Yet another dose algorithm (YODA) for independent computations of dose and dose changes due to anatomical changes.

Objective:To assess the viability of a physics-based, deterministic and adjoint-capable algorithm for performing treatment planning system independent dose calculations and for computing dosimetric differences caused by anatomical changes. Approach:A semi-numerical approach is employed to solve two partial differential equations for the proton phase-space density which determines the deposited dose. Lateral hetereogeneities are accounted for by an optimized (Gaussian) beam splitting scheme. Adjoint theory is applied to approximate the change in the deposited dose caused by a new underlying patient anatomy. Main results:The quality of the dose engine was benchmarked through three-dimensional gamma index comparisons against Monte Carlo simulations done in TOPAS. The worst passing rate for the gamma index with (1 mm, 1 %, 10 % dose cut-off) criteria is 94.55 %. The effect of delivering treatment plans on repeat CTs was also tested. For a non-robustly optimized plan the adjoint component was accurate to 5.7 % while for a robustly optimized plan it was accurate to 4.8 %. Significance:YODA is capable of accurate dose computations in both single and multi spot irradiations when compared to TOPAS. Moreover, it is able to compute dosimetric differences due to anatomical changes with small to moderate errors thereby facilitating its use for patient-specific quality assurance in online adaptive proton therapy.

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 (offlineTBre-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 offlineTBre-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, offlineTBre-planning resulted in <50% probability ofD98%≥ 95% of the prescribed dose (Dpres) in one or both CTVs, which never happened with online re-optimization. With offlineTBre-planning, eight repeat-CTs had zero probability of obtainingD98%≥ 95%Dpresfor 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< 10-5for 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.

Robustness analysis of CTV and OAR dose in clinical PBS-PT of neuro-oncological tumors: prescription-dose calibration and inter-patient variation with the Dutch proton robustness evaluation protocol.

Objective. The Dutch proton robustness evaluation protocol prescribes the dose of the clinical target volume (CTV) to the voxel-wise minimum (VWmin) dose of 28 scenarios. This results in a consistent but conservative near-minimum CTV dose (D98%,CTV). In this study, we analyzed (i) the correlation between VWmin/voxel-wise maximum (VWmax) metrics and actually delivered dose to the CTV and organs at risk (OARs) under the impact of treatment errors, and (ii) the performance of the protocol before and after its calibration with adequate prescription-dose levels.Approach. Twenty-one neuro-oncological patients were included. Polynomial chaos expansion was applied to perform a probabilistic robustness evaluation using 100,000 complete fractionated treatments per patient. Patient-specific scenario distributions of clinically relevant dosimetric parameters for the CTV and OARs were determined and compared to clinical VWmin and VWmax dose metrics for different scenario subsets used in the robustness evaluation protocol.Main results. The inclusion of more geometrical scenarios leads to a significant increase of the conservativism of the protocol in terms of clinical VWmin and VWmax values for the CTV and OARs. The protocol could be calibrated using VWmin dose evaluation levels of 93.0%-92.3%, depending on the scenario subset selected. Despite this calibration of the protocol, robustness recipes for proton therapy showed remaining differences and an increased sensitivity to geometrical random errors compared to photon-based margin recipes.Significance. The Dutch proton robustness evaluation protocol, combined with the photon-based margin recipe, could be calibrated with a VWmin evaluation dose level of 92.5%. However, it shows limitations in predicting robustness in dose, especially for the near-maximum dose metrics to OARs. Consistent robustness recipes could improve proton treatment planning to calibrate residual differences from photon-based assumptions.

PTV-based VMAT vs. robust IMPT for head-and-neck cancer: A probabilistic uncertainty analysis of clinical plan evaluation with the Dutch model-based selection.

