Clinical Implementation of Robust Optimization for Craniospinal Irradiation

With robust optimization for spot scanning proton therapy now commercially available, the ability exists to account for setup, range, and interfield uncertainties during optimization. Robust optimization is particularly beneficial for craniospinal irradiation (CSI) where the large target volume lends itself to larger setup uncertainties and the need for robust match lines can all be handled with the uncertainty parameters found inside the optimizer. Suggested robust optimization settings, parameters, and image guidance for CSI patients using proton therapy spot scanning are provided. Useful structures are defined and described. Suggestions are given for perturbations to be entered into the optimizer in order to achieve a plan that provides robust target volume coverage and critical structure sparing as well as a robust match line. Interfield offset effects, a concern when using multifield optimization, can also be addressed within the robust optimizer. A robust optimizer can successfully be employed to produce robust match lines, target volume coverage, and critical structure sparing under specified uncertainties. The robust optimizer can also be used to reduce effects arising from interfield uncertainties. Using robust optimization, a plan robust against setup, range, and interfield uncertainties for craniospinal treatments can be created. Utilizing robust optimization allows one to ensure critical structures are spared and target volumes are covered under the desired uncertainty parameters.

Robust intensity-modulated proton therapy to reduce high linear energy transfer in organs at risk

PURPOSE

We propose a robust treatment planning model that simultaneously considers proton range and patient setup uncertainties and reduces high linear energy transfer (LET) exposure in organs at risk (OARs) to minimize the relative biological effectiveness (RBE) dose in OARs for intensity-modulated proton therapy (IMPT). Our method could potentially reduce the unwanted damage to OARs.

METHODS

We retrospectively generated plans for 10 patients including two prostate, four head and neck, and four lung cancer patients. The "worst-case robust optimization" model was applied. One additional term as a "biological surrogate (BS)" of OARs due to the high LET-related biological effects was added in the objective function. The biological surrogate was defined as the sum of the physical dose and extra biological effects caused by the dose-averaged LET. We generated nine uncertainty scenarios that considered proton range and patient setup uncertainty. Corresponding to each uncertainty scenario, LET was obtained by a fast LET calculation method developed in-house and based on Monte Carlo simulations. In each optimization iteration, the model used the worst-case BS among all scenarios and then penalized overly high BS to organs. The model was solved by an efficient algorithm (limited-memory Broyden-Fletcher-Goldfarb-Shanno) in a parallel computing environment. Our new model was benchmarked with the conventional robust planning model without considering BS. Dose-volume histograms (DVHs) of the dose assuming a fixed RBE of 1.1 and BS for tumor and organs under nominal and uncertainty scenarios were compared to assess the plan quality between the two methods.

RESULTS

For the 10 cases, our model outperformed the conventional robust model in avoidance of high LET in OARs. At the same time, our method could achieve dose distributions and plan robustness of tumors assuming a fixed RBE of 1.1 almost the same as those of the conventional robust model.

CONCLUSIONS

Explicitly considering LET in IMPT robust treatment planning can reduce the high LET to OARs and minimize the possible toxicity of high RBE dose to OARs without sacrificing plan quality. We believe this will allow one to design and deliver safer proton therapy.

Planning low-carbon electricity systems under uncertainty considering operational flexibility and smart grid technologies

Electricity grid operators and planners need to deal with both the rapidly increasing integration of renewables and an unprecedented level of uncertainty that originates from unknown generation outputs, changing commercial and regulatory frameworks aimed to foster low-carbon technologies, the evolving availability of market information on feasibility and costs of various technologies, etc. In this context, there is a significant risk of locking-in to inefficient investment planning solutions determined by current deterministic engineering practices that neither capture uncertainty nor represent the actual operation of the planned infrastructure under high penetration of renewables. We therefore present an alternative optimization framework to plan electricity grids that deals with uncertain scenarios and represents increased operational details. The presented framework is able to model the effects of an array of flexible, smart grid technologies that can efficiently displace the need for conventional solutions. We then argue, and demonstrate via the proposed framework and an illustrative example, that proper modelling of uncertainty and operational constraints in planning is key to valuing operationally flexible solutions leading to optimal investment in a smart grid context. Finally, we review the most used practices in power system planning under uncertainty, highlight the challenges of incorporating operational aspects and advocate the need for new and computationally effective optimization tools to properly value the benefits of flexible, smart grid solutions in planning. Such tools are essential to accelerate the development of a low-carbon energy system and investment in the most appropriate portfolio of renewable energy sources and complementary enabling smart technologies.This article is part of the themed issue 'Energy management: flexibility, risk and optimization'.

Toward robust adaptive radiation therapy strategies

PURPOSE

To set up a framework combining robust treatment planning with adaptive re-optimization in order to maintain high treatment quality, to respond to interfractional geometric variations and to identify those patients who will benefit the most from an adaptive fractionation schedule.

