In recent years, various systems have been developed which integrate a linear accelerator with an MR system, enabling high quality imaging during radiotherapy. However, these systems produce strong magnetic fields that cause the secondary electrons to deflect. This leads to significant changes in the dose distribution since the path of the electrons is altered in this magnetic field. Several methods have been developed to accurately determine the influence of a magnetic field on the dose distribution, however, these methods are impractical due to their long computation times. In this work we develop a deterministic DGFEM method for solving the Linear Boltzmann transport equation (LBTE) in magnetic fields for photon therapy. For this purpose, we first developed a deterministic Boltzmann solver based on the discrete ordinate methods. This algorithm was extended to use the DGFEM method and finally a magnetic field term was implemented to determine the influence of a magnetic field on the dose distribution.

The results acquired with the algorithm based on the DGFEM method were compared to exact solutions, these results were consistent with the exact solutions and reported high levels of accuracy. The accuracy of these methods was comparable to those achieved by using discrete ordinates. Furthermore, the cost of the DGFEM algorithm were compared to those of the discrete ordinate method, here it has been shown that the DGFEM algorithm is only slightly more computationally expensive.

The DGFEM based solution algorithm was extended by implementing the magnetic field operator into the algorithm. The deterministic results in the presence of a magnetic field were compared against the MCNP and TOPAS Monte Carlo codes. These results showed similar dose distributions compared to MCNP, however, the deterministic results were not in accordance with the TOPAS simulation. It is suspected that the discrepancy in dose distribution originates from the difference in source spectrum between the two methods.

In order to investigate the influence of a magnetic field, dose distributions were determined with a magnetic field perpendicular to the photon beam. The results showed that the buildup region decreases for stronger magnetic fields and that higher values for the dose are formed at the boundaries between materials with different densities. This increased dose is caused by the electron return effect and becomes more condensed for stronger magnetic fields. Furthermore, a lateral shift in the dose distribution has been observed in the direction of the Lorentz force. These results show that the developed deterministic Boltzmann solver is able to generate accurate dose distributions in the presence of a magnetic field.

Background: While intensity modulated proton therapy (IMPT) plans allow for increased normal tissue sparing in comparison to photon radiotherapy, IMPT is also more sensitive to treatment uncertainties, including geometrical shifts in patient anatomy and range errors. Additionally, for thoracic treatment sites, e.g. the oesophagus, interference between breathing motion and IMPT treatment delivery, ‘the interplay effect’, can significantly degrade the quality of the dose distribution. To ensure IMPT plans are robust against treatment uncertainties, the dose distribution should ideally be evaluated in a high number of error scenarios. In this way, probabilistic robustness evaluation (PRE) enables the derivation of the probability distribution of relevant dose distribution parameters. Previous research has shown that polynomial chaos expansion (PCE) methods can efficiently perform PRE for head-and-neck and neurological IMPT plans, accounting for geometrical shifts and range errors. The goal of this thesis was to extend the PCE methodology for PRE to include the interplay effect, in addition to geometrical shifts and range errors, for evaluation of clinical IMPT plans of oesophageal cancer patients.
Methods: To include the interplay effect in the PCE methodology, we simulated 4D dynamic dose distributions with 1 set of PCE models per breathing signal. Sinusoidal breathing signals with a period between 3 s and 7 s were assumed. For 1 patient, we studied the effect of PCE parameters – Monte Carlo (MC) noise level, grid order (GO), polynomial order (PO), and PCE coefficient calculation methods – on PCE model accuracy. PCE model parameters and PRE parameters were selected with cost-accuracy analysis and validated for 2 patients. To evaluate the performance of the clinical protocol that was used to create the IMPT plans, PRE was performed including geometrical shifts, range errors, and different breathing signals for 20 clinical IMPT plans of oesophageal cancer patients treated at Holland PTC. We evaluated the probability of adequate CTV dose and scenario distributions of OAR (heart) dose and normal tissue complication probability (NTCP). Finally, we analysed the effect of several factors on PRE outcomes for 1 patient, including presence/absence of fractionation and repainting, extreme breathing signals, and presence/absence of geometrical shifts and range errors.
Results: Lowering the MC noise level improved PCE model accuracy. Selection of the GO3E1PO4 MC1.0% regression model resulted in accurate models for acceptable computational costs. Cost-accuracy analysis showed that 10 000 fully fractionated scenarios and 5 included breathing signals were statistically adequately for PRE, resulting in a total computation time of < 1 day per patient. For all patients, we found a probability of adequate clinical target volume dose (CTV D99.8% > 0.95 Dprescribed) larger than the criterium of 90%, with a population mean 99.56% (minimum – maximum: 98.75% – 99.96%). If fractionation and/or repainting are not considered, ≥ 20 breathing signals could be required for statistically adequate PRE.
Conclusion: We established and validated a pipeline for extending the PCE methodology for PRE to account for breathing motion. Our selected PCE models were as accurate as previously reported models. However, the number of included breathing signals required for statistically adequate PRE could vary depending on the IMPT treatment planning protocol. Our results show that the protocol used to create the included IMPT plans leads to safe, but conservative treatment plans. A lower prescription dose level could be used to significantly reduce the heart dose and NTCP, while still ensuring adequate dose to the CTV.

