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.