Probability of normal tissue complications for hematologic and gastrointestinal toxicity in postoperative whole pelvic radiotherapy for gynecologic malignancies using intensity-modulated proton therapy with robust optimization

This retrospective treatment-planning study was conducted to determine whether intensity-modulated proton therapy with robust optimization (ro-IMPT) reduces the risk of acute hematologic toxicity (H-T) and acute and late gastrointestinal toxicity (GI-T) in postoperative whole pelvic radiotherapy for gynecologic malignancies when compared with three-dimensional conformal radiation therapy (3D-CRT), intensity-modulated X-ray (IMXT) and single-field optimization proton beam (SFO-PBT) therapies. All plans were created for 13 gynecologic-malignancy patients. The prescribed dose was 45 GyE in 25 fractions for 95% planning target volume in 3D-CRT, IMXT and SFO-PBT plans and for 99% clinical target volume (CTV) in ro-IMPT plans. The normal tissue complication probability (NTCP) of each toxicity was used as an in silico surrogate marker. Median estimated NTCP values for acute H-T and acute and late GI-T were 0.20, 0.94 and 0.58 × 10-1 in 3D-CRT; 0.19, 0.65 and 0.24 × 10-1 in IMXT; 0.04, 0.74 and 0.19 × 10-1 in SFO-PBT; and 0.06, 0.66 and 0.15 × 10-1 in ro-IMPT, respectively. Compared with 3D-CRT and IMXT plans, the ro-IMPT plan demonstrated significant reduction in acute H-T and late GI-T. The risk of acute GI-T in ro-IMPT plan is equivalent with IMXT plan. The ro-IMPT plan demonstrated potential clinical benefits for reducing the risk of acute H-T and late GI-T in the treatment of gynecologic malignances by reducing the dose to the bone marrow and bowel bag while maintaining adequate dose coverage to the CTV. Our results indicated that ro-IMPT may reduce acute H-T and late GI-T risk with potentially improving outcomes for postoperative gynecologic-malignancy patients with concurrent chemotherapy.

Comparing Efficacy Between Robust and PTV Margin-based Optimizations for Interfractional Anatomical Variations in Prostate Tomotherapy

BACKGROUND/AIM

Interfractional anatomical variations cause considerable differences between planned and actual radiotherapy doses. This study aimed to investigate the efficacy of robust and planning target volume (PTV) margin-based optimizations for the anatomical variations in helical tomotherapy for prostate cancer.

PATIENTS AND METHODS

Ten patients underwent treatment-planning kilovolt computed tomography (kVCT) and daily megavolt computed tomography (MVCT). Two types of nominal plans, with a prescription of 60 Gy/20 fractions, were created using robust and PTV margin-based optimizations on kVCT for each patient. Subsequently, the daily estimated doses were recalculated using nominal plans, and all available MVCTs modified the daily patient-setup errors. Due to the difference in dose calculation accuracy between kVCT and MVCT, three scenarios with dose corrections of 1, 2, and 3% were considered in the recalculation process. The dosimetric metrics, including target coverage with the prescription dose, Paddick's conformity index, homogeneity index, and mean dose to the rectum, were analyzed.

RESULTS

A dosimetric comparison of the nominal plans demonstrated that the robust plans had better dose conformity, lower target coverage, and dose homogeneity than the PTV plans. In the daily estimated doses of any dose-corrected scenario, the target coverage and dose sparing to the rectum in the robust plans were significantly higher than those in the PTV plans, whereas dose conformity and homogeneity were identical to those of the nominal case.

CONCLUSION

Robust optimization is recommended as it accounts for anatomical variations during treatment regarding target coverage in helical tomotherapy plans for prostate cancer.

A robust treatment planning approach for chest motion in postmastectomy chest wall intensity modulated radiation therapy

PURPOSE

Chest wall postmastectomy radiation therapy (PMRT) should consider the effects of chest wall respiratory motion. The purpose of this study is to evaluate the effectiveness of robustness planning intensity modulated radiation therapy (IMRT) for respiratory movement, considering respiratory motion as a setup error.

MATERIAL AND METHODS

This study analyzed 20 patients who underwent PMRT (10 left and 10 right chest walls). The following three treatment plans were created for each case and compared. The treatment plans are a planning target volume (PTV) plan (PP) that covers the PTV within the body contour with the prescribed dose, a virtual bolus plan (VP) that sets a virtual bolus in contact with the body surface and prescribing the dose that includes the PTV outside the body contour, and a robust plan (RP) that considers respiratory movement as a setup uncertainty and performs robust optimization. The isocenter was shifted to reproduce the chest wall motion pattern and the doses were recalculated for comparison for each treatment plan.

RESULT

No significant difference was found between the PP and the RP in terms of the tumor dose in the treatment plan. In contrast, VP had 3.5% higher PTV Dmax and 5.5% lower PTV V95% than RP (p < 0.001). The RP demonstrated significantly higher lung V20Gy and Dmean by 1.4% and 0.4 Gy, respectively, than the PP. The RP showed smaller changes in dose distribution affected by chest wall motion and significantly higher tumor dose coverage than the PP and VP.

CONCLUSION

We revealed that the RP demonstrated comparable tumor doses to the PP in treatment planning and was robust for respiratory motion compared to both the PP and the VP. However, the organ at risk dose in the RP was slightly higher; therefore, its clinical use should be carefully considered.

Robust stochastic optimization of needle configurations for robotic HDR prostate brachytherapy

BACKGROUND

Ideally, inverse planning for HDR brachytherapy (BT) should include the pose of the needles which define the trajectory of the source. This would be particularly interesting when considering the additional freedom and accuracy in needle pose which robotic needle placement enables. However, needle insertion typically leads to tissue deformation, resulting in uncertainty regarding the actual pose of the needles with respect to the tissue.

PURPOSE

To efficiently address uncertainty during inverse planning for HDR BT in order to robustly optimize the pose of the needles before insertion, that is, to facilitate path planning for robotic needle placement.

METHODS

We use a form of stochastic linear programming to model the inverse treatment planning problem. To account for uncertainty, we consider random tissue displacements at the needle tip to simulate tissue deformation. Conventionally for stochastic linear programming, each simulated deformation is reflected by an addition to the linear programming problem which increases problem size and computational complexity substantially and leads to impractical runtime. We propose two efficient approaches for stochastic linear programming. First, we consider averaging dose coefficients to reduce the problem size. Second, we study weighting of the slack variables of an adjusted linear problem to approximate the full stochastic linear program. We compare different approaches to optimize the needle configurations and evaluate their robustness with respect to different amounts of tissue deformation.

RESULTS

Our results illustrate that stochastic planning can improve the robustness of the treatment with respect to deformation. The proposed approaches approximating stochastic linear programming better conform to the tissue deformation compared to conventional linear programming. They show good correlation with the plans computed after deformation while reducing the runtime by two orders of magnitude compared to the complete stochastic linear program. Robust optimization of needle configurations takes on average 59.42 s. Skew needle configurations lead to mean coverage improvements compared to parallel needles from 0.39 to 2.94 percentage points, when 8 mm tissue deformation is considered. Considering tissue deformations from 4  to 10 mm during planning with weighted stochastic optimization and skew needles generally results in improved mean coverage from 1.77 to 4.21 percentage points.

CONCLUSIONS

We show that efficient stochastic optimization allows selecting needle configurations which are more robust with respect to potentially negative effects of target deformation and displacement on the achievable prescription dose coverage. The approach facilitates robust path planning for robotic needle placement.

The LET trilemma: Conflicts between robust target coverage, uniform dose, and dose-averaged LET in carbon therapy

BACKGROUND

Linear energy transfer (LET) is closely related to the biological effect of ionizing radiation. Increasing the dose-averaged LET (LETd ) within the target volume has been proposed as a means to improve clinical outcome for hypoxic tumors. However, doing so can lead to reduced robustness to range uncertainty.

PURPOSE

To quantify the relationship between robust target coverage, target dose uniformity, and LETd , we employ robust optimization using dose-based and LETd -based functions and allow varying amounts of target non-uniformity.

METHODS AND MATERIALS

Robust carbon therapy optimization is used to create plans for phantom cases with increasing target sizes (radii 1, 3, and 5 cm). First, the influence of respectively range and setup uncertainty on the LETd in the target is studied. Second, we employ strategies allowing overdosage in the clinical target volume (CTV) or gross tumor volume (GTV), which enable increased LETd in the target. The relationship between robust target coverage and LETd in the target is illustrated by tradeoff curves generated by optimization using varying weights for the LETd -based functions.

RESULTS

As the range uncertainty used in the robust optimization increased from 0% to 5%, the near-minimum nominal LETd decreased by 17%-29% (9-21 keV/µm) for the different target sizes. The effect of increasing setup uncertainty was marginal. Allowing 10% overdosage in the CTV enabled 9%-29% (6-12 keV/µm) increased near-minimum worst case LETd for the different target sizes, compared to uniform dose plans. When 10% overdosage was allowed in the GTV only, the increase was 1%-20% (1-8 keV/µm).

CONCLUSIONS

There is an inherent conflict between range uncertainty robustness and high LETd in the target, which is aggravated with increasing target size. For large tumors, it is possible to simultaneously achieve two of the three qualities range robustness, uniform dose, and high LETd in the target.

