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…

Hyperthermia is a form of thermal therapy used in combination with radiotherapy (RT) or chemotherapy (CTx) to enhance their effects. By using electromagnetic (EM) waves, tissue can be locally heated to temperatures between 39−44 ◦C. When applied to tumor tissue, this heating induces various biological responses that enhance both RT and CTx. The clinical workflow includes a hyperthermia treatment planning (HTP) stage, where treatment parameters are optimized to determine the phase and amplitude settings for the applicator antennas. HTP is subject to significant uncertainties. Variability in patient anatomy, dielectric and thermal tissue properties, patient positioning, and applicator modeling causes variations in the temperature distribution and thus affects the treatment. This study uses polynomial chaos expansion (PCE) to model these uncertainties and evaluate their impact on treatment parameters. PCE serves as a meta-model of the simulation software within a defined range of input variables. This meta-model allows for rapid calculation of temperature distributions, enabling the sampling of numerous scenarios to achieve statistical accuracy regarding the impact of treatment uncertainties. We successfully created a pipeline including patient modeling, treatment planning and uncertainty analysis using PCE. We developed separate smaller sub-models for different sources of uncertainty, including positioning, dielectric conductivity (σ), dielectric permittivity (ϵ), thermal conductivity (k), and perfusion rate (ω). Using these models we assessed the feasibility of building a PCE model for each uncertainty and determine the optimal settings for a comprehensive model combining input variables from different uncertainty sources. A high impact on the temperature achieved in 90% of the target volume (T90) was observed, with standard deviations observed up to 1.36 ◦C. Uncertainties in positioning, σ and ω had the largest impact, the impact of ϵ and k was significantly lower. The final model incorporated 31 parameters selected based on their impact on treatment parameters in a univariate analysis. This model was used to evaluate the combined effect of all treatment uncertainties, we did not succeed in maintaining the same accuracy as we show for the sub-models. We show that uncertainties are not necessarily additive, and that the combined effect of these uncertainties induced larger deviations in T90. The results demonstrated the potential of PCE to effectively handle complex uncertainty analysis in HTP, providing a robust framework for analyzing HTP. Future work should focus on validating these findings with a larger patient cohort to enhance the generalizability and reliability of the approach.

To reduce the probability of complications in proton therapy, while maintaining a high tumor control probability, adaptive treatment can be applied. In adaptive treatments, the treatment plans are frequently assessed and adjusted to, for example, account for anatomical changes. Ideally, daily adaptive treatment would be implemented, where every day a repeat scan is made and the treatment plan is adjusted. However, due to computational limitations, daily adaptive treatment is not possible yet. Quality assurance (QA) is a vital part of the proton therapy workflow. Intending to implement daily adaptive treatment, fast-working quality assurance tools are necessary. The goal of this thesis is to calibrate and adapt a deterministic proton transport algorithm to reconstruct the delivered dose using log files, which can be compared to the planned dose as a QA tool.

To achieve this, Yet anOther Dose Algorithm (YODA) was calibrated to the popular planning software RayStation, by optimizing the input parameters of YODA to minimize the difference in dose between YODA and RayStation for a 0° gantry angle single spot in a homogeneous water phantom. From this calibration, beam data library (BDL) files were created for cases without a range shifter and with range shifters of thicknesses 2 cm, 3 cm and 5 cm and planned spot energies ranging from 70 MeV to 190 MeV. An approximation to improve the inclusion of the effect of nuclear interactions was added to YODA. The lowest passing rate found was 99.47% for a 190 MeV spot without a range shifter, therefore the calibration was successful. The passing rate decreased for high energies, likely due to the crude approximation to deal with nuclear interactions. Other ways to include
the effect of nuclear interaction should be investigated to further improve the calibration results. After the calibration was complete, three experiments were performed.

First, simple treatment plan comparisons were performed using the BDL files and a homogeneous water phantom, including plans containing a single spot irradiated from gantry angles ranging from 10° to 90°. To account for the angled beams, a beam splitting algorithm was used. It was observed that the BDL files are specific for the isocenter to CT volume surface distance, as the boundary conditions of YODA are at the CT volume surface while the treatment plans define spots at the isocenter in air. To include this effect, the BDLs should contain beamlet parameters at the isocenter, from which the beamlet parameters at the CT volume surface can be calculated. The calibration procedure for the spatial spread, angular spread and correlation needs to be adjusted. Alternatives to the beam splitting algorithm should be investigated, as this algorithm inadequately reflects reality when a beam enters the CT volume under an angle.