As humanity prepares to return to the Moon, understanding its complex radiation environment becomes increasingly critical. Radiation hardness assurance is essential to ensure that the payload remains operational and reliable under prolonged exposure to harsh space conditions. This thesis investigates the performance of the Floating Gate Dosimeter (FGDOS) as part of the Lunar Zebro nano-rover payload developed at TU Delft. The sensor’s response was evaluated through a series of irradiation campaigns: low-dose gamma radiation at the Reactor Institute Delft (RID), proton irradiation at HollandPTC, and mixed-field exposure at CERN’s CHARM facility. While the FGDOS demonstrated linear dose-response behavior and potential for spaceborne dosimetry, several limitations were identified, including reduced sensitivity, temperature dependence, and a firmware-related recharging issue.

A preliminary investigation into the use of a boron carbide layer showed a measurable increase in neutron sensitivity, suggesting its relevance for shielding strategies in mixed-field environments. Although the current payload is not yet flight-ready, it provides a robust foundation for further development. Future work should focus on high-flux gamma testing and refinement of both hardware and firmware to improve measurement reliability and system resilience in the lunar radiation environment.

Proton therapy is a form of radiation therapy, that leverages the unique properties of protons to maximize dose deposition in treatment volumes. The usefulness of proton therapy treatment, in sparing healthy tissue, becomes even more evident with the incorporation of the FLASH effect. FLASH delivers ultra-high dose rates with minimal treatment time while maintaining therapeutic efficiency in eradicating tumours. How- ever, due to practical challenges such as energy layer switching in pencil beam scanning systems the clinical applications are limited. This thesis researched the development of patient-specific ridge filters (RFs) for proton therapy using an optimization algorithm. Ridge filters are energy modulators that help enable dose delivery without energy layer switching, making the FLASH effect feasible as was shown in 2018 [1]. Previous studies used static and dynamic methods [2] and fluence-based optimization [3] to construct patient-specific RFs. This study presents a novel framework for optimizing patient-specific RFs using a combination of TOPAS, a Monte Carlo particle simulation software that accurately models particle transport, and PyGAD, a Python-based genetic algorithm (GA) module. This class of optimizers is effective in cases where no derivatives are avail- able or are very difficult to compute. GAs do this by testing various simulations and evaluating these using a fitness function. The methodology involves simulating dose distribution in a scoring volume, optimizing ridge pin geometry, and evaluating performance using fitness functions. The results demonstrate that the proposed framework effectively generates patient-specific RFs with min- imal deviation from the desired dose distribution in simple cases, with a maximum dose difference of 2.66 % and mean dose of 99.21 % over the region of interest. Comparative analysis with prior approaches shows that the framework achieves similar results. However, applying the framework to cases with obstructions in the scoring volume requires further refinement of the algorithm. The findings provide a basis for using GAs for constructing patient-specific RFs for FLASH proton therapy. Future work should be aimed at refining the GA and Monte Carlo simulation and assessing the viability of producing the generated RFs.

External beam radiotherapy (EBRT) is a method for treating cancer in which the tumor is targeted by beams of radiation originating from the patient’s exterior. The two main particles employed for EBRT are photons and protons, with electrons and carbon ions also being in use. Both photons and protons are capable of achieving adequate tumor coverage, but protons can theoretically achieve lower doses in the surrounding tissues (at the expense of increased economical costs). Regardless of the chosen modality, the radiotherapy (RT) workflow is similar. It consists of determining the patient anatomy via imaging, usually via computed tomography (CT) scans, contouring (delineating) the organs at risk (OARs) and the target, creating a treatment plan, performing quality assurance (QA) and delivering the plan safely. In classical (also called non-adaptive) RT this workflow is performed once and the treatment is delivered over several (around 30) daily sessions (also called fractions).

Theoretically, the best radiotherapy treatment is the one in which the tumor is completely eradicated, while the surrounding tissue is not irradiated at all. Given that this is physically impossible, due to the nature of photon and proton propagation and interaction with matter, the next best result is maximal tumor coverage and minimal radiation damage to OARs. As the patient anatomy changes on different time scales ranging from weeks (e.g., weight loss, tumor shrinkage) to days (e.g., day to day variations of cavity fillings or neck pose changes) to seconds (due to for example breathing and slight movements) it becomes apparent that the offline approach to RT is suboptimal. To improve on this, the radiotherapy workflow must be adjusted such that imaging, delineation and treatment planning are performed several times over the course of the treatment, resulting in adaptive radiotherapy (ART). ART results in better targeting of the tumor and lower OAR doses. If adaptation is performed without the patient on the treatment table, the process is called offline adaptation. The next time-scale is online, which refers to a daily adaptation regime where the patient remains online (on the treatment table) after imaging. In such a workflow, on a given day the patient is imaged and within a short time (from tens of seconds to several minutes) the complete offline workflow (contouring, treatment planning, quality assurance, safe delivery) is performed. The time between imaging and delivery should be as short as possible, in order to minimize inter-fractional and patient set-up errors and to maximize clinical output. The ideal scenario would be real-time adaptation, in which all the steps of the radiotherapy workflow (including imaging and irradiation adaptations) are performed in real-time…