Setup Uncertainty of Pediatric Brain Tumor Patients Receiving Proton Therapy: A Prospective Study

This study quantifies setup uncertainty in brain tumor patients who received image-guided proton therapy. Patients analyzed include 165 children, adolescents, and young adults (median age at radiotherapy: 9 years (range: 10 months to 24 years); 80 anesthetized and 85 awake) enrolled in a single-institution prospective study from 2020 to 2023. Cone-beam computed tomography (CBCT) was performed daily to calculate and correct manual setup errors, once per course after setup correction to measure residual errors, and weekly after treatments to assess intrafractional motion. Orthogonal radiographs were acquired consecutively with CBCT for paired comparisons of 40 patients. Translational and rotational errors were converted from 6 degrees of freedom to a scalar by a statistical approach that considers the distance from the target to the isocenter. The 95th percentile of setup uncertainty was reduced by daily CBCT from 10 mm (manual positioning) to 1-1.5 mm (after correction) and increased to 2 mm by the end of fractional treatment. A larger variation existed between the roll corrections reported by radiographs vs. CBCT than for pitch and yaw, while there was no statistically significant difference in translational variation. A quantile mixed regression model showed that the 95th percentile of intrafractional motion was 0.40 mm lower for anesthetized patients (p=0.0016). Considering additional uncertainty in radiation-imaging isocentricity, the commonly used total plan robustness of 3 mm against positional uncertainty would be appropriate for our study cohort.

A spot-specific range uncertainty framework for robust optimization of proton therapy treatments

PURPOSE

An accurate estimation of range uncertainties is essential to exploit the potential of proton therapy. According to Paganetti's study, a value of 2.4% (1.5 standard deviation) is currently recommended for planning robust treatments with Monte Carlo dose engines. This number is based on a dominant contribution from the mean excitation energy of tissues. However, it was recently shown that expressing tissues as a mixture of water and "dry" material in the CT calibration process allowed for a significant reduction of this uncertainty. We thus propose an adapted framework for pencil beam scanning robust optimization. First, we move towards a spot-specific range uncertainty (SSRU) determination. Second, we use the water-based formalism to reduce range uncertainties and, potentially, to spare better the organs at risk.

METHODS

The stoichiometric calibration was adapted to provide a molecular decomposition (including water) of each voxel of the CT. The SSRU calculation was implemented in MCsquare, a fast Monte Carlo dose engine dedicated to proton therapy. For each spot, a ray-tracing method was used to propagate molecular I-values uncertainties and obtain the corresponding effective range uncertainty. These were then combined with other sources of range uncertainties, according to Paganetti's study of 2012. The method was then assessed on three head-and-neck patients. Two plans were optimized for each patient: the first one with the classical 2.4% flat range uncertainty (FRU), the second one with the variable range uncertainty. Both plans were then compared in terms of target coverage and OAR mean dose reduction. Robustness evaluations were also performed, using the SSRU for both plans in order to simulate errors as realistically as possible.

RESULTS

For patient 1, it was found that the median SSRU was 1.04% (1.5 standard deviation), yielding, therefore, a very large reduction from the 2.4% FRU. All three SSRU plans were found to have a very good robustness level at a 90% confidence interval while sparing OAR better than the classical plan. For instance, in nominal cases, average reductions in the mean dose of 15.7, 8.4, and 13.2% were observed in the left parotid, right parotid, and pharyngeal constrictor muscle, respectively. As expected, the classical plans showed a higher but unnecessary level of robustness.

CONCLUSIONS

Promising results of the SSRU framework were observed on three head-and-neck cases, and more patients should now be considered. The method could also benefit to other tumor sites and, in the long run, the variable part of the range uncertainty could be generalized to other sources of uncertainty in order to move towards more and more patient-specific treatments.

Our journeys through the fascinating world of proton radiation therapy

The purpose of this article is to share the excitement of the science of proton therapy, told by two physicists, who started their career in this area at different times. The authors' journey spans the evolution of proton therapy over the past 30 years, taking the reader from the time when it was an extremely exotic treatment modality until its more common use today. Over this time period, the authors' research and development aimed at an improved understanding of the physical benefits of intensity-modulated proton therapy and arc therapy, treatment planning and optimization to take proton-specific uncertainties into account, and imaging to measure the proton range in the patient. The final section focuses on emerging themes to democratize proton therapy by substantially reducing its size and price, for much greater affordability and global availability of this treatment modality.

An uncertainty-incorporated method for fast beam angle selection in intensity-modulated proton therapy

Aim

We propose a novel metric called ψ - score to rank the Intensity Modulated Proton Therapy (IMPT) beams in the order of their optimality and robustness. The beams ranked based on this metric were accordingly chosen for IMPT optimization. The objective of this work is to study the effectiveness of the proposed method in various clinical cases.

Methods and Materials

We have used Pinnacle TPS (Philips Medical System V 16.2) for performing the optimization. To validate our approach, we have applied it in four clinical cases: Lung, Pancreas, Prostate+Node and Prostate. Basically, for all clinical cases, four set of plans were created using Multi field optimization (MFO) and Robust Optimization (RO) with same clinical objectives, namely (1) Conventional angle plan without Robust Optimization (CA Plan), (2) Suitable angle Plan without Robust Optimization (SA Plan), (3) Conventional angle plan with Robust Optimization (CA-RO Plan), (4) Suitable angle Plan with Robust Optimization (SA-RO Plan). Initial plan was generated with 20 equiangular beams starting from the gantry angle of 0°. In the corresponding SA Plan and SA-RO Plan, the beam angles were obtained using the guidance provided by ψ - score.

Results

All CA plans were compared against the SA plans in terms of Dose distribution, Dose volume histogram (DVH) and percentage of dose difference. The results obtained from the clinical cases indicate that the plan quality is considerably improved without significantly compromising the robustness when the beam angles are optimized using the proposed method. It takes approximately 10-15 min to find the suitable beam angles without Robust Optimization (RO), while it takes approximately 20-30 min to find the suitable beam angles with RO. However, the inclusion of RO in BAO did not result in a change in the final beam angles for anatomies other than lung.

Conclusion

The results obtained in different anatomic sites demonstrate the usefulness of our approach in improving the plan quality by determining optimal beam angles in IMPT.

Dosimetric impact of a robust optimization approach to mitigate effects from rotational uncertainty in prostate intensity-modulated brachytherapy

BACKGROUND

Intensity-modulated brachytherapy (IMBT) is an emerging technology for cancer treatment, in which radiation sources are shielded to shape the dose distribution. The rotatable shields provide an additional degree of freedom, but also introduce an additional, directional, type of uncertainty, compared to conventional high-dose-rate brachytherapy (HDR BT).

PURPOSE

We propose and evaluate a robust optimization approach to mitigate the effects of rotational uncertainty in the shields with respect to planning criteria.

METHODS

A previously suggested prototype for platinum-shielded prostate ¹⁶⁹ Yb-based dynamic IMBT is considered. We study a retrospective patient data set (anatomical contours and catheter placement) from two clinics, consisting of six patients that had previously undergone conventional ¹⁹² Ir HDR BT treatment. The Monte Carlo-based treatment planning software RapidBrachyMCTPS is used for dose calculations. In our computational experiments, we investigate systematic rotational shield errors of ±10° and ±20°, and the same systematic error is applied to all dwell positions in each scenario. This gives us three scenarios, one nominal and two with errors. The robust optimization approach finds a compromise between the average and worst-case scenario outcomes.

RESULTS

We compare dose plans obtained from standard models and their robust counterparts. With dwell times obtained from a linear penalty model (LPM), for 10° errors, the dose to urethra ( D 0.1 c c $D_{0.1cc}$ ) and rectum ( D 0.1 c c $D_{0.1cc}$ and D 1 c c $D_{1cc}$ ) increase with up to 5% and 7%, respectively, in the worst-case scenario, while with the robust counterpart, the corresponding increases were 3% and 3%. For all patients and all evaluated criteria, the worst-case scenario outcome with the robust approach had lower deviation compared to the standard model, without compromising target coverage. We also evaluated shield errors up to 20° and while the deviations increased to a large extent with the standard models, the robust models were capable of handling even such large errors.

CONCLUSIONS

We conclude that robust optimization can be used to mitigate the effects from rotational uncertainty and to ensure the treatment plan quality of IMBT.

Proton liver stereotactic body radiation therapy: Treatment techniques and dosimetry feasibility from a single institution

Purpose

To assess the resulting dosimetry characteristics of simulation and planning techniques for proton stereotactic body radiation therapy (SBRT) of primary and secondary liver tumors.

Methods

Consecutive patients treated under volumetric daily image guidance with liver proton SBRT between September 2019 and March 2022 at Emory Proton Therapy Center were included in this study. Prescriptions ranged from 40 Gy to 60 Gy in 3- or 5-fraction regimens, and motion management techniques were used when target motion exceeded 5 mm. 4D robust optimization was used when necessary. Dosimetry evaluation was conducted for ITV V100, D99, Dmax, and liver-ITV mean dose and D700cc. Statistical analysis was performed using independent-samples Mann-Whitney U tests.

Results

Thirty-six tumors from 29 patients were treated. Proton therapy for primary and secondary liver tumors using motion management techniques and robust optimization resulted in high target coverage and low doses to critical organs. The median ITV V100% was 100.0%, and the median ITV D99% was 111.3%. The median liver-ITV mean dose and D700cc were 499 cGy and 5.7 cGy, respectively. The median conformity index (CI) was 1.03, and the median R50 was 2.56. Except for ITV D99% (primary 118.1% vs. secondary 107.2%, p = 0.005), there were no significant differences in age, ITV volume, ITV V100%, ITV maximum dose, liver-ITV mean dose, or D700cc between primary and secondary tumor groups.

Conclusion

The study demonstrated that proton therapy with motion management techniques and robust optimization achieves excellent target coverage with low normal liver doses for primary and secondary liver tumors. The results showed high target coverage, high conformality, and low doses to the liver.

Robust optimization for casualty scheduling considering injury deterioration and point-edge mixed failures in early stage of post-earthquake relief

Objective

Scientifically organizing emergency rescue activities to reduce mortality in the early stage of earthquakes.

Methods

A robust casualty scheduling problem to reduce the total expected death probability of the casualties is studied by considering scenarios of disrupted medical points and routes. The problem is described as a 0-1 mixed integer nonlinear programming model. An improved particle swarm optimization (PSO) algorithm is introduced to solve the model. A case study of the Lushan earthquake in China is conducted to verify the feasibility and effectiveness of the model and algorithm.

