The partial adaptation strategy for online-adaptive proton therapy: A proof of concept study in head and neck cancer patients.

BACKGROUND: The accuracy of intensity-modulated proton therapy (IMPT) is greatly affected by anatomy variations that might occur during the treatment course. Online plan adaptations have been proposed as a solution to intervene promptly during a treatment session once the anatomy changes are detected. The implementation of online-adaptive proton therapy (OAPT) is still hindered by time-consuming tasks in the workflow. PURPOSE: The study introduces the novel concept of partial adaptation and aims at investigating its feasibility as a potential solution to parallelize tasks during an OAPT workflow for saving valuable in-room time. METHODS: The proof-of-principle simulation study includes datasets from six head and neck cancer (HNC) patients, each consisting of one planning CT (pCT) and three contoured control CTs (cCTs). Robust 3-field normo-fractionated initial IMPT plans were generated on the pCTs with a standardized field configuration, delivering 66 Gy and 54 Gy to the high-risk and low-risk clinical target volume (CTVHigh and CTVLow), respectively. For each cCT, a dose-mimicking-based partial adaptation was applied: two fields were adapted on the current anatomy taking into account the background dose of the first non-adapted field supposedly delivered in the meantime. Fraction doses on the cCTs resulting from partially adapted plans with different first (non-adapted) field assignments were compared against those from non-adapted and fully adapted plans regarding target coverage and organs at risk (OARs) sparing. The robustness of partially adapted plans was also evaluated. RESULTS: Partially adapted plans showed comparable results to fully adapted plans and were superior to non-adapted plans for both target coverage and OAR sparing. Target coverage degradation in the non-adapted plans (median D98%: 95.9% and 97.5% for CTVLow and CTVHigh, respectively) was recovered by both partial (98.0% and 98.5%) and full adaptation (98.2% and 98.7%) in comparison to the initial plans (98.7% and 98.8%). The initial hotspot dose for the CTVHigh (median D2%: 101.8%) increased in the non-adapted plans (102.9%) and was recovered by the adaptive strategies (partial: 102.5%, full: 101.9%). The near-maximum dose (D0.01cc) to brainstem and spinal cord was within clinical constraints for all investigated dose distributions, but clearly increased for no adaptation and improved in the (both partially and fully) adapted plans with respect to the non-adapted ones. The parotids' median doses (D50) were mainly patient-specific depending on the proximity to the target region, but anyway lower for the partially and fully adapted plans compared to the non-adapted ones. OAR sparing was furthermore improved for the partially adapted plans in comparison to full adaptation. Robustness of the target dose metrics was preserved in all evaluated scenarios. CONCLUSIONS: For OAPT of HNC patients, partial adaptation is able to generate plans of superior conformity to non-adapted plans and of comparable conformity as fully adapted plans, while having the potential to speed up the online-adaptive workflows. Thus, partial adaptation represents an intermediate approach until fast online adaptation workflows become available. Furthermore, it can be applied in workflows where online treatment verification stops the delivery and triggers an online adaptation for the remaining fraction.

Generation and evaluation of anatomy-preserving virtual CT for online adaptive proton therapy.