The goal of the thesis is to find a Reduced Order Modelling method that speeds up burnup simulations—as encountered in the core of a Molten Salt Fast Reactor—while keeping
accuracy loss minimal. Four different methods have been tested: Proper Orthogonal Decomposition (POD), heuristically corrected POD, Balanced Truncation (BT), and Balanced
Proper Orthogonal Decomposition (BPOD). The first two methods are inadequate, because
of stability issues. The third is stable, but fails to execute for burnup simulations. The
fourth, a midway method between the first and third, does work for burnup simulations.
Using BPOD with 4 orders for a 10 year burnup simulation of 1650 nuclides with 1000
simulation steps, we find a normalised relative error of 10^-5 both for the total model and
each nuclide individually. The execution time per simulation step is reduced to 10^-5 s.
These results are a factor 1000 better than known alternatives such as the ORIGEN burnup
program.

The conclusion contains recommendations for incorporating different fuel mixtures and non-
linearity of the burnup equation in the BPOD. The method could be generalised to handle
arbitrary burnup problems with a single Reduced Order Model.

Background: Real-time adaptive radiotherapy workflows require fast spatial dose calculations with clinical accuracy. Modern physics-based dose calculation algorithms often compromise between speed and accuracy. In contrast, deep learning methods have shown to be effective at predicting spatial dose distributions with high accuracy in sub-second times. Very High Energy Electrons (VHEE) have shown potential as a treatment modality in recent years due to their penetrative ability and conformality. Creating a need for fast and accurate VHEE spatial dose calculations.
Purpose: This study presents a deep learning-based algorithm that utilizes convolutional layers and the self-attention mechanism to predict VHEE beam spatial dose distributions in sub-second times.
Methods: The presented Electron-Dose Transformer Algorithm (E-DoTA) maps the 3D patient geometry and beam characteristics (using a vector representing the beam energy and a 3D Gaussian with a specific Gaussian positional spread representing the beam shape) to
a 3D dose distribution. E-DoTA uses a series of 3D convolutional layers to extract features from the patient geometries and beam shape, followed by a transformer to route information between the extracted features and the added energy vector, which are then upsampled to
the 3D dose distribution. E-DoTA is trained on 60,000 combinations of patient geometries and beam characteristics, derived from 15,000 independent patient geometries based on 12 distinct patient CT scans from the abdomen region. The model’s accuracy and prediction
speed are assessed using 8,000 previously unseen patient geometries and beam characteristics.
Results: E-DoTA predicts dose distributions of VHEE beams with high accuracy, achieving a gamma pass rate of 97.05% ± 3% (3mm, 1%) and an average relative dose error of 0.254% ± 0.096% in approximately 131 ms.
Conclusions: The fast and high-accuracy dose predictions allow the speed-up of VHEE spatial dose distribution calculations, which is currently only provided by slow Monte Carlo algorithms. Further optimizations to E-DoTA could allow for more accurate and faster dose calculations, thereby potentially accelerating VHEE radiotherapy workflows.

In this thesis, Boltzmann's H-theorem is studied and applied to prove a general convergence to equilibrium for the adiabatic piston paradox, governed by a specially-derived kinetic Fokker-Planck equation. We review general results in kinetic theory on the Boltzmann collision operator, and rates of convergence to equilibrium. Furthermore, we turn our attention to simulations of the piston paradox, and apply the algorithm of Sigureirsson et al. for particle-particle collision dynamics to the piston setting, determining empirically the optimal parameters.

In this thesis, a predictive non-intrusive reduced order model of a high-temperature gas-cooled reactor has been created. We first set out to create a representative multi-physics model coupling the neutronics and thermodynamics in the HTGR. To this end we first made a representative model of neutronics and thermodynamics separately in the HTGR. These representative models were used to train and test our reduced order models (ROMs). It has been found that the representative model converges spatially and temporally to the expected values of analytical and pseudo analytical solutions for the neutronics, the temperature, and the coupled model. However, the convergence in the spatial domain was found to be slower than the mathematical expectation from the implemented finite volume method, converging at a rate of Δx1.5, instead of Δx2. The temporal convergence rate was Δt as is expected from the implemented first order backward differentiation formula. In literature review, we have found that Operator Inference provides a way to construct ROMs that are both predictive and non-intrusive. We used Operator Inference to create three ROMs. A ROM of the temperature model, a ROM of the neutronics model, and lastly a ROM of the coupled model. The temperature ROM created with 12 modi and 1500 snapshots was found to be accurate to the representative model for any sort of power input, achieving a root mean square error below 10−5 compared to the representative model, while predicting 3000 seconds longer than the training at Δt = 1 s. for 1000 random power inputs not included in training. The neutronics ROM created with 7 modi and 3960 snapshots retrieved accurate results, with a root mean square error around 10−4 compared to the representative model if we used a homogeneous temperature in the reactor. If we defined more temperature zones in the reactor we used a different interpolation technique. For this we found the results to be of lesser quality with an average root mean square error closer to 10−2 for a temperature profile far from a steady state temperature profile, while the results were of greater quality with an average root mean square error of 10−5 for temperature profiles close to a steady state temperature profile. Finally, we developed two methods of creating a reduced order model of the coupled model. First, we created a sequential model, where the outputs of the individual temperature ROM and neutronics ROM fed into each other. Second, we created a merged model, in which both the temperature and neutronics were determined by our reduced order model in one single model. A loss of forced cooling was simulated by changing the heat transfer coefficient at the coolant channel boundary. We trained the ROMs for 50 seconds with Δt = 10−3 s, with 5 different heat transfer coefficient equidistant between 0 and 0.03 Wcm−2K−1. It has been found that the merged model was robust and provided accurate results, it could predict to 200 seconds estimating for a heat transfer coefficient of 0.00375 Wcm−2K−1. with an average root mean square error in time for both the neutron flux profile and the temperature profile of less than 10−2. The sequential model was unstable, with root mean square errors orders of magnitude higher than the merged model.