Results

The results show that the proposed PSO algorithm is superior to the compared genetic algorithm, immune optimization algorithm, and differential evolution algorithm. The optimization results are still robust and reliable even if some medical points fail and routes are disrupted in affected areas when considering point-edge mixed failure scenarios.

Conclusion

Decision makers can balance casualty treatment and system reliability based on the degree of risk preference considering the uncertainty of casualties, to achieve the optimal casualty scheduling effect.

Distributed and scalable optimization for robust proton treatment planning

BACKGROUND

The importance of robust proton treatment planning to mitigate the impact of uncertainty is well understood. However, its computational cost grows with the number of uncertainty scenarios, prolonging the treatment planning process.

PURPOSE

We developed a fast and scalable distributed optimization platform that parallelizes the robust proton treatment plan computation over the uncertainty scenarios.

METHODS

We modeled the robust proton treatment planning problem as a weighted least-squares problem. To solve it, we employed an optimization technique called the alternating direction method of multipliers with Barzilai-Borwein step size (ADMM-BB). We reformulated the problem in such a way as to split the main problem into smaller subproblems, one for each proton therapy uncertainty scenario. The subproblems can be solved in parallel, allowing the computational load to be distributed across multiple processors (e.g., CPU threads/cores). We evaluated ADMM-BB on four head-and-neck proton therapy patients, each with 13 scenarios accounting for 3 mm setup and 3.5% range uncertainties. We then compared the performance of ADMM-BB with projected gradient descent (PGD) applied to the same problem.

RESULTS

For each patient, ADMM-BB generated a robust proton treatment plan that satisfied all clinical criteria with comparable or better dosimetric quality than the plan generated by PGD. However, ADMM-BB's total runtime averaged about 6 to 7 times faster. This speedup increased with the number of scenarios.

CONCLUSIONS

ADMM-BB is a powerful distributed optimization method that leverages parallel processing platforms, such as multicore CPUs, GPUs, and cloud servers, to accelerate the computationally intensive work of robust proton treatment planning. This results in (1) a shorter treatment planning process and (2) the ability to consider more uncertainty scenarios, which improves plan quality.

Introduce a rotational robust optimization framework for spot-scanning proton arc (SPArc) therapy

Objective. Proton dosimetric uncertainties resulting from the patient's daily setup errors in rotational directions exist even with advanced image-guided radiotherapy techniques. Thus, we developed a new rotational robust optimization SPArc algorithm (SPArc_rot) to mitigate the dosimetric impact of the rotational setup error in Raystation ver. 6.02 (RaySearch Laboratory AB, Stockholm, Sweden).Approach.The initial planning CT was rotated ±5° simulating the worst-case setup error in the roll direction. The SPArc_rotuses a multi-CT robust optimization framework by taking into account of such rotational setup errors. Five cases representing different disease sites were evaluated. Both SPArc_originaland SPArc_rotplans were generated using the same translational robust optimized parameters. To quantitatively investigate the mitigation effect from the rotational setup errors, all plans were recalculated using a series of pseudo-CT with rotational setup error (±1°/±2°/±3°/±5°). Dosimetric metrics such as D98% of CTV, and 3D gamma analysis were used to assess the dose distribution changes in the target and OARs.Main results.The magnitudes of dosimetric changes in the targets due to rotational setup error were significantly reduced by the SPArc_rotcompared to SPArc in all cases. The uncertainties of the max dose to the OARs, such as brainstem, spinal cord and esophagus were significantly reduced using SPArc_rot. The uncertainties of the mean dose to the OARs such as liver and oral cavity, parotid were comparable between the two planning techniques. The gamma passing rate (3%/3 mm) was significantly improved for CTV of all tumor sites through SPArc_rot.Significance.Rotational setup error is one of the major issues which could lead to significant dose perturbations. SPArc_rotplanning approach can consider such rotational error from patient setup or gantry rotation error by effectively mitigating the dose uncertainties to the target and in the adjunct series OARs.

ALERT-RA: an aperture library-enabled real-time respiratory motion adaptive framework for 4D-VMAT

PURPOSE

To develop a framework for robust optimization of real-time respiratory motion adaptive VMAT treatment plans, and to evaluate the robustness of resulting plans to variations in tumor trajectory during delivery.

METHODS

The proposed framework is called aperture library-enabled real-time robust adaptation (ALERT-RA). A patient-specific library of optimized MLC apertures is defined for each combination of gantry angle and respiratory phase. The method assumes that the tumor is tracked in real-time throughout delivery, and the aperture corresponding to the current phase and gantry angle will be delivered. The aperture library is optimized by considering all possible tumor trajectories determined by a probabilistic respiratory motion model. Plan robustness to trajectory variations was evaluated by sampling a trajectory, and determining the corresponding dose, from the respiratory model for each fraction. The cumulative dose of the full treatment course was simulated 50 times. Percentile dose-volume histograms (PDVHs) were computed from these simulated treatments. The resulting plan quality and robustness of this method were compared to other previously published motion 4D-VMAT methods, including: an optimized tracking approach that assumes reproducible tumor motion, conformal tracking with aperture deformation, and a motion-encompassing method. Two fractionation schemes were tested to determine the possible effect on robustness: a conventional fractionation of 66 Gy in 33 fractions, and an SBRT course with 60 Gy in 5 fractions.

RESULTS

When considering target coverage, the ALERT-RA method was found to produce a plan which was more robust than those produced using the optimized or conformal tracking methods. Using the PDVH analysis, the 5th and 95th percentiles of the prescription dose volume for the conventionally fractioned plan were found to be (respectively) 79% and 82% for the optimized tracking approach, 81% and 83% for the conformal tracking approach, and 92% and 97% using the new ALERT-RA method. The motion-encompassing plan was slightly more robust than the ALERT-RA plan, with 5th and 95th percentiles at 94% and 95%, respectively. This came at a cost of higher dose to OARs, with the volume of lung receiving 5 Gy or more equal to 48% for the motion-encompassing plan versus 44% for the ALERT-RA plan. For the SBRT plan, the conformal tracking plan was similarly not robust, with 5th and 95th percentiles of the prescription dose volume equal to 88% and 89%. The optimized tracking SBRT plan gave values of 93% and 95%, and the motion-encompassing plan 94% and 95%, while the ALERT-RA gave values of 93% and 96%. The volume of lung receiving 20 Gy or more was slightly higher for the optimized tracking and motion-encompassing plans compared to the ALERT-RA plan, at 15%, 15%, and 14%, respectively.

CONCLUSIONS

Compared to other motion-adaptive VMAT approaches, the ALERT-RA algorithm is capable of delivering high-quality plans which are robust to variations in tumor motion trajectories.

A Robust Power Allocation Algorithm for Cognitive Radio Networks Based on Hybrid PSO

The use of a cognitive radio power allocation algorithm is an effective method to improve spectral utilization. However, there are three problems with traditional cognitive radio power allocation algorithms: (1) based on the ideal channel model analysis, channel fluctuation is not considered; (2) they do not consider fairness among cognitive users; and (3) some algorithms are complex and locating the optimal power allocation scheme is not an easy task. For the above problems, this study establishes a robust model which adds the cognitive user transmission rate variance constraint to solve the maximum channel capacity time power allocation scheme by considering the worst-case channel transmission model, and finally solves this complex non-convex optimization problem by using the hybrid particle swarm algorithm. Simulation results show that the algorithm has good robustness, improves the fairness among the cognitive users, makes full use of the channel resources under the constraints, and has a simple algorithm, fast convergence, and good optimization results.

Robust optimization of VMAT for prostate cancer accounting for geometric uncertainty

The aim of this study was to propose optimal robust planning by comparing the robustness with setup error with the robustness of a conventional planning target volume (PTV)‐based plan and to compare the robust plan to the PTV‐based plan for the target and organ at risk (OAR). Data from 13 patients with intermediate‐to‐high‐risk localized prostate cancer who did not have T3b disease were analyzed. The dose distribution under multiple setup error scenarios was assessed using a conventional PTV‐based plan. The clinical target volume (CTV) and OAR dose in moving coordinates were used for the dose constraint with the robust plan. The hybrid robust plan added the dose constraint of the PTV‐rectum to the static coordinate system. When the isocenter was shifted by 10 mm in the superior–inferior direction and 8 mm in the right‐left and anterior directions, the doses to the CTV, bladder, and rectum of the PTV‐based plan, robust plan, and hybrid robust plan were compared. For the CTV D_99% in the PTV‐based plan and hybrid robust plan, over 95% of the prescribed dose was secured in all directions, except in the inferior direction. There was no significant difference between the PTV‐based plan and the hybrid robust plan for rectum V_70Gy, V_60Gy, and V_40Gy. This study proposed an optimization method for patients with prostate cancer. When the setup error occurred within the PTV margin, the dose robustness of the CTV for the hybrid robust plan was higher than that of the PTV‐based plan, while maintaining the equivalent OAR dose.

Range uncertainty reductions in proton therapy may lead to the feasibility of novel beam arrangements which improve organ-at-risk sparing

PURPOSE

In proton therapy, dose distributions are currently often conformed to organs at risk (OARs) using the less sharp dose fall-off at the lateral beam edge to reduce the effects of uncertainties in the in vivo proton range. However, range uncertainty reductions may make greater use of the sharper dose fall-off at the distal beam edge feasible, potentially improving OAR sparing. We quantified the benefits of such novel beam arrangements.

METHODS

For each of 10 brain or skull base cases, five treatment plans robust to 2 mm setup and 0%-4% range uncertainty were created for the traditional clinical beam arrangement and a novel beam arrangement making greater use of the distal beam edge to conform the dose distribution to the brainstem. Metrics including the brainstem normal tissue complication probability (NTCP) with the endpoint of necrosis were determined for all plans and all setup and range uncertainty scenarios.

