Technical note: Optimization functions for re-irradiation treatment planning.

BACKGROUND: Although re-irradiation is increasingly used in clinical practice, almost no dedicated planning software exists. PURPOSE: Standard dose-based optimization functions were adjusted for re-irradiation planning using accumulated equivalent dose in 2-Gy fractions (EQD2) with rigid or deformable dose mapping, tissue-specific α/ß, treatment-specific recovery coefficients, and voxelwise adjusted EQD2 penalization levels based on the estimated previously delivered EQD2 (EQD2deliv ). METHODS: To demonstrate proof-of-concept, 35 Gy in 5 fractions was planned to a fictitious spherical relapse planning target volume (PTV) in three separate locations following previous prostate treatment on a virtual human phantom. The PTV locations represented one repeated irradiation scenario and two re-irradiation scenarios. For each scenario, three re-planning strategies with identical PTV dose-functions but various organ at risk (OAR) EQD2-functions was used: 1) reRTregular : Regular functions with fixed EQD2 penalization levels larger than EQD2deliv for all OAR voxels. 2) reRTreduce : As reRTregular , but with lower fixed EQD2 penalization levels aiming to reduce OAR EQD2. 3) reRTvoxelwise : As reRTregular and reRTreduce , but with voxelwise adjusted EQD2 penalization levels based on EQD2deliv . PTV near-minimum and near-maximum dose (D98% /D2% ), homogeneity index (HI), conformity index (CI) and accumulated OAR EQD2 (α/ß = 3 Gy) were evaluated. RESULTS: For the repeated irradiation scenario, all strategies resulted in similar dose distributions. For the re-irradiation scenarios, reRTreduce and reRTvoxelwise reduced accumulated average and near-maximum EQD2 by ˜1-10 Gy for all relevant OARs compared to reRTregular . The reduced OAR doses for reRTreduce came at the cost of distorted dose distributions with D98% = 92.3%, HI = 12.0%, CI = 73.7% and normal tissue hot spots ≥150% for the most complex scenario, while reRTregular (D98% = 98.1%, HI = 3.2%, CI = 94.2%) and reRTvoxelwise (D98%  = 96.9%, HI = 6.1%, CI = 93.7%) fulfilled PTV coverage without hot spots. CONCLUSIONS: The proposed re-irradiation-specific EQD2-based optimization functions introduce novel planning possibilities with flexible options to guide the trade-off between target coverage and OAR sparing with voxelwise adapted penalization levels based on EQD2deliv .

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.

Brain Re-Irradiation Robustly Accounting for Previously Delivered Dose.

(1) Background: The STRIDeR (Support Tool for Re-Irradiation Decisions guided by Radiobiology) planning pathway aims to facilitate anatomically appropriate and radiobiologically meaningful re-irradiation (reRT). This work evaluated the STRIDeR pathway for robustness compared to a more conservative manual pathway. (2) Methods: For ten high-grade glioma reRT patient cases, uncertainties were applied and cumulative doses re-summed. Geometric uncertainties of 3, 6 and 9 mm were applied to the background dose, and LQ model robustness was tested using α/ß variations (values 1, 2 and 5 Gy) and the linear quadratic linear (LQL) model δ variations (values 0.1 and 0.2). STRIDeR robust optimised plans, incorporating the geometric and α/ß uncertainties during optimisation, were also generated. (3) Results: The STRIDeR and manual pathways both achieved clinically acceptable plans in 8/10 cases but with statistically significant improvements in the PTV D98% (p < 0.01) for STRIDeR. Geometric and LQ robustness tests showed comparable robustness within both pathways. STRIDeR plans generated to incorporate uncertainties during optimisation resulted in a superior plan robustness with a minimal impact on PTV dose benefits. (4) Conclusions: Our results indicate that STRIDeR pathway plans achieved a similar robustness to manual pathways with improved PTV doses. Geometric and LQ model uncertainties can be incorporated into the STRIDeR pathway to facilitate robust optimisation.

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.

Technical note: Evaluation of a spatial optimization model for prostate high dose-rate brachytherapy in a clinical treatment planning system.