Introduction and purpose: Long-term xerostomia and dysphagia affect the quality of life (QoL) of head and neck (HN) cancer patients treated with radiotherapy (RT). However, xerostomia is subjectively measured with questionnaires, which has several limitations. It is of interest to investigate whether quantitative magnetic resonance imaging (qMRI) techniques can capture radiation-induced damage to organs in the HN area. This study uses diffusion-weighted imaging (DWI) to measure the apparent diffusion coefficient (ADC), mDIXON Quant to measure the fat fraction (FF), and T2-mapping to map T2 values. All three qMRI parameters are expected to increase with dose and, therefore, differ for different patient-reported xerostomia scores. In addition, recent literature emphasizes the relevance of the stem cell rich (SCR) region in the parotid glands, but the delineation methods are not patient-specific and incorporate a large margin to account for differences between patients.

Methods: 26 healthy controls (HC) and 54 HNC patients treated with RT have been included. MRI acquisition was performed 6 months to 3 years after the last RT fraction. 19 patients were scanned in a test-retest fashion to calculate the repeatability coefficient (RC). In addition, planning CT with dose distributions were available for all but two patients. Pearson’s correlation with a simple linear regression was performed to investigate the relationship between qMRI values and dose. A linear mixed-effects model (LMM) analysis was performed to assess the effect of subject characteristics on qMRI values. The fixed-effects estimates of this LMM were used to correct for subject characteristics in the correlation analysis. Cohorts were defined based on patient-reported scores for xerostomia (score 1 or score ≥ 2) and sticky saliva (score 1 or score ≥ 2). A one-way ANOVA with Tukey’s HSD post-hoc test was performed to test for differences in qMRI histogram parameters between HC and xerostomia cohorts, and between HC and sticky saliva cohorts. The hybrid and biomechanical deformable image registration (DIR) were performed for one patient to map the parotid glands from T2-weighted TSE to planning CT and similarity metrics were calculated. The best performing DIR algorithm was used in the delineation process of the SCR region, to delineate the SCR region on MR sialography imaging and map the delineations from MRI to planning CT. Volume and qMRI values were extracted.

Results: The difference in RC between HCs as reported in literature and patients ranged from -0.10 to 0.02 · 103 mm2/s for ADC, -0.4 to 1.6 % for FF, and -2.6 to 2.0 ms for T2, showing sufficient and comparable repeatability. Overall, ADC positively correlated with the dose for several relevant organs, while T2 only positively correlated with the dose of the submandibular glands and the superior pharyngeal constrictor muscle. FF did not show a positive correlation with dose. The LMM analysis showed that age affects the FF and T2 values of several organs related to xerostomia or dysphagia. BMI was also shown to affect the FF and T2 values of the submandibular glands. The fixed-effects estimates were not sufficient to correct for the effect of subject characteristics on qMRI values. Comparison of HC and patient cohorts showed differences in ADC, FF, and T2 for the parotid and submandibular glands, which can partly be explained by the effect of age. For the submandibular glands, the xerostomia cohorts also differed in ADC and T2 values, which can be due to the effects of dose, since the mean dose of the glands differed for the two patient cohorts. This effect was not observed for the sticky saliva cohorts. The hybrid DIR outperformed the biomechanical DIR and was therefore used in the delineation process of the SCR region. It was feasible to delineate the SCR region based on MR sialography imaging and map the delineation to qMRI maps and planning CT.

Conclusion: The findings of this study show the promise of ADC and T2 values in quantifying radiation-induced toxicity long-term after treatment, providing a basis for an improved understanding of long-term toxicities in head and neck cancer patients treated with RT.

Over the next couple of decades, the world will face the challenge of drastically reducing carbon emissions. Innovative Generation-IV nuclear reactor designs can play an important role in driving this energy transition. One of these designs is the Molten Salt Fast Reactor (MSFR), characterized by a fast neutron spectrum and the use of a liquid fuel. Because of the liquid fuel, melting and solidification phenomena need to be considered. To this end, this thesis presents a combined experimental and numerical investigation of melting and solidification phenomena in the MSFR. The experimental part was primarily motivated by the lack of suitable experimental data for the transient development of an ice-layer in internal flow, which is a relevant case for the analysis of accident scenarios in a MSFR where solidification may pose a risk. The main focus of the numerical part was to improve the computational efficiency of current state-of-the-art melting and solidification models.

