Partial Differential Equations (PDEs) are central to science and engineering. Since solving them is computationally expensive, a lot of effort has been put into approximating their solution operator via both traditional and recently increasingly Deep Learning (DL) techniques. In this paper, we propose an autoregressive and data-driven method using the analogy with classical numerical solvers for time-dependent, parametric and (typically) nonlinear PDEs. We present how Dimensionality Reduction (DR) can be coupled with Neural Ordinary Differential Equations (NODEs) in order to learn the solution operator of arbitrary PDEs accounting both for (continuous) time and parameter dependency. The idea of our work is that it is possible to map the high-fidelity (i.e., high-dimensional) PDE solution space into a reduced (low-dimensional) space, which subsequently exhibits dynamics governed by a (latent) Ordinary Differential Equation (ODE). Solving this (easier) ODE in the reduced space allows avoiding solving the PDE in the high-dimensional solution space, thus decreasing the computational burden for repeated calculations for e.g., uncertainty quantification or design optimization purposes. The main outcome of this work is the importance of exploiting DR as opposed to the recent trend of building large and complex architectures: we show that by leveraging DR we can deliver not only more accurate predictions, but also a considerably lighter and faster DL model compared to existing methodologies.

Deterministically solving charged particle transport problems at a sufficient spatial and angular resolution is often prohibitively expensive, especially due to their highly forward peaked scattering. We propose a model order reduction approach which evolves the solution on a low-rank manifold in time, making computations feasible at much higher resolutions and reducing the overall run-time and memory footprint. For this, we use a hybrid dynamical low-rank approach based on a collided-uncollided split, i.e., the transport equation is split through a collision source method. Uncollided particles are described using a ray tracer, facilitating the inclusion of boundary conditions and straggling, whereas collided particles are represented using a moment method combined with the dynamical low-rank approximation. Here the energy is treated as a pseudo-time and a rank adaptive integrator is chosen to dynamically adapt the rank in energy. We can reproduce the results of a full-rank reference code at a much lower rank and thus computational cost and memory usage. The solution further achieves comparable accuracy with respect to TOPAS MC as previous deterministic approaches.

Real-time proton therapy range verification is a technique that can potentially reduce uncertainty margins around the treatment volume and enable prompt corrections during treatment, making proton therapy a safer cancer treatment modality. Imaging secondary particles resulting from proton-beam nuclear interactions with tissue serves as a means of range verification. The NOVO project recently (2023) presented a compact detector array (NOVCoDA) range verification system designed to image secondary prompt-gamma rays (PGs) and fast neutrons (FNs). The position resolution and arrangement of detector elements within the NOVCoDA influences the reconstructed particle distributions and in turn the system's range shift detection capabilities. Through Monte-Carlo simulations, we investigate the effects of four different detector element arrangements and the utilization of optically segmented scintillator volumes within detector elements, for improved position resolution, on NOVCoDA's range shift determination capability for proton therapy. We limit our study to the detection of FNs produced by an 85-MeV proton beam interacting within a homogeneous water phantom. Results indicate that a parallel array with detector elements oriented perpendicular to the proton beam axis and line-of-sight direction yields the highest double FN scattering efficiency, on order of 10−6 per proton. Furthermore, optically segmented detector elements resulted in improved minimum detectable range shift, reducing required proton intensity by 30%–60% to discern a 1 mm shift.

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.

Objective. A dynamic model is developed to predict the impact of radiotherapy on circulating lymphocyte counts in women with locally advanced cervical cancer (LACC). This study aims to compare the effects of photon and proton therapy, as well as the influence of bone marrow sparing (BMS) techniques, on relative lymphocyte preservation over time. Approach. A dynamic lymphocyte flow model was developed to simulate the migration of lymphocytes based on seven compartments. Biological cell death and lymphocyte production were integrated across compartments. The lymphocyte flow model was applied to 19 LACC patients. Volumetric modulated arc therapy (VMAT) and intensity modulated proton therapy (IMPT) treatment plans were created for each patient without BMS and with BMS. The model calculated radiation dose to lymphocytes to estimate radiation-induced cell death over time. The output of the model was the relative lymphocyte count relative to baseline (RLC) over time and the RLC nadir in the blood and total body. Main results. According to the model, IMPT resulted in lower doses to lymphocyte and higher RLC nadirs compared to VMAT for all 19 patients. The total RLC nadir (mean ± SD) was 48.4% ± 4.0% for VMAT and 62.5% ± 5.1% for IMPT. In the blood compartment, the RLC nadir was 32.7% ± 3.5% for VMAT and 47.7% ± 5.9% for IMPT. The RLC nadir in the blood compartment improved with 3Gy BMS from 32.7% ± 3.5% to 33.0% ± 3.5% , while it decreased for IMPT from 47.7% ± 5.9% to 46.6% ± 6.0%. Total RLC nadir decreased with BMS for VMAT from 48.4% ± 4.0% to 48.2% ± 3.9% and for IMPT from 62.5% ± 5.1% to 60.9% ± 5.3%. Significance. By incorporating a dynamic flow model, we predicted the RLC over time. The model predicted a substantial sparing effect IMPT has on the lymphocytes compared to VMAT. This sparing was both present in the blood and the total body. Sparing the bone marrow showed only a minimal effect on the RLC.