BACKGROUND: Spatial properties of a dose distribution, such as volumes of contiguous hot spots, are of clinical importance in treatment planning for high dose-rate brachytherapy (HDR BT). We have in an earlier study developed an optimization model that reduces the prevalence of contiguous hot spots by modifying a tentative treatment plan. PURPOSE: The aim of this study is to incorporate the correction of hot spots in a standard inverse planning workflow and to validate the integrated model in a clinical treatment planning system. The spatial function is included in the objective function for the inverse planning, as opposed to in the previous study where it was applied as a separate post-processing step. Our aim is to demonstrate that fine-adjustments of dose distributions, which are often performed manually in today's clinical practice, can be automated. METHODS: A spatial optimization function was introduced in the treatment planning system RayStation (RaySearch Laboratories AB, Stockholm, Sweden) via a research interface. A series of 10 consecutive prostate patients treated with HDR BT was retrospectively replanned with and without the spatial function. RESULTS: Optimization with the spatial function decreased the volume of the largest contiguous hot spot by on average 31%, compared to if the function was not included. The volume receiving at least 200% of the prescription dose decreased by on average 11%. Target coverage, measured as the fractions of the clinical target volume (CTV) and the planning target volume (PTV) receiving at least the prescription dose, was virtually unchanged (less than a percent change for both metrics). Organs-at-risk received comparable or slightly decreased doses if the spatial function was included in the optimization model. CONCLUSIONS: Optimization of spatial properties such as the volume of contiguous hot spots can be integrated in a standard inverse planning workflow for brachytherapy, and need not be conducted as a separate post-processing step.

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.

Probabilistic Pareto plan generation for semiautomated multicriteria radiation therapy treatment planning.

Objective.We propose a semiautomatic pipeline for radiation therapy treatment planning, combining ideas from machine learning-automated planning and multicriteria optimization (MCO).Approach.Using knowledge extracted from historically delivered plans, prediction models for spatial dose and dose statistics are trained and furthermore systematically modified to simulate changes in tradeoff priorities, creating a set of differently biased predictions. Based on the predictions, an MCO problem is subsequently constructed using previously developed dose mimicking functions, designed in such a way that its Pareto surface spans the range of clinically acceptable yet realistically achievable plans as exactly as possible. The result is an algorithm outputting a set of Pareto optimal plans, either fluence-based or machine parameter-based, which the user can navigate between in real time to make adjustments before a final deliverable plan is created.Main results.Numerical experiments performed on a dataset of prostate cancer patients show that one may often navigate to a better plan than one produced by a single-plan-output algorithm.Significance.We demonstrate the potential of merging MCO and a data-driven workflow to automate labor-intensive parts of the treatment planning process while maintaining a certain extent of manual control for the user.

Probabilistic feature extraction, dose statistic prediction and dose mimicking for automated radiation therapy treatment planning.

PURPOSE: We propose a general framework for quantifying predictive uncertainties of dose-related quantities and leveraging this information in a dose mimicking problem in the context of automated radiation therapy treatment planning. METHODS: A three-step pipeline, comprising feature extraction, dose statistic prediction and dose mimicking, is employed. In particular, the features are produced by a convolutional variational autoencoder and used as inputs in a previously developed nonparametric Bayesian statistical method, estimating the multivariate predictive distribution of a collection of predefined dose statistics. Specially developed objective functions are then used to construct a probabilistic dose mimicking problem based on the produced distributions, creating deliverable treatment plans. RESULTS: The numerical experiments are performed using a dataset of 94 retrospective treatment plans of prostate cancer patients. We show that the features extracted by the variational autoencoder capture geometric information of substantial relevance to the dose statistic prediction problem and are related to dose statistics in a more regularized fashion than hand-crafted features. The estimated predictive distributions are reasonable and outperforms a non-input-dependent benchmark method, and the deliverable plans produced by the probabilistic dose mimicking agree better with their clinical counterparts than for a non-probabilistic formulation. CONCLUSIONS: We demonstrate that prediction of dose-related quantities may be extended to include uncertainty estimation and that such probabilistic information may be leveraged in a dose mimicking problem. The treatment plans produced by the proposed pipeline resemble their original counterparts well, illustrating the merits of a holistic approach to automated planning based on probabilistic modeling.

Direct optimization of dose-volume histogram metrics in radiation therapy treatment planning.

