A fast and robust constraint-based online re-optimization approach for automated online adaptive intensity modulated proton therapy in head and neck cancer

Objective. In head-and-neck cancer intensity modulated proton therapy, adaptive radiotherapy is currently restricted to offline re-planning, mitigating the effect of slow changes in patient anatomies. Daily online adaptations can potentially improve dosimetry. Here, a new, fully automated online re-optimization strategy is presented. In a retrospective study, this online re-optimization approach was compared to our trigger-based offline re-planning (offlineTB re-planning) schedule, including extensive robustness analyses. Approach. The online re-optimization method employs automated multi-criterial re-optimization, using robust optimization with 1 mm setup-robustness settings (in contrast to 3 mm for offlineTB re-planning). Hard planning constraints and spot addition are used to enforce adequate target coverage, avoid prohibitively large maximum doses and minimize organ-at-risk doses. For 67 repeat-CTs from 15 patients, fraction doses of the two strategies were compared for the CTVs and organs-at-risk. Per repeat-CT, 10.000 fractions with different setup and range robustness settings were simulated using polynomial chaos expansion for fast and accurate dose calculations. Main results. For 14/67 repeat-CTs, offlineTB re-planning resulted in <50% probability of D 98% ≥ 95% of the prescribed dose (D pres) in one or both CTVs, which never happened with online re-optimization. With offlineTB re-planning, eight repeat-CTs had zero probability of obtaining D 98% ≥ 95%D pres for CTV7000, while the minimum probability with online re-optimization was 81%. Risks of xerostomia and dysphagia grade ≥ II were reduced by 3.5 ± 1.7 and 3.9 ± 2.8 percentage point [mean ± SD] (p < 10−5 for both). In online re-optimization, adjustment of spot configuration followed by spot-intensity re-optimization took 3.4 min on average. Significance. The fast online re-optimization strategy always prevented substantial losses of target coverage caused by day-to-day anatomical variations, as opposed to the clinical trigger-based offline re-planning schedule. On top of this, online re-optimization could be performed with smaller setup robustness settings, contributing to improved organs-at-risk sparing.