RESULTS

For the traditional beam arrangement, reducing the range uncertainty from the current level of approximately 4% to a potentially achievable level of 1% reduced the brainstem NTCP by up to 0.9 percentage points in the nominal and up to 1.5 percentage points in the worst-case scenario. Switching to the novel beam arrangement at 1% range uncertainty improved these values by a factor of 2, that is, to 1.8 percentage points and 3.2 percentage points, respectively. The novel beam arrangement achieved a lower brainstem NTCP in all cases starting at a range uncertainty of 2%.

CONCLUSION

The benefits of novel beam arrangements may be of the same magnitude or even exceed the direct benefits of range uncertainty reductions. Indirect effects may therefore contribute markedly to the benefits of reducing proton range uncertainties.

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.

A study to determine the impact of IMPT optimization techniques on prostate synthetic CT image sets dose comparison against CT image sets

Background

The objective of this study is to determine the impact of intensity modulated proton therapty (IMPT) optimization techniques on the proton dose comparison of commercially available magnetic resonance for calculating attenuation (MRCA T) images, a synthetic computed tomography CT (sCT) based on magnetic resonance imaging (MRI) scan against the CT images and find out the optimization technique which creates plans with the least dose differences against the regular CT image sets.

Material and methods

Regular CT data sets and sCT image sets were obtained for 10 prostate patients for the study. Six plans were created using six distinct IMPT optimization techniques including multi-field optimization (MFO), single field uniform dose (SFUD) optimization, and robust optimization (RO) in CT image sets. These plans were copied to MRCA T, sCT datasets and doses were computed. Doses from CT and MRCA T data sets were compared for each patient using 2D dose distribution display, dose volume histograms (DVH), homogeneity index (HI), conformation number (CN) and 3D gamma analysis. A two tailed t-test was conducted on HI and CN with 5% significance level with a null hypothesis for CT and sCT image sets.

Results

Analysis of ten CT and sCT image sets with different IMPT optimization techniques shows that a few of the techniques show significant differences between plans for a few evaluation parameters. Isodose lines, DVH, HI, CN and t-test analysis shows that robust optimizations with 2% range error incorporated results in plans, when re-computed in sCT image sets results in the least dose differences against CT plans compared to other optimization techniques. The second best optimization technique with the least dose differences was robust optimization with 5% range error.

Conclusion

This study affirmatively demonstrates the impact of IMPT optimization techniques on synthetic CT image sets dose comparison against CT images and determines the robust optimization with 2% range error as the optimization technique which gives the least dose difference when compared to CT plans.

Robust automated radiation therapy treatment planning using scenario-specific dose prediction and robust dose mimicking

Purpose

We present a framework for robust automated treatment planning using machine learning, comprising scenario‐specific dose prediction and robust dose mimicking.

Methods

The scenario dose prediction pipeline is divided into the prediction of nominal dose from input image and the prediction of scenario dose from nominal dose, each using a deep learning model with U‐net architecture. By using a specially developed dose–volume histogram–based loss function, the predicted scenario doses are ensured sufficient target coverage despite the possibility of the training data being non‐robust. Deliverable plans may then be created by solving a robust dose mimicking problem with the predictions as scenario‐specific reference doses.

Results

Numerical experiments are performed using a data set of 52 intensity‐modulated proton therapy plans for prostate patients. We show that the predicted scenario doses resemble their respective ground truth well, in particular while having target coverage comparable to that of the nominal scenario. The deliverable plans produced by the subsequent robust dose mimicking were showed to be robust against the same scenario set considered for prediction.

Conclusions

We demonstrate the feasibility and merits of the proposed methodology for incorporating robustness into automated treatment planning algorithms.

Dosimetric advantages of daily adaptive strategy in IMPT for high-risk prostate cancer

Purpose

To evaluate the dosimetric advantages of daily adaptive radiotherapy (DART) in intensity‐modulated proton therapy (IMPT) for high‐risk prostate cancer by comparing estimated doses of the conventional non‐adaptive radiotherapy (NART) that irradiates according to an original treatment plan through the entire treatment and the DART that uses an adaptive treatment plan generated by using daily CT images acquired before each treatment.

Methods

Twenty‐three patients with prostate cancer were included. A treatment plan with 63 Gy (relative biological effectiveness (RBE)) in 21 fractions was generated using treatment planning computed tomography (CT) images assuming that all patients had high‐risk prostate cancer for which the clinical target volume (CTV) needs to include prostate and the seminal vesicle (SV) in our treatment protocol. Twenty‐one adaptive treatment plans for each patient (total 483 data sets) were generated using daily CT images, and dose distributions were calculated. Using a 3 mm set‐up uncertainty in the robust optimization, the doses to the CTV, prostate, SV, rectum, and bladder were compared.

Results

Estimated accumulated doses of NART and DART in the 23 patients were 60.81 ± 3.47 Gy (RBE) and 63.24 ± 1.04 Gy (RBE) for CTV D99 (p < 0.01), 62.99 ± 1.28 Gy (RBE) and 63.43 ± 1.33 Gy (RBE) for the prostate D99 (p = 0.2529), and 59.07 ± 5.19 Gy (RBE) and 63.17 ± 1.04 Gy (RBE) for SV D99 (p < 0.001). No significant differences were observed between NART and DART in the estimated accumulated dose for the rectum and bladder.

Conclusion

Compared with the NART, DART was shown to be a useful approach that can maintain the dose coverage to the target without increasing the dose to the organs at risk (OAR) using the 3 mm set‐up uncertainty in the robust optimization in patients with high‐risk prostate cancer.

Robust Security Beamforming for SWIPT-Assisted Relay System with Channel Uncertainty

This paper considers the physical layer security (PLS) of a simultaneous wireless information and power transfer (SWIPT) relay communication system composed of a legitimate source-destination pair and some eavesdroppers. Supposing a disturbance of channel status information (CSI) between relay and eavesdroppers in a bounded ellipse, we intend to design a robust beamformer to maximum security rate in the worst case on the constraints of relay energy consumption. To handle this non-convex optimization problem, we introduce a slack variable to transform the original problem into two sub-problems firstly, then an algorithm employing a semidefinite relaxation (SDR) technique and S-procedure is proposed to tackle above two sub-problems. Although our study was conducted in the scene of a direct link among source, destination, and eavesdroppers that is non-existing, we demonstrate that our conclusions can be easily extended to the scene for which a direct link among source, destination and eavesdroppers exist. Numerical simulation results compared with the benchmark scheme are provided to prove the effectiveness and superior performance of our algorithm.

Knowledge-Based Planning for Robustly Optimized Intensity-Modulated Proton Therapy of Head and Neck Cancer Patients

PURPOSE

To assess the performance of a proton-specific knowledge-based planning (KBP) model in the creation of robustly optimized intensity-modulated proton therapy (IMPT) plans for treatment of advanced head and neck (HN) cancer patients.

METHODS

Seventy-three patients diagnosed with advanced HN cancer previously treated with volumetric modulated arc therapy (VMAT) were selected and replanned with robustly optimized IMPT. A proton-specific KBP model, RapidPlanPT (RPP), was generated using 53 patients (20 unilateral cases and 33 bilateral cases). The remaining 20 patients (10 unilateral and 10 bilateral cases) were used for model validation. The model was validated by comparing the target coverage and organ at risk (OAR) sparing in the RPP-generated IMPT plans with those in the expert plans. To account for the robustness of the plan, all uncertainty scenarios were included in the analysis.

RESULTS

All the RPP plans generated were clinically acceptable. For unilateral cases, RPP plans had higher CTV_primary V100 (1.59% ± 1.24%) but higher homogeneity index (HI) (0.7 ± 0.73) than had the expert plans. In addition, the RPP plans had better ipsilateral cochlea Dmean (-5.76 ± 6.11 Gy), with marginal to no significant difference between RPP plans and expert plans for all other OAR dosimetric indices. For the bilateral cases, the V100 for all clinical target volumes (CTVs) was higher for the RPP plans than for the expert plans, especially the CTV_primary V100 (5.08% ± 3.02%), with no significant difference in the HI. With respect to OAR sparing, RPP plans had a lower spinal cord Dmax (-5.74 ± 5.72 Gy), lower cochlea Dmean (left, -6.05 ± 4.33 Gy; right, -4.84 ± 4.66 Gy), lower left and right parotid V20Gy (left, -6.45% ± 5.32%; right, -6.92% ± 3.45%), and a lower integral dose (-0.19 ± 0.19 Gy). However, RPP plans increased the Dmax in the body outside of CTV (body-CTV) (1.2 ± 1.43 Gy), indicating a slightly higher hotspot produced by the RPP plans.

CONCLUSION

IMPT plans generated by a broad-scope RPP model have a quality that is, at minimum, comparable with, and at times superior to, that of the expert plans. The RPP plans demonstrated a greater robustness for CTV coverage and better sparing for several OARs.

Implementation and experimental validation of a robust hybrid direct aperture optimization approach for mixed-beam radiotherapy

Purpose

The objectives of the work presented in this paper were to (1) implement a robust‐optimization method for deliverable mixed‐beam radiotherapy (MBRT) plans within a previously developed MBRT planning framework; (2) perform an experimental validation of the delivery of robust‐optimized MBRT plans; and (3) compare PTV‐based and robust‐optimized MBRT plans in terms of target dose robustness and organs at risk (OAR) sparing for clinical head and neck and brain patient cases.