BACKGROUND AND PURPOSE: In the Netherlands, head-and-neck cancer (HNC) patients are referred for proton therapy (PT) through model-based selection (MBS). However, treatment errors may compromise adequate CTV dose. Our aims are: (i) to derive probabilistic plan evaluation metrics on the CTV consistent with clinical metrics; (ii) to evaluate plan consistency between photon (VMAT) and proton (IMPT) planning in terms of CTV dose iso-effectiveness and (iii) to assess the robustness of the OAR doses and of the risk toxicities involved in the MBS. MATERIALS AND METHODS: Sixty HNC plans (30 IMPT/30 VMAT) were included. A robustness evaluation with 100,000 treatment scenarios per plan was performed using Polynomial Chaos Expansion (PCE). PCE was applied to determine scenario distributions of clinically relevant dosimetric parameters, which were compared between the 2 modalities. Finally, PCE-based probabilistic dose parameters were derived and compared to clinical PTV-based photon and voxel-wise proton evaluation metrics. RESULTS: Probabilistic dose to near-minimum volume v = 99.8% for the CTV correlated best with clinical PTV-D98% and VWmin-D98%,CTV doses for VMAT and IMPT respectively. IMPT showed slightly higher nominal CTV doses, with an average increase of 0.8 GyRBE in the median of the D99.8%,CTV distribution. Most patients qualified for IMPT through the dysphagia grade II model, for which an average NTCP gain of 10.5 percentages points (%-point) was found. For all complications, uncertainties resulted in moderate NTCP spreads lower than 3 p.p. on average for both modalities. CONCLUSION: Despite the differences between photon and proton planning, the comparison between PTV-based VMAT and robust IMPT is consistent. Treatment errors had a moderate impact on NTCPs, showing that the nominal plans are a good estimator to qualify patients for PT.

A probabilistic deep learning model of inter-fraction anatomical variations in radiotherapy.

Objective. In radiotherapy, the internal movement of organs between treatment sessions causes errors in the final radiation dose delivery. To assess the need for adaptation, motion models can be used to simulate dominant motion patterns and assess anatomical robustness before delivery. Traditionally, such models are based on principal component analysis (PCA) and are either patient-specific (requiring several scans per patient) or population-based, applying the same set of deformations to all patients. We present a hybrid approach which, based on population data, allows to predict patient-specific inter-fraction variations for an individual patient.Approach. We propose a deep learning probabilistic framework that generates deformation vector fields warping a patient's planning computed tomography (CT) into possible patient-specific anatomies. This daily anatomy model (DAM) uses few random variables capturing groups of correlated movements. Given a new planning CT, DAM estimates the joint distribution over the variables, with each sample from the distribution corresponding to a different deformation. We train our model using dataset of 312 CT pairs with prostate, bladder, and rectum delineations from 38 prostate cancer patients. For 2 additional patients (22 CTs), we compute the contour overlap between real and generated images, and compare the sampled and 'ground truth' distributions of volume and center of mass changes.Results. With a DICE score of 0.86 ± 0.05 and a distance between prostate contours of 1.09 ± 0.93 mm, DAM matches and improves upon previously published PCA-based models, using as few as 8 latent variables. The overlap between distributions further indicates that DAM's sampled movements match the range and frequency of clinically observed daily changes on repeat CTs.Significance. Conditioned only on planning CT values and organ contours of a new patient without any pre-processing, DAM can accurately deformations seen during following treatment sessions, enabling anatomically robust treatment planning and robustness evaluation against inter-fraction anatomical changes.

Sub-second photon dose prediction via transformer neural networks.