Objective: Scenario-based evaluation in proton therapy often relies on a small number of error scenarios, leading to limited insight into the DVH values under uncertainty and suboptimal trade-offs. In this study, we investigated if re-optimization based on probabilistic evaluation improves the trade-off between OAR sparing and target coverage in neuro-oncological patients. Materials and methods: 22 neuro-oncological patients were included. 18 met their original target goals (group A), while in 4, target coverage was compromised to spare OARs (group B). The probabilistic goal for the CTV was calibrated to be consistent with PTV-based photon plans, resulting in D_99.8%,CTV = 0.95D_pres with a 90 % confidence level. The probabilistic OAR constraints were set to meet the clinical constraints with a 95 % confidence level. For both groups, the clinical plans were re-optimized, keeping the clinical objectives and constraints, but reducing robustness for the CTV objective (group A) to meet the probabilistic goal, or for the dose-limiting OAR objectives (group B) without exceeding the constraints. For the original and re-optimized plans, polynomial chaos expansion was applied to simulate 10,000 fractionated treatments, deriving probability distributions for relevant DVH parameters. Results: For group A, re-optimization resulted in a population median decrease of 8.2 (range: 0.4–20.8) Gy RBE in the total OAR-related clinical goal values. For group B, re-optimization resulted in a population median increase of 2.7 (range: 1.3–6.8) Gy RBE in the D_99.8%,CTV. The population median V_95%,CTV improved from 97.4 % to 99.1 %. Conclusion: We demonstrated that probabilistic evaluation guided IMPT planning enables either OAR sparing or target coverage enhancement.

This paper presents an experimental study for the transient growth of an ice layer in a square channel under laminar flow conditions and a mixed convection heat transfer regime. The ice layer was grown from a cold plate located at the bottom of the channel, capable of reaching temperatures between 0 and −20 °C. The onset of ice formation was marked by a sudden sharp increase of the cold plate temperature followed by a rapid spreading of the ice over the cold plate surface. This was attributed to subcooling effects within the thermal boundary layer of the flow. The flow field was measured using particle image velocimetry (PIV) and the ice profiles were measured at several instances of time after the onset of freezing by a visual tracing of the solid–liquid interface. In addition, a parametric study was performed regarding the effect of the cold plate temperature and the flow rate on the ice growth rate. Suitable approximations to the experimental boundary conditions were found after a detailed analysis of the cold plate's transient temperature response, which could be readily implemented in numerical software. An important novelty of the present work is the measurement of the transient ice development of the ice-layer near the inlet of the channel, in addition to the centre of the channel where the flow is more developed. As such, a comprehensive and well-described experimental data set was generated for transient freezing in laminar internal flow. With this approach, a very good agreement was obtained between the experimental results and numerical simulations which were included to indicate the suitability of the current experimental campaign for numerical benchmarking purposes.

Objective. This study investigates the use of list-mode (LM) maximum a posteriori (MAP) expectation maximization (EM) incorporating prior information predicted by a convolutional neural network for image reconstruction in fast neutron (FN)-based proton therapy range verification. Approach. A conditional generative adversarial network (pix2pix) was trained on progressively noisier data, where detector resolution effects were introduced gradually to simulate realistic conditions. FN data were generated using Monte Carlo simulations of an 85 MeV proton pencil beam in a computed tomography-based lung cancer patient model, with range shifts emulating weight gain and loss. The network was trained to estimate the expected two-dimensional ground truth FN production distribution from simple back-projection images. Performance was evaluated using mean squared error, structural similarity index (SSIM), and the correlation between shifts in predicted distributions and true range shifts. Main results. Our results show that pix2pix performs well on noise-free data but suffers from significant degradation when detector resolution effects are introduced. Among the LM-MAP-EM approaches tested, incorporating a mean prior estimate into the reconstruction process improved performance, with LM-MAP-EM using a mean prior estimate outperforming naïve LM maximum likelihood EM (LM-MLEM) and conventional LM-MAP-EM with a smoothing quadratic energy function in terms of SSIM. Significance. Findings suggest that deep learning techniques can enhance iterative reconstruction for range verification in proton therapy. However, the effectiveness of the model is highly dependent on data quality, limiting its robustness in high-noise scenarios.