Introduction
Daily online plan adaptation has the potential to reduce dose degradation caused by inter-fraction anatomy and position variability (Bertholet et al 2020, Qiu et al 2023, Trnkova et al 2023).This is particularly relevant for intensity modulated proton therapy (IMPT), where the delivered dose is substantially more sensitive to these variations.For head-and-neck (H&N) cancer patients, the large setup robustness settings required to achieve the desired target coverage in the absence of online plan adaptations can result in significantly increased toxicity risks (van de Water et al 2016, Oud et al 2022).Therefore, there have been continuous efforts to investigate the potential and feasibility of various online adaptation strategies.
Several studies have highlighted the feasibility of fast online adaptation for IMPT.Table 1 provides an overview of proposed online adaptive strategies, and dosimetric evaluations of such strategies, explicitly for H&N IMPT.Approaches can be divided in four categories, depending on the amount of information inherited from the original plan (Paganetti et al 2021): (1) online re-planning strategies entail the generation of a full new treatment plan with the original treatment planning pipeline, as introduced by Matter et al (2019), Nenoff et al (2019).( 2) Online re-optimization strategies adapt the original plan to obtain similar or improved plan quality, without aiming at reproducing the original dose distribution (Botas et al 2018, Bobić et al 2021, 2023, Lalonde et al 2021).(3) Online dose restoration strategies adapt the original plan to obtain a similar dose distribution for the daily anatomy (Bernatowicz et al 2018, Borderías-Villarroel et al 2022, 2023, Miyazaki et al 2022).(4) Plan library strategies do not adapt the original plans.Instead, a pre-treatment generated library of plans is employed with daily selection of the library plan that best fits the geometry-of-the-day (Oud et al 2022).
Effective and efficient online adaptation requires a fully automated algorithm that guarantees adequate target coverage.However, existing methods can fall short, primarily related to two main factors.First, adapted plans may not have guaranteed robustness against residual errors such as intra-fraction motion, beam alignment to the isocenter of the CT, and range errors.Second, the in-room plan re-optimization workflow may be inefficient, especially in the presence of large anatomical variations.Manual tweaking of objective weights to balance multiple objectives (target coverage, maximum doses to the CTVs, and organ-at-risk (OAR) doses) may be required to achieve adequate target coverage.Constraining the minimum robust target coverage of the CTV during optimization could offer a solution.So far, none of the published online adaptation approaches for H&N cancer have incorporated a combined approach that integrates robust optimization with imposed hard constraints on target coverage.
Furthermore, accurate and systematic evaluation of the dosimetric impact of online adaptation is crucial for the decision-making process regarding its introduction in clinical practice, given the considerable resources associated with online procedures.The potential dosimetric benefit is currently unclear because published assessments do not meet one or both of the following two requirements, (1) no evaluation of robustness of adapted plans against unavoidable residual errors.The omission of such analyzes bears the potential of bias in the conclusions regarding truly delivered doses in CTVs and OARs.Recently, studies employing polynomial chaos expansion (PCE) on the planning-CT have shown that large numbers of dose distributions under the influence of potential residual errors can be generated rapidly and used for statistically accurate plan robustness analysis (Perkó et al 2016, Rojo-Santiago et al 2021, 2023).This has not yet been employed to evaluate plan adaptation strategies, (2) no comparison with current state-of-the-art clinical treatment planning strategy, such as robust optimization with trigger-based offline adaptive re-planning.Bobić et al (2023) compared their online re-optimization strategy to their clinical offline adaptation strategy.However, robustness evaluation was not performed and they exclusively included patients that needed an offline adaptation, not providing a representative sample of the patient population.In Oud et al (2022), our plan library strategy was compared in compliance with the two requirements.However, online dose restoration, re-optimization, and re-planning strategies can potentially further improve dosimetry.
In this study, a fully automated online re-optimization strategy is proposed that guarantees CTV coverage by using hard planning constraints and by employing mini-max robust optimization (Fredriksson et al 2011).Setup robustness settings of 1 mm and automated multi-criterial optimization are used to maximally reduce OAR doses.Spots are added to the original spot distribution in poorly covered areas of the CTV, to ensure a good spot distribution while maintaining the original spot configuration as much as possible.Our novel online reoptimization strategy was validated for H&N cancer by dosimetric comparisons to our current clinical treatment strategy, which entails trigger-based offline robust re-planning.Dosimetric comparisons between the novel online re-optimization strategy and trigger-based offline re-planning included extensive robustness analyzes on repeat-CTs using PCE evaluations (Perkó et al 2016, Rojo-Santiago et al 2021).

Patient data
In this retrospective study, CT-scans of fifteen primary H&N cancer patients treated with IMPT at Holland Proton Therapy Center in 2019 and 2020 were included.The following inclusion criteria had to be met: (1) availability of three or more repeat-CTs in treatment position, acquired during the fractionated treatment to verify the need for offline re-planning due to anatomical changes; and (2) Robust CTV coverage constraints Table 1.Overview of publications on overview of proposed online adaptive strategies, and dosimetric evaluations of such strategies in head-and-neck IMPT.PCE = Polynomial chaos expansion (see text).RS = Robustness setting (setup robustness/range robustness).* Only patients with offline plan adaptations, ** only used when target coverage constraints were not met on repeat-CTs.could be met on the planning-CT without exceeding constraints on serial OARs due to proximity of the CTV.Prescribed doses (D pres ) were 70 GyRBE to the high-dose CTV, including the GTV and positive lymph nodes (CTV 7000 ) and 54.25 GyRBE to the elective areas (CTV 5425 ) in 35 fractions.A constant relative biological effectiveness (RBE) of 1.1 was used in planning.For each patient, 3-6 repeat-CTs were available.The acquisition of repeat-CTs was part of the standard protocol, and the frequency per patient was mostly based on the availability of personnel and CT scanner.
CTV contours were propagated from the planning-CT to the corresponding repeat-CTs.The CTV 7000 and the part of the CTV 5425 that was within a 5 mm margin to the CTV 7000 were rigidly propagated from the planning-CT to the repeat-CTs and were manually adjusted if contours were outside the external patient contour or inside bone or if large discrepancies occurred (e.g. the hyoid bone moved resulting in a different position of the GTV).The remainder of the CTV 5425 was deformably propagated to the repeat-CTs and manually adjusted in case of noticeable mismatches with the repeat-CTs.The contours were checked for consistency by expert clinicians.Contours of the OARs were deformably propagated to the repeat-CTs, and manually adjusted.