Second, YODA assumes that spots are laterally symmetrical, however, in reality, spots are ellipse-shaped. To solve this, the asymmetrical spot solution to the Fermi-Eyges equation was derived. The difference in integrated Fermi-Eyges flux between the symmetrical and asymmetrical spot was calculated for realistic combinations of lateral spread, angular spread and correlation. The mean error in integrated Fermi-Eyges flux, relative to the maximum, induced by assuming lateral spot symmetry, around the central beam axis is significant, as it ranges from 0.6853% to 3.071% at the entrance of the CT volume and from 0.4710% to 4.957% at the Bragg peak. Therefore the asymmetrical spot solution should be implemented, after which, YODA should be re-calibrated

Third, the error induced by systematic errors in the log file was investigated. The plan contains a target cube centered in the homogeneous water phantom irradiated by a 0° gantry angle beam. By perturbing each energy layer randomly using a uniform distribution, where the maximum perturbation was 0.8 mm in spot position, 1% for MU and 0.1% for energy, the magnitude of the dose difference was calculated. The mean differences in dose in the target cube induced by randomly perturbing each energy layer were 0.1204% ± 0.0408% in x, 0.1700% ± 0.0324% in z, 0.2592% ± 0.1595% in MU and 0.4802% ± 0.1558% in energy. These differences are small compared to the error induced by assuming symmetrical spots, note that the differences in spatial spread were an order of magnitude bigger than the perturbation in spot position. Before this investigation on the effect of systematic errors can continue, the asymmetrical spot solution needs to be implemented and the problems discovered with angled beams should be solved.

The calibration was successful, and additional extensions and alterations have been identified to further improve YODA before it can be used as the described patient-specific quality assurance tool.

The dose computation algorithm, or dose engine, is one of the fundamental parts of radiotherapy treatment planning. These algorithms predict how the dose will be distributed inside the patient.
Current dose engines are mainly based on either Monte Carlo simulations (MC) or pencil beam algorithms (PBA). MC being very precise, but relatively slow. PBA being quicker, but generally lacking accuracy. Since treatment planning requires both high speed and accuracy, one would prefer MC accuracy with even higher speeds than PBA. A recent study showed a possible solution based on deep-learning called the Dose Transformation Algorithm (DoTA). This deep-learning algorithm is capable of doing MC accurate dose calculations and is faster than PBA (Pastor-Serrano and Perk ́o 2022).
In this project, a feasibility study has been performed on the integration of DoTA as a dose engine in actual treatment planning. The treatment planning system (TPS) in this study is Erasmus- iCycle (Breedveld, Storchi, et al. 2012). This study included the creation of an algorithm to do dose computations with DoTA for any given set of parameters given by the TPS. Subsequently, the dose computations by DoTA have been compared to those computed by Erasmus-iCycle’s current dose engine, ASTROID (Kooy et al. 2010). Analyses on these dose computations included comparisons in a homogeneous water box, alternative homogeneous matter and patient geometries. Two main sources of discrepancy between DoTA and ASTROID where the beam’s range and the beam model used by ASTROID, compared to what DoTA was trained on. Both dose engines likely use a different interpretation of the proton stopping power, leading to range discrepancies up to 14.9% for 200 MeV beamlets when projected in a homogeneous matter of 1000 Hounsfield Units (HUs). Comparing the dose distributions in water, the maximum dose discrepancy around the Bragg peak (BP) for a 80 MeV beam was about 60.0%, due to the width of the beam being larger for DoTA. The mean dose discrepancy in water reached a maximum of 18.9%. In a patient geometry, the range differences made the mean discrepancies go up to a maximum of 22.9%, as expected from the range discrepancies found earlier. Implementation of different gantry and beamlet angles increased the discrepancies, likely caused by the interpolation required to perform calculations under these angles. In terms of distributed energy, the models were closer, with the mean discrepancy decreasing to maximum of 7.1%. Computations of two treatment plan dose distributions showed that the discrepancies arising from this beam model and range difference were to large to achieve viable dose volume histograms. A two lateral beam plan showed the better results of the two plans with an under dosing of 20.8%, likely due to robustness occasionally compensating for the range discrepancy.

Radiotherapy is one of the main treatments for cancer and relies heavily on CT images to calculate radiation dose. With research on radiotherapy moving to adaptive treatments aiming to calculate these doses at real-time speeds while maintaining high precision, a need for accurate CT imaging at comparable real-time speeds has emerged. Currently, the best performing CT image reconstruction methods are iterative reconstruction (IR) methods, which suffer from slow reconstruction speed. Faster methods are accompanied by artifacts due to the implementation of simplified physics models.