METHODS

The authors propose robust adaptive strategies based on stochastic minimax optimization for a series of simulated treatments on a one-dimensional patient phantom. The plan applied during the first fractions should be able to handle anticipated systematic and random errors. Information on the individual geometric variations is gathered at each fraction. At scheduled fractions, the impact of the measured errors on the delivered dose distribution is evaluated. For a patient having received a dose that does not satisfy specified plan quality criteria, the plan is re-optimized based on these individually measured errors. The re-optimized plan is then applied during subsequent fractions until a new scheduled adaptation becomes necessary. In this study, three different adaptive strategies are introduced and investigated. (a) In the first adaptive strategy, the measured systematic and random error scenarios and their assigned probabilities are updated to guide the robust re-optimization. (b) In the second strategy, the degree of conservativeness is adapted in response to the measured dose delivery errors. (c) In the third strategy, the uncertainty margins around the target are recalculated based on the measured errors. The simulated treatments are subjected to systematic and random errors that are either similar to the anticipated errors or unpredictably larger in order to critically evaluate the performance of these three adaptive strategies.

RESULTS

According to the simulations, robustly optimized treatment plans provide sufficient treatment quality for those treatment error scenarios similar to the anticipated error scenarios. Moreover, combining robust planning with adaptation leads to improved organ-at-risk protection. In case of unpredictably larger treatment errors, the first strategy in combination with at most weekly adaptation performs best at notably improving treatment quality in terms of target coverage and organ-at-risk protection in comparison with a non-adaptive approach and the other adaptive strategies.

CONCLUSION

The authors present a framework that provides robust plan re-optimization or margin adaptation of a treatment plan in response to interfractional geometric errors throughout the fractionated treatment. According to the simulations, these robust adaptive treatment strategies are able to identify candidates for an adaptive treatment, thus giving the opportunity to provide individualized plans, and improve their treatment quality through adaptation. The simulated robust adaptive framework is a guide for further development of optimally controlled robust adaptive therapy models.

Evaluating Intensity Modulated Proton Therapy Relative to Passive Scattering Proton Therapy for Increased Vertebral Column Sparing in Craniospinal Irradiation in Growing Pediatric Patients

PURPOSE

At present, proton craniospinal irradiation (CSI) for growing children is delivered to the whole vertebral body (WVB) to avoid asymmetric growth. We aimed to demonstrate the feasibility and potential clinical benefit of delivering vertebral body sparing (VBS) versus WVB CSI with passively scattered (PS) and intensity modulated proton therapy (IMPT) in growing children treated for medulloblastoma.

METHODS AND MATERIALS

Five plans were generated for medulloblastoma patients, who had been previously treated with CSI PS proton radiation therapy: (1) single posteroanterior (PA) PS field covering the WVB (PS-PA-WVB); (2) single PA PS field that included only the thecal sac in the target volume (PS-PA-VBS); (3) single PA IMPT field covering the WVB (IMPT-PA-WVB); (4) single PA IMPT field, target volume including thecal sac only (IMPT-PA-VBS); and (5) 2 posterior-oblique (-35°, +35°) IMPT fields, with the target volume including the thecal sac only (IMPT2F-VBS). For all cases, 23.4 Gy (relative biologic effectiveness [RBE]) was prescribed to 95% of the spinal canal. The dose, linear energy transfer, and variable-RBE-weighted dose distributions were calculated for all plans using the tool for particle simulation, version 2, Monte Carlo system.

RESULTS

IMPT VBS techniques efficiently spared the anterior vertebral bodies (AVBs), even when accounting for potential higher variable RBE predicted by linear energy transfer distributions. Assuming an RBE of 1.1, the V10 Gy(RBE) decreased from 100% for the WVB techniques to 59.5% to 76.8% for the cervical, 29.9% to 34.6% for the thoracic, and 20.6% to 25.1% for the lumbar AVBs, and the V20 Gy(RBE) decreased from 99.0% to 17.8% to 20.0% for the cervical, 7.2% to 7.6% for the thoracic, and 4.0% to 4.6% for the lumbar AVBs when IMPT VBS techniques were applied. The corresponding percentages for the PS VBS technique were higher.

CONCLUSIONS

Advanced proton techniques can sufficiently reduce the dose to the vertebral body and allow for vertebral column growth for children with central nervous system tumors requiring CSI. This was true even when considering variable RBE values. A clinical trial is planned for VBS to the thoracic and lumbosacral spine in growing children.