Online re-optimization
The novel online re-optimization strategy consisted of daily adaptation of the initial treatment plan using contoured repeat-CTs.The initial treatment plan was obtained through full multi-criterial optimization (see below).The re-optimization algorithm was embedded in our in-house system for automated treatment planning (Erasmus-iCycle), and used a weighted-sum cost-function and hard constraints for plan generation.Weights in the applied weighted-sum cost-function were Lagrange parameters obtained from the initial treatment plan (Breedveld et al 2009).Such weight extractions could be done automatically, prior to the first treatment fraction.Online re-optimization for repeat-CTs then consisted of five steps: (1) restoration of spot Bragg peak positions to their intended positions by adjusting their energies to account for changes in waterequivalent-path-lengths (WEPL) (Jagt et al 2017).Restored energies were interpolated to the same energy grid as used for initial treatment planning, (2) the online re-optimization strategy employs a novel method to improve the established original spot distribution, in which new spots were added specifically to target areas that were not covered by spots after step 1 due to anatomical changes.Hereto, a dense candidate spot distribution with spots originating from all beam directions was first placed over the CTV + 5 mm expansion, followed by an iterative selection of 2000 of these spots with a Bragg peak location at 8 mm or more from restored original spots, (3) computation of dose-deposition matrices for the repeat-CT anatomy for all spots (restored original and added), (4) constrained robust optimization of the intensities of all spots using the weighted-sum cost-function.The same robustness settings as the initial plan were used (1 mm/3% setup/range robustness settings in 29 scenarios, see below).The constraints ensured appropriate coverage of the two CTVs, (5) spots that had an intensity below the minimum required monitor units were removed to ensure deliverability of the treatment plan.
Trigger-based offline re-planning schedule Our current clinical adaptation strategy consists of trigger-based offline re-planning (offline TB re-planning).For the simulation of this strategy, treatment plans were generated with full multi-criterial optimization (see below), and the clinical offline re-planning schedule was followed.In our clinical workflow, triggering offline adaptations is guided by dose assessments on repeat-CTs and the evaluation of sequential daily CBCTs.In this dataset, nine plan offline adaptations were performed for seven patients in total.Four of these plan adaptations were performed on the last repeat-CT.In the simulations, offline adapted plans were used from the next repeat-CT onwards.Adaptations based on the last repeat-CT were therefore not taken into account in the evaluations.This resulted in a total of 5 plan adaptations for 5 patients that were taken into account.In supplementary data A, a schematic representation of the treatment planning schedule in the online re-optimization and offline TB replanning strategies is shown.

