 vs 0.54). The WCA showed similar results between IMRT and VMAT plans (D95%: 3.28 vs 3.00; D5%: 1.68 vs 1.95). The RVH showed the area under the RVH curve of IMRT was comparable to that of VMAT (1.13 vs 1.15). No statistical significance was found in plan robustness between IMRT and VMAT.

CONCLUSIONS

The VMAT is comparable to IMRT in terms of plan robustness. For the 3 quantification methods, WCA and DVHB are DVH parameter-dependent, whereas RVH captures the overall effect of uncertainties.

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

PURPOSE

Robust optimization leads to intensity-modulated proton therapy (IMPT) plans that are less sensitive to uncertainties and superior in terms of organs-at-risk (OARs) sparing, target dose coverage, and homogeneity compared to planning target volume (PTV)-based optimized plans. Robust optimization incorporates setup and range uncertainties, which implicitly adds margins to both targets and OARs and is also able to compensate for perturbations in dose distributions within targets and OARs caused by uncertainties. In contrast, the traditional PTV-based optimization considers only setup uncertainties and adds a margin only to targets but no margins to the OARs. It also ignores range uncertainty. The purpose of this work is to determine if robustly optimized plans are superior to PTV-based plans simply because the latter do not assign margins to OARs during optimization.

METHODS

The authors retrospectively selected from their institutional database five patients with head and neck (H&N) cancer and one with prostate cancer for this analysis. Using their original images and prescriptions, the authors created new IMPT plans using three methods: PTV-based optimization, optimization based on the PTV and planning risk volumes (PRVs) (i.e., "PTV+PRV-based optimization"), and robust optimization using the "worst-case" dose distribution. The PRVs were generated by uniformly expanding OARs by 3 mm for the H&N cases and 5 mm for the prostate case. The dose-volume histograms (DVHs) from the worst-case dose distributions were used to assess and compare plan quality. Families of DVHs for each uncertainty for all structures of interest were plotted along with the nominal DVHs. The width of the "bands" of DVHs was used to quantify the plan sensitivity to uncertainty.

RESULTS

Compared with conventional PTV-based and PTV+PRV-based planning, robust optimization led to a smaller bandwidth for the targets in the face of uncertainties {clinical target volume [CTV] bandwidth: 0.59 [robust], 3.53 [PTV+PRV], and 3.53 [PTV] Gy (RBE)}. It also resulted in higher doses to 95% of the CTV {D(95%): 60.8 [robust] vs 59.3 [PTV+PRV] vs 59.6 [PTV] Gy (RBE)}, smaller D(5%) (doses to 5% of the CTV) minus D(95%) {D(5%) - D(95%): 13.2 [robust] vs 17.5 [PTV+PRV] vs 17.2 [PTV] Gy (RBE)}. At the same time, the robust optimization method irradiated OARs less {maximum dose to 1 cm(3) of the brainstem: 48.3 [robust] vs 48.8 [PTV+PRV] vs 51.2 [PTV] Gy (RBE); mean dose to the oral cavity: 22.3 [robust] vs 22.9 [PTV+PRV] vs 26.1 [PTV] Gy (RBE); maximum dose to 1% of the normal brain: 66.0 [robust] vs 68.0 [PTV+PRV] vs 69.3 [PTV] Gy (RBE)}.

CONCLUSIONS

For H&N cases studied, OAR sparing in PTV+PRV-based optimization was inferior compared to robust optimization but was superior compared to PTV-based optimization; however, target dose robustness and homogeneity were comparable in the PTV+PRV-based and PTV-based optimizations. The same pattern held for the prostate case. The authors' data suggest that the superiority of robust optimization is not due simply to its inclusion of margins for OARs, but that this is due mainly to the ability of robust optimization to compensate for perturbations in dose distributions within target volumes and normal tissues caused by uncertainties.