BACKGROUND: Fast dose calculation is critical for online and real-time adaptive therapy workflows. While modern physics-based dose algorithms must compromise accuracy to achieve low computation times, deep learning models can potentially perform dose prediction tasks with both high fidelity and speed. PURPOSE: We present a deep learning algorithm that, exploiting synergies between transformer and convolutional layers, accurately predicts broad photon beam dose distributions in few milliseconds. METHODS: The proposed improved Dose Transformer Algorithm (iDoTA) maps arbitrary patient geometries and beam information (in the form of a 3D projected shape resulting from a simple ray tracing calculation) to their corresponding 3D dose distribution. Treating the 3D CT input and dose output volumes as a sequence of 2D slices along the direction of the photon beam, iDoTA solves the dose prediction task as sequence modeling. The proposed model combines a Transformer backbone routing long-range information between all elements in the sequence, with a series of 3D convolutions extracting local features of the data. We train iDoTA on a dataset of 1700 beam dose distributions, using 11 clinical volumetric modulated arc therapy (VMAT) plans (from prostate, lung, and head and neck cancer patients with 194-354 beams per plan) to assess its accuracy and speed. RESULTS: iDoTA predicts individual photon beams in ≈50 ms with a high gamma pass rate of 97.72 ± 1.93 % $97.72\pm 1.93\%$ (2 mm, 2%). Furthermore, estimating full VMAT dose distributions in 6-12 s, iDoTA achieves state-of-the-art performance with a 99.51 ± 0.66 % $99.51\pm 0.66\%$ (2 mm, 2%) pass rate and an average relative dose error of 0.75 ± 0.36%. CONCLUSIONS: Offering the millisecond speed prediction per beam angle needed in online and real-time adaptive treatments, iDoTA represents a new state of the art in data-driven photon dose calculation. The proposed model can massively speed-up current photon workflows, reducing calculation times from few minutes to just a few seconds.

An online adaptive plan library approach for intensity modulated proton therapy for head and neck cancer.

BACKGROUND AND PURPOSE: In intensity modulated proton therapy (IMPT), the impact of setup errors and anatomical changes is commonly mitigated by robust optimization with population-based setup robustness (SR) settings and offline replanning. In this study we propose and evaluate an alternative approach based on daily plan selection from patient-specific pre-treatment established plan libraries (PLs). Clinical implementation of the PL strategy would be rather straightforward compared to daily online re-planning. MATERIALS AND METHODS: For 15 head-and-neck cancer patients, the planning CT was used to generate a PL with 5 plans, robustly optimized for increasing SR: 0, 1, 2, 3, 5 mm, and 3% range robustness. Repeat CTs (rCTs) and realistic setup and range uncertainty distributions were used for simulation of treatment courses for the PL approach, treatments with fixed SR (fSR3) and a trigger-based offline adaptive schedule for 3 mm SR (fSR3OfA). Daily plan selection in the PL approach was based only on recomputed dose to the CTV on the rCT. RESULTS: Compared to using fSR3 and fSR3OfA, the risk of xerostomia grade ≥ II & III and dysphagia ≥ grade III were significantly reduced with the PL. For 6/15 patients the risk of xerostomia and/or dysphagia ≥ grade II could be reduced by > 2% by using PL. For the other patients, adherence to target coverage constraints was often improved. fSR3OfA resulted in significantly improved coverage compared to PL for selected patients. CONCLUSION: The proposed PL approach resulted in overall reduced NTCPs compared to fSR3 and fSR3OfA at limited cost in target coverage.

Millisecond speed deep learning based proton dose calculation with Monte Carlo accuracy.

Objective.Next generation online and real-time adaptive radiotherapy workflows require precise particle transport simulations in sub-second times, which is unfeasible with current analytical pencil beam algorithms (PBA) or Monte Carlo (MC) methods. We present a deep learning based millisecond speed dose calculation algorithm (DoTA) accurately predicting the dose deposited by mono-energetic proton pencil beams for arbitrary energies and patient geometries.Approach.Given the forward-scattering nature of protons, we frame 3D particle transport as modeling a sequence of 2D geometries in the beam's eye view. DoTA combines convolutional neural networks extracting spatial features (e.g. tissue and density contrasts) with a transformer self-attention backbone that routes information between the sequence of geometry slices and a vector representing the beam's energy, and is trained to predict low noise MC simulations of proton beamlets using 80 000 different head and neck, lung, and prostate geometries.Main results.Predicting beamlet doses in 5 ± 4.9 ms with a very high gamma pass rate of 99.37 ± 1.17% (1%, 3 mm) compared to the ground truth MC calculations, DoTA significantly improves upon analytical pencil beam algorithms both in precision and speed. Offering MC accuracy 100 times faster than PBAs for pencil beams, our model calculates full treatment plan doses in 10-15 s depending on the number of beamlets (800-2200 in our plans), achieving a 99.70 ± 0.14% (2%, 2 mm) gamma pass rate across 9 test patients.Significance.Outperforming all previous analytical pencil beam and deep learning based approaches, DoTA represents a new state of the art in data-driven dose calculation and can directly compete with the speed of even commercial GPU MC approaches. Providing the sub-second speed required for adaptive treatments, straightforward implementations could offer similar benefits to other steps of the radiotherapy workflow or other modalities such as helium or carbon treatments.