Full multi-criterial optimization of treatment plans
For the online re-optimization strategy, initial treatment plans for the planning-CTs were generated with full multi-objective optimization.For the offline TB re-planning strategy, all treatment plans on the planning-CT and the 5 plan adaptations were generated with this approach.Wish-list driven fully-automated software was used for generation of the treatment plans: Erasmus-iCycle (Breedveld et al 2012, van de Water et al 2013).To simultaneously also ensure plan robustness, these optimizations were mini-max scenario-based (Fredriksson et al 2011, Liu et al 2013).Smaller setup robustness settings were applied for treatment plans used in the online re-optimization strategy.A resampling approach was used for spot selection (van de Water et al 2013), where candidate spots are iteratively selected from a dense grid and added to the optimization problem.After each iteration of optimization, non-contributing spots are removed from the optimization problem.Details on the applied wish-list, sequential minimization of prioritized objectives subject to hard constraints, and treatmentsite specific configuration of the employed treatment planning system can be found in Breedveld et al (2012), van de Water et al (2013), Heijmen et al (2018).Details on the specific configuration of automated plan generation in this study are described in the supplementary data of Oud et al (2022).
During optimization, the nominal scenario and 28 uncertainty scenarios were used to account for variations in patient setup and uncertainties in proton ranges (Korevaar et al 2019).For offline TB re-planning, 3 mm/3% robustness settings (setup robustness/range robustness) were used, while 1 mm/3% was used for online reoptimization.The selected setup robustness setting of 3 mm for offline TB re-planning is the same as currently used in our clinic.The 1 mm setup robustness setting for online re-optimization was based on literature (Nenoff et al 2021, Bobić et al 2023).Both for CTV 7000 and for CTV 5425 , generated treatment plans had to meet a coverage constraint: V 95% > 98% in the voxelwise minimum dose distribution (Korevaar et al 2019).Note that voxelwise dose distributions were only used in the planning phase, not for plan evaluations and comparisons (below).
Evaluation and comparison of online re-optimization and offline TB re-planning Dosimetric evaluations and comparisons of the two investigated adaptive strategies were performed for the available repeat-CTs.The impact of inter-fraction anatomical changes was incorporated through repeat-CTs.While adaptive approaches can mitigate anatomical changes, they cannot compensate for residual errors: errors in matching the gantry to the isocenter of the CT, uncertainties in couch positioning, registration errors with the MR that was used for target delineation, registration errors with the CT, intra-fraction motion and proton range uncertainties (supplementary data B).On the other hand, dosimetric variations caused by these uncertainties will in reality occur and need to be accounted for in evaluations and comparisons of optimized/predicted doses.
PCE (Perkó et al 2016, Rojo-Santiago et al 2021) was used for extensive evaluation of robustness of generated dose distributions against residual uncertainties.The rationale to use PCE comes from its ability to accurately approximate 3D dose distributions for all (i.e.thousands of) uncertainty scenarios of a treatment plan in a matter of seconds, allowing statistical robustness evaluation instead of using the common nominal or 29 scenarios.Instead of executing forward dose computations to obtain the 3D dose distribution for all the scenarios, PCE constructs and employs a computational model to predict dose distributions.This model is a multi-dimensional polynomial function of the stochastic input variables (geometrical errors and proton range-errors in this study).Expansion coefficients of the function are obtained by linear regression, see Perkó et al (2016), Rojo-Santiago et al (2021) for details.Our PCE approach is implemented in Matlab (version 2021b) and was previously validated for the employed ASTROID dose engine (Kooy et al 2010, Perkó et al 2016, van der Voort et al 2016).In this study, the expansion coefficients were obtained based on the input of 208 dose distributions computed in fixed uncertainty scenarios.Once these computations are completed, computing the expansion coefficients took around 2 s, and the generation of 10.000 scenario dose distributions for a structure took around 2 s.Time required for assessment of the DVHs highly depends on the employed settings and organ size.In our case, DVH computation for the two CTVs took around 30 min for an average patient (analysis performed on an Intel ® Xeon ® Gold 6248).PCE models were constructed for each repeat-CT, for both online re-optimization and offline TB re-planning strategy.
Both for online re-optimization and offline TB re-planning, PCE was used to calculate for each repeat-CT 10.000 dose distributions, each for a randomly selected total residual setup error for each of the three principal directions, and a randomly selected range error for offline TB re-planning and online re-optimization.These errors were sampled from Gaussian distributions describing total residual geometric uncertainties.The standard deviations (SD) of these Gaussian distributions were derived from quality assurance (QA) and treatment data at Holland Proton Therapy Center by quadratically adding SDs of the various residual errors involved.This resulted in total SDs of 1.18, 1.16, and 1.22 mm for the setup errors in lateral, longitudinal, and vertical directions, respectively.A description of the residual errors and the employed SD can be found in supplementary data B. The Gaussian distribution of range errors was assumed to have a SD of 1.5% in correspondence to Taasti et al (2018).
For each repeat-CT, the obtained dosimetric values were multiplied by 35 to arrive at values for full treatments to improve interpretability.The probabilities for adequate CTV coverage and for exceeding preferred maximum doses in a fraction were established with the 10.000 PCE dose distributions.The D 98% was evaluated as it is an ICRU-recommended metric that is numerically more robust than point minimum doses.Reported OAR mean doses were obtained by averaging achieved mean doses in the 10.000 PCE dose distributions.For each repeat-CT, NTCPs were calculated using these OAR doses.The risks of xerostomia and dysphagia grade II and III were evaluated.We used NTCP models described in the Dutch National Indication protocol (National Association for Radiotherapy in the Netherlands 2019), which were constructed using the data of 750 patients using multivariable regression analysis and were validated on an independent dataset.
Online re-optimization times were evaluated on an Intel ® Xeon ® Gold 6248, ignoring dose computation and contouring times.
Statistical significance of differences between online re-optimization and offline TB re-planning was tested using paired Wilcoxon signed-rank tests for paired data, and Wilcoxon rank sum tests for unpaired data (α < 0.05).