We present a method of directly optimizing on deviations in clinical goal values in radiation therapy treatment planning. Using a new mathematical framework in which metrics derived from the dose-volume histogram are regarded as functionals of an auxiliary random variable, we are able to obtain volume-at-dose and dose-at-volume as infinitely differentiable functions of the dose distribution with easily evaluable function values and gradients. Motivated by the connection to risk measures in finance, which is formalized in this framework, we also derive closed-form formulas for mean-tail-dose and demonstrate its capability of reducing extreme dose values in tail distributions. Numerical experiments performed on a prostate and a head-and-neck patient case show that the direct optimization of dose-volume histogram metrics produced marginally better results than or outperformed conventional planning objectives in terms of clinical goal fulfilment, control of low- and high-dose tails of target distributions and general plan quality defined by a pre-specified evaluation measure. The proposed framework eliminates the disconnect between optimization functions and evaluation metrics and may thus reduce the need for repetitive user interaction associated with conventional treatment planning. The method also has the potential of enhancing plan optimization in other settings such as multicriteria optimization and automated treatment planning.

Dynamic conformal arcs for lung stereotactic body radiation therapy: A comparison with volumetric-modulated arc therapy.

This study constitutes a feasibility assessment of dynamic conformal arc (DCA) therapy as an alternative to volumetric-modulated arc therapy (VMAT) for stereotactic body radiation therapy (SBRT) of lung cancer. The rationale for DCA is lower geometric complexity and hence reduced risk for interplay errors induced by respiratory motion. Forward planned DCA and inverse planned DCA based on segment-weight optimization were compared to VMAT for single arc treatments of five lung patients. Analysis of dose-volume histograms and clinical goal fulfillment revealed that DCA can generate satisfactory and near equivalent dosimetric quality to VMAT, except for complex tumor geometries. Segment-weight optimized DCA provided spatial dose distributions qualitatively similar to those for VMAT. Our results show that DCA, and particularly segment-weight optimized DCA, may be an attractive alternative to VMAT for lung SBRT treatments if the patient anatomy is favorable.

Technical Note: Improving VMAT delivery efficiency by optimizing the dynamic collimator trajectory.

PURPOSE: To provide a method for optimizing the multileaf collimator angle trajectory in volumetric modulated arc therapy (VMAT) in order to make VMAT delivery and planning more efficient. METHODS: Static fluence maps are optimized at a 10-degree spacing around the patient. Sliding window delivery time of each of these fields is computed for a large set of possible collimator orientations. An optimal trajectory, which selects a collimator angle for each field and assures that the collimator angles do not differ excessively between adjacent fields, is computed by solving a network flow model of a shortest path problem. RESULTS: For four clinical cases (two brains, an anal, and a spine), we demonstrate time reductions from 6% to 32% (average: 24%) for the optimal static angle vs the worst static angle. Further reductions from 3% to 17% (average 9%) are achievable when dynamic collimator trajectories are allowed. CONCLUSIONS: Dynamic collimator trajectories, which can be computed with an efficient linear programming formulation, can improve the efficiency of VMAT delivery.

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.

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.

Projections onto the Pareto surface in multicriteria radiation therapy optimization.

PURPOSE: To eliminate or reduce the error to Pareto optimality that arises in Pareto surface navigation when the Pareto surface is approximated by a small number of plans. METHODS: The authors propose to project the navigated plan onto the Pareto surface as a postprocessing step to the navigation. The projection attempts to find a Pareto optimal plan that is at least as good as or better than the initial navigated plan with respect to all objective functions. An augmented form of projection is also suggested where dose-volume histogram constraints are used to prevent that the projection causes a violation of some clinical goal. The projections were evaluated with respect to planning for intensity modulated radiation therapy delivered by step-and-shoot and sliding window and spot-scanned intensity modulated proton therapy. Retrospective plans were generated for a prostate and a head and neck case. RESULTS: The projections led to improved dose conformity and better sparing of organs at risk (OARs) for all three delivery techniques and both patient cases. The mean dose to OARs decreased by 3.1 Gy on average for the unconstrained form of the projection and by 2.0 Gy on average when dose-volume histogram constraints were used. No consistent improvements in target homogeneity were observed. CONCLUSIONS: There are situations when Pareto navigation leaves room for improvement in OAR sparing and dose conformity, for example, if the approximation of the Pareto surface is coarse or the problem formulation has too permissive constraints. A projection onto the Pareto surface can identify an inaccurate Pareto surface representation and, if necessary, improve the quality of the navigated plan.