Methods

A robust‐optimization method, which accounts for translational setup errors, was implemented within a previously developed treatment planning framework for MBRT. The framework uses a hybrid direct aperture optimization method combining column generation and simulated annealing. A robust plan was developed and then delivered to an anthropomorphic head phantom using the Developer Mode of a TrueBeam linac. Planar dose distributions were measured and compared to the planned dose. Robust‐optimized and PTV‐based plans were developed for three clinical patient cases consisting of two head and neck cases and one brain case. The plans were compared in terms of the robustness to 5 mm shifts of the target volume dose as well as in terms of OAR sparing.

Results

Using a gamma criterion of 3%/2 mm and a dose threshold of 10%, the agreement between film measurements and dose calculations was better than 97.7% for the total plan and better than 95.5% for the electron component of the plan. For the two head and neck patient cases, the average clinical target volume (CTV) dose homogeneity index (V95%–V107%) over all the considered setup error scenarios was on average 19% lower for the PTV‐based plans and it had a larger standard deviation. The robust‐optimized plans achieved, on average, a 20% reduction in the OAR doses compared to the PTV‐based plans. For the brain patient case, the CTV dose homogeneity index was similar for the two plans, while the OAR doses were 22% lower, on average, for the robust‐optimized plan. No clear trend in terms of electron contributions was found across the three patient cases, although robust‐optimized plans tended toward higher electron beam energies.

Conclusions

A framework for robust optimization of deliverable MBRT plans has been developed and validated. PTV‐based MBRT were found to not be robust to setup errors, while the dose delivered by the robust‐optimized plans were clinically acceptable for all considered error scenarios and had better OAR sparing. This study shows that the robust optimization is a promising alternative to conventional PTV margins for MBRT.

Proton range uncertainty reduction benefits for skull base tumors in terms of normal tissue complication probability (NTCP) and healthy tissue doses

PURPOSE

Proton therapy allows for more conformal dose distributions and lower organ at risk and healthy tissue doses than conventional photon-based radiotherapy, but uncertainties in the proton range currently prevent proton therapy from making full use of these advantages. Numerous developments therefore aim to reduce such range uncertainties. In this work, we quantify the benefits of reductions in range uncertainty for treatments of skull base tumors.

METHODS

The study encompassed 10 skull base patients with clival tumors. For every patient, six treatment plans robust to setup errors of 2 mm and range errors from 0% to 5% were created. The determined metrics included the brainstem and optic chiasm normal tissue complication probability (NTCP) with the endpoints of necrosis and blindness, respectively, as well as the healthy tissue volume receiving at least 70% of the prescription dose.

RESULTS

A range uncertainty reduction from the current level of 4% to a potentially achievable level of 1% reduced the probability of brainstem necrosis by up to 1.3 percentage points in the nominal scenario in which neither setup nor range errors occur and by up to 2.9 percentage points in the worst-case scenario. Such a range uncertainty reduction also reduced the optic chiasm NTCP with the endpoint of blindness by up to 0.9 percentage points in the nominal scenario and by up to 2.2 percentage points in the worst-case scenario. The decrease in the healthy tissue volume receiving at least 70% of the prescription dose ranged from -7.8 to 24.1 cc in the nominal scenario and from -3.4 to 38.4 cc in the worst-case scenario.

CONCLUSION

The benefits quantified as part of this study serve as a guideline of the OAR and healthy tissue dose benefits that range monitoring techniques may be able to achieve. Benefits were observed between all levels of range uncertainty. Even smaller range uncertainty reductions may therefore be beneficial.

Introducing a probabilistic definition of the target in a robust treatment planning framework

The 'clinical target distribution' (CTD) has recently been introduced as a promising alternative to the binary clinical target volume (CTV). However, a comprehensive study that considers the CTD, together with geometric treatment uncertainties, was lacking. Because the CTD is inherently a probabilistic concept, this study proposes a fully probabilistic approach that integrates the CTD directly in a robust treatment planning framework. First, the CTD is derived from a reported microscopic tumor infiltration model such that it explicitly features the probability of tumor cell presence in its target definition. Second, two probabilistic robust optimization methods are proposed that evaluate CTD coverage under uncertainty. The first method minimizes the expected-value (EV) over the uncertainty scenarios and the second method minimizes the sum of the expected value and standard deviation (EV-SD), thereby penalizing the spread of the objectives from the mean. Both EV and EV-SD methods introduce the CTD in the objective function by using weighting factors that represent the probability of tumor presence. The probabilistic methods are compared to a conventional worst-case approach that uses the CTV in a worst-case optimization algorithm. To evaluate the treatment plans, a scenario-based evaluation strategy is implemented that combines the effects of microscopic tumor infiltrations with the other geometric uncertainties. The methods are tested for five lung tumor patients, treated with intensity-modulated proton therapy. The results indicate that for the studied patient cases, the probabilistic methods favor the reduction of the esophagus dose but compensate by increasing the high-dose region in a low conflicting organ such as the lung. These results show that a fully probabilistic approach has the potential to obtain clinical benefits when tumor infiltration uncertainties are taken into account directly in the treatment planning process.

A Review of the Robust Optimization Process and Advances with Monte Carlo in the Proton Therapy Management of Head and Neck Tumors

In intensity-modulated proton therapy, robust optimization processes have been developed to manage uncertainties associated with (1) range, (2) setup, (3) anatomic changes, (4) dose calculation, and (5) biological effects. Here we review our experience using a robust optimization technique that directly incorporates range and setup uncertainties into the optimization process to manage those sources of uncertainty. We also review procedures for implementing adaptive planning to manage the anatomic uncertainties. Finally, we share some early experiences regarding the impact of uncertainties in dose calculation and biological effects, along with techniques to manage and potentially reduce these uncertainties.

Impact of errors in spot size and spot position in robustly optimized pencil beam scanning proton-based stereotactic body radiation therapy (SBRT) lung plans

Purpose

The purpose of the current study was threefold: (a) investigate the impact of the variations (errors) in spot sizes in robustly optimized pencil beam scanning (PBS) proton‐based stereotactic body radiation therapy (SBRT) lung plans, (b) evaluate the impact of spot sizes and position errors simultaneously, and (c) assess the overall effect of spot size and position errors occurring simultaneously in conjunction with either setup or range errors.

Methods

In this retrospective study, computed tomography (CT) data set of five lung patients was selected. Treatment plans were regenerated for a total dose of 5000 cGy(RBE) in 5 fractions using a single‐field optimization (SFO) technique. Monte Carlo was used for the plan optimization and final dose calculations. Nominal plans were normalized such that 99% of the clinical target volume (CTV) received the prescription dose. The analysis was divided into three groups. Group 1: The increasing and decreasing spot sizes were evaluated for ±10%, ±15%, and ±20% errors. Group 2: Errors in spot size and spot positions were evaluated simultaneously (spot size: ±10%; spot position: ±1 and ±2 mm). Group 3: Simulated plans from Group 2 were evaluated for the setup (±5 mm) and range (±3.5%) errors.

Results

Group 1: For the spot size errors of ±10%, the average reduction in D_99% for −10% and +10% errors was 0.7% and 1.1%, respectively. For −15% and +15% spot size errors, the average reduction in D_99% was 1.4% and 1.9%, respectively. The average reduction in D_99% was 2.1% for −20% error and 2.8% for +20% error. The hot spot evaluation showed that, for the same magnitude of error, the decreasing spot sizes resulted in a positive difference (hotter plan) when compared with the increasing spot sizes. Group 2: For a 10% increase in spot size in conjunction with a −1 mm (+1 mm) shift in spot position, the average reduction in D_99% was 1.5% (1.8%). For a 10% decrease in spot size in conjunction with a −1 mm (+1 mm) shift in spot position, the reduction in D_99% was 0.8% (0.9%). For the spot size errors of ±10% and spot position errors of ±2 mm, the average reduction in D_99% was 2.4%. Group 3: Based on the results from 160 plans (4 plans for spot size [±10%] and position [±1 mm] errors × 8 scenarios × 5 patients), the average D_99% was 4748 cGy(RBE) with the average reduction of 5.0%. The isocentric shift in the superior–inferior direction yielded the least homogenous dose distributions inside the target volume.

Conclusion

The increasing spot sizes resulted in decreased target coverage and dose homogeneity. Similarly, the decreasing spot sizes led to a loss of target coverage, overdosage, and degradation of dose homogeneity. The addition of spot size and position errors to plan robustness parameters (setup and range uncertainties) increased the target coverage loss and decreased the dose homogeneity.

Analysis of acute-phase toxicities of intensity-modulated proton therapy using a model-based approach in pharyngeal cancer patients

Pharyngeal cancer patients treated with intensity-modulated proton therapy (IMPT) using a model-based approach were retrospectively reviewed, and acute toxicities were analyzed. From June 2016 to March 2019, 15 pharyngeal (7 naso-, 5 oro- and 3 hypo-pharyngeal) cancer patients received IMPT with robust optimization. Simulation plans for IMPT and intensity-modulated X-ray therapy (IMXT) were generated before treatment. We also reviewed 127 pharyngeal cancer patients with IMXT in the same treatment period. In the simulation planning comparison, all of the normal-tissue complication probability values for dysphagia, dysgeusia, tube-feeding dependence and xerostomia were lower for IMPT than for IMXT in the 15 patients. After completing IMPT, 13 patients completed the evaluation, and 12 of these patients had a complete response. The proportions of patients who experienced grade 2 or worse acute toxicities in the IMPT and IMXT cohorts were 21.4 and 56.5% for dysphagia (P < 0.05), 46.7 and 76.3% for dysgeusia (P < 0.05), 73.3 and 62.8% for xerostomia (P = 0.43), 73.3 and 90.6% for mucositis (P = 0.08) and 66.7 and 76.4% for dermatitis (P = 0.42), respectively. Multivariate analysis revealed that IMPT was independently associated with a lower rate of grade 2 or worse dysphagia and dysgeusia. After propensity score matching, 12 pairs of IMPT and IMXT patients were selected. Dysphagia was also statistically lower in IMPT than in IMXT (P < 0.05). IMPT using a model-based approach may have clinical benefits for acute dysphagia.