Results
CTV coverage for example repeat-CT Figures 1 and 2 illustrate results for an example repeat-CT.Figure 1 presents the 90%-worst-case obtained with online re-optimization for CTV 5425 .This particular repeat-CT was selected because it shows the efficacy of online re-optimization in areas of large anatomical variations (top panels): underdosage in the CTV 5425 with offline TB re-planning, while coverage was maintained with online re-optimization.The example also shows the ability of online re-optimization to maintain good conformity, which is reduced with offline TB re-planning (bottom panels).
Figures 2(a) and (b) show the D 98% histogram and the corresponding cumulative D 98% histogram for the example repeat-CT in figure 1, derived from the 10.000 fractions obtained with the PCE simulations.With offline TB re-planning, the probabilities of obtaining at least 95% D pres in CTV 5425 and CTV 7000 were 50% and 98% (points A1 and A2 in figure 2(b)) while for online re-optimization they were 88% and 83% (points A3, A4 in figure 2(b)).

CTV coverage in population of repeat-CTs
Figure 3 shows for each repeat-CT for the two adaptive strategies separately, the percentage of the 10.000 PCE dose distributions with a D 98% of at least 95%D pres , both for CTV 5425 and CTV 7000 .While for the majority of repeat-CTs the chances of reaching D 98% 95%D pres were higher with offline TB re-planning, for a large minority of repeat-CTs, the probability for adequate coverage was zero or close to zero with offline TB replanning because of large changes in patient geometry, while online re-optimization was able to guarantee high coverage probabilities.For 14/67 repeat-CTs, offline TB re-planning resulted in <50% probability of D 98% 95%D pres in one or both CTVs, which never happened with online re-optimization.With offline TB re-planning, eight repeat-CTs had zero coverage probability for CTV 7000 , while the minimum repeat-CT coverage probability with online re-optimization was 81%.For online re-optimization, the mean percentages with [10th, 90th percentile] were 93.6% [84.7%, 91.1%] for CTV 5425 and 87.9% [86.0%, 98.2%] for CTV 7000 .For offline TB re-planning, this was 87.7% [46.6%, 100%] and 83.0%[0, 99.9%], for CTV 5425 and CTV 7000 .Comparing the 10th and 90th percentiles of the distributions for offline TB re-planning and online re-optimization, target coverage is more consistent across the repeat-CTs for online re-optimization.With online re-optimization, probabilities for adequate target coverage in repeat-CTs were highly similar to those in the corresponding planning-CT plans (supplementary data C), meaning that the intended target coverage from the planning-CTs was maintained for repeat-CTs.This was certainly not achieved with offline TB re-planning, as in a large minority the probability was extremely low.
Figure 4(a) shows cumulative D 98% histograms for CTV 5425 and CTV 7000 for the 95th, 90th, 85th, and 5th percentiles of the population of 67 repeat-CTs.For both CTVs, comparison of the 95th percentile curves points to enhanced rates of adequate coverage with online re-optimization compared to offline TB re-planning.Comparisons of the 5th percentile curves' intersections with 90% probability of D 98% above dose (B1 with B3 and B2 with B4) in figure 4(a) further point at clear coverage advantages for online re-optimization, as 95% of the repeat-CTs had 90% chance of receiving a D 98% of 49.4 Gy in the CTV 5425 and 64.0 Gy in the CTV 7000 for offline TB re-planning, while this was 51.1 Gy and 66.1 Gy for online re-optimization.The 95%D pres intersections with the 5th percentile also highlight the advantage of online re-optimization, showing that for 95% of the patient population online re-optimization ensures a minimum CTV 5425 coverage probability as high Figure 3.For each of the 67 repeat-CT, the percentage of the 10.000 PCE dose distributions with D 98% > 95% of the prescribed dose for the two investigated adaptive strategies, for CTV 7000 (top) and CTV 5425 (bottom).Repeat-CTs were sorted based on CTV 7000 D 98% in the trigger-based offline adaptive (offline TB re-planning) strategy.as 84%, while this drops to 31% with offline TB re-planning (points C1 and C3), and for CTV 7000 online reoptimization ensures a minimum coverage probability of 84% versus 0% with offline TB re-planning (points C2 and C4).Furthermore, comparisons of the difference between the 5th percentile curves and the 95th percentile curves between the two adaptive strategies in figure 4(a) show enhanced consistency in target coverage across the patient population with online re-optimization.
Figure 4(b) displays cumulative population D 2% histograms for CTV 7000 for the two strategies with corresponding 5th and 95th percentile curves.The 95th percentile curves (right dashed curves) show a slight disadvantage for online re-optimization: for 95% of the repeat-CTs the probability that D 2% exceeded 74.9 Gy (107%D pres ) was only limited at 3%, while this probability was zero for offline TB re-planning (see points D1 and D2 in figure 4(b)).