Optimization approaches to volumetric modulated arc therapy planning.

Volumetric modulated arc therapy (VMAT) has found widespread clinical application in recent years. A large number of treatment planning studies have evaluated the potential for VMAT for different disease sites based on the currently available commercial implementations of VMAT planning. In contrast, literature on the underlying mathematical optimization methods used in treatment planning is scarce. VMAT planning represents a challenging large scale optimization problem. In contrast to fluence map optimization in intensity-modulated radiotherapy planning for static beams, VMAT planning represents a nonconvex optimization problem. In this paper, the authors review the state-of-the-art in VMAT planning from an algorithmic perspective. Different approaches to VMAT optimization, including arc sequencing methods, extensions of direct aperture optimization, and direct optimization of leaf trajectories are reviewed. Their advantages and limitations are outlined and recommendations for improvements are discussed.

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.

Advantages and limitations of navigation-based multicriteria optimization (MCO) for localized prostate cancer IMRT planning.

Efficacy of inverse planning is becoming increasingly important for advanced radiotherapy techniques. This study's aims were to validate multicriteria optimization (MCO) in RayStation (v2.4, RaySearch Laboratories, Sweden) against standard intensity-modulated radiation therapy (IMRT) optimization in Oncentra (v4.1, Nucletron BV, the Netherlands) and characterize dose differences due to conversion of navigated MCO plans into deliverable multileaf collimator apertures. Step-and-shoot IMRT plans were created for 10 patients with localized prostate cancer using both standard optimization and MCO. Acceptable standard IMRT plans with minimal average rectal dose were chosen for comparison with deliverable MCO plans. The trade-off was, for the MCO plans, managed through a user interface that permits continuous navigation between fluence-based plans. Navigated MCO plans were made deliverable at incremental steps along a trajectory between maximal target homogeneity and maximal rectal sparing. Dosimetric differences between navigated and deliverable MCO plans were also quantified. MCO plans, chosen as acceptable under navigated and deliverable conditions resulted in similar rectal sparing compared with standard optimization (33.7 ± 1.8 Gy vs 35.5 ± 4.2 Gy, p = 0.117). The dose differences between navigated and deliverable MCO plans increased as higher priority was placed on rectal avoidance. If the best possible deliverable MCO was chosen, a significant reduction in rectal dose was observed in comparison with standard optimization (30.6 ± 1.4 Gy vs 35.5 ± 4.2 Gy, p = 0.047). Improvements were, however, to some extent, at the expense of less conformal dose distributions, which resulted in significantly higher doses to the bladder for 2 of the 3 tolerance levels. In conclusion, similar IMRT plans can be created for patients with prostate cancer using MCO compared with standard optimization. Limitations exist within MCO regarding conversion of navigated plans to deliverable apertures, particularly for plans that emphasize avoidance of critical structures. Minimizing these differences would result in better quality treatments for patients with prostate cancer who were treated with radiotherapy using MCO plans.

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.

Distributed approximation of Pareto surfaces in multicriteria radiation therapy treatment planning.

We consider multicriteria radiation therapy treatment planning by navigation over the Pareto surface, implemented by interpolation between discrete treatment plans. Current state of the art for calculation of a discrete representation of the Pareto surface is to sandwich this set between inner and outer approximations that are updated one point at a time. In this paper, we generalize this sequential method to an algorithm that permits parallelization. The principle of the generalization is to apply the sequential method to an approximation of an inexpensive model of the Pareto surface. The information gathered from the model is sub-sequently used for the calculation of points from the exact Pareto surface, which are processed in parallel. The model is constructed according to the current inner and outer approximations, and given a shape that is difficult to approximate, in order to avoid that parts of the Pareto surface are incorrectly disregarded. Approximations of comparable quality to those generated by the sequential method are demonstrated when the degree of parallelization is up to twice the number of dimensions of the objective space. For practical applications, the number of dimensions is typically at least five, so that a speed-up of one order of magnitude is obtained.