The Role of Plan Robustness Evaluation in Comparing Protons and Photons Plans - An Application on IMPT and IMRT Plans in Skull Base Chordomas

Purpose:

To analyze robustness of treatment plans optimized using different approaches in intensity modulated proton therapy (IMPT) and investigate the necessity of robust optimization and evaluation in intensity modulated radiotherapy (IMRT) plans for skull base chordomas.

Materials and Methods:

Two photon plans, standard IMRT and robustly optimized IMRT (RB-IMRT), and two IMPT plans, robustly optimized multi field optimization (MFO) and hybrid-MFO (HB-MFO), were created in RayStation TPS for five patients previously treated using single field uniform optimization (SFO). Both set-up and range uncertainties were incorporated during robust optimization of IMPT plans whereas only set-up uncertainty was used in RB-IMRT. The dosimetric outcomes from the five planning techniques were compared for every patient using standard dose volume indices and integral dose (ID) estimated for target and organs at risk (OARs). Robustness of each treatment plan was assessed by introducing set-up uncertainties of ±3 mm along the three translational axes and, only in protons, an additional range uncertainty of ±3.5%.

Results:

All the five nominal plans provided comparable and clinically acceptable target coverage. In comparison to nominal plans, worst case decrease in D_95% of clinical target volume-high risk (CTV-HR) were 11.1%, 13.5%, and 13.6% for SFO, MFO, and HB-MFO plans respectively. The corresponding values were 13.7% for standard IMRT which improved to 11.5% for RB-IMRT. The worst case increased in high dose (D_1%) to CTV-HR was highest in IMRT (2.1%) and lowest in SFO (0.7%) plans. Moreover, IMRT showed worst case increases in D_1% for all neurological OARs and were lowest for SFO plans. The worst case D_1% for brainstem, chiasm, spinal cord, optic nerves, and temporal lobes were increased by 29%, 41%, 30%, 41% and 14% for IMRT and 18%, 21%, 21%, 24%, and 7% for SFO plans, respectively. In comparison to IMRT, RB-IMRT improved D_1% of all neurological OARs ranging from 5% to 14% in worst case scenarios.

Conclusion:

Based on the five cases presented in the current study, all proton planning techniques (SFO, MFO and HB-MFO) were robust both for target coverage and OARs sparing. Standard IMRT plans were less robust than proton plans in regards to high doses to neurological OARs. However, robust optimization applied to IMRT resulted in improved robustness in both target coverage and high doses to OARs. Robustness evaluation may be considered as a part of plan evaluation procedure even in IMRT.

Robust optimization approach to emergency mobile facility routing

Emergency events such as natural disasters, environmental events, sudden illness, and social security events pose tremendous threats to people's lives and property security. In order to meet emergency service demands by rationally allocating mobile facilities, an emergency mobile facility routing model is proposed to maximize the total served demand by the available mobile facilities. Based on the uninterruptible feature of emergency services, the model abstracts emergency events act as a combination of multiple uncertain variables. To overcome the computational difficulty, a robust optimization approach and genetic algorithm are employed to obtain solutions. Illustrative examples show that it provides an effective method for solving the emergency mobile facility routing problem, and that the risk factor and penalty factor of the model can further guide decision-making.

Effectiveness of robust optimization in volumetric modulated arc therapy using 6 and 10 MV flattening filter-free beam therapy planning for lung stereotactic body radiation therapy with a breath-hold technique

We investigated the feasibility of a robust optimization with 6 MV X-ray (6X) and 10 MV X-ray (10X) flattening filter-free (FFF) beams in a volumetric modulated arc therapy (VMAT) plan for lung stereotactic body radiation therapy (SBRT) using a breath-holding technique. Ten lung cancer patients were selected. Four VMAT plans were generated for each patient; namely, an optimized plan based on the planning target volume (PTV) margin and a second plan based on a robust optimization of the internal target volume (ITV) with setup uncertainties, each for the 6X- and 10X-FFF beams. Both optimized plans were normalized by the percentage of the prescription dose covering 95% of the target volume (D95%) to the PTV (1050 cGy × 4 fractions). All optimized plans were evaluated using perturbed doses by specifying user-defined shifted values from the isocentre. The average perturbed D99% doses to the ITV, compared to the nominal plan, decreased by 369.1 (6X-FFF) and 301.0 cGy (10X-FFF) for the PTV-based optimized plan, and 346.0 (6X-FFF) and 271.6 cGy (10X-FFF) for the robust optimized plan, respectively. The standard deviation of the D99% dose to the ITV were 163.6 (6X-FFF) and 158.9 cGy (10X-FFF) for the PTV-based plan, and 138.9 (6X-FFF) and 128.5 cGy (10X-FFF) for the robust optimized plan, respectively. Robust optimized plans with 10X-FFF beams is a feasible method to achieve dose certainty for the ITV for lung SBRT using a breath-holding technique.

Technical Note: Integrating an open source Monte Carlo code "MCsquare" for clinical use in intensity-modulated proton therapy

PURPOSE

To commission an open source Monte Carlo (MC) dose engine, "MCsquare" for a synchrotron-based proton machine, integrate it into our in-house C++-based I/O user interface and our web-based software platform, expand its functionalities, and improve calculation efficiency for intensity-modulated proton therapy (IMPT).

METHODS

We commissioned MCsquare using a double Gaussian beam model based on in-air lateral profiles, integrated depth dose of 97 beam energies, and measurements of various spread-out Bragg peaks (SOBPs). Then we integrated MCsquare into our C++-based dose calculation code and web-based second check platform "DOSeCHECK." We validated the commissioned MCsquare based on 12 different patient geometries and compared the dose calculation with a well-benchmarked GPU-accelerated MC (gMC) dose engine. We further improved the MCsquare efficiency by employing the computed tomography (CT) resampling approach. We also expanded its functionality by adding a linear energy transfer (LET)-related model-dependent biological dose calculation.

RESULTS

Differences between MCsquare calculations and SOBP measurements were <2.5% (<1.5% for ~85% of measurements) in water. The dose distributions calculated using MCsquare agreed well with the results calculated using gMC in patient geometries. The average 3D gamma analysis (2%/2 mm) passing rates comparing MCsquare and gMC calculations in the 12 patient geometries were 98.0 ± 1.0%. The computation time to calculate one IMPT plan in patients' geometries using an inexpensive CPU workstation (Intel Xeon E5-2680 2.50 GHz) was 2.3 ± 1.8 min after the variable resolution technique was adopted. All calculations except for one craniospinal patient were finished within 3.5 min.

CONCLUSIONS

MCsquare was successfully commissioned for a synchrotron-based proton beam therapy delivery system and integrated into our web-based second check platform. After adopting CT resampling and implementing LET model-dependent biological dose calculation capabilities, MCsquare will be sufficiently efficient and powerful to achieve Monte Carlo-based and LET-guided robust optimization in IMPT, which will be done in the future studies.

On adaptation cost and tractability in robust adaptive radiation therapy optimization

PURPOSE

In this paper, a framework for online robust adaptive radiation therapy (ART) is discussed and evaluated. The purpose of the presented approach to ART is to: (a) handle interfractional geometric variations following a probability distribution different from the a priori hypothesis, (b) address adaptation cost, and (c) address computational tractability.

METHODS

A novel framework for online robust ART using the concept of Bayesian inference and scenario reduction is introduced and evaluated in a series of simulated cases on a one-dimensional phantom geometry. The initial robust plan is generated from a robust optimization problem based on either expected-value or worst-case optimization approach using the a priori hypothesis of the probability distribution governing the interfractional geometric variations. Throughout the course of treatment, the simulated interfractional variations are evaluated in terms of their likelihood with respect to the a priori hypothesis of their distribution and violation of user-specified tolerance limits by the accumulated dose. If an adaptation is considered, the a posteriori distribution is computed from the actual variations using Bayesian inference. Then, the adapted plan is optimized to better suit the actual interfractional variations of the individual case. This adapted plan is used until the next adaptation is triggered. To address adaptation cost, the proposed framework provides an option for increased adaptation frequency. Computational tractability in robust planning and ART is addressed by an approximation algorithm to reduce the size of the optimization problem.

RESULTS

According to the simulations, the proposed framework may improve target coverage compared to the corresponding nonadaptive robust approach. In particular, Bayesian inference may be useful to individualize plans to the actual interfractional variations. Concerning adaptation cost, the results indicate that mathematical methods like Bayesian inference may have a greater impact on improving individual treatment quality than increased adaptation frequency. In addition, the simulations suggest that the concept of scenario reduction may be useful to address computational tractability in ART and robust planning in general.

CONCLUSIONS

The simulations indicate that the adapted plans may improve target coverage and OAR protection at manageable adaptation and computational cost within the novel framework. In particular, adaptive strategies using Bayesian inference appear to perform best among all strategies. This proof-of-concept study provides insights into the mathematical aspects of robustness, tractability, and ART, which are a useful guide for further development of frameworks for online robust ART.

Beamforming Optimization in Internet of Things Applications Using Robust Swarm Algorithm in Conjunction with Connectable and Collaborative Sensors

The integration of the Internet of Things (IoT) with Wireless Sensor Networks (WSNs) typically involves multihop relaying combined with sophisticated signal processing to serve as an information provider for several applications such as smart grids, industrial, and search-and-rescue operations. These applications entail deploying many sensors in environments that are often random which motivated the study of beamforming using random geometric topologies. This paper introduces a new algorithm for the synthesis of several geometries of Collaborative Beamforming (CB) of virtual sensor antenna arrays with maximum mainlobe and minimum sidelobe levels (SLL) as well as null control using Canonical Swarm Optimization (CPSO) algorithm. The optimal beampattern is achieved by optimizing the current excitation weights for uniform and non-uniform interelement spacings based on the network connectivity of the virtual antenna arrays using a node selection scheme. As compared to conventional beamforming, convex optimization, Genetic Algorithm (GA), and Particle Swarm Optimization (PSO), the proposed CPSO achieves significant reduction in SLL, control of nulls, and increased gain in mainlobe directed towards the desired base station when the node selection technique is implemented with CB.

