Background and purpose: In online-adaptive proton therapy planning based on cone beam computed tomography (CBCT), CT number errors can pose challenges. We propose an approach for coping with CT number uncertainties by increasing range robustness settings (RRS) in online-adaptive planning. This was compared to our trigger-based offline (TB-Offline) adaptive approach, and to daily replanning using in-room CT-on-rails (CTOR). Material and methods: For 23 head-and-neck cancer patients, a CTOR and CBCT were acquired in a single fraction. CTOR contours were copied rigidly onto the CBCT. CBCT-based plans were generated with 3, 6, 8, 10, and 12 % RRS, each with 1 mm setup-RS, followed by a forward dose calculation on the reference CTOR. This was compared to dose distributions from our TB-Offline approach (3 mm/3% SRS/RRS), also recomputed on the CTOR. Coverage (voxelwise-minimum) of the primary clinical target volume (CTV₇₀₀₀) and elective lymph nodes (CTV₅₄₂₅) and grade ≥ II normal tissue complication probabilities were compared between strategies. Results: When going from RRS = 3 % to RRS = 10 %, the population 90th percentiles of CTV₅₄₂₅ V_94% improved from 89.6 % to 96.4 %, and CTV₇₀₀₀ V_94% from 92.8 % to 96.4 %. Substantial coverage loss (V_94%<95 %) with CBCT-based online adaptive and RRS = 10 % was observed in 1/23 evaluated patients for CTV₇₀₀₀ and 2/23 for CTV₅₄₂₅. This was an improvement compared to 3/23 and 4/23 with TB-Offline. Moreover, for RRS = 10 % the average risk of xerostomia improved by 2.4 percentage point compared to TB-Offline. Conclusions: Robust optimization with increased range robustness settings effectively mitigated dose degradation from CT number errors in CBCT-based online-adaptive proton therapy.

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Objective. To assess the performance of a probabilistic deep learning based algorithm for predicting inter-fraction anatomical changes in head and neck patients. Approach. A probabilistic daily anatomy model (DAM) for head and neck patients DAM (DAMHN) is built on the variational autoencoder architecture. The model approximates the generative joint conditional probability distribution of the repeat computed tomography (rCT) images and their corresponding masks on the planning CT images (pCT) and their masks. The model outputs deformation vector fields, which are used to produce possible rCTs and associated masks. The dataset is composed of 93 patients (i.e. 315 pCT–rCT pairs), 9 (i.e. 27 pairs) of which were set aside for final testing. The performance of the model is assessed based on the reconstruction accuracy and the generative performance for the set aside patients. Main results. The model achieves a DICE score of 0.83 and an image similarity score normalized cross-correlation of 0.60 on the test set. The generated parotid glands, spinal cord and constrictor muscle volume change distributions and center of mass shift distributions were also assessed. For all organs, the medians of the distributions are close to the true ones, and the distributions are broad enough to encompass the real observed changes. Moreover, the generated images display anatomical changes in line with the literature reported ones, such as the medial shifts of the parotids glands. Significance. DAMHN is capable of generating realistic anatomies observed during the course of the treatment and has applications in anatomical robust optimization, treatment planning based on plan library approaches and robustness evaluation against inter-fractional changes.@en

Background and purpose: In the Netherlands, 2 protocols have been standardized for PT among the 3 proton centers: a robustness evaluation (RE) to ensure adequate CTV dose and a model-based selection (MBS) approach for IMPT patient-selection. This multi-institutional study investigates (i) inter-patient and inter-center variation of target dose from the RE protocol and (ii) the robustness of the MBS protocol against treatment errors for a cohort of head-and-neck cancer (HNC) patients treated in the 3 Dutch proton centers. Materials and methods: Clinical treatment plans of 100 HNC patients were evaluated. Polynomial Chaos Expansion (PCE) was used to perform a comprehensive robustness evaluation per plan, enabling the probabilistic evaluation of 100,000 complete fractionated treatments. PCE allowed to derive scenario distributions of clinically relevant dosimetric parameters to assess CTV dose (D_99.8%/D_0.2%, based on a prior photon plan calibration) and tumour control probabilities (TCP) as well as the evaluation of the dose to OARs and normal tissue complication probabilities (NTCP) per center. Results: For the CTV_70.00, doses from the RE protocol were consistent with the clinical plan evaluation metrics used in the 3 centers. For the CTV_54.25, D_99.8% were consistent with the clinical plan evaluation metrics at center 1 and 2 while, for center 3, a reduction of 1 GyRBE was found on average. This difference did not impact modelled TCP at center 3. Differences between expected and nominal NTCP were below 0.3 percentage point for most patients. Conclusion: The standardization of the RE and MBS protocol lead to comparable results in terms of TCP and the NTCPs. Still, significant inter-patient and inter-center variation in dosimetric parameters remained due to clinical practice differences at each institution. The MBS approach is a robust protocol to qualify patients for PT.