BACKGROUND: Daily CTs generated by CBCT correction are required for daily replanning in online-adaptive proton therapy (APT) to effectively deal with inter-fractional changes. Out of the currently available methods, the suitability of a daily CT generation method for proton dose calculation also depends on the anatomical site. PURPOSE: We propose an anatomy-preserving virtual CT (APvCT) method as a hybrid method of CBCT correction, which is especially suitable for large anatomy deformations. The accuracy of the hybrid method was assessed by comparison with the corrected CBCT (cCBCT) and virtual CT (vCT) methods in the context of online APT. METHODS: Seventy-one daily CBCTs of four prostate cancer patients treated with intensity modulated proton therapy (IMPT) were converted to daily CTs using cCBCT, vCT, and the newly proposed APvCT method. In APvCT, planning CT (pCT) were mapped to CBCT geometry using deformable image registration with boundary conditions on controlling regions of interest (ROIs) created with deep learning segmentation on cCBCT. The relative frequency distribution (RFD) of HU, mass density and stopping power ratio (SPR) values were assessed and compared with the pCT. The ROIs in the APvCT and vCT were compared with cCBCT in terms of Dice similarity coefficient (DSC) and mean distance-to-agreement (mDTA). For each patient, a robustly optimized IMPT plan was created on the pCT and subsequent daily adaptive plans on daily CTs. For dose distribution comparison on the same anatomy, the daily adaptive plans on cCBCT and vCT were recalculated on the corresponding APvCT. The dose distributions were compared in terms of isodose volumes and 3D global gamma-index passing rate (GPR) at γ(2%, 2 mm) criterion. RESULTS: For all patients, no noticeable difference in RFDs was observed amongst APvCT, vCT, and pCT except in cCBCT, which showed a noticeable difference. The minimum DSC value was 0.96 and 0.39 for contours in APvCT and vCT respectively. The average value of mDTA for APvCT was 0.01 cm for clinical target volume and ≤0.01 cm for organs at risk, which increased to 0.18 cm and ≤0.52 cm for vCT. The mean GPR value was 90.9%, 64.5%, and 67.0% for APvCT versus cCBCT, vCT versus cCBCT, and APvCT versus vCT, respectively. When recalculated on APvCT, the adaptive cCBCT and vCT plans resulted in mean GPRs of 89.5 ± 5.1% and 65.9 ± 19.1%, respectively. The mean DSC values for 80.0%, 90.0%, 95.0%, 98.0%, and 100.0% isodose volumes were 0.97, 0.97, 0.97, 0.95, and 0.91 for recalculated cCBCT plans, and 0.89, 0.88, 0.87, 0.85, and 0.81 for recalculated vCT plans. Hausdorff distance for the 100.0% isodose volume in some cases of recalculated cCBCT plans on APvCT exceeded 1.00 cm. CONCLUSIONS: APvCT contours showed good agreement with reference contours of cCBCT which indicates anatomy preservation in APvCT. A vCT with erroneous anatomy can result in an incorrect adaptive plan. Further, slightly lower values of GPR between the APvCT and cCBCT-based adaptive plans can be explained by the difference in the cCBCT's SPR RFD from the pCT.

Treatment planning of scanned proton beams in RayStation.

The use of scanned proton beams in external beam radiation therapy has seen a rapid development over the past decade. This technique places new demands on treatment planning, as compared to conventional photon-based radiation therapy. In this article, several proton specific functions as implemented in the treatment planning system RayStation are presented. We will cover algorithms for energy layer and spot selection, basic optimization including the handling of spot weight limits, optimization of the linear energy transfer (LET) distribution, robust optimization including the special case of 4D optimization, proton arc planning, and automatic planning using deep learning. We will further present the Monte Carlo (MC) proton dose engine in RayStation to some detail, from the material interpretation of the CT data, through the beam model parameterization, to the actual MC transport mechanism. Useful tools for plan evaluation, including robustness evaluation, and the versatile scripting interface are also described. The overall aim of the paper is to give an overview of some of the key proton planning functions in RayStation, with example usages, and at the same time provide the details about the underlying algorithms that previously have not been fully publicly available.

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.

Partitioning of discrete proton arcs into interlaced subplans can bring proton arc advances to existing proton facilities.