How should we model and evaluate breathing interplay effects in IMPT?

Breathing interplay effects in Intensity Modulated Proton Therapy (IMPT) arise from the interaction between target motion and the scanning beam. Assessing the detrimental effect of interplay and the clinical robustness of several mitigation techniques requires statistical evaluation procedures that take into account the variability of breathing during dose delivery. In this study, we present such a statistical method to model intra-fraction respiratory motion based on breathing signals and assess clinical relevant aspects related to the practical evaluation of interplay in IMPT such as how to model irregular breathing, how small breathing changes affect the final dose distribution, and what is the statistical power (number of different scenarios) required for trustworthy quantification of interplay effects. First, two data-driven methodologies to generate artificial patient-specific breathing signals are compared: a simple sinusoidal model, and a precise probabilistic deep learning model generating very realistic samples of patient breathing. Second, we investigate the highly fluctuating relationship between interplay doses and breathing parameters, showing that small changes in breathing period result in large local variations in the dose. Our results indicate that using a limited number of samples to calculate interplay statistics introduces a bigger error than using simple sinusoidal models based on patient parameters or disregarding breathing hysteresis during the evaluation. We illustrate the power of the presented statistical method by analyzing interplay robustness of 4DCT and Internal Target Volume (ITV) treatment plans for a 8 lung cancer patients, showing that, unlike 4DCT plans, even 33 fraction ITV plans systematically fail to fulfill robustness requirements.

Accurate assessment of a Dutch practical robustness evaluation protocol in clinical PT with pencil beam scanning for neurological tumors.

BACKGROUND AND PURPOSE: Scenario-based robust optimization and evaluation are commonly used in proton therapy (PT) with pencil beam scanning (PBS) to ensure adequate dose to the clinical target volume (CTV). However, a statistically accurate assessment of the clinical application of this approach is lacking. In this study, we assess target dose in a clinical cohort of neuro-oncological patients, planned according to the DUPROTON robustness evaluation consensus, using polynomial chaos expansion (PCE). MATERIALS AND METHODS: A cohort of the first 27 neuro-oncological patients treated at HollandPTC was used, including realistic error distributions derived from geometrical and stopping-power prediction (SPP) errors. After validating the model, PCE-based robustness evaluations were performed by simulating 100.000 complete fractionated treatments per patient to obtain accurate statistics on clinically relevant dosimetric parameters and population-dose histograms. RESULTS: Treatment plans that were robust according to clinical protocol and treatment plansin which robustness was sacrificed are easily identified. For robust treatment plans on average, a CTV dose of 3 percentage points (p.p.) more than prescribed was realized (range +2.7 p.p. to +3.5 p.p.) for 98% of the sampled fractionated treatments. For the entire patient cohort on average, a CTV dose of 0.1 p.p. less than prescribed was achieved (range -2.4 p.p. to +0.5 p.p.). For the 6 treatment plans in which robustness was clinically sacrificed, normalized CTV doses of 0.98, 0.94(7)1, 0.94, 0.91, 0.90 and 0.89 were realized. The first of these was clinically borderline non-robust. CONCLUSION: The clinical robustness evaluation protocol is safe in terms of CTV dose as all plans that fulfilled the clinical robustness criteria were also robust in the PCE evaluation. Moreover, for plans that were non-robust in the PCE-based evaluation, CTV dose was also lower than prescribed in the clinical evaluation.

A semi-supervised autoencoder framework for joint generation and classification of breathing.