Background and purpose:
Understanding the cellular and molecular effect of proton radiation, particularly the increased DNA damage complexity at the distal end of the Bragg curve, is current topic of investigation. This work aims to study in vitro clonogenic survival and DNA damage foci kinetics of a head and neck squamous cell carcinoma cell line at various positions along a double passively scattered Bragg curve. Complementary in silico studies are conducted to gain insights into the link between cell survival variations, experimentally yielded foci and the number and complexity of double strand breaks (DSBs).

Materials and methods:
Proton irradiations are performed at the HollandPTC R&D proton beamline, using a double passively scattered setup. A custom water phantom setup is employed to accurately position the samples within the Bragg curve. FaDu cells are irradiated at the proximal 36 % point of the Bragg peak, (P36), proximal 80 % point of the Bragg peak (P80) and distal 20 % point of the Bragg peak (D20), with dose-averaged mean lineal energies (yD¯) of 1.10 keV/μm, 1.80 keV/μm and 7.25 keV/μm, respectively.

Results:
Clonogenic survival correlates strongly with yD¯, showing similar survival for P36 (D37%=3.0 Gy) and P80 (D37%=2.9 Gy), but decreased survival for D20 (D37% = 1.6 Gy). D20 irradiated samples exhibit increased 53BP1 foci shortly after irradiation, slower resolution of the foci, and larger residual 53BP1 foci after 24 h, indicating unrepaired complex breaks. These experimental observations are supported by the in silico study which demonstrates that irradiation at D20 leads to a 1.7-fold increase in complex DSBs with respect to the total number of strand breaks compared to P36 and P80.

Conclusions:
This combined approach provides valuable insights into the cellular and molecular effect of proton radiation, emphasizing the increased DNA damage complexity at the distal end of the Bragg curve, and has the potential to enhance the efficacy of proton therapy.

A three-dimensional whole-core transient coupled thermal-hydraulic and neutronics code system for modeling prismatic high-temperature gas-cooled reactors (HTGRs) is presented. The discrete ordinates method code PHANTOM-SN was used to solve the multigroup neutron transport problem with cross sections generated with Serpent. The new finite element code OPERA was developed to solve the heat equation in the core and includes simplified subcodes for the coolant, reactor pressure vessel, and concrete containment building, as well as the power conversion cycle. Core graphite thermal conductivity degradation is included as a function of temperature and irradiation temperature. A 20-MW(thermal) HTGR design was modeled using the coupled multiphysics code to prove inherent safety. We simulated steady state, a depressurized loss of forced cooling (DLOFC), a partial blockage, and a reactivity insertion incident. We show that the DLOFC is not the most severe scenario for the fuel temperature in this prismatic micro HTGR. Upon a DLOFC, the peak fuel temperature remains well below the tri-structural isotropic (TRISO) fuel limits, even when the power is increased to 40 MW(thermal). However, during a partial blockage incident of one fuel assembly stack, the maximum fuel temperature reaches 2300°C, severely exceeding the limits. We furthermore contend that the graphite thermal conductivity values used in modeling should always be made explicit and that the temperature of irradiation should be included as a parameter since it can cause a sharp decrease (up to 97%) in the conductivity. We show that using unirradiated graphite parameters leads to an underestimation in peak temperature of 165°C while using a relatively low power density compared to other HTGRs. Finally, we argue that for prismatic HTGRs with a central reflector, bypass flow may lower the maximum fuel temperature.

HollandPTC is an independent outpatient center for proton therapy, scientific research, and education. Patients with different types of cancer are treated with Intensity Modulated Proton Therapy (IMPT). Additionally, the HollandPTC R&D consortium conducts scientific research into the added value and improvements of proton therapy. To this end, HollandPTC created clinical and pre-clinical research facilities including a versatile R&D proton beamline for various types of biologically and technologically oriented research. In this work, we present the characterization of the R&D proton beamline of HollandPTC. Its pencil beam mimics the one used for clinical IMPT, with energy ranging from 70 up to 240 MeV, which has been characterized in terms of shape, size, and intensity. For experiments that need a uniform field in depth and lateral directions, a dual ring passive scattering system has been designed, built, and characterized. With this system, field sizes between 2 × 2 cm² and 20 × 20 cm² with 98 % uniformity are produced with dose rates ranging from 0.5 Gy/min up to 9 Gy/min. The unique and customized support of the dual ring system allows switching between a pencil beam and a large field in a very simple and fast way, making the HollandPTC R&D proton beam able to support a wide range of different applications.