As part of the experimental investigation, a new experimental facility (ESPRESSO) was designed and built. The ESPRESSO facility consists of a water tunnel capable of reaching both laminar and turbulent flow rates, in which ice is grown from a cold plate at the bottom of a square channel. The ESPRESSO facility was designed to have well-described experimental boundary conditions, through careful consideration of the inflow and cold-plate specifications. Subsequently, experimental data was generated for the transient development of an ice layer in laminar internal flow using particle image velocimetry (PIV), which may be used for numerical validation. The onset of ice formation was found to coincide with a sudden increase of the cold-plate temperature, which was therefore used to identify the zero time instant in our experiments. This was attributed to subcooling effects prior to nucleation, of which evidence was obtained using laser induced fluorescence (LIF) temperature measurements.

In addition, non-intrusive temperature measurements have been performed for the transient development of an ice layer in laminar channel flow using LIF, which is so far only the second application of LIF as a non-intrusive temperature measurement technique in solid-liquid phase change experiments. The LIF method presented in this thesis is a novel approach for solid-liquid phase change experiments because of the use of a two color (instead of a one color) technique, the use of a post-processing algorithm to remove top to bottom striations and reduce other measurement noise, and a detailed analysis of the uncertainty in the temperature fields. Good results were obtained for sufficiently large temperature differences of approximately C with an uncertainty of σ=0.3-0.5 °C, however further improvements are needed to remove artefacts as a result of laser light scattering from the solid-liquid interface, and to obtain a sufficiently high accuracy for numerical validation purposes, especially for smaller temperature differences.

The numerical work performed as part of this thesis aims to address the need for more efficient melting and solidification models, which can accurately capture the solid-liquid interface and resolve the recirculation zones in the fluid region at a lower computational cost. To this end, an energy-conservative DG-FEM approach based on the `linearized enthalpy melting/solidification model' was developed and validated. Although certain solid-liquid phase change problems with strong gradients in the flowfield can benefit from the use of the higher order DG-FEM method, overall a suboptimal O(h) mesh convergence rate was obtained due to an inaccurate numerical solution of the discontinuities at the solid-liquid interface. Therefore, further development of the DG-FEM solid-liquid phase change solver is needed to fully benefit from the arbitrarily high order of accuracy of the hierarchical polynomial basis function set.

Very promising results were obtained with a parallel finite volume adaptive mesh refinement method for solid-liquid phase. Cells were refined based on the maximum difference in the liquid fraction over the cell faces and the estimated numerical discretization error in the flow and temperature fields, using the cell residual method. With this approach, a very good agreement was obtained between the adaptive mesh results and the reference solutions on a uniformly refined grid with significantly less degrees of freedom. This demonstrates the potential of the proposed finite volume adaptive mesh refinement approach as a more computationally efficient numerical method for solid-liquid phase change problems.

The final part of this thesis details a five-stage benchmark for modelling phase change in molten salt reactors, modelled after the MS(F)R freeze-valve design. With each stage, an additional layer of complexity is added, which enabled the identification of potential sources of discrepancy between different numerical modelling approaches. Results were obtained with three different codes: STAR-CCM+, OpenFOAM and DGFlows (inhouse DG-FEM based code for computational fluid dynamics). The results from the benchmark showed an overall good agreement between the three codes, although some discrepancies were observed when adding conjugate heat transfer effects. Therefore, we recommend some caution when coupling different solid-liquid phase change and conjugate heat transfer modelling approaches.

To summarize, this thesis presents new experimental data for the transient ice-growth in laminar internal flow, driven by a general lack hereof. In addition, this thesis illustrates the potential of LIF as a non-intrusive temperature measurement technique for solid-liquid phase change experiments. Two new numerical methods were developed and validated for solid-liquid phase change problems, and especially the finite volume adaptive mesh refinement approach showed promising results in terms of enhanced computational efficiency. On a final note: solid-liquid phase change is a vast and ongoing field of research. We believe this thesis is a substantial addition to the field, yet there are still a lot of opportunities for future work. Some suggestions are given in the concluding chapter.

With FLASH proton radiotherapy, healthy tissue is spared more compared to conventional proton therapy. The FLASH effect is present at high fractional doses of more than 8 Gy, at ultra-high mean dose rates of more than 40 Gy per second and at dose delivery times of less than 200 milliseconds. However, particle accelerator intrinsic uncertainties can influence the FLASH effect negatively. FLASH proton therapy is affected by pencil beam positioning errors and by proton beam current fluctuations. In this work, these two types of uncertainties were added to a Gaussian two-dimensional analytical dose model. The impact of pencil beam placement errors was evaluated on dose deposition and related to clinically used metrics. These are the V95, V107, D2 and D98. The constraint on the V95 was violated for 5\% of patients first. For all evaluated FLASH dose fields, the allowed Gaussian pencil beam placement error is less than 1.0-mm in standard deviation. A trade-off between target coverage and the level of FLASH effect was found. Proton beam current fluctuations were coupled to the pencil beam scanning dose rate (PBSDR98), the minimum dose rate for 98\% of the target volume. For all evaluated FLASH fields the permitted beam current fluctuation was 6.8\%. This is considered more achievable than the limit on pencil beam placement errors. Proton FLASH radiotherapy is feasible, but proton beam characterisation is required to quantify for which patients this is the case.