BACKGROUND AND OBJECTIVE: One of the main problems with biomedical signals is the limited amount of patient-specific data and the significant amount of time needed to record the sufficient number of samples needed for diagnostic and treatment purposes. In this study, we present a framework to simultaneously generate and classify biomedical time series based on a modified Adversarial Autoencoder (AAE) algorithm and one-dimensional convolutions. Our work is based on breathing time series, with specific motivation to capture breathing motion during radiotherapy lung cancer treatments. METHODS: First, we explore the potential in using the Variational Autoencoder (VAE) and AAE algorithms to model breathing signals from individual patients. We then extend the AAE algorithm to allow joint semi-supervised classification and generation of different types of signals within a single framework. To simplify the modeling task, we introduce a pre-processing and post-processing compressing algorithm that transforms the multi-dimensional time series into vectors containing time and position values, which are transformed back into time series through an additional neural network. RESULTS: The resulting models are able to generate realistic and varied samples of breathing. By incorporating 4% and 12% of the labeled samples during training, our model outperforms other purely discriminative networks in classifying breathing baseline shift irregularities from a dataset completely different from the training set, achieving an average macro F1-score of 94.91% and 96.54%, respectively. CONCLUSION: To our knowledge, the presented framework is the first approach that unifies generation and classification within a single model for this type of biomedical data, enabling both computer aided diagnosis and augmentation of labeled samples within a single framework.

Technical Note: Investigating interplay effects in pencil beam scanning proton therapy with a 4D XCAT phantom within the RayStation treatment planning system.

PURPOSE: Pencil beam scanning (PBS) for moving targets is known to be impacted by interplay effects. Four-dimensional computed tomography (4DCT)-based motion evaluation is crucial for understanding interplay and developing mitigation strategies. Availability of high-quality 4DCTs with variable breathing traces is limited. Purpose of this work is the development of a framework for interplay analysis using 4D-XCAT phantoms in conjunction with time-resolved irradiation patterns in a commercial treatment planning system (TPS). Four-dimensional dynamically accumulated dose distributions (4DDDs) are simulated in an in-silico study for a PBS liver treatment. METHODS: An XCAT phantom with 50 phases, varying linearly in amplitude each by 1 mm, was combined with the RayStation TPS (7.99.10). Deformable registration was used with time-resolved dose calculation, mapping XCAT phases to motion signals. To illustrate the applicability of the method a two-field liver irradiation plan was used. A variety sin4 type motion signals, varying in amplitude (1-20 mm), period (1.6-5.2 s) and phase (0-2π) were applied. Either single variable variations or random combinations were selected. The interplay effect within a clinical target (5 cm diameter) was characterized in terms of homogeneity index (HI5), with and without five paintings. In total 2092 scenarios were analyzed within RayStation. RESULTS: A framework is presented for interplay research, allowing for flexibility in determining motion management techniques, increasing reproducibility, and enabling comparisons of different methods. A case study showed the interplay effect was correlated with amplitude and strongly affected by the starting phase, leading to large variance. The average of all scenarios (single fraction) resulted in HI5 of 0.31 (±0.11), while introduction of five times layered repainting reduced this to 0.11(±0.03). CONCLUSION: The developed framework, which uses the XCAT phantom and RayStation, allows detailed analysis of motion in context of PBS with comparable results to clinical cases. Flexibility in defining motion patterns for detailed anatomies in combination with time-resolved dose calculation, facilitates investigation of optimal treatment and motion mitigation strategies.

Fast and fully-automated multi-criterial treatment planning for adaptive HDR brachytherapy for locally advanced cervical cancer.