Accounting for multiple ecosystem services in a simulation of land-use decisions: Does it reduce tropical deforestation?

Conversion of tropical forests is among the primary causes of global environmental change. The loss of their important environmental services has prompted calls to integrate ecosystem services (ES) in addition to socio-economic objectives in decision-making. To test the effect of accounting for both ES and socio-economic objectives in land-use decisions, we develop a new dynamic approach to model deforestation scenarios for tropical mountain forests. We integrate multi-objective optimization of land allocation with an innovative approach to consider uncertainty spaces for each objective. These uncertainty spaces account for potential variability among decision-makers, who may have different expectations about the future. When optimizing only socio-economic objectives, the model continues the past trend in deforestation (1975-2015) in the projected land-use allocation (2015-2070). Based on indicators for biomass production, carbon storage, climate and water regulation, and soil quality, we show that considering multiple ES in addition to the socio-economic objectives has heterogeneous effects on land-use allocation. It saves some natural forest if the natural forest share is below 38%, and can stop deforestation once the natural forest share drops below 10%. For landscapes with high shares of forest (38%-80% in our study), accounting for multiple ES under high uncertainty of their indicators may, however, accelerate deforestation. For such multifunctional landscapes, two main effects prevail: (a) accelerated expansion of diversified non-natural areas to elevate the levels of the indicators and (b) increased landscape diversification to maintain multiple ES, reducing the proportion of natural forest. Only when accounting for vascular plant species richness as an explicit objective in the optimization, deforestation was consistently reduced. Aiming for multifunctional landscapes may therefore conflict with the aim of reducing deforestation, which we can quantify here for the first time. Our findings are relevant for identifying types of landscapes where this conflict may arise and to better align respective policies.

Accelerated robust optimization algorithm for proton therapy treatment planning

PURPOSE

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.

METHODS

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.

RESULTS

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).

CONCLUSIONS

The proposed worst-case 4D robust optimization algorithm achieves a significant optimization time gain of 84%, without compromising target coverage or normal tissue sparing.

Automated proton treatment planning with robust optimization using constrained hierarchical optimization

PURPOSE

We present a method for fully automated generation of high quality robust proton treatment plans using hierarchical optimization. To fill the gap between the two common extreme robust optimization approaches, that is, stochastic and worst-case, a robust optimization approach based on the p-norm function is used whereby a single parameter, p , can be used to control the level of robustness in an intuitive way.

METHODS

A fully automated approach to treatment planning using Expedited Constrained Hierarchical Optimization (ECHO) is implemented in our clinic for photon treatments. ECHO strictly enforces critical (inviolable) clinical criteria as hard constraints and improves the desirable clinical criteria sequentially, as much as is feasible. We extend our in-house developed ECHO codes for proton therapy and integrate it with a new approach for robust optimization. Multiple scenarios accounting for both setup and range uncertainties are included (13scenarios), and the maximum/mean/dose-volume constraints on organs-at-risk (OARs) and target are fulfilled in all scenarios. We combine the objective functions of the individual scenarios using the p-norm function. The p-norm with a parameter p = 1 or p = ∞ result in the stochastic or the worst-case approach, respectively; an intermediate robustness level is obtained by employing p -values in-between. While the worst-case approach only focuses on the worst-case scenario(s), the p-norm approach with a large p value ( p ≈ 20 ) resembles the worst-case approach without completely neglecting other scenarios. The proposed approach is evaluated on three head-and-neck (HN) patients and one water phantom with different parameters, p ∈ 1 , 2 , 5 , 10 , 20 . The results are compared against the stochastic approach (p-norm approach with p = 1 ) and the worst-case approach, as well as the nonrobust approach (optimized solely on the nominal scenario).

RESULTS

The proposed algorithm successfully generates automated robust proton plans on all cases. As opposed to the nonrobust plans, the robust plans have narrower dose volume histogram (DVH) bands across all 13 scenarios, and meet all hard constraints (i.e., maximum/mean/dose-volume constraints) on OARs and the target for all scenarios. The spread in the objective function values is largest for the stochastic approach ( p = 1 ) and decreases with increasing p toward the worst-case approach. Compared to the worst-case approach, the p-norm approach results in DVH bands for clinical target volume (CTV) which are closer to the prescription dose at a negligible cost in the DVH for the worst scenario, thereby improving the overall plan quality. On average, going from the worst-case approach to the p-norm approach with p = 20 , the median objective function value across all the scenarios is improved by 15% while the objective function value for the worst scenario is only degraded by 3%.

CONCLUSION

An automated treatment planning approach for proton therapy is developed, including robustness, dose-volume constraints, and the ability to control the robustness level using the p-norm parameter p , to fit the priorities deemed most important.

Difference in LET-based biological doses between IMPT optimization techniques: Robust and PTV-based optimizations

Purpose

While a large amount of experimental data suggest that the proton relative biological effectiveness (RBE) varies with both physical and biological parameters, current commercial treatment planning systems (TPS) use the constant RBE instead of variable RBE models, neglecting the dependence of RBE on the linear energy transfer (LET). To conduct as accurate a clinical evaluation as possible in this circumstance, it is desirable that the dosimetric parameters derived by TPS (DRBE=1.1) are close to the “true” values derived with the variable RBE models (DvRBE). As such, in this study, the closeness of DRBE=1.1 to DvRBE was compared between planning target volume (PTV)‐based and robust plans.

Methods

Intensity‐modulated proton therapy (IMPT) treatment plans for two Radiation Therapy Oncology Group (RTOG) phantom cases and four nasopharyngeal cases were created using the PTV‐based and robust optimizations, under the assumption of a constant RBE of 1.1. First, the physical dose and dose‐averaged LET (LET_d) distributions were obtained using the analytical calculation method, based on the pencil beam algorithm. Next, DvRBE was calculated using three different RBE models. The deviation of DvRBE from DRBE=1.1 was evaluated with D₉₉ and D_max, which have been used as the evaluation indices for clinical target volume (CTV) and organs at risk (OARs), respectively. The influence of the distance between the OAR and CTV on the results was also investigated. As a measure of distance, the closest distance and the overlapped volume histogram were used for the RTOG phantom and nasopharyngeal cases, respectively.

Results

As for the OAR, the deviations of DmaxvRBE from DmaxRBE=1.1 were always smaller in robust plans than in PTV‐based plans in all RBE models. The deviation would tend to increase as the OAR was located closer to the CTV in both optimization techniques. As for the CTV, the deviations of D99vRBE from D99RBE=1.1 were comparable between the two optimization techniques, regardless of the distance between the CTV and the OAR.

Conclusion

Robust optimization was found to be more favorable than PTV‐based optimization in that the results presented by TPS were closer to the “true” values and that the clinical evaluation based on TPS was more reliable.

A fast robust optimizer for intensity modulated proton therapy using GPU

Robust optimization has been shown to be effective for stabilizing treatment planning in intensity modulated proton therapy (IMPT), but existing algorithms for the optimization process is time‐consuming. This paper describes a fast robust optimization tool that takes advantage of the GPU parallel computing technologies. The new robust optimization model is based on nine boundary dose distributions — two for ±range uncertainties, six for ±set‐up uncertainties along anteroposterior (A‐P), lateral (R‐L) and superior‐inferior (S‐I) directions, and one for nominal situation. The nine boundary influence matrices were calculated using an in‐house finite size pencil beam dose engine, while the conjugate gradient method was applied to minimize the objective function. The proton dose calculation algorithm and the conjugate gradient method were tuned for heterogeneous platforms involving the CPU host and GPU device. Three clinical cases — one head and neck cancer case, one lung cancer case, and one prostate cancer case — were investigated to demonstrate the clinical feasibility of the proposed robust optimizer. Compared with results from Varian Eclipse (version 13.3), the proposed method is found to be conducive to robust treatment planning that is less sensitive to range and setup uncertainties. The three tested cases show that targets can achieve high dose uniformity while organs at risks (OARs) are in better protection against setup and range errors. Based on the CPU + GPU heterogeneous platform, the execution times of the head and neck cancer case and the prostate cancer case are much less than half of Eclipse, while the run time of the lung cancer case is similar to that of Eclipse. The fast robust optimizer developed in this study can improve the reliability of traditional proton treatment planning in a much faster speed, thus making it possible for clinical utility.

A robust bi-objective multi-trip periodic capacitated arc routing problem for urban waste collection using a multi-objective invasive weed optimization

Urban waste collection is one of the principal processes in municipalities with large expenses and laborious operations. Among the important issues raised in this regard, the lack of awareness of the exact amount of generated waste makes difficulties in the processes of collection, transportation and disposal. To this end, investigating the waste collection issue under uncertainty can play a key role in the decision-making process of managers. This paper addresses a novel robust bi-objective multi-trip periodic capacitated arc routing problem under demand uncertainty to treat the urban waste collection problem. The objectives are to minimize the total cost (i.e. traversing and vehicles' usage costs) and minimize the longest tour distance of vehicles (makespan). To validate the proposed bi-objective robust model, the ε-constraint method is implemented using the CPLEX solver of GAMS software. Furthermore, a multi-objective invasive weed optimization algorithm is then developed to solve the problem in real-world sizes. The parameters of the multi-objective invasive weed optimization are tuned optimally using the Taguchi design method to enhance its performance. The computational results conducted on different test problems demonstrate that the proposed algorithm can generate high-quality solutions considering three indexes of mean of ideal distance, number of solutions and central processing unit time. It is proved that the ε-constraint method and multi-objective invasive weed optimization can efficiently solve the small- and large-sized problems, respectively. Finally, a sensitivity analysis is performed on one of the main parameters of the problem to study the behavior of the objective functions and provide the optimal policy.