Recently, the Dose Transformer Algorithm (DoTA) [47], [48] and improved DoTA (iDoTA) [49] have shown to successfully calculate radiation therapy dose by modelling particle transport in 3D with the use of a neural network. By implementing a Transformer architecture [62], DoTA is able to capture the relationship between elements in a 3D CT volume while processing it as an input sequence. This results in an accurate prediction of particle transport, while significantly reducing computation times compared to other methods.

A neural network based on the DoTA-architecture is presented. It predicts projection data from CT input, modelling the x-ray photon transport. The network processes 2D CT images as a sequence of 1D lines. The ground truth data contains Monte Carlo projections of cylindrical water phantoms with inserts composed of five different materials.

The predictions are compared to Monte Carlo projections and raytracing projections generated with Astra Toolbox [45], as well as a Two-Angle Convolution (TAC) network [11]. The average NRMSE of the Transformer predictions was 0.725% compared to 2.20% and 1.09% respectively for the raytracer and TAC. The Transformer showed the ability to predict from unseen types of geometries and intensity values. Due to bias in the training data, it does not generalize well to input phantoms with an unseen outer shape.

Two phantoms were reconstructed using the network within an IR algorithm. For the Transformer and raytracer, the highest achieved CNR values are similar for low-contrast regions (6.88 and 8.28 for the raytracer compared to 7.10 and 7.35 for the Transformer) as well as high-contrast regions (37.40 and 41.94 for the raytracer compared to 39.01 and 39.80 for the Transformer). Convergence rates based on low-contrast CNR are higher for the raytracer (39 and 34 iterations compared to 41 and 41 iterations for the Transformer, respectively). The Transformer performs significantly better than the raytracer with respect to beam-hardening artefacts. The IR algorithm has not been tuned for use with the Transformer, suggesting that a higher performance is obtainable with adjustments such as the implementation of a different backprojector or a different value for correction factors used in the algorithm.

Limitations in prediction quality are likely related to factors outside of the model predictions, such as biases in the input data and resolution loss due to interpolation of the input data. When its prediction speed is optimised, the CT Transformer model has potential to replace conventional forward projections in IR methods, achieving Monte Carlo-level accuracy with a fraction of the computation time.

The goal of radiotherapy is to maximize the dose to the target while minimizing the dose to normal tissue. Treatment plans are optimized for this goal and dose delivery is improved in accuracy and precision. The optimization is based on the delineations of the volumes of interest on the medical images of the patient. The problem is that these delineations contain uncertainties and the effect of these uncertainties become more pronounced as the accuracy and precision of dose delivery improves. The delineation uncertainties are caused by various factors such as knowledge and experience of the observers, guidelines, and image quality and modality. The goal of this thesis is to research the effects of delineation uncertainties. Uncertainties are characterized using a rolling ball algorithm (RBA) to modify the delineation. The radius of the ball represents the uncertainty and ranges from -5 mm to 5 mm for the clinical target volume (CTV) and -2 mm to 2 mm for the brain stem. The effect of these uncertainties will be researched for both fixed and re-optimized dose distributions. These are then used as input to create a model that will simulate the dose distributions for different uncertainties using Polynomial Chaos Expansion (PCE). PCE will be used to model dose volume histograms (DVH) of the CTV and the brain stem. The dosimetric effect will be determined by setting confidence intervals in D98% of the CTV and D2% of the brain stem. The widths of the confidence intervals in these two metrics represent the dose uncertainty. This thesis uses three sets of patient data. Each patient had a CTV close to the brain stem. Dose uncertainty in the two metrics was found to increase as the uncertainty of CTV and brain stem delineation increases. For a fixed dose distribution, a delineation uncertainty of 0.75 mm to 1.25 mm in the CTV would lead to a dose uncertainty of 2 Gy in the D98% of the CTV. A delineation uncertainty of 0.25 mm to 0.5 mm in the brain stem would lead to the same dose uncertainty in D2% of the brain stem. For a re-optimized dose distribution, a combined delineation uncertainty of 1.25 mm for two patients and 4.5 mm for one patient would lead to a dose uncertainty of 2 Gy in D98% of the CTV. For the same dose uncertainty in the D2% of the brain stem, there would be a combined delineation uncertainty between 1.0 mm and 4.5 mm. For all three patients, the dose uncertainty in the D2% was more sensitive to delineation uncertainties in the brain stem. The effects of these uncertainties will depend on the nominal situation. For all patients a 2 Gy dose uncertainty corresponds to 2.85% of the prescribed dose to the CTV and 3.33% of the maximum dose constraint of the brain stem. One patient was on the boundary of underdosing the CTV in the nominal situation and a 2 Gy uncertainty would be sufficient to underdose the CTV. The nominal D2% for all three patients was sufficiently low that it is unlikely it would exceed the maximum dose constraint.