The PBSDR is sensitive to added uncertainties and contradicts our current understanding of the FLASH effect. In this thesis, a more robust metric is developed which depends on the radiolytic oxygen depletion hypothesis for the FLASH effect. This metric is called the FER_eff. The oxygen concentration over time in a cell is modelled with an ordinary differential equation (ODE) involving an oxygen depletion and re-oxygenation term. The FER_eff can be calculated with the oxygen concentration over time for a treatment plan. Currently, The onset of the FLASH effect lies between a prescribed dose of 8 Gy and 16 Gy. This is in line with the FLASH dose threshold. The shortcomings of the PBSDR are dealt with.

A three-dimensional uncertainty analysis can be done with a semi-analytical dose engine from the TUD. With this engine, changes in dose deposition are coupled to Hounsfield unit (HU) perturbations without the necessity of a full dose re-computation. To study the machine uncertainties, an EMC FLASH treatment plan formed with iCycle was recreated with the TUD dose engine. The iCycle optimisation results contain all the required information for a dose calculation. The gamma pass rates between the iCycle dose and engine dose were satisfactory for the target but not good enough for an organ-at-risk (OAR) yet. Similarity can be improved by adjusting the dose recreation procedure. When the iCycle dose and engine dose are comparable, a trustworthy clinical uncertainty analysis can be done. The idea is to simulate field and individual pencil beam placement errors by shifting the original patient CT to a virtual CT. First, it should be studied if the computed dose response is valid for a combination of CT shifts and HU perturbations. In a later stage, pencil beam placement errors should be coupled to the clinically used ICRU metrics and constraints. The impact of beam current fluctuations can also be studied in the future.

Introduction: Head and neck cancer (HNC) is a common and diverse group of tumors located in the region from the nasopharynx down to the upper part of the esophagus. Radiotherapy plays a crucial role in HNC treatment. In this thesis the particular focus is on external photon beam radiotherapy. The research is conducted in collaboration with the radiotherapy department of the Leiden University Medical Center (LUMC).
Theoretical background: The quality of a radiation treatment plan significantly affects patient outcomes in radiotherapy. Excessive radiation to organs at risk (OARs) can lead to complications, while insufficient dose to the tumor may increase the risk of recurrence. Automating the treatment planning process has gained attention in recent years, aiming to improve plan consistency, quality, and planning time. This study focuses on the optimization of treatment planning using RayStation’s deep learning autoplanning (DLAP) for patients with HNC.
Method: The study consists of three patient cohorts. The first and largest cohort includes 43 oropharynx patients. The second cohort includes eleven hypopharynx patients and eight larynx patients. The third cohort consists of nine unilateral oropharynx patients. Dosimetric analysis and normal tissue complication probability (NTCP) analysis are performed for both the clinical and DLAP plans in all cohorts. Dosimetric analysis uses parameters from dose volume histograms (DVH), while the NTCP analysis follows the Dutch National Indication Protocol for Proton Therapy for HNC.
Results: An initial sub-study determines the optimal tuning for the DLAP model, which is not only used in this study but also chosen for clinical implementation at the LUMC. In the following comparison study, all patient cohorts demonstrate higher Planning Target Volume (PTV) coverage in the DLAP compared to the clinical plans. The OAR dosimetric parameters show varying results, with DLAP generally demonstrating similar or better sparing of the OARs in oropharynx, hypopharynx, and larynx tumors. However, DLAP show a significantly higher dose in the brain stem core for larynx patients. Furthermore, an increased dose is observed in the mandible across all patient cohorts. Unilateral oropharynx patients treated with DLAP show a significant increase in dose to several OARs, particularly the contra-lateral salivary glands and swallowing muscles. The NTCP analysis does not reveal notable improvements or worsening across all patient cohorts.
Conclusion: DLAP demonstrates promising results for oropharynx patients, raising the question if further improvements in PTV coverage to achieve lower doses in the OARs are necessary. Although the patient cohorts for hypopharynx and larynx are small, the study’s findings indicate the potential for generating adequate treatment plans in these HNC regions. Furthermore, the results also highlight the need for further investigation in unilateral oropharynx cases, as DLAP did not sufficiently spare the contra-lateral side. The divergence in treatment technique suggests waiting for a specifically trained and designed DLAP for unilateral oropharynx patients.

Intensity modulated proton therapy is an advanced radiotherapy technique that is used to treat cancer patients. In order to successfully treat a patient, sufficient dose to the tumor is required. However, during the fractionated treatment, multiple errors can cause a difference between the planned and actual dose delivery. To ensure adequate dose delivery in potential error scenarios, robust treatment plans are acquired as these are less sensitive to uncertainties inherent to proton therapy. However, robust optimization is challenging.

First, as robust optimization accounts for multiple error scenarios, the time needed to generate optimal treatment plans increases significantly. Therefore, it is investigated in this thesis if the optimization time can be reduced while preserving treatment plan quality. This is investigated through two different methods. In the first method, the number of error scenarios accounted for during optimization is reduced. We found that this can significantly reduce optimization time, while improved target coverage and lower risk on side effects are obtained. However, the near-maximum dose to the tumor was found to be less favourable. The second method investigated is variance optimization. This method significantly reduces optimization time. However, for similar target coverage, the risk of side effects increases.