Comparison of linear and nonlinear programming approaches for "worst case dose" and "minmax" robust optimization of intensity-modulated proton therapy dose distributions

Robust optimization of intensity‐modulated proton therapy (IMPT) takes uncertainties into account during spot weight optimization and leads to dose distributions that are resilient to uncertainties. Previous studies demonstrated benefits of linear programming (LP) for IMPT in terms of delivery efficiency by considerably reducing the number of spots required for the same quality of plans. However, a reduction in the number of spots may lead to loss of robustness. The purpose of this study was to evaluate and compare the performance in terms of plan quality and robustness of two robust optimization approaches using LP and nonlinear programming (NLP) models. The so‐called “worst case dose” and “minmax” robust optimization approaches and conventional planning target volume (PTV)‐based optimization approach were applied to designing IMPT plans for five patients: two with prostate cancer, one with skull‐based cancer, and two with head and neck cancer. For each approach, both LP and NLP models were used. Thus, for each case, six sets of IMPT plans were generated and assessed: LP‐PTV‐based, NLP‐PTV‐based, LP‐worst case dose, NLP‐worst case dose, LP‐minmax, and NLP‐minmax. The four robust optimization methods behaved differently from patient to patient, and no method emerged as superior to the others in terms of nominal plan quality and robustness against uncertainties. The plans generated using LP‐based robust optimization were more robust regarding patient setup and range uncertainties than were those generated using NLP‐based robust optimization for the prostate cancer patients. However, the robustness of plans generated using NLP‐based methods was superior for the skull‐based and head and neck cancer patients. Overall, LP‐based methods were suitable for the less challenging cancer cases in which all uncertainty scenarios were able to satisfy tight dose constraints, while NLP performed better in more difficult cases in which most uncertainty scenarios were hard to meet tight dose limits. For robust optimization, the worst case dose approach was less sensitive to uncertainties than was the minmax approach for the prostate and skull‐based cancer patients, whereas the minmax approach was superior for the head and neck cancer patients. The robustness of the IMPT plans was remarkably better after robust optimization than after PTV‐based optimization, and the NLP‐PTV‐based optimization outperformed the LP‐PTV‐based optimization regarding robustness of clinical target volume coverage. In addition, plans generated using LP‐based methods had notably fewer scanning spots than did those generated using NLP‐based methods.

On how to deal with deep uncertainties in a risk assessment and management context

Recently, several authors have presented interesting contributions on how to meet deep or severe uncertainties in a risk analysis setting. In this article, we provide some reflections on some of the foundational pillars that this work is based on, including the meaning of concepts such as deep uncertainty, known probabilities, and correct models, the aim being to contribute to a strengthening of the scientific platform of the work, as well as providing new insights on how to best implement management policies meeting these uncertainties. We also provide perspectives on the boundaries and limitations of analytical approaches for supporting decision making in cases of deep uncertainties. A main conclusion of the article is that deep uncertainties call for managerial review and judgment that sees beyond the analytical frameworks studied in risk assessment and risk management contexts, including those now often suggested to be used, such as robust optimization techniques. This managerial review and judgment should be seen as a basic element of the risk management.

A Hybrid Interval-Robust Optimization Model for Water Quality Management

In water quality management problems, uncertainties may exist in many system components and pollution-related processes (i.e., random nature of hydrodynamic conditions, variability in physicochemical processes, dynamic interactions between pollutant loading and receiving water bodies, and indeterminacy of available water and treated wastewater). These complexities lead to difficulties in formulating and solving the resulting nonlinear optimization problems. In this study, a hybrid interval-robust optimization (HIRO) method was developed through coupling stochastic robust optimization and interval linear programming. HIRO can effectively reflect the complex system features under uncertainty, where implications of water quality/quantity restrictions for achieving regional economic development objectives are studied. By delimiting the uncertain decision space through dimensional enlargement of the original chemical oxygen demand (COD) discharge constraints, HIRO enhances the robustness of the optimization processes and resulting solutions. This method was applied to planning of industry development in association with river-water pollution concern in New Binhai District of Tianjin, China. Results demonstrated that the proposed optimization model can effectively communicate uncertainties into the optimization process and generate a spectrum of potential inexact solutions supporting local decision makers in managing benefit-effective water quality management schemes. HIRO is helpful for analysis of policy scenarios related to different levels of economic penalties, while also providing insight into the tradeoff between system benefits and environmental requirements.

Re-irradiation of recurrent head and neck carcinomas: comparison of robust intensity modulated proton therapy treatment plans with helical tomotherapy

BACKGROUND

To test the hypothesis that the therapeutic ratio of intensity-modulated photon therapy using helical tomotherapy (HT) for retreatment of head and neck carcinomas can be improved by robust intensity-modulated proton therapy (IMPT).

METHODS

Comparative dose planning with robust IMPT was performed for 7 patients retreated with HT.

RESULTS

On average, HT yielded dose gradients steeper in a distance ≤ 7.5 mm outside the target (p<0.0001, F-test) and more conformal high dose regions down to the 50% isodose than IMPT. Both methods proved comparably robust against set-up errors of up to 2 mm, and normal tissue exposure was satisfactory. The mean body dose was smaller with IMPT.

CONCLUSIONS

IMPT was found not to be uniformly superior to HT and the steeper average dose fall-off around the target volume is an argument pro HT under the methodological implementations used. However, looking at single organs at risk, the normal tissue sparing of IMPT can surpass tomotherapy for an individual patient. Therefore, comparative dose planning is recommended, if both methods are available.