PURPOSE: To develop and evaluate a fast, automated multi-criterial treatment planning approach for adaptive high-dose-rate (HDR) intracavitary + interstitial brachytherapy (BT) for locally advanced cervical cancer. METHODS AND MATERIALS: Twenty-two previously delivered single fraction MRI-based HDR treatment plans (SFclin) were used to guide training of our in-house system for multi-criterial autoplanning, aiming for an autoplan quality superior to the training plans, while respecting the clinically desired "pear-shaped" dose distribution. Next, the configured algorithm was used to automatically generate treatment plans for 63 other fractions (SFauto). The SFauto plans were compared to the corresponding SFclin plans in blind pairwise comparisons by an expert clinician. Then, the effect of adaptive autoplanning on total treatment (TT) plans (external beam + 3 BT fractions) was evaluated for 16 patients by simulating the clinically applied adaptive strategy to generate TTauto plans and compare them with the corresponding clinical treatments (TTclin). RESULTS: In the blind comparisons, all SFauto plans were considered clinically acceptable. In 62/63 comparisons, SFauto plans were considered at least as good as, or better than the corresponding SFclin. The average optimization time for autoplanning was 20.5 ± 19.2 s (range 4.4-106.4 s) per plan. In 14 of 16 TTauto plans, the desired total dose of 90 Gy (EQD2) was obtained, compared to only 9 in the corresponding TTclin, while autoplanning also decreased bladder and rectum doses. CONCLUSIONS: Fast, fully-automated multi-criterial treatment planning for adaptive HDR-BT for locally advanced cervical cancer is feasible. Autoplans were superior to corresponding clinical plans.

The Relative Biological Effect of Spread-Out Bragg Peak Protons in Sensitive and Resistant Tumor Cells.

PURPOSE: Variations in the radiosensitivity of tumor cells within and between tumors impact tumor response to radiation, including the dose required to achieve permanent local tumor control. The increased expression of DNA-PKcs, a key component of a major DNA damage repair pathway in tumors treated by radiation, suggests that DNA-PKcs-dependent repair is likely a cause of tumor cell radioresistance. This study evaluates the relative biological effect of spread-out Bragg-peak protons in DNA-PKcs-deficient cells and the same cells transfected with a functional DNA-PKcs gene. MATERIALS AND METHODS: A cloned radiation-sensitive DNA-PKcs-deficient tumor line and its DNA-PKcs-transfected resistant counterpart were used in this study. The presence of functional DNA-PKcs was evaluated by DNA-PKcs autophosphorylation. Cells to be proton irradiated or x-irradiated were obtained from the same single cell suspension and dilution series to maximize precision. Cells were concurrently exposed to 6-MV x-rays or mid 137-MeV spread-out Bragg peak protons and cultured for colony formation. RESULTS: The surviving fraction data were well fit by the linear-quadratic model for each of 8 survival curves. The results suggest that the relative biological effectiveness of mid spread-out Bragg peak protons is approximately 6% higher in DNA-PKcs-mediated resistant tumor cells than in their DNA-PKcs-deficient and radiation-sensitive counterpart. CONCLUSION: DNA-PKcs-dependent repair of radiation damage is less capable of repairing mid spread-out Bragg peak proton lesions than photon-induced lesions, suggesting protons may be more efficient at sterilizing DNA-PKcs-expressing cells that are enriched in tumors treated by conventional fractionated dose x-irradiation.

Derivation of mean dose tolerances for new fractionation schemes and treatment modalities.

Avoiding toxicities in radiotherapy requires the knowledge of tolerable organ doses. For new, experimental fractionation schemes (e.g. hypofractionation) these are typically derived from traditional schedules using the biologically effective dose (BED) model. In this report we investigate the difficulties of establishing mean dose tolerances that arise since the mean BED depends on the entire spatial dose distribution, rather than on the dose level alone. A formula has been derived to establish mean physical dose constraints such that they are mean BED equivalent to a reference treatment scheme. This formula constitutes a modified BED equation where the influence of the spatial dose distribution is summarized in a single parameter, the dose shape factor. To quantify effects we analyzed 24 liver cancer patients for whom both proton and photon IMRT treatment plans were available. The results show that the standard BED equation-neglecting the spatial dose distribution-can overestimate mean dose tolerances for hypofractionated treatments by up to 20%. The shape difference between photon and proton dose distributions can cause 30-40% differences in mean physical dose for plans having identical mean BEDs. Converting hypofractionated, 5/15-fraction proton doses to mean BED equivalent photon doses in traditional 35-fraction regimens resulted in up to 10 Gy higher doses than applying the standard BED formula. The dose shape effect should be accounted for to avoid overestimation of mean dose tolerances, particularly when estimating constraints for hypofractionated regimens. Additionally, tolerances established for one treatment modality cannot necessarily be applied to other modalities with drastically different dose distributions, such as proton therapy. Last, protons may only allow marginal (5-10%) dose escalation if a fraction-size adjusted organ mean dose is constraining instead of a physical dose.