Computational power is a challenge when it comes to the high-fidelity modeling of nuclear reactors. Detailed simulations of reactor physics involve complex calculations that require significant computing resources, which can be time-consuming and expensive. Reduced Order Modeling (ROM) allows for an approximation of a complex model by only capturing the essential features, thereby reducing the computational load. A reduced order model provides computationally efficient approximations of a system, but it requires still many evaluations of a high-fidelity model to capture all the dynamics. Using the adaptive sparse grid can reduce the number of evaluations needed, though the construction of the reduced order model is still computationally intensive.

The aim is to minimize the computational workload involved in constructing a reduced-order model during the offline phase. This is achieved by decreasing the number of high-fidelity model evaluations necessary for building the reduced order model while maintaining accurate results. To this end, the existing adaptive proper orthogonal decomposition algorithm is enhanced by employing multi-fidelity techniques. Multi-fidelity methods aim to combine large amount of low-fidelity data with a limited amount of high-fidelity data to compute accurate, yet computationally inexpensive approximations. Two novel multi-fidelity reduced order model methods based on proper orthogonal decomposition are proposed; Filtered Bi-Fidelity Adaptive Proper Orthogonal Decomposition (FB-POD) algorithm and Adapted Bi-Fidelity Proper Orthogonal Decomposition (AB-POD). These models are evaluated on two different test cases, and the balance between the accuracy of each multi-fidelity ROM and the computational cost, measured by the number of high-fidelity evaluations, is investigated. In specific cases, the proposed methods significantly reduce the number of high-fidelity evaluations compared to the single high-fidelity ROM, while yielding comparable accuracy.

To evaluate the effect of interplay due to breathing of the patient during proton treatment of lung tumors Interplay dose calculation techniques have been proposed in literature. The proposed method requires the deformation vector field (DVF) to register dose distributions of different phases in the breathing cycle to a reference phase. The DVF is obtained by registering 4DCT lung scans between the phases. Current methods of image registration are too slow to make the interplay dose calculation techniques clinically feasible.

Advances in deep learning have allowed for models that predict the DVF in orders of magnitude quicker than traditional methods. In this research, two model architectures, previously applied for registration of brain MRI images, will be evaluated to predict the DVF between scans at different phases of a 4DCT lung scan. The quality of the registration is evaluated based on the mean absolute error between the images and contour metrics of organs including the Dice score, Hausdorff distance and the mean surface distance. In addition, the amount of grid folding was evaluated based on the number of voxels with a negative Jacobean determinant.

The first model architecture, VoxelMorph, is an unsupervised model with an U-net architecture. Two hyperparameters were varied: the maximum size of the DVF limited by a HardTanh, and secondly the weight of the loss function for the divergence of the DVF during training. The model performed poorly in predicting the DVF, the values of the DVF were too small. Varying the hyperparameter seems to have no significant impact on the prediction quality of the model. Limiting the maximum of the DVF prevents the registration of large deformations, which is not favorable.

The second model architecture has a multi-resolution approach. The images are downsampled to 1/2 and 1/4 the resolution. Multiple sub-network predict a DVF at each of the resolutions in a coarse to fine order. Each of the networks consisted of a feature encoder, residual blocks and a feature decoder. By upsampling and combining the multiple DVFs, the final DVF is obtained. Hyperparameter search is performed: The number of residuals blocks and their filters were varied. At first only for the coarses network, and later for all the networks. Lastly, an additional resolution was added to the model. The model was capable of predicting good-quality DVFs. Only varying the number of residual blocks and their filters for all resolutions resulted in a significant difference in the quality of the prediction.