Another challenge related to robust optimization is the increase in delivered dose to healthy tissues surrounding the tumor, which increases the risk of side effects. Therefore, it is investigated in this thesis if the risk of side effects can be lowered by allowing higher maximum dose to the tumor. It is found that this method indeed reduces the risk of side effects. However, the increased maximum dose to the tumor may not be clinically desired as the increase may lead to higher risks of other side effects: edema and fibrosis. The clinically desired trade-off between near-maximum dose and normal tissue sparing should be established.

Proton irradiation therapy is a powerful form of cancer treatment, promising better dose conformity as compared to conventional radiotherapy. Due to the complex scattering properties of protons, the optimization process that is needed to accurately target the cancer cells whilst causing minimal damage to
the surrounding healthy tissue and minimizing detrimental effects, is very time-consuming. This means that the CT scan it is based on has lost part of its accuracy in describing the to be irradiated tissue. To account for this, the surrounding tissue is irradiated more to ensure effective treatment, reducing dose conformity and thus increasing the probability of detrimental side effects.
To solve this problem, a new proton therapy method concept, called Online Adaptive Proton Therapy, or OAPT, calls for a CT scan to be taken about 30 seconds before the treatment, allowing the planned treatment to be adapted to any anatomical changes that have occurred since the previous scan where the original treatment planning was based on. The computations required for this adaptation, and the required quality assurance, currently still take significantly longer than 30 seconds on current computational hardware, making the concept not yet viable in its current form. However, using GPU-acceleration, parts of the algorithm that is used for this can be significantly sped up to reduce overall computational time, potentially making the concept viable for real world application. In this thesis, the research question ”How can GPU-offloading decrease computation time for proton therapy dose calculations?” is answered by accelerating two model algorithms representative of two time-consuming steps in the proton therapy optimization process and analyzing the performance, on
an NVIDIA V100S GPU, of the accelerated code. Furthermore, a model is postulated and validated to characterize and predict the performance of a GPU accelerated algorithm. Using OpenACC, both algorithms achieved speedups between 30x and 440x excluding data transfer time, and between 0.88x and 40x including data transfer time, with both values depending on the problem size, with larger problems yielding larger speedups. Further research is needed on the validity of the derived model on different hardware and for different algorithms. Furthermore, additional research on the effect of implementing these accelerated algorithms on the total computation time of the real world algorithm is advised.

Over 50% of cancer patients will receive radiotherapy treatment at least once. Most patients are receiving photon radiotherapy. In this work very high energy electron (VHEE) radiotherapy is being studied as a potential replacement for photon radiotherapy. VHEE beams have a favorable depth dependence and the penumbra of VHEE pencil beams stays small deep inside the patient. Therefore, using VHEE radiotherapy can potentially result in a lower dose being delivered to the organs at risk (OAR) in comparison with clinically used volumetric modulated arc therapy (VMAT). New accelerator techniques allow VHEE beam generators to fit in standard radiotherapy treatment bunkers. Therefore, VHEE therapy can reduce the equipment costs in comparison with proton therapy and it can increase the treatment quality in comparison with photon therapy. In this work the VHEE treatment plans are compared with clinically used VMAT treatment plans for prostate and lung cancer.

VHEE treatment plans were generated for 6 patients with prostate cancer and 3 patients with lung cancer. First, the pencil beam dose distributions were calculated for each patients using a Monte Carlo particle simulation tool called TOPAS MC. Thereafter, the optimal intensities of the pencil beams were calculated using iCycle, an automated optimization tool, which calculates the optimal treatment plan. The VHEE treatment plans are generated with 9, 18 and 36 beams and the energies that are used are: 100, 200, 300 and 400 MeV. The treatment plans were normalized to a 99% PTV coverage of 95% of the prescribed dose.

For the prostate case, the 100 MeV VHEE treatment plans deliver more dose to the organs at risk (OARs) than the VMAT plan. The 18 beam 300 and 400 MeV VHEE treatment plans showed a dose reduction in the mean dose of the patient, the rectum, the anus and the bladder, but a dose increase to the left and right femoral heads. The 18 beam 400 MeV treatment plan reduced the dose to all OARs in comparison with the VMAT plan, for the lung cases. Increasing the number of beams of the VHEE treatment plan reduces the dose to the OARs, for both the prostate and the lung cases. Increasing the energy of the electron beams also reduces the OAR dose for both cases.

VHEE plans reduce the dose to the healthy tissue, while keeping the PTV dose constant and can therefore be considered as a possible replacement for photon radiotherapy.

The Molten Salt Fast Reactor (MSFR) is a next generation nuclear reactor. The MSFR may play an important role in combatting global warming whilst ensuring energy safety considering fossil fuels’ finiteness. A key safety mechanism for the MSFR is the freeze plug, a valve underneath the reactor core designed to melt during reactor malfunction, letting the fuel salt drain into an emergency draining system.