We present a finite volume adaptive mesh refinement method for solid-liquid phase change problems with convection. The refinement criterion consisted of three different error estimators for the solid-liquid interface, the flow field, and the temperature field respectively. For the solid-liquid interface, the cells undergoing phase change were refined based on the maximum difference in the liquid fraction over the cell faces. For the flow field and the temperature field, an error indicator was used based on the cell residual method. To maintain a high parallelization efficiency, a dynamic load balancing procedure was used. The adaptive mesh refinement strategy was verified through three different test cases, these are the gallium melting in both 2D and 3D cavities, and the molten salt reactor freeze valve. For all three cases, very good agreement was obtained between the adaptive mesh results and the reference solutions. In addition, more accurate results were obtained with the adaptive meshes compared to static meshes with a similar amount of mesh cells. This illustrated the potential of the current approach for developing computationally efficient numerical methods for solid-liquid phase change problems.

This study aims to investigate the capability of U-Nets in improving image reconstruction accuracy for proton range verification within the framework of the NOVO (Next generation imaging for real-time dose verification enabling adaptive proton therapy) project. NOVO aims to enhance the accuracy of proton range verification by imaging the distribution of prompt gamma-rays (PGs) and fast neutrons (FNs) produced by nuclear interactions within tissue. In this work, focus lies on FNs, leaving PGs as future work. A dataset consisting of Monte Carlo-based simple back-projection and ground truth images of FN production distributions in a homogeneous water phantom was utilized. Various U-Net models were trained to predict FN distributions, and a set of range landmark (RL) metrics were computed for evaluation. Linear regression models were established to correlate shifts in mean RL with true range shift magnitudes. Our findings demonstrate a strong linear correlation between the shifts in mean RL in U-Net predictions and the true range shift magnitudes. Multiple RL metrics, including weighted average, inflection point, edge, and peak, were explored. This study highlights the potential utility of U-Nets in enhancing image reconstruction accuracy for proton range verification. The observed correlations between RL shifts and true range shifts provide evidence of the ability of U-Nets to accurately predict images containing range information. Future research will focus on generating more realistic training data incorporating more clinically relevant phantoms, including tissue heterogeneities.

This work presents two color LIF temperature measurements for the transient freezing in a square channel under laminar flow conditions. This is the first time non-intrusive temperature measurements were performed within the thermal boundary layer during the transient growth of an ice layer in internal flow. A combination of a local outlier factor algorithm and a smoothing operation was used to remove the top to bottom striations and reduce the other measurement noise. The temperature uncertainty in our measurements was between σ=0.3∘C and σ=0.5∘C. For the largest temperature difference between the bulk and the melting point of 14.6 °C, good results were obtained. As such, the current campaign demonstrates the potential of LIF as a non-intrusive temperature measurement technique for solid–liquid phase change experiments. However, some artefacts were present within the vicinity of the ice-layer due to the scattering of the laser light, especially near the inlet of the channel where the ice-layer is curved instead of flat. LIF measurements taken within a short time span prior to the onset of ice freezing showed approximately 2 °C of subcooling, consistent with previous findings. In addition, an anomalous behavior within the thermal boundary layer was observed, with a much smaller temperature gradient within the first few mm above the cold plate and a point of inflection in the temperature profile. The anomalous temperature behavior is possibly attributed to enhanced natural convection as a result of the subcooling at the cold plate surface.