Fast and accurate sensitivity analysis of IMPT treatment plans using Polynomial Chaos Expansion.

The highly conformal planned dose distribution achievable in intensity modulated proton therapy (IMPT) can severely be compromised by uncertainties in patient setup and proton range. While several robust optimization approaches have been presented to address this issue, appropriate methods to accurately estimate the robustness of treatment plans are still lacking. To fill this gap we present Polynomial Chaos Expansion (PCE) techniques which are easily applicable and create a meta-model of the dose engine by approximating the dose in every voxel with multidimensional polynomials. This Polynomial Chaos (PC) model can be built in an automated fashion relatively cheaply and subsequently it can be used to perform comprehensive robustness analysis. We adapted PC to provide among others the expected dose, the dose variance, accurate probability distribution of dose-volume histogram (DVH) metrics (e.g. minimum tumor or maximum organ dose), exact bandwidths of DVHs, and to separate the effects of random and systematic errors. We present the outcome of our verification experiments based on 6 head-and-neck (HN) patients, and exemplify the usefulness of PCE by comparing a robust and a non-robust treatment plan for a selected HN case. The results suggest that PCE is highly valuable for both research and clinical applications.

Robustness Recipes for Minimax Robust Optimization in Intensity Modulated Proton Therapy for Oropharyngeal Cancer Patients.

PURPOSE: We aimed to derive a "robustness recipe" giving the range robustness (RR) and setup robustness (SR) settings (ie, the error values) that ensure adequate clinical target volume (CTV) coverage in oropharyngeal cancer patients for given gaussian distributions of systematic setup, random setup, and range errors (characterized by standard deviations of Σ, σ, and ρ, respectively) when used in minimax worst-case robust intensity modulated proton therapy (IMPT) optimization. METHODS AND MATERIALS: For the analysis, contoured computed tomography (CT) scans of 9 unilateral and 9 bilateral patients were used. An IMPT plan was considered robust if, for at least 98% of the simulated fractionated treatments, 98% of the CTV received 95% or more of the prescribed dose. For fast assessment of the CTV coverage for given error distributions (ie, different values of Σ, σ, and ρ), polynomial chaos methods were used. Separate recipes were derived for the unilateral and bilateral cases using one patient from each group, and all 18 patients were included in the validation of the recipes. RESULTS: Treatment plans for bilateral cases are intrinsically more robust than those for unilateral cases. The required RR only depends on the ρ, and SR can be fitted by second-order polynomials in Σ and σ. The formulas for the derived robustness recipes are as follows: Unilateral patients need SR = -0.15Σ(2) + 0.27σ(2) + 1.85Σ - 0.06σ + 1.22 and RR=3% for ρ = 1% and ρ = 2%; bilateral patients need SR = -0.07Σ(2) + 0.19σ(2) + 1.34Σ - 0.07σ + 1.17 and RR=3% and 4% for ρ = 1% and 2%, respectively. For the recipe validation, 2 plans were generated for each of the 18 patients corresponding to Σ = σ = 1.5 mm and ρ = 0% and 2%. Thirty-four plans had adequate CTV coverage in 98% or more of the simulated fractionated treatments; the remaining 2 had adequate coverage in 97.8% and 97.9%. CONCLUSIONS: Robustness recipes were derived that can be used in minimax robust optimization of IMPT treatment plans to ensure adequate CTV coverage for oropharyngeal cancer patients.