OARs
Differences between online re-optimization and offline TB re-planning in OAR mean doses are shown in figure 5(a).Online re-optimization was superior for all dose differences (p < 10 5 for all).The highest reduction was observed for the middle constrictor muscle (−5.0 Gy on average, ranging from −23.8 to 3.8 Gy). Figure 5(b) shows to what extent the superiority of online re-optimization in OAR doses impacts NTCPs.The risk of xerostomia and dysphagia grade II could be reduced significantly by 3.5 ± 1.7 percentage point and 3.9 ± 2.8 percentage point [mean ± SD] (p < 10 5 for both).The risk of xerostomia and dysphagia grade III could be reduced by 1.1 ± 0.6 percentage point and 1.0 ± 1.0 percentage point (p < 10 5 for both).

Optimization times
In the online re-optimization strategy, restoration of the planned WEPL took 2.5 ± 0.6 s [mean ± SD] per repeat-CT.Spot addition took 14.8 ± 2.8 s.Re-optimization times were 189 ± 31 s.

Discussion
In this study, we have proposed a novel approach for online adaptive dose re-optimization in IMPT and evaluated this for patients with H&N cancer.To enforce adequate target coverage and minimize OAR dose, the online re-optimization method employs automated constraint-based multi-criterial re-optimization, mini-max robust optimization with a 1 mm setup-robustness setting, spot restoration and spot addition.Dose distributions obtained with online re-optimization were benchmarked against our current offline adaptive replanning protocol.To obtain an accurate and relevant comparison of the two strategies, a representative patient population and realistic robustness settings during optimization were used, and a comprehensive statistical analysis of the robustness against residual errors was performed.
Three important advantages of the online re-optimization strategy compared to offline TB re-planning were identified: first, with the novel online re-optimization strategy, the intended planning-CT target coverage was maintained in the repeat-CTs.Second, online re-optimization resulted in full avoidance of very low probabilities for adequate target coverage, while with offline TB re-planning in 21% of the analyzed repeat-CTs the chance of adequate target coverage was <50% in one or both CTVs.Third, online re-optimization significantly reduced OAR doses, which resulted in reduced NTCPs.On the other hand, two dosimetric advantages of offline TB replanning were found: first, near-maximum doses in the CTV 7000 were slightly advantageous with offline TB replanning.Second, apart from very low coverage probabilities with offline TB re-planning for some repeat-CTs (above), there is also a substantial fraction of repeat-CTs with coverage probabilities approaching 100% (48% of repeat-CTs with 100% CTV 7000 coverage probability, see figure 3).However, very high coverage probabilities in the latter are a result of the population-based setup robustness settings determined by the near-worst performing patients.The overall increased NTCPs with offline TB re-planning are likely (partly) related to these high coverages.With online re-optimization such higher-than-requested coverage probabilities were avoided: they were more in line with intended coverage probabilities in the corresponding planning-CT plans.
For online re-optimization, obtained probabilities for adequate target coverage (D 98% >95%D pres ) on the repeat-CTs were 87.9% [86.0%, 98.2%] (mean [10th, 90th percentile]) for CTV 7000 and 93.6% [84.7%,91.1%]for CTV 5425 .Further research, including dose accumulation studies, is needed to establish the optimal choice for the metrics used to assess adequate target coverage, as well as for the optimal probabilities of obtaining adequate target coverage.With the proposed online re-optimization approach, steering the D 98% is possible with the applied setup robustness settings in planning-CT plan generations (1 mm in the current study, as proposed in literature).
Guaranteeing adequate target coverage without prohibitively high maximum doses requires an appropriate spot distribution.An improved spot distribution in the daily situation can be obtained by complete replacement of the spot configuration (Borderias Villarroel et al 2023), but generating this distribution can be timeconsuming and large changes in spot configurations are undesirable for online QA purposes.Previous studies found that restoration could be performed by keeping the original spot distribution (Bobić et al 2021, Lalonde et al 2021) or only changing the energies of the spots (Botas et al 2018).However, our findings were that spot addition was necessary to achieve dose distributions with acceptable target coverages and acceptable maximum doses in targets and surroundings.This is related to the imposed dosimetric constraints on target coverage in our strategy.Contrary to our findings, imposed constraints on target coverage in Lalonde et al (2021) without the use of spot addition resulted in acceptable near-maximum doses in the high-dose CTV.Possibly, this is related to their larger number of spots in original treatment plans, the omission of robust optimization and evaluation, or a different degree of variability in patient anatomies.Although the near-maximum doses with our online reoptimization strategy were still slightly higher compared to offline TB re-planning, it may not be clinically relevant to further improve these.