BACKGROUND: Proton arcs have shown potential to reduce the dose to organs at risks (OARs) by delivering the protons from many different directions. While most previous studies have been focused on dynamic arcs (delivery during rotation), an alternative approach is discrete arcs, where step-and-shoot delivery is used over a large number of beam directions. The major advantage of discrete arcs is that they can be delivered at existing proton facilities. However, this advantage comes at the expense of longer treatment times. PURPOSE: To exploit the dosimetric advantages of proton arcs, while achieving reasonable delivery times, we propose a partitioning approach where discrete arc plans are split into subplans to be delivered over different fractions in the treatment course. METHODS: For three oropharyngeal cancer patients, four different arc plans have been created and compared to the corresponding clinical IMPT plan. The treatment plans are all planned to be delivered in 35 fractions, but with different delivery approaches over the fractions. The first arc plan (1×30) has 30 directions to be delivered every fraction, while the others are partitioned into subplans with 10 and 6 beam directions, each to be delivered every third (3×10), fifth fraction (5×6), or seventh fraction (7×10). All plans are assessed with respect to delivery time, target robustness over the treatment course, doses to OARs and NTCP for dysphagia and xerostomia. RESULTS: The delivery time (including an additional delay of 30 s between the discrete directions to simulate manual interaction with the treatment control system) is reduced from on average 25.2 min for the 1×30 plan to 9.2 min for the 3×10 and 7×10 plans and 5.7 min for the 5×6 plans. The delivery time for the IMPT plan is 7.9 min. When accounting for the combination of delivery time, target robustness, OAR sparing, and NTCP reduction, the plans with 10 directions in each fraction are the preferred choice. Both the 3×10 and 7×10 plans show improved target robustness compared to the 1×30 plans, while keeping OAR doses and NTCP values at almost as low levels as for the 1×30 plans. For all patients the NTCP values for dysphagia are lower for the partitioned plans with 10 directions compared to the IMPT plans. NTCP reduction for xerostomia compared to IMPT is seen in two of the three patients. The best results are seen for the first patient, where the NTCP reductions for the 7×10 plan are 1.6 p.p. (grade 2 xerostomia) and 1.5 p.p. (grade 2 dysphagia). The corresponding NTCP reductions for the 1×30 plan are 2.7 p.p. (xerostomia, grade 2) and 2.0 p.p. (dysphagia, grade 2). CONCLUSIONS: Discrete proton arcs can be implemented at any proton facility with reasonable treatment times using a partitioning approach. The technique also makes the proton arc treatments more robust to changes in the patient anatomy.

Implications of using the clinical target distribution as voxel-weights in radiation therapy optimization.

Objective.Delineating and planning with respect to regions suspected to contain microscopic tumor cells is an inherently uncertain task in radiotherapy. The recently proposedclinical target distribution(CTD) is an alternative to the conventionalclinical target volume(CTV), with initial promise. Previously, using the CTD in planning has primarily been evaluated in comparison to a conventionally defined CTV. We propose to compare the CTD approach against CTV margins of various sizes, dependent on the threshold at which the tumor infiltration probability is considered relevant.Approach.First, a theoretical framework is presented, concerned with optimizing the trade-off between the probability of sufficient target coverage and the penalties associated with high dose. From this framework we derive conventional CTV-based planning and contrast it with the CTD approach. The approaches are contextualized further by comparison with established methods for managing geometric uncertainties. Second, for both one- and three-dimensional phantoms, we compare a set of CTD plans created by varying the target objective function weight against a set of plans created by varying both the target weight and the CTV margin size.Main results.The results show that CTD-based planning gives slightly inefficient trade-offs between the evaluation criteria for a case in which near-minimum target dose is the highest priority. However, in a case when sparing a proximal organ at risk is critical, the CTD is better at maintaining sufficiently high dose toward the center of the target.Significance.We conclude that CTD-based planning is a computationally efficient method for planning with respect to delineation uncertainties, but that the inevitable effects on the dose distribution should not be disregarded.

Fast robust optimization of proton PBS arc therapy plans using early energy layer selection and spot assignment.

Objective.Proton pencil-beam scanning arcs (PBS arcs) have gained much attention during the past years, due to its potential for increased clinical benefit compared to conventional proton therapy. Previous studies on PBS arcs have primarily been focused on plan quality, and lately efforts have been made to reduce the delivery time. However, the methods presented so far suffer from slow optimization processes.Approach.We present a new method for fast robust optimization of PBS arc plans. The new method assigns a single energy layer per discretized direction prior to spot weight optimization and reduces the number of initial spots considerably compared to conventional methods. We used the new method for three prostate cancer patients with a prescribed dose to the CTV of 77 GyRBEin 35 fractions. For each of the patients, four plans were created: 2-beam IMPT (2IMPT), 1-beam PBS arc (1Arc), 1-beam PBS arc without focus on reducing upward energy jumps (1Arc_unseq) and two-beam PBS arc (2Arc).Main results.All PBS arc plans show a reduced integral dose compared to their respective 2IMPT plans. In the nominal case, the average CTV D98 and D2 metrics over the three patients were best for the 2Arc, followed by 2IMPT (D98¯/D2¯:7523/7986 cGyRBE(2IMPT), 7478/7984 cGy (1Arc), 7486/7951 cGy (1Arc_unseq), 7531/7951 cGyRBE(2Arc)). The average robust target coverage in terms of V95 of the voxelwise minimum dose distribution (evaluated over 42 scenarios) was: 98.0% (2IMPT), 88.6% (1Arc), 92.5% (1Arc_unseq), 97.3% (2Arc). The optimization time, including spot selection and spot dose computation, is longest for the 2Arc plan, but is below 6 min for all patients. The maximum estimated delivery time for all types of arc plans is just above 5 minSignificance.The ability for efficient treatment planning constitutes an important step towards clinical introduction of proton PBS arcs.