A Robust Approach for Mitigating Risks in Cyber Supply Chains

In recent years, there have been growing concerns regarding risks in federal information technology (IT) supply chains in the United States that protect cyber infrastructure. A critical need faced by decisionmakers is to prioritize investment in security mitigations to maximally reduce risks in IT supply chains. We extend existing stochastic expected budgeted maximum multiple coverage models that identify "good" solutions on average that may be unacceptable in certain circumstances. We propose three alternative models that consider different robustness methods that hedge against worst-case risks, including models that maximize the worst-case coverage, minimize the worst-case regret, and maximize the average coverage in the ( 1 - α ) worst cases (conditional value at risk). We illustrate the solutions to the robust methods with a case study and discuss the insights their solutions provide into mitigation selection compared to an expected-value maximizer. Our study provides valuable tools and insights for decisionmakers with different risk attitudes to manage cybersecurity risks under uncertainty.

Advanced Treatment Planning

Treatment planning for protons and heavier ions is adapting technologies originally developed for photon dose optimization, but also has to meet its particular challenges. Since the quality of the applied dose is more sensitive to geometric uncertainties, treatment plan robust optimization has a much more prominent role in particle therapy. This has led to specific planning tools, approaches, and research into new formulations of the robust optimization problems. Tools for solution space navigation and automatic planning are also being adapted to particle therapy. These challenges become even greater when detailed models of relative biological effectiveness (RBE) are included into dose optimization, as is required for heavier ions.

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.

A Pilot Study on the Comparison between Planning Target Volume-based Intensity-Modulated Proton Therapy Plans and Robustly Optimized Intensity-Modulated Proton Therapy Plans

The objective of this work is to compare the planning target volume (PTV)-based intensity-modulated proton therapy (IMPT) plans with robustly optimized IMPT plans using the robust optimization tools available in Pinnacle Treatment Planning System. We performed the study in five cases of different anatomic sites (brain, head and neck, lung, pancreas, and prostate). Pinnacle IMPT nonclinical version was used for IMPT planning. Two types of IMPT plans were created for each case. One is PTV-based conventionally optimized IMPT plan and the other is robustly optimized plan considering setup uncertainties. For the PTV-based plans, margins were on top of clinical target volume (CTV) to account for the setup errors, whereas in the robustly optimized plan, the setup errors were directly incorporated into the optimization process. The plan evaluation included target (CTV) coverage and dose uniformity. Our interest was to see how the target coverage and dose uniformity were perturbed on imposing setup errors in +X, −X, +Y, −Y, +Z, and −Z directions for both PTV-based and robust optimization (RO)-based plans. On the average, RO-based IMPT plans have shown a good consistency of target coverage and dose uniformity for all six setup errors scenarios as compared to PTV-based plans. In addition, RO-based plans have a better target coverage and dose uniformity under uncertainty conditions as compared to the PTV-based plans. The study demonstrates the superiority of robustly optimized IMPT plans over the PTV-based IMPT plans in terms of dose distribution under the uncertainty conditions.

Four-dimensional Plan Optimization for the Treatment of Lung Tumors Using Pencil-beam Scanning Proton Radiotherapy

Purpose 

This study aimed to evaluate the effectiveness of four-dimensional (4D) robust optimization for proton pencil-beam scanning (PBS) treatment of lung tumors.

Patients and methods 

In seven patients with lung cancer, proton beam therapy was planned using 4D robust optimization over 4D computed tomography (CT) data sets. The gross target volume (GTV) was contoured based on individual breathing phases, and a 5-mm expansion was used to generate the clinical target volume (CTV) for each phase. The 4D optimization was conducted directly on the 4D CT data set. The robust optimization settings included a CT Hounsfield unit (HU) uncertainty of 4% and a setup uncertainty of 5 mm to obtain the CTV. Additional target dose objectives such as those for the internal target volume (ITV) as well as the organ-at-risk (OAR) dose requirements were placed on the average CT. For comparison, three-dimensional (3D) robust optimization was also performed on the average CT. An additional verification 4D CT was performed to verify plan robustness against inter-fractional variations.

Results 

Target coverages were generally higher for 4D optimized plans. The difference was most pronounced for ITV V70Gy when evaluating individual breathing phases. The 4D optimized plans were shown to be able to maintain the ITV coverage at full prescription, while 3D optimized plans could not. More importantly, this difference in ITV V70Gy between the 4D and 3D optimized plans was also consistently observed when evaluating the verification 4D CT, indicating that the 4D optimized plans were more robust against inter-fractional variations. Less difference was seen between the 4D and 3D optimized plans in the lungs criteria: V5Gy and V20Gy.

Conclusion 

The proton PBS treatment plans optimized directly on the 4D CT were shown to be more robust when compared to those optimized on a regular 3D CT. Robust 4D optimization can improve the target coverage for the proton PBS lung treatments.

Stem cell biomanufacturing under uncertainty: A case study in optimizing red blood cell production

As breakthrough cellular therapy discoveries are translated into reliable, commercializable applications, effective stem cell biomanufacturing requires systematically developing and optimizing bioprocess design and operation. This article proposes a rigorous computational framework for stem cell biomanufacturing under uncertainty. Our mathematical tool kit incorporates: high‐fidelity modeling, single variate and multivariate sensitivity analysis, global topological superstructure optimization, and robust optimization. The advantages of the proposed bioprocess optimization framework using, as a case study, a dual hollow fiber bioreactor producing red blood cells from progenitor cells were quantitatively demonstrated. The optimization phase reduces the cost by a factor of 4, and the price of insuring process performance against uncertainty is approximately 15% over the nominal optimal solution. Mathematical modeling and optimization can guide decision making; the possible commercial impact of this cellular therapy using the disruptive technology paradigm was quantitatively evaluated. © 2017 American Institute of Chemical Engineers AIChE J, 64: 3011–3022, 2018

4D robust optimization including uncertainties in time structures can reduce the interplay effect in proton pencil beam scanning radiation therapy

PURPOSE

Interplay effects in proton radiotherapy can create large distortions in the dose distribution and severely degrade the plan quality. Standard methods to mitigate these effects include abdominal compression, gating, and rescanning. We propose a new method to include the time structures of the delivery and organ motion in the framework of four-dimensional (4D) robust optimization to generate plans that are robust against interplay effects.

METHODS

The method considers multiple scenarios reflecting the uncertainties in the delivery and in the organ motion. In each scenario, the pencil beam scanning spots are distributed to different phases of the breathing cycle according to each individual spot time stamp, and a partial beam dose is calculated for each phase. The partial beam doses are accumulated on a reference phase through deformable image registrations. Minimax optimization is performed to take all scenarios into account simultaneously. For simplicity, the uncertainties in this proof of concept study are limited to variations in the breathing pattern. The method is evaluated for three different nonsmall cell lung cancer patients and compared to plans using conventional 4D robust optimization both with and without rescanning. We assess the ability of the method to mitigate distortions from the interplay effect over multiple evaluation scenarios using 4D dose calculations. This interplay evaluation is performed in an experimentally validated framework, which is independent of the optimization in the plan generation step.

RESULTS

For the three studied patients, 4D optimization including time structures is efficient, especially for large tumor motions, where rescanning of conventional 4D robustly optimized plans is not sufficient to mitigate the interplay effect. The most efficient approach of the new method is achieved when it is combined with rescanning. For the patient with the largest motion, the mean V95% is 99.2% and mean V107% is 3.65% for the best rescanned 4D plan optimized with time structure. This can be compared to conventional 4D optimized plans with mean V95% of 92.7% and mean V107% of 13.1%.

CONCLUSIONS

The current study shows the potential of reducing interplay effects in proton pencil beam scanning radiotherapy by incorporating organ motion and delivery characteristics in a 4D robust optimization.

Robust optimization in lung treatment plans accounting for geometric uncertainty

Robust optimization generates scenario‐based plans by a minimax optimization method to find optimal scenario for the trade‐off between target coverage robustness and organ‐at‐risk (OAR) sparing. In this study, 20 lung cancer patients with tumors located at various anatomical regions within the lungs were selected and robust optimization photon treatment plans including intensity modulated radiotherapy (IMRT) and volumetric modulated arc therapy (VMAT) plans were generated. The plan robustness was analyzed using perturbed doses with setup error boundary of ±3 mm in anterior/posterior (AP), ±3 mm in left/right (LR), and ±5 mm in inferior/superior (IS) directions from isocenter. Perturbed doses for D₉₉, D₉₈, and D₉₅ were computed from six shifted isocenter plans to evaluate plan robustness. Dosimetric study was performed to compare the internal target volume‐based robust optimization plans (ITV‐IMRT and ITV‐VMAT) and conventional PTV margin‐based plans (PTV‐IMRT and PTV‐VMAT). The dosimetric comparison parameters were: ITV target mean dose (D_mean), R₉₅(D₉₅/D_prescription), Paddick's conformity index (CI), homogeneity index (HI), monitor unit (MU), and OAR doses including lung (D_mean, V_{20 Gy} and V_{15 Gy}), chest wall, heart, esophagus, and maximum cord doses. A comparison of optimization results showed the robust optimization plan had better ITV dose coverage, better CI, worse HI, and lower OAR doses than conventional PTV margin‐based plans. Plan robustness evaluation showed that the perturbed doses of D₉₉, D₉₈, and D₉₅ were all satisfied at least 99% of the ITV to received 95% of prescription doses. It was also observed that PTV margin‐based plans had higher MU than robust optimization plans. The results also showed robust optimization can generate plans that offer increased OAR sparing, especially for normal lungs and OARs near or abutting the target. Weak correlation was found between normal lung dose and target size, and no other correlation was observed in this study.