In our comparisons, the clinical trigger for offline re-planning was based on plans generated with a 5 mm setup robustness setting while we used 3 mm setup robustness settings as this complies with current standard clinical care of H&N proton treatment in the Netherlands.This may have contributed to a relatively lower coverage in the trigger-based offline adaptive approach.For both strategies, all treatment plans were generated with Erasmus-iCycle, intentionally omitting the use of the clinical treatment plan.The rationale behind this decision was to allow for fully-automated plan generation for both adaptive strategies and to keep optimization differences between the strategies minimal, e.g. using the same dose calculation algorithm, the same implementation of cost functions, etc. Employing treatment plan generation with identical optimization settings (except the setup robustness setting) ensured a systematic and consistent dosimetric evaluation.Erasmus-iCycle generates treatment plans with comparableto-better quality compared to clinical treatment plans, as shown by Huiskes et al (2023).
Our comparison of online re-optimization and offline TB re-planning was based on 3-6 repeat-CTs per patient, while other studies (table 1) performed their analyzes of online re-optimization using corrected CBCTs.A limitation of our study was that evaluating with a limited number of repeat-CTs may have led to the possibility that offline adaptations were initiated earlier in clinical practice, potentially resulting in an overrepresentation of the number of fractions with inadequate target coverage in this study.On the other hand, corrected CBCTs provide daily information on the anatomy.However, HU in corrected CBCTs are less accurate compared to repeat-CTs (Park et al 2015, Lalonde et al 2020, Thummerer et al 2020).Therefore, using corrected CBCT also introduces potential bias because online re-optimization will compensate for inaccuracies in HU in contrast to offline re-planning.
This study only compared single-fraction delivered doses.For interpretability, fraction doses were multiplied by the number of fractions during the complete treatment.Analyzes of accumulated dose would provide insight in the total delivered dose during the treatment.Currently, single-fraction dosimetric constraints in adaptive treatments are not available.Accumulated doses, in combination with comparisons to current clinically applied strategies, could potentially aid in determining whether the obtained coverage with online re-optimization is adequate.Investigation of accumulated dose was hampered in this study by manual contour adjustments that invalidated deformable vector fields obtained from HU matching.
The contours that were used on the repeat-CTs were obtained by automatic propagation of planning-CT contours, followed by manual correction in case of observed inaccuracies.Editing of the automatically propagated contours was performed to enhance the accuracy of the performed dosimetric analyzes for the comparison of online re-optimization with offline TB re-planning.In an online setting, available time for editing may be limited.Further enhancement of image quality and contour propagation algorithms may limit the time needed for editing.Possibly, the dosimetric impact of using non-edited or minimally-edited contours for online adaptive IMPT obtained from propagation or AI-based solutions is small and only CTV contours may require manual adjustments (Guo et al 2021, Smolders et al 2023).
In this study, the impact of inter and intra-observer variations in contouring on planning and repeat-CTs was ignored during simulations.Inter and intra-observer variations in target volume delineations are one of the largest contributors to variations in dose delivery (Barbara Segedin 2016, Apolle et al 2019, van der Veen et al 2019, Nash et al 2022).Furthermore, contouring on repeat-CTs without MRI also introduces extra uncertainty as the target is not always well visible.
Implementation of this online re-optimization strategy requires not only fast re-optimization, high quality imaging, and appropriate contours, but also fast online QA procedures, which are currently unavailable in clinical settings.However, recent advancements in independent dose computations and log-file-based QA strategies have been made (Li et al 2013, Meier et al 2015, Meijers et al 2020, Burlacu et al 2023).Clinical application of online adaptive approaches also requires fast dose computation algorithms.Fortunately, algorithms that provide fast dose computations are becoming available (Pastor-Serrano and Perkó 2022).