Technical Note: Collimator angle optimization for multiple brain metastases in dynamic conformal arc treatment planning.

PURPOSE: To reduce the exposed area by the multileaf collimator between lesions for single-isocenter dynamic conformal arc (DCA) therapy for stereotactic radiosurgery treatment of multiple brain metastases by optimizing the collimator angle orientation. In particular, this is achieved by the avoidance of collimator angles where multiple lesions are exposed by the same leaf pairs. METHODS: An algorithm that estimates the quality of an arc by considering the target projections onto the plane perpendicular to the central axis of the arc beam. A penalty proportional to the exposure of healthy tissue between metastases is assigned to each control point and each feasible collimator angle from a discretized set of angles. The algorithm can generate two outputs: the fixed optimal collimator angle over all the control points, or the optimal collimator angle trajectory through all the control points considering the rotation speed of the collimator. The first output is based on explicit enumeration of all collimator angles, and the second one generates the optimal trajectory using dynamic programming to find the globally optimal solution with respect to the objective function cost. The algorithm was validated on eight clinical cases having a different number of cranial metastases: two metastases (n = 1), three metastases (n = 5), four metastases (n = 1), and five metastases (n = 1). Plans with optimized fixed collimator angles and plans with optimized dynamic collimator trajectories were compared between each other. RESULTS: When comparing optimal dynamic trajectories to fixed optimal collimator trajectories, the resulting plans demonstrated a total reduction of the exposed area between lesions over the entire beam configuration from 21.7% up to 71.3%; similarly, beam-wise reductions ranging from 5.83% to over 90% have been registered. CONCLUSION: Collimator angle optimization has the potential to reduce the magnitude of the exposed area between lesions in an efficient way for non-isocentric treatments where multiple lesions are treated simultaneously. Dynamic trajectories are capable of limiting the island blocking problem more than optimal fixed trajectories by exploiting the extra degree of freedom of rotating the multileaf collimator. The algorithm can also lead to time saving during the treatment planning process.

Robust radiation therapy optimization using simulated treatment courses for handling deformable organ motion.

We describe a radiation therapy treatment plan optimization method that explicitly considers the effects of interfraction organ motion through optimization on the clinical target volume (CTV), and investigate how it compares to conventional planning using a planning target volume (PTV). The method uses simulated treatment courses generated using patient images created by a deformable registration algorithm to replicate the effects of interfraction organ motion, and performs robust optimization aiming to achieve CTV coverage under all simulated treatment courses. The method was applied to photon-mediated treatments of three prostate cases and compared to conventional, PTV-based planning with margins selected to achieve similar CTV coverage as the robustly optimized plans. Clinical goals for the CTV and healthy tissue were used in comparison between the two types of plans. Out of the two clinical goals for overdosage of the CTV, the three robustly optimized plans violated respectively 2, 2, and 0 goals in the mean over the scenarios, whereas none of the PTV plans violated these goals. Of the ten clinical goals for rectum, bladder, anal canal, and bulbus, the robustly optimized plans violated respectively 0, 1, and 1 goals in the mean, whereas the PTV plans violated 5, 7, and 4 goals. Compared to PTV-based planning, the inclusion of treatment course scenarios in the optimization has the potential to reduce the dose to healthy tissues while retaining a high probability of target coverage. This may reduce the need for adaptive replanning.

Automated Robust Proton Planning Using Dose-Volume Histogram-Based Mimicking of the Photon Reference Dose and Reducing Organ at Risk Dose Optimization.