Objective. Oxygen depletion is generally believed to play an important role in the FLASH effect—a differential reduction of the radiosensitivity of healthy tissues, relative to that of the tumour under ultra-high dose-rate (UHDR) irradiation conditions. In proton therapy (PT) with pencil-beam scanning (PBS), the deposition of dose, and, hence, the degree of (radiolytic) oxygen depletion varies both spatially and temporally. Therefore, the resulting oxygen concentration and the healthy-tissue sparing effect through radiation-induced hypoxia varies both spatially and temporally as well. Approach. We propose and numerically solve a physical oxygen diffusion model to study these effects and their dependence on tissue parameters and the scan pattern in pencil-beam delivery. Since current clinical FLASH PT (FLASH-PT) is based on 250 MeV shoot-through (transmission) beams, for which dose and dose rate (DR) hardly vary with depth compared to the variation transverse to the beam axis, we focus on the two-dimensional case. We numerically integrate the model to obtain the oxygen concentration in each voxel as a function of time and extract voxel-based and spatially and temporarily integrated metrics for oxygen (FLASH) enhanced dose. Furthermore, we evaluate the impact on oxygen enhancement of standard pencil-beam delivery patterns and patterns that were optimised on dose-rate. Our model can contribute to the identification of tissue properties and pencil-beam delivery parameters that are critical for FLASH-PT and it may be used for the optimisation of FLASH-PT treatment plans and their delivery. Main results. (i) the diffusive properties of oxygen are critical for the steady state concentration and therefore the FLASH effect, even more so in two dimensions when compared to one dimension. (ii) The FLASH effect through oxygen depletion depends primarily on dose and less on other parameters. (iii) At a fixed fraction dose there is a slight dependence on DR. (iv) Scan patterns optimised on DR slightly increase the oxygen induced FLASH effect. Significance. To our best knowledge, this is the first study assessing the impact of scan-pattern optimization (SPO) in FLASH-PT with PBS on a biological FLASH model. While the observed impact of SPO is relatively small, a larger effect is expected for larger target volumes. A better understanding of the FLASH effect and the role of oxygen (depletion) therein is essential for the further development of FLASH-PT with PBS, and SPO.

Objective.The integration of proton beamlines with x-ray imaging/irradiation platforms has opened up possibilities for image-guided Bragg peak irradiations in small animals. Such irradiations allow selective targeting of normal tissue substructures and tumours. However, their small size and location pose challenges in designing experiments. This work presents a simulation framework useful for optimizing beamlines, imaging protocols, and design of animal experiments. The usage of the framework is demonstrated, mainly focusing on the imaging part.Approach.The fastCAT toolkit was modified with Monte Carlo (MC)-calculated primary and scatter data of a small animal imager for the simulation of micro-CT scans. The simulated CT of a mini-calibration phantom from fastCAT was validated against a full MC TOPAS CT simulation. A realistic beam model of a preclinical proton facility was obtained from beam transport simulations to create irradiation plans in matRad. Simulated CT images of a digital mouse phantom were generated using single-energy CT (SECT) and dual-energy CT (DECT) protocols and their accuracy in proton stopping power ratio (SPR) estimation and their impact on calculated proton dose distributions in a mouse were evaluated.Main results.The CT numbers from fastCAT agree within 11 HU with TOPAS except for materials at the centre of the phantom. Discrepancies for central inserts are caused by beam hardening issues. The root mean square deviation in the SPR for the best SECT (90 kV/Cu) and DECT (50 kV/Al-90 kV/Al) protocols are 3.7% and 1.0%, respectively. Dose distributions calculated for SECT and DECT datasets revealed range shifts <0.1 mm, gamma pass rates (3%/0.1 mm) greater than 99%, and no substantial dosimetric differences for all structures. The outcomes suggest that SECT is sufficient for proton treatment planning in animals.Significance.The framework is a useful tool for the development of an optimized experimental configuration without using animals and beam time.

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.

Particle therapy (PT) used for cancer treatment can spare healthy tissue and reduce treatment toxicity. However, full exploitation of the dosimetric advantages of PT is not yet possible due to range uncertainties, warranting development of range-monitoring techniques. This study proposes a novel range-monitoring technique introducing the yet unexplored concept of simultaneous detection and imaging of fast neutrons and prompt-gamma rays produced in beam-tissue interactions. A quasi-monolithic organic detector array is proposed, and its feasibility for detecting range shifts in the context of proton therapy is explored through Monte Carlo simulations of realistic patient models and detector resolution effects. The results indicate that range shifts of 1mm can be detected at relatively low proton intensities (22.30 (13) × 10 ⁷ protons/spot) when spatial information obtained through imaging of both particle species are used simultaneously. This study lays the foundation for multi-particle detection and imaging systems in the context of range verification in PT.

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.

The design of a molten salt reactor is largely based on CFD simulations. Phase change plays an important role in the safety of the reactor, but numerical modelling of phase change is particularly challenging. Therefore, the knowledge of the margin of error of CFD simulations involving phase change is very important. Relevant experimental validation data is lacking. For this reason, a numerical benchmark designed after the freeze valve is proposed. The benchmark consists of five stages, where with each step more complexity is added. The step-wise addition of complexity allows for pinpointing potential sources of discrepancy. Results were obtained with three different codes: STAR-CCM+, OpenFOAM, and DGFlows. The results were found to be largely consistent between the codes, however the addition of conjugate heat transfer introduced some discrepancies. These results indicate that careful consideration is needed when coupling conjugate heat transfer solvers with solid–liquid phase change models.