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.@en

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.

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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.@en

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.

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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.@en

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.@en

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.

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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.

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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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We present a discontinuous Galerkin method for melting/solidification problems based on the “linearized enthalpy approach,” which is derived from the conservative form of the energy transport equation and does not depend on the use of a so-called mushy zone. We use the symmetric interior penalty method and the Lax–Friedrichs flux to discretize diffusive and convective terms, respectively. Time is discretized with a second-order implicit backward differentiation formula, and two outer iterations with second-order extrapolation predictors are used for the coupling of the momentum and energy. The numerical method was validated with three different benchmark cases, i.e., the one-dimensional Stefan problem, octadecane melting in a square cavity and gallium melting in a rectangular cavity. The performance of the method was quantified based on the L ² norm error and the number of iterations needed to convergence the energy equation at each time step. For all three validation cases, a mesh convergence rate of approximately O(h) was obtained, which is below the expected accuracy of the numerical method. Only for the gallium melting case, the use of a higher-order method proved to be beneficial. The results from the present numerical campaign demonstrate the promise of the discontinuous Galerkin finite element method for modeling certain solid–liquid phase change problems where large gradients in the flow field are present or the phase change is highly localized, however, further enhancement of the method is needed to fully benefit from the use of a higher-order numerical method when solving solid–liquid phase change problems.

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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.

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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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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. 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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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.

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A Geant4 based simulation platform of the Holland Proton Therapy Centre (HollandPTC, Netherlands) R&D beamline (G4HPTC-R&D) was developed to enable the planning, optimisation and advanced dosimetry for radiobiological studies. It implemented a six parameter non-symmetrical Gaussian pencil beam surrogate model to simulate the R&D beamline in both a pencil beam and passively scattered field configuration. Three different experimental proton datasets (70 MeV, 150 MeV, and 240 MeV) of the pencil beam envelope evolution in free air and depth-dose profiles in water were used to develop a set of individual parameter surrogate functions to enable the modelling of the non-symmetrical Gaussian pencil beam properties with only the ProBeam isochronous cyclotron mean extraction proton energy as input. This refined beam model was then benchmarked with respect to three independent experimental datasets of the R&D beamline operating in both a pencil beam configuration at 120 and 200 MeV, and passively scattered field configuration at 150 MeV. It was shown that the G4HPTC-R&D simulation platform can reproduce the pencil beam envelope evolution in free air and depth-dose profiles to within an accuracy on the order of ±5% for all tested energies, and that it was able to reproduce the 150 MeV passively scattered field to the specifications need for clinical and radiobiological applications.

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For image-guided small animal irradiations, the whole workflow of imaging, organ contouring, irradiation planning, and delivery is typically performed in a single session requiring continuous administration of anaesthetic agents. Automating contouring leads to a faster workflow, which limits exposure to anaesthesia and thereby, reducing its impact on experimental results and on animal wellbeing. Here, we trained the 2D and 3D U-Net architectures of no-new-Net (nnU-Net) for autocontouring of the thorax in mouse micro-CT images. We trained the models only on native CTs and evaluated their performance using an independent testing dataset (i.e., native CTs not included in the training and validation). Unlike previous studies, we also tested the model performance on an external dataset (i.e., contrast-enhanced CTs) to see how well they predict on CTs completely different from what they were trained on. We also assessed the interobserver variability using the generalized conformity index (CI _gen) among three observers, providing a stronger human baseline for evaluating automated contours than previous studies. Lastly, we showed the benefit on the contouring time compared to manual contouring. The results show that 3D models of nnU-Net achieve superior segmentation accuracy and are more robust to unseen data than 2D models. For all target organs, the mean surface distance (MSD) and the Hausdorff distance (95p HD) of the best performing model for this task (nnU-Net 3d_fullres) are within 0.16 mm and 0.60 mm, respectively. These values are below the minimum required contouring accuracy of 1 mm for small animal irradiations, and improve significantly upon state-of-the-art 2D U-Net-based AIMOS method. Moreover, the conformity indices of the 3d_fullres model also compare favourably to the interobserver variability for all target organs, whereas the 2D models perform poorly in this regard. Importantly, the 3d_fullres model offers 98% reduction in contouring time.

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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.

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Over the past two decades, there has been much development in discontinuous Galerkin methods for incompressible flows and for compressible flows with a positive Mach number, but almost no attention has been paid to variable-density flows at low speeds. This paper presents a pressure-based discontinuous Galerkin method for flow in the low-Mach number limit. We use a variable-density pressure correction method, which is simplified by solving for the mass flux instead of the velocity. The fluid properties do not depend significantly on the pressure, but may vary strongly in space and time as a function of the temperature. We pay particular attention to the temporal discretization of the enthalpy equation, and show that the specific enthalpy needs to be ‘offset’ with a constant in order for the temporal finite difference method to be stable. We also show how one can solve for the specific enthalpy from the conservative enthalpy transport equation without needing a predictor step for the density. These findings do not depend on the spatial discretization. A series of manufactured solutions with variable fluid properties demonstrate full second-order temporal accuracy, without iterating the transport equations within a time step. We also simulate a Von Kármán vortex street in the wake of a heated circular cylinder, and show good agreement between our numerical results and experimental data.

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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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