Predictions are performed in 260±4 ms and 24±4 ms for the first and second architectures respectively. Which is faster than other deep learning methods found in literature, and significantly faster compared to traditional registration methods

Dose calculations in proton therapy need to be computed as fast as possible for successful cancer treatment planning and execution. The dose calculation algorithms that provide enough accuracy for treatment planning, takes too much time to utilise; therefore there is a need for faster alternatives. One of the alternatives is using a deterministic semi-analytic numerical algorithm for EM interactions. This alternative in its current state is not accurate enough, and therefore it is sought to include the effects of secondary protons on the total dose distribution of the deterministic semi-analytic numerical algorithm, using convolutional methods. In this thesis an attempt is made to find a kernel that, when convoluted with a primary proton flux, produces the desired secondary proton dose. The parameters of two different types of kernels, the Gaussian kernel and Fractional Filter kernel, are optimised and their resulting shapes are presented. Furthermore, the secondary proton dose through the convolution of the primary proton flux and the different kernels are presented. The doses obtained from the optimal kernels are compared with the target dose on the shape and a measure of quality: the gamma index passing rate. Found was that the Fractional Filter kernel can produce both asymmetric doses and symmetric doses, while the Gaussian kernel can only produce symmetric doses. The passing rate was found to be 29.41% for the Fractional Filter kernel and 17.65% for the Gaussian kernel. Thus, the Fractional Filter is better for estimating secondary proton dose distribution through convolutional methods than using a Gaussian kernel. but insufficient due to the low passing rate. A suggestion for improvement is applying skew-Gaussians in the Fractional Filter kernel or by applying other asymmetric kernels.

High-fidelity models are computationally intensive to work with in many-query applications, such as the design process of small modular reactors. A reduced order model of the high-fidelity model can still accurately determine the quantities of interest with only a fraction of the computational cost, and thus can potentially solve the aforementioned problem. However, reducing a high-fidelity model of a small modular reactor is complicated due to the large number of parameters involved in nuclear reactor models, as that leads to an exponentially increasing parameter space needed to be surveyed.

Disregarding the parameters with the smallest impact on the output and thereby reducing the total number of variables can limit the parameter space, and thus speed up the model reduction at the cost of some accuracy. Perturbation theory utilizes the benefits of adjoint theory to efficiently determine sensitivities of responses to all the variables in the model, which allows one to find the influence on the output of the different variables without the need for evaluating them all repeatedly. It is then possible to apply a reduced order modeling technique such as proper orthogonal decomposition to determine and select only the most important eigenmodes of the high-fidelity model and build a reduced model.

This approach is applied to three different neutronics model of the U-Battery, varying in complexity. The presented method has shown to alleviate computational cost significantly for all examined reduced models. However, the upfront cost of building the reduced models by sampling the high-fidelity models has been considerable, especially when evaluating the resulting accuracy of the reduced models. A proper selection of the proper orthogonal decomposition tolerances must be made to ensure sufficient accuracy and to prevent oversampling. Nonetheless, combining proper orthogonal decomposition with perturbation theory showed to be a promising way of selecting only a few parameters for participation in the building of reduced order models while minimizing the loss of accuracy compared to the high-fidelity model.

In this report, a transformer based deep learning proton dose calculation algorithm called Dose Transformer Algorithm (DoTA) is described. This model learns to predict proton dose distributions by being trained with Monte Carlo generated data. Monte Carlo is the golden standard of proton dose calculation because it is very accurate, but it has relatively long computation times. In current proton therapy treatment programmes, Monte Carlo algorithms are the most commonly used models to perform dose calculation. The goal of the DoTA model is to predict proton dose distributions with Monte Carlo accuracy in the fraction of the computation time of Monte Carlo algorithms to speed up the dose calculation process in proton therapy treatment. The DoTA model can take patient geometry, random proton beam energy and random proton beam shape (2D Gaussian with different major and minor axes) as input. The addition of the random proton beam shape input is discussed in this report, together with a detailed explanation of the DoTA model. The DoTA model is trained with data from 9 lung cancer patients and 9 head & neck cancer patients. Being used on an Intel(R) Core(TM) i7-8565U CPU, the DoTA model managed to produce results with a gamma pass rate of 98.45 ± 2.60 % with an average computation time of 0.3 seconds. The gamma pass rate determines how similar the DoTA predicted dose is to the reference (Monte Carlo generated) dose. Compared to the average computation time of the Monte Carlo algorithm that was used to generate the training data, which is 20 seconds on the same CPU, we can conclude that the DoTA model has the potential to greatly improve dose calculation times in proton therapy treatment, especially when used on a system with greater processing power. Because the DoTA model is able to deliver accurate results in a small amount of time, it has the potential to be used for real-time dose calculation. Real-time dose calculation could account for small changes in patient geometry during treatment, which increases the accuracy of the treatment and minimizes side effects. The DoTA model can also be used for other radiotherapy types like phonon therapy and electron therapy (in that case it needs to be trained with
different data).