PURPOSE: Patient selection for proton therapy is increasingly based on proton to photon plan comparisons. To improve efficient decision making, we developed a dose mimicking and reducing (DMR) algorithm to automatically generate a robust proton plan from a reference photon dose, as well as target and organ at risk (OAR) delineations. METHODS AND MATERIALS: The DMR algorithm was evaluated in 40 patients with head and neck cancer. The first step of the DMR algorithm comprises dose-volume histogram-based mimicking of the photon dose distribution in the clinical target volumes and OARs. Target robustness is included by mimicking the nominal photon dose in 21 perturbed scenarios. The second step of the optimization aims to reduce the OAR doses while retaining the robust target coverage as achieved in the first step. We evaluated each DMR plan against the manually robustly optimized reference proton plan in terms of plan robustness (voxel-wise minimum dose). Furthermore, the DMR plans were evaluated against the reference photon plan using normal tissue complication probability (NTCP) models of xerostomia, dysphagia, and tube feeding dependence. Consequently, ΔNTCPs were defined as the difference between the NTCPs of the photon and proton plans. RESULTS: The dose distributions of the DMR and reference proton plans were very similar in terms of target robustness and OAR dose values. Regardless of proton planning technique (ie, DMR or reference proton plan), the same treatment modality was selected in 80% (32 of 40) of cases based on the ∑ΔNTCPs. In 15% (6 of 40) of cases, a conflicting decision was made based on relatively small dose differences to the OARs (<2.0 Gy). CONCLUSIONS: The DMR algorithm automatically optimized robust proton plans from a photon reference dose that were comparable to the dosimetrist-optimized proton plans in patients with head and neck cancer. This algorithm has been successfully embedded into a framework to automatically select patients for proton therapy based on NTCPs.

Robust radiotherapy planning.

Motion and uncertainty in radiotherapy is traditionally handled via margins. The clinical target volume (CTV) is expanded to a larger planning target volume (PTV), which is irradiated to the prescribed dose. However, the PTV concept has several limitations, especially in proton therapy. Therefore, robust and probabilistic optimization methods have been developed that directly incorporate motion and uncertainty into treatment plan optimization for intensity modulated radiotherapy (IMRT) and intensity modulated proton therapy (IMPT). Thereby, the explicit definition of a PTV becomes obsolete and treatment plan optimization is directly based on the CTV. Initial work focused on random and systematic setup errors in IMRT. Later, inter-fraction prostate motion and intra-fraction lung motion became a research focus. Over the past ten years, IMPT has emerged as a new application for robust planning methods. In proton therapy, range or setup errors may lead to dose degradation and misalignment of dose contributions from different beams - a problem that cannot generally be addressed by margins. Therefore, IMPT has led to the first implementations of robust planning methods in commercial planning systems, making these methods available for clinical use. This paper first summarizes the limitations of the PTV concept. Subsequently, robust optimization methods are introduced and their applications in IMRT and IMPT planning are reviewed.

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.

Scenario-based radiation therapy margins for patient setup, organ motion, and particle range uncertainty.

This work extends and validates the scenario-based generalization of margins presented in Fredriksson and Bokrantz (2016 Phys. Med. Biol. 61 2067-82). Scenario-based margins are, in their original form, a method for robust planning under setup uncertainty where the sum of a plan evaluation criterion over a set of scenarios is optimized. The voxelwise penalties in the summands are weighted by a distribution of coefficients defined such that the method is mathematically equivalent to the use of conventional geometric margins if the scenario doses are calculated using the static dose cloud approximation. The purpose of this work is to extend scenario-based margins to general types of geometric uncertainty and to validate their use on clinical cases. Specifically, we outline how to incorporate density heterogeneity in the calculation of coefficients and demonstrate the extended method's ability to safeguard against setup errors, organ motion, and range shifts (and combinations thereof). For a water phantom with a high-density slab partly covering the target, the extended form of scenario-based margins method led to improved target coverage robustness compared to the original method. At most minor differences in robustness were, however, observed between the extended and original method for a prostate and two lung patients, all treated with intensity-modulated proton therapy, yielding evidence that the calculation of weighting coefficients is generally insensitive to tissue heterogeneities. The scenario-based margins were, furthermore, verified to provide a comparable level of robustness to expected value and worst case optimization while circumventing some known shortcomings of these methods.

The scenario-based generalization of radiation therapy margins.

We give a scenario-based treatment plan optimization formulation that is equivalent to planning with geometric margins if the scenario doses are calculated using the static dose cloud approximation. If the scenario doses are instead calculated more accurately, then our formulation provides a novel robust planning method that overcomes many of the difficulties associated with previous scenario-based robust planning methods. In particular, our method protects only against uncertainties that can occur in practice, it gives a sharp dose fall-off outside high dose regions, and it avoids underdosage of the target in 'easy' scenarios. The method shares the benefits of the previous scenario-based robust planning methods over geometric margins for applications where the static dose cloud approximation is inaccurate, such as irradiation with few fields and irradiation with ion beams. These properties are demonstrated on a suite of phantom cases planned for treatment with scanned proton beams subject to systematic setup uncertainty.