Influence of robust optimization in intensity-modulated proton therapy with different dose delivery techniques

PURPOSE

The distal edge tracking (DET) technique in intensity-modulated proton therapy (IMPT) allows for high energy efficiency, fast and simple delivery, and simple inverse treatment planning; however, it is highly sensitive to uncertainties. In this study, the authors explored the application of DET in IMPT (IMPT-DET) and conducted robust optimization of IMPT-DET to see if the planning technique's sensitivity to uncertainties was reduced. They also compared conventional and robust optimization of IMPT-DET with three-dimensional IMPT (IMPT-3D) to gain understanding about how plan robustness is achieved.

METHODS

They compared the robustness of IMPT-DET and IMPT-3D plans to uncertainties by analyzing plans created for a typical prostate cancer case and a base of skull (BOS) cancer case (using data for patients who had undergone proton therapy at our institution). Spots with the highest and second highest energy layers were chosen so that the Bragg peak would be at the distal edge of the targets in IMPT-DET using 36 equally spaced angle beams; in IMPT-3D, 3 beams with angles chosen by a beam angle optimization algorithm were planned. Dose contributions for a number of range and setup uncertainties were calculated, and a worst-case robust optimization was performed. A robust quantification technique was used to evaluate the plans' sensitivity to uncertainties.

RESULTS

With no uncertainties considered, the DET is less robust to uncertainties than is the 3D method but offers better normal tissue protection. With robust optimization to account for range and setup uncertainties, robust optimization can improve the robustness of IMPT plans to uncertainties; however, our findings show the extent of improvement varies.

CONCLUSIONS

IMPT's sensitivity to uncertainties can be improved by using robust optimization. They found two possible mechanisms that made improvements possible: (1) a localized single-field uniform dose distribution (LSFUD) mechanism, in which the optimization algorithm attempts to produce a single-field uniform dose distribution while minimizing the patching field as much as possible; and (2) perturbed dose distribution, which follows the change in anatomical geometry. Multiple-instance optimization has more knowledge of the influence matrices; this greater knowledge improves IMPT plans' ability to retain robustness despite the presence of uncertainties.

Robust optimization of intensity modulated proton therapy

PURPOSE

Intensity modulated proton therapy (IMPT) is highly sensitive to range uncertainties and uncertainties caused by setup variation. The conventional inverse treatment planning of IMPT optimized based on the planning target volume (PTV) is not often sufficient to ensure robustness of treatment plans. In this paper, a method that takes the uncertainties into account during plan optimization is used to mitigate the influence of uncertainties in IMPT.

METHODS

The authors use the so-called "worst-case robust optimization" to render IMPT plans robust in the face of uncertainties. For each iteration, nine different dose distributions are computed-one each for ± setup uncertainties along anteroposterior (A-P), lateral (R-L) and superior-inferior (S-I) directions, for ± range uncertainty, and the nominal dose distribution. The worst-case dose distribution is obtained by assigning the lowest dose among the nine doses to each voxel in the clinical target volume (CTV) and the highest dose to each voxel outside the CTV. Conceptually, the use of worst-case dose distribution is similar to the dose distribution achieved based on the use of PTV in traditional planning. The objective function value for a given iteration is computed using this worst-case dose distribution. The objective function used has been extended to further constrain the target dose inhomogeneity.

RESULTS

The worst-case robust optimization method is applied to a lung case, a skull base case, and a prostate case. Compared with IMPT plans optimized using conventional methods based on the PTV, our method yields plans that are considerably less sensitive to range and setup uncertainties. An interesting finding of the work presented here is that, in addition to reducing sensitivity to uncertainties, robust optimization also leads to improved optimality of treatment plans compared to the PTV-based optimization. This is reflected in reduction in plan scores and in the lower normal tissue doses for the same coverage of the target volume when subjected to uncertainties.

CONCLUSIONS

The authors find that the worst-case robust optimization provides robust target coverage without sacrificing, and possibly even improving, the sparing of normal tissues. Our results demonstrate the importance of robust optimization. The authors assert that all IMPT plans should be robustly optimized.