Adaptive proton therapy (APT) removes one of the most significant sources of inaccuracy in treatment delivery, which is using a treatment plan based on an outdated patient anatomy. Adapting the plan throughout the treatment is crucial for delivering an optimal dose to the patient, whose anatomy is constantly changing. This is especially true for proton therapy, where the delivered dose is highly dependent on the range accuracy. Imaging and plan adaptation must be performed online, immediately before the dose delivery, to take maximum advantage of the benefits of APT. The main problem with online APT is that adaptation of the treatment plan takes too long. Therefore, automation of the processes is required to ensure they can be executed adequately in a short time frame.

Deep learning methods have been successfully applied in two processes required for adaptation, namely the definition of structure contours on a CT scan and determining an optimal dose distribution for a given anatomy. Since a treatment plan is dependent on the locations of the different structures, dose prediction methods rely on manually defined contours, which are not available for daily CT scans in APT due to time limitations. This research aims to develop an approach that determines an optimal dose distribution for prostate cancer patients without using manual structure contours.

We use 3D U-Nets for image segmentation and registration as methods for defining the contours on an image. We use another 3D U-Net to predict an optimal dose distribution, which can use predicted or manually defined contours as input. In addition to this, we use two multitask learning approaches that allow one network to perform both contour definition and dose prediction, which makes it possible to share information between the tasks. The first approach is a cross-stitch network that allows two networks to share feature maps if this is beneficial and the second approach is a w-net that consecutively performs contour definition and dose prediction, using the predicted contours for the dose prediction.

The manual contour based dose prediction performed well in the area around the structures, resulting in a test set average 2%/2mm gamma pass rate of 93.4% ± 3.2% and a Dmean prediction error of 0.45% ± 0.36% in the prostate. The average errors for predicting measures such as D95 and V95% in the targets range from 1% to 3%.

The best method for predicting optimal dose distributions without manual contours is to first predict the contours on the CT scan and use those contours for the dose prediction. However, dose predictions based on predicted contours are significantly worse than those based on manual contours, having a 2%/2mm gamma pass rate of 83.8% ± 6.9% and a Dmean prediction error of 0.92% ± 0.7% in the prostate. Their average errors for predicting measures such as D95 and V95% range from 7% to 20%, which makes these predicted dose distributions too inaccurate to be helpful for treatment planning. This shows that dose prediction relies heavily on accurate knowledge of the structure locations, considering the predicted contours have similar quality as those from state-of-the-art methods.

Dose predictions have not improved by additionally learning a network the contour definition task. Using feature maps from other networks via cross-stitch units had no advantageous effect on the predicted dose distributions, mainly because dose predictions not based on structure masks were too bad for it to have any effect. The dose predictions from the w-net did not improve after the segmentation and dose prediction networks were trained together, which could be because the dose prediction loss could not improve the segmentation sufficiently. The main conclusion is that multi-task learning can only benefit related tasks if they can already be performed independently to a certain extent. It is not a substitute for missing information required to perform the task.

Sensitivity analysis and uncertainty quantification of nuclear reactors requires many expensive high-fidelity simulations. To approximate the dynamics of such a time and parameter dependent system efficiently and effectively, reduced order modelling (ROM) is used. In previous research, a ROM was constructed which used a combination of proper orthogonal decomposition (POD) and a locally adaptive sampling strategy based on sparse grids. To improve the representation of the physics in local parts of the parameter domain, in this thesis, the previous ROM is altered to use multiple local bases instead of one fixed global basis covering the entire parameter domain.

The spatially dependent local bases and local time dependent coefficients are interpolated separately in the parameter domain using the method of interpolation on a tangent space to the Grassmann manifold (ITSGM). The separate interpolators of the local bases and local coefficients are coupled in a space-time coupled approach. The algorithm based on sparse grids is modified so that it can adaptively draw new tangent planes in the parameter domain in a hierarchical manner. This results in the domain being split up into into smaller overlapping subdomains, each having their own tangent plane, number of basis vectors, and interpolators that use radial basis functions (RBF). The algorithm was tested on the Burgers Equation and the Molenkamp test which have an analytical solution. Then, the algorithm was tested on a numerically solved 2D neutron diffusion problem. First the parametric dependence of the modes and coefficients was analyzed, after which the performance of the algorithm was evaluated on these models via different experiments.

The results of the experiments on the 1D Burgers equation and the 2D neutron diffusion problem showed that the algorithm can adaptively and hierarchically draw new tangent planes and can accurately interpolate to new unknown solutions in the subdomains in both a 1D and 2D parameter setting. Higher order non-linear modes and coefficients are harder to interpolate than lower order modes and coefficients. The performance of the interpolator also depends on a combination of the chosen RBF and the size of the subdomains. The results from the Molenkamp test showed that in the smooth setting the new algorithm achieved a higher error with a higher number of evaluations, while in the steep setting the new algorithm performed on par with the previous algorithm, only if the interpolation accuracy threshold is set lower. The results from the neutron
diffusion problem indicate that the first principal angle can act as an indicator of which parts of the parameter domain contain more relatable physics than other parts of the domain.