Maximizing the probability of satisfying the clinical goals in radiation therapy treatment planning under setup uncertainty.

PURPOSE: This paper introduces a method that maximizes the probability of satisfying the clinical goals in intensity-modulated radiation therapy treatments subject to setup uncertainty. METHODS: The authors perform robust optimization in which the clinical goals are constrained to be satisfied whenever the setup error falls within an uncertainty set. The shape of the uncertainty set is included as a variable in the optimization. The goal of the optimization is to modify the shape of the uncertainty set in order to maximize the probability that the setup error will fall within the modified set. Because the constraints enforce the clinical goals to be satisfied under all setup errors within the uncertainty set, this is equivalent to maximizing the probability of satisfying the clinical goals. This type of robust optimization is studied with respect to photon and proton therapy applied to a prostate case and compared to robust optimization using an a priori defined uncertainty set. RESULTS: Slight reductions of the uncertainty sets resulted in plans that satisfied a larger number of clinical goals than optimization with respect to a priori defined uncertainty sets, both within the reduced uncertainty sets and within the a priori, nonreduced, uncertainty sets. For the prostate case, the plans taking reduced uncertainty sets into account satisfied 1.4 (photons) and 1.5 (protons) times as many clinical goals over the scenarios as the method taking a priori uncertainty sets into account. CONCLUSIONS: Reducing the uncertainty sets enabled the optimization to find better solutions with respect to the errors within the reduced as well as the nonreduced uncertainty sets and thereby achieve higher probability of satisfying the clinical goals. This shows that asking for a little less in the optimization sometimes leads to better overall plan quality.

A critical evaluation of worst case optimization methods for robust intensity-modulated proton therapy planning.

PURPOSE: To critically evaluate and compare three worst case optimization methods that have been previously employed to generate intensity-modulated proton therapy treatment plans that are robust against systematic errors. The goal of the evaluation is to identify circumstances when the methods behave differently and to describe the mechanism behind the differences when they occur. METHODS: The worst case methods optimize plans to perform as well as possible under the worst case scenario that can physically occur (composite worst case), the combination of the worst case scenarios for each objective constituent considered independently (objectivewise worst case), and the combination of the worst case scenarios for each voxel considered independently (voxelwise worst case). These three methods were assessed with respect to treatment planning for prostate under systematic setup uncertainty. An equivalence with probabilistic optimization was used to identify the scenarios that determine the outcome of the optimization. RESULTS: If the conflict between target coverage and normal tissue sparing is small and no dose-volume histogram (DVH) constraints are present, then all three methods yield robust plans. Otherwise, they all have their shortcomings: Composite worst case led to unnecessarily low plan quality in boundary scenarios that were less difficult than the worst case ones. Objectivewise worst case generally led to nonrobust plans. Voxelwise worst case led to overly conservative plans with respect to DVH constraints, which resulted in excessive dose to normal tissue, and less sharp dose fall-off than the other two methods. CONCLUSIONS: The three worst case methods have clearly different behaviors. These behaviors can be understood from which scenarios that are active in the optimization. No particular method is superior to the others under all circumstances: composite worst case is suitable if the conflicts are not very severe or there are DVH constraints whereas voxelwise worst case is advantageous if there are severe conflicts but no DVH constraints. The advantages of composite and voxelwise worst case outweigh those of objectivewise worst case.

Deliverable navigation for multicriteria IMRT treatment planning by combining shared and individual apertures.

We consider the problem of deliverable Pareto surface navigation for step-and-shoot intensity-modulated radiation therapy. This problem amounts to calculation of a collection of treatment plans with the property that convex combinations of plans are directly deliverable. Previous methods for deliverable navigation impose restrictions on the number of apertures of the individual plans, or require that all treatment plans have identical apertures. We introduce simultaneous direct step-and-shoot optimization of multiple plans subject to constraints that some of the apertures must be identical across all plans. This method generalizes previous methods for deliverable navigation to allow for treatment plans with some apertures from a collective pool and some apertures that are individual. The method can also be used as a post-processing step to previous methods for deliverable navigation in order to improve upon their plans. By applying the method to subsets of plans in the collection representing the Pareto set, we show how it can enable convergence toward the unrestricted (non-navigable) Pareto set where all apertures are individual.