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Introduction
In head-and-neck IMPT, trigger-based offline plan adaptation (Offline trigger-based) is often used. Our goal was to compare this to four alternative adaptive strategies for dosimetry, workload and treatment time, considering also foreseen further technological advancements, including anticipated automation.

Materials and methods
Alternative strategies included weekly offline re-planning (Offline weekly), daily plan selection from a library (Library static and Library progressive) and a fast, approximate daily online re-optimization approach (Online re-opt). Impact on CTV coverage and NTCPs was assessed by simulations based on repeat-CTs from 15 patients. Full daily re-planning was used as dosimetric benchmark. Increases in workload and treatment time were estimated.

Results
Both for coverage and NTCPs, fast Online re-opt performed as well as full re-planning. Compared to current practice, Online re-opt showed enhanced probabilities for high coverage, and resulted in reductions in grade ≥ II NTCPs of 4.6 ± 1.7 %-point for xerostomia and 4.2 ± 2.3 %-point for dysphagia. Offline weekly and library strategies did not show coverage enhancements and resulted in smaller NTCP improvements. Further automation can largely limit workload and treatment time increases. With anticipated further automation, adaptation-related workload of Offline weekly, Library static, Library progressive, and Online re-opt was expected to increase by 3, 8, 21, and 66 h for 35 fraction treatment courses compared to Offline trigger-based. The corresponding adaptation-related prolonged treatment times were estimated to be 0, 4, 6, and 29 min/fraction.

Conclusion
Online adaptive strategies could approach dosimetric quality of full re-planning at the cost of additional workload and prolonged treatment time compared to the current offline adaptive strategy. Automation needs to play a key role in making more complex adaptive approaches feasible.@en

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 (offline _TB 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 offline _TB 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, offline _TB 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 offline _TB re-planning, eight repeat-CTs had zero probability of obtaining D _98% ≥ 95%D _pres for CTV ₇₀₀₀, 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.

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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 dose engine’s accuracy was benchmarked through three-dimensional gamma index comparisons against Monte Carlo simulations done in TOPAS. For a lung test case, the worst passing rate 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 non-robustly optimized plans the adjoint component was accurate to 5.7% while for a robustly optimized plan it was accurate to 4.8%. Significance. Yet anOther Dose Algorithm 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.

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Radiation therapy plays a crucial role in cancer treatment, necessitating precise delivery of radiation to tumors while sparing healthy tissues over multiple days. Computed tomography (CT) is integral for treatment planning, offering electron density data crucial for accurate dose calculations. However, accurately representing patient anatomy is challenging, especially in adaptive radiotherapy, where CT is not acquired daily. Magnetic resonance imaging (MRI) provides superior soft-tissue contrast. Still, it lacks electron density information, while cone beam CT (CBCT) lacks direct electron density calibration and is mainly used for patient positioning.

Adopting MRI-only or CBCT-based adaptive radiotherapy eliminates the need for CT planning but presents challenges. Synthetic CT (sCT) generation techniques aim to address these challenges by using image synthesis to bridge the gap between MRI, CBCT, and CT. The SynthRAD2023 challenge was organized to compare synthetic CT generation methods using multi-center ground truth data from 1080 patients, divided into two tasks: (1) MRI-to-CT and (2) CBCT-to-CT. The evaluation included image similarity and dose-based metrics from proton and photon plans.

The challenge attracted significant participation, with 617 registrations and 22/17 valid submissions for tasks 1/2. Top-performing teams achieved high structural similarity indices (≥ 0.87/0.90) and gamma pass rates for photon (≥ 98.1%/99.0%) and proton (≥ 97.3%/97.0%) plans. However, no significant correlation was found between image similarity metrics and dose accuracy, emphasizing the need for dose evaluation when assessing the clinical applicability of sCT.