The dependence of RBF interpolator on the subdomain size is caused by how the RBF values scale for further distanced points from the point of interpolation interest. Also more higher order modes than necessary can be included in the local basis interpolation method without worsening the interpolation accuracy of lower order modes, given that no numerical noise is present in the local bases or coefficients. Interpolating the time-dependent behaviour can be easier in the
space-time coupled approach than in the approach based on the global basis. However, a lower interpolation accuracy threshold should be chosen as full time evolutions are being interpolated instead of single state vectors. The current interpolation method scales worse than the previous algorithm, as the corner points of the parameter domain will always have to be sampled when using the RBF interpolator compared to local linear basis functions. Additionally, far more data is needed to represent this ROM compared to the ROM based on the global basis.

This research presented a method that generalizes reduced order modelling of time and parameter dependent problems on sparse grids, by using multiple local bases instead of a fixed global basis to represent the underlying physics of a model. The novel local basis interpolation scheme was competitive with the global basis approach on test problems, showing that manifold methods
such as ITSGM have great potential to be utilized in reduced order models. However, more research on matrix interpolation methods is needed to improve the overall performance, scalability and efficiency of the algorithm.

Treatment planning for radiation therapy is a complex process, as there are many machine parameters to determine for a treatment. To decrease the required labour and improve the plan quality, auto-planning systems have been developed, which can automatically generate high-quality treatment plans. These plans still have to be checked to ensure their quality, which means an independent and automatic quality assurance method is needed. This is where deep learning comes in, as recent advancements in computer hardware and artificial intelligence make it possible to quickly train neural networks for fast predictions of dose distributions based on the anatomy of a certain patient. Even though these models have proven capable of generating predictions comparable to the actual delivered dose, there is no guarantee that the distributions are actually deliverable. Therefore, this study is conducted to develop a novel deep learning model that uses physical information of how dose is delivered to constrain the neural networks and force realistic and deliverable dose distributions. The models presented in this study are implemented on prostate cancer patients treated with the Volumetric-Modulated Arc Therapy (VMAT) delivery technique.

First, the conventional Anatomy-based dose prediction model is further developed to improve the quality of the predicted dose distributions. The goal is to assess how accurate the predicted dose is from a deep learning model without any physical constraint. The model with U-net architecture has shown to be capable of predicting dose distributions of very high quality with average DVH differences of less than 1 Gy and errors in the dose coverage statistics on the PTV of less than 1\%. Furthermore, the lack of deliverability was confirmed due to the missing ray effects in the dose distributions, showing no clear entry points of the external photon beam. This lack of ray effects was quantified and confirmed using the dip in the S\o rensen-Dice Index around the 30\% isodose contours, where the ray effects are most apparent.

Second, the Physics-guided prediction model was developed by combining the Anatomy-based dose prediction model with the newly developed Segment prediction model, which predicts Multi-Leaf Collimator (MLC) positions and beam intensity values for all directions from which the dose is delivered. These predictions are based on the prediction from the Anatomy-based dose prediction model and the Beam's Eye View images of the CT and the delineated structures. The segment prediction is used in a stand-alone dose engine, based on the Matrad dose calculation algorithm, to calculate a dose distribution from the predicted treatment plan, which is deliverable by definition. The performance of the Physics-guided prediction model is underwhelming, scoring considerably worse on most evaluation metrics compared to the Anatomy-based dose prediction model. The lack of performance is mainly caused by the poor performance of the Segment prediction model component.

To circumvent the issue of the Segment prediction model, a dose mimicking model has been developed and investigated, where a dose mimicking algorithm is used to mimic a prediction from the Anatomy-based dose prediction model by optimizing the segments on which the dose is delivered. This model has only been tested on a single patient but seems to be performing better than the Physics-guided prediction model, with the downside that an optimisation process is involved. Still, the performance is not on par with the Anatomy-based dose prediction model.

Further investigation on the Segment prediction model will be needed before the Physics-guided prediction model can be considered as a serious quality assessment tool. Once performance of the Segment prediction model has increased, it could prove an interesting model that could even replace an auto-planning system in the far future.