In this thesis, the effect of the inclination angle of the freeze plug on its melting behaviour was investigated. This was done via the Linearised Enthalpy Method for phase change in OpenFOAM 8, a Finite Volume Method software package. First, two benchmark cases - one of inclined gallium melting and one of a heater copper fin in air - were performed. These showed reasonable agreement with established results.

A cylindrical freeze plug consisting of LiF-ThF4 salt was defined, with copper and hastelloy annuli around it to simulate the cooling and the draining pipe, respectively. Steady-state simulations were performed for inclination angles of 𝜃 = 0°, 15°, 30°, 45°, 60°, and 90°. Via simulations on meshes with 40,500 and 1.1 million cells, it was shown that the freeze plug did not form at 𝜃 = 60° and 90°. For the other four inclination angles, the resulting freeze plug was found to be mesh convergent via a third mesh of 3.6 million cells.

Then, a transient simulation mimicking reactor malfunction was performed for the inclination angles 0° ≤ 𝜃 ≤ 45°. It was found that the start and end opening times - the times where the melt front first and last reached the freeze plug’s bottom - were reduced by 74% and 52%, respectively for 𝜃 = 45° with respect to 𝜃 = 0°. The other two 𝜃’s also showed lower opening times compared to 𝜃 = 0°. The inclination angle thus was found to have a significant effect on the freeze plug’s melting behaviour, shortening the opening times.

Physical improvements for the model include the incorporation of molten salt leakage after start opening time, and settling. Computational improvements are also possible, such as the refinement of the mesh near the salt boundary or adaptive mesh refinement near the solid-liquid boundary. Symmetry can be exploited to speed up results.

The aim of this thesis is to study the dosimetric feasibility of FLASH proton therapy for early-stage breast cancer patients. The biological effect of FLASH is seen under ultra-high dose-rates conditions and is beneficial in the damage to healthy tissue. The FLASH effect could enable the clinical feasibility of definitive radiotherapy for low-risk early-stage breast cancer patients. Some of these patients can not receive surgery for medical reasons and definitive conventional radiotherapy carries a high risk of toxicities. FLASH proton therapy could be a viable option for these patients. The biological FLASH effect enables to reduce the risk of toxicities by sparing healthy tissue and proton therapy enables to deliver dose to the cancer cells effectively.
This thesis proposes a pencil beam scanning (PBS) ridge filter simulation set-up to achieve ultra-high dose-rates. The ridge filter generates spread-out Bragg peak (SOBP) beams that cover a broader depth of the tumor, avoiding the time-consuming energy switching of conventional PBS. An optimization is performed with intensity-modulated ridge filtered beams. SOBP beams with a width of 3 cm are implemented in the in-house treatment planning software Erasmus-iCycle to generate ridge filter treatment plans for two patients.
In this study, the dosimetric feasibility is determined by comparing the ridge filter treatment plans to conventional intensity-modulated proton therapy (IMPT) treatment plans. The clinical acceptability of the treatment plans is assessed by dose uniformity and dose coverage. Furthermore, toxicity-model endpoints for fat necrosis and fibrosis are used to evaluate the treatment plans. The generated ridge filter treatment plans outperform the generated IMPT treatment plans for a FLASH enhancement ratio between 1.19-1.39 for one of the patients. The other patient required a FER in the order of magnitude of 2.0.
The results of the study suggest that it is feasible to generate ridge filter treatment plans with the proposed set-up. However, the dosimetric feasibility comes with limitations in the tumor characteristics (size and position) and needs further investigation. More knowledge is needed of the optimal ridge filter, the optimization of SOBP beams, and the FLASH effect before clinically acceptable FLASH-compatible ridge filter treatment plans can be achieved.

In this report, the conversion from spin-echo signals, obtained with a low-field hand-held MRI scanner that was designed and built at the Leiden University, to images of the proton density within the sample is considered. This scanner does not make use of switchable gradient coils, but instead relies solely on the natural inhomogeneity of the field and on translations of the sample over this field for its spatial encoding. Specifically, an attempt is made to answer the question of how we can reconstruct a phantom using this kind of scanner. This is done by deriving a signal model, discretising it and writing it as a linear least squares problem. Then, we can make use of the techniques of Cojugate Gradient for Least Squares (CGLS) wih `2-regularization and Generalized Conjugate Gradient Minimal Error (GCGME) with `1-regularization for the difference between neighbouring pixels in order to solve this inverse problem. Firstly, we theoretically consider combinations for magnetic field geometry and measurement strategy for their usability for image reconstruction. After this, the obtained strategies are tested in three experiments, with two magnets and two samples. We start by doing this numerically, using a simulated phantom in combination with a measured magnetic field and the translation strategy. By doing this, we can determine if reconstruction is possible using that combination of field and strategy. Finally, the strategy is tested on real samples. Using numerical phantoms in combination with the magnetic field and translation strategy used in the measurements, we were able to correctly reconstruct the phantoms. However, the reconstruction broke down when data from real samples was considered. A variety of possible improvements is discussed. The improvement that would have the most impact would be to design a magnet that has a less uniform gradient in the z-direction, and instead has some locations in the xy-plane where the field falls slowly as function of z, but quickly in other locations.