SynthRAD2023 facilitated the investigation and benchmarking of sCT generation techniques, providing insights for developing MRI-only and CBCT-based adaptive radiotherapy. It showcased the growing capacity of deep learning to produce high-quality sCT, reducing reliance on conventional CT for treatment planning.@en

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 (Formula presented.) (2 mm, 2%). Furthermore, estimating full VMAT dose distributions in 6–12 s, iDoTA achieves state-of-the-art performance with a (Formula presented.) (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.

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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-D_98% and VWmin-D_98%,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 D_99.8%,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.

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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.

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In this paper we propose a solution to the need for a fast particle transport algorithm in Online Adaptive Proton Therapy capable of cheaply, but accurately computing the changes in patient dose metrics as a result of changes in the system parameters. We obtain the proton phase-space density through the product of the numerical solution to the one-dimensional Fokker-Planck equation and the analytical solution to the Fermi-Eyges equation. Moreover, a corresponding adjoint system was derived and solved for the adjoint flux. The proton phase-space density together with the adjoint flux and the metric (chosen as the energy deposited by the beam in a variable region of interest) allowed assessing the accuracy of our algorithm to different perturbation ranges in the system parameters and regions of interest. The algorithm achieved negligible errors ((Formula presented.)) for small Hounsfield unit (HU) perturbation ranges (–40 HU to 40 HU) and small to moderate errors (3% to 17%)–in line with the well-known limitation of adjoint approaches–for large perturbation ranges (–400 HU to 400 HU) in the case of most clinical interest where the region of interest surrounds the Bragg peak. Given these results coupled with the capability of further improving the timing performance it can be concluded that our algorithm presents a viable solution for the specific purpose of Online Adaptive Proton Therapy.

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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.

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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.

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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.

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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.

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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.

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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.

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In this paper, we present a reduced-order modeling approach to study the Molten Salt Fast Reactor (MSFR). Our approach is nonintrusive and based on the proper orthogonal decomposition method. We include adaptivity in selecting the sampling points both in time and parameter space. Steady-state and transient analysis were both performed using the developed models. In the steady-state analysis, we capture the effect of 30 model parameters on the spatial distributions of fission power and temperature, and on the multiplication factor. The dimensionality of the fission power was reduced from the 104288 nominal dimensions in the physical space to 10 dimensions in the reduced space, whereas the temperature was reduced from 220972 dimensions to 3. The reduced model was then used for uncertainty and sensitivity study of the maximum temperature in the reactor and the multiplication factor. In the transient analysis, the reduced model captured the effect of perturbations in the flow rate of salt in the intermediate circuit on the fission power density and temperature. The reduced models were successfully tested on a set of points that were not part of the snapshots used during the construction stage.

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We present an approach to build a reduced-order model for nonlinear, time-dependent, parametrized partial differential equations in a nonintrusive manner. The approach is based on combining proper orthogonal decomposition (POD) with a Smolyak hierarchical interpolation model for the POD coefficients. The sampling of the high-fidelity model to generate the snapshots is based on a locally adaptive sparse grid method. The novelty of the work is in the adaptive sampling of time, which is treated as an additional parameter. The goal is to have a robust and efficient sampling strategy that minimizes the risk of overlooking important dynamics of the system while disregarding snapshots at times when the dynamics are not contributing to the construction of the reduced model. The developed algorithm was tested on three numerical tests. The first was an advection problem parametrized with a five-dimensional space. The second was a lid-driven cavity test, and the last was a neutron diffusion problem in a subcritical nuclear reactor with 11 parameters. In all tests, the algorithm was able to detect and include more snapshots in important transient windows, which produced accurate and efficient representations of the high-fidelity models.

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In this work, we present the results of a preliminary uncertainty quantification and sensitivity analysis study of the Molten Salt Fast Reactor (MSFR) behavior at steady-state performed by applying a non-intrusive Polynomial Chaos Expansion (PCE) approach. An in-house high-fidelity multi-physics simulation tool is used as reactor reference model. Considering several thermal-hydraulics and neutronics parameters as stochastic inputs, with a limited number of samples we build a PCE meta-model able to reproduce he reactor response in terms of effective multiplication factor, maximum, minimum, and average salt temperatures, and complete salt temperature distribution. The probability density functions of the responses are constructed and analyzed, highlighting strengths and issues of the current MSFR design. The sensitivity study highlights the relative importance of each input parameter, thus providing useful indications for future research efforts. The analysis on the whole temperature field shows that the heat exchanger can be a critical component, so its design requires particular care.

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