Conclusion
In this study, we introduced a fast and fully automated online robust re-optimization strategy for daily adaptation of initial treatment plans to cope with day-to-day anatomical variations for H&N IMPT.Hard constraints and spot addition were used to maintain adequate CTV dose.Based on a comprehensive robustness evaluation, we conclude that substantial loss of target coverage, as observed with our current clinical triggerbased offline adaptive (offline TB re-planning) strategy, could be fully avoided with the online re-optimization strategy, while using small setup robustness settings.This resulted in improved OAR doses and reduced NTCPs compared to offline TB re-planning.

Figure 1 .
Figure 1.Slices of an example repeat-CT (#38 in figure 3), showing the dose distribution corresponding to the scenario having the 90%-worst-case D 98% among the 10 000 simulated fractions for the CTV 5425 in the trigger-based offline re-planning (offline TB replanning) strategy.The arrow in the upper left panel points at an underdose in CTV 5425 with the offline TB re-planning strategy, while proper dose is delivered with online re-optimization (upper right).Arrows in the lower panels point at too wide high dose delivery around CTV 7000 with offline TB re-planning, which does not happen with online re-optimization.

Figure 2 .
Figure 2.For the example repeat-CT in figure 1, histograms showing distributions of D 98% values in the 10.000 polynomial chaos expansion (PCE) dose distributions (a) and the corresponding D 98% -histogram.(b) Points A1-4 are discussed in the text.

Figure 4 .
Figure 4.For the population of 67 repeat-CTs, D 98% -(a) and D 2% -(b) cumulative histograms obtained from the 10.000 PCE dose distributions for each of the repeat-CT scans.For each of the CTVs, the construction of the presented cumulative histograms started by establishing the cumulative histogram for each repeat-CT separately.Next, the 95%, 90%, 85%, and 5% of these 67 cumulative histograms were taken and displayed.Points B1-4, C1-4 and D1-2 are discussed in the text.

Figure 5 .
Figure 5. Differences between online re-optimization and trigger-based offline adaptive planning (offline TB re-planning) in (top) OAR mean doses and (bottom) resulting NTCPs.Box plots show distributions for the 67 evaluated repeat-CTs, every dot indicates a repeat-CT.Whiskers extend to the 10th and 90th percentiles of the distributions.All differences in OAR mean doses and in NTCPs were statistically significant with p < 10 5 .