Automated improvement of radiation therapy treatment plans by optimization under reference dose constraints.

A method is presented that automatically improves upon previous treatment plans by optimization under reference dose constraints. In such an optimization, a previous plan is taken as reference and a new optimization is performed toward some goal, such as minimization of the doses to healthy structures under the constraint that no structure can become worse off than in the reference plan. Two types of constraints that enforce this are discussed: either each voxel or each dose-volume histogram of the improved plan must be at least as good as in the reference plan. These constraints ensure that the quality of the dose distribution cannot deteriorate, something that constraints on conventional physical penalty functions do not. To avoid discontinuous gradients, which may restrain gradient-based optimization algorithms, the positive part operators that constitute the optimization functions are regularized. The method was applied to a previously optimized plan for a C-shaped phantom and the effects of the choice of regularization parameter were studied. The method resulted in reduced integral dose and reduced doses to the organ at risk while maintaining target homogeneity. It could be used to improve upon treatment plans directly or as a means of quality control of plans.

A characterization of robust radiation therapy treatment planning methods-from expected value to worst case optimization.

PURPOSE: To characterize a class of optimization formulations used to handle systematic and random errors in radiation therapy, and to study the differences between the methods within this class. METHODS: The class of robust methods that can be formulated as minimax stochastic programs is studied. This class generalizes many previously used methods, ranging between optimization of the expected and the worst case objective value. The robust methods are used to plan intensity-modulated proton therapy (IMPT) treatments for a case subject to systematic setup and range errors, random setup errors with and without uncertain probability distribution, and combinations thereof. As reference, plans resulting from a conventional method that uses a margin to account for errors are shown. RESULTS: For all types of errors, target coverage robustness increased with the conservativeness of the method. For systematic errors, best case organ at risk (OAR) doses increased and worst case doses decreased with the conservativeness. Accounting for random errors of fixed probability distribution resulted in heterogeneous dose. The heterogeneities were reduced when uncertainty in the probability distribution was accounted for. Doing so, the OAR doses decreased with the conservativeness. All robust methods studied resulted in more robust target coverage and lower OAR doses than the conventional method. CONCLUSIONS: Accounting for uncertainties is essential to ensure plan quality in complex radiation therapy such as IMPT. The utilization of more information than conventional in the optimization can lead to robust target coverage and low OAR doses. Increased target coverage robustness can be achieved by more conservative methods.

Minimax optimization for handling range and setup uncertainties in proton therapy.

PURPOSE: Intensity modulated proton therapy (IMPT) is sensitive to errors, mainly due to high stopping power dependency and steep beam dose gradients. Conventional margins are often insufficient to ensure robustness of treatment plans. In this article, a method is developed that takes the uncertainties into account during the plan optimization. METHODS: Dose contributions for a number of range and setup errors are calculated and a minimax optimization is performed. The minimax optimization aims at minimizing the penalty of the worst case scenario. Any optimization function from conventional treatment planning can be utilized by the method. By considering only scenarios that are physically realizable, the unnecessary conservativeness of other robust optimization methods is avoided. Minimax optimization is related to stochastic programming by the more general minimax stochastic programming formulation, which enables accounting for uncertainties in the probability distributions of the errors. RESULTS: The minimax optimization method is applied to a lung case, a paraspinal case with titanium implants, and a prostate case. It is compared to conventional methods that use margins, single field uniform dose (SFUD), and material override (MO) to handle the uncertainties. For the lung case, the minimax method and the SFUD with MO method yield robust target coverage. The minimax method yields better sparing of the lung than the other methods. For the paraspinal case, the minimax method yields more robust target coverage and better sparing of the spinal cord than the other methods. For the prostate case, the minimax method and the SFUD method yield robust target coverage and the minimax method yields better sparing of the rectum than the other methods. CONCLUSIONS: Minimax optimization provides robust target coverage without sacrificing the sparing of healthy tissues, even in the presence of low density lung tissue and high density titanium implants. Conventional methods using margins, SFUD, and MO do not utilize the full potential of IMPT and deliver unnecessarily high doses to healthy tissues.