Numerical solving a full order model can be computationally and time expensive. For real time control problems, it may be infeasible to solve full order models. Reduced order models can be used in order to reduce the time and computational cost while maintaining a high enough accuracy. In this thesis, it will be researched if a convolutional autoencoder based reduced order model is a feasible reduced order modelling method. Reduced order models will be constructed and applied for three different steady state neutron diffusion problems. Every autoencoder receives full order model solutions at its input. Convolutional layers are employed to process the high dimensional input to lower layers. The encoder will map the input data to the low dimensional latent space. The decoder will subsequently reconstruct the high dimensional input at its output from the low dimensional latent space. The latent space between the encoder and decoder forces the autoencoder to capture all necessary information in the few latent variables in such a way that the decoder can reconstruct the full order solution as good as possible. In order to find the optimal values for the model parameters, the autoencoder is trained on a set of full order solutions via gradient descent. After the training, the decoder can be used separately to map from the latent variables to the full order solutions. By joining the decoder with a regression model from the full order model parameters to the latent variables, one can find the full order solution without having to use a full order model solution method, like the finite element approach. In this thesis, a multivariate polynomial regression model is used for the regression from the full order model parameters to the latent variables. The convolutional autoencoder based reduced order model which incorporates residual blocks and parallel residual blocks in its structure, managed to outperform its proper orthogonal decomposition based counterpart by having an approx. 2.5 smaller mean squared error and a 1.4 times smaller mean absolute error. This shows that the proposed method is feasible in terms of prediction performance. Research should be done on the feasibility in terms of the computational costs and time costs. Additional recommendations are the extension of the proposed method to time dependent problems and the application to problems which are harder to capture with proper orthogonal decomposition based models.

Treatment of early stage breast cancer is generally invasive to a patient's daily life while being treated. Therefore, to diminish the physical and psychological impact during and after recovery, a newly proposed minimally invasive therapy for early-stage breast cancer treatment is proposed. Within this study, this proposed treatment is modelled to gain more knowledge of the behavior of the treatment material in tissue. The treatment includes magnetic thermal ablation, which is combined with permanent Low Dose Rate (LDR) brachytherapy, both performed simultaneously.
The goal of the treatment is to diminish the physical and psychological impact during treatment and after recovery, since it requires only a single medical intervention. The treatment material consists of radioactive palladium-103 superparamagnetic iron-oxide nanoparticles (Pd-103 SPIONs) incorporated in a solid gel, forming a seed that is implanted into the tumor. To investigate the effectiveness and limitations of the combined therapy, computational simulations were performed in Matlab using the Finite Element Method (FEM).
These simulations allowed for the prediction of the treatment results, by calculating the temperature distribution based on Pennes' bioheat equation, the nanoparticle concentration distribution and the dose distribution over time. The sensitivity of the results to the relevant physical properties and optimization parameters was analyzed. The latter resulted in a recommended optimization approach that ultimately could be used for treatment planning. First, an initial simulation was performed using property values from literature. Then, the temperature and dose results were tested on their sensitivity to model parameter changes. The temperature model was found to be most sensitive to changes in the nanoparticle heat source value Qnp, to an increased heat conduction coefficient k and to a decreased blood perfusion rate wb. The cumulative dose results are sensitive to both the initial concentration ci and to a decreased diffusion coefficient D. It is concluded that accurate values for these temperature and concentration model parameters are necessary to perform relevant simulations.
Furthermore, the possible optimization parameters were identified. For dose optimization, these parameters are the activity of the nanoparticles A, which is not easily modified, and the initial nanoparticle concentration in the seeds ci, which affects the temperature distribution as well. The temperature distribution specific variables that were found, are the strength of the magnetic field H and the time t of magnetic field application, which both can be adjusted during the treatment. The seed location and number of seeds are two additional adjustable variables used for optimization of both temperature and dose distribution. Lastly, it was concluded that the internal radiation part of the treatment is limiting in the reaching treatment goals and in number of optimization possibilities, compared to the thermal ablation part. Therefore, treatment optimization should be performed on the dose distribution first. Because most limitations of the models are a result of the 2D representation and because these limitations strongly affect the outcomes of the models, it is recommended to transform these models to 3D. These limitations make it impossible to do proper treatment planning with the 2D model, which requires a 3D view of the results. With all these findings, this study has contributed by providing basic knowledge of the state-of-the-art early stage breast cancer combined therapy, bringing it one step closer to clinical implementation.

This thesis investigates the tissue sparing effect of FLASH (>40 Gy/s) radiation, as opposed to CONV (conventional, dose rates typically between 0.01­0.1 Gy/s) radiation. We irradiated zebrafish embryos (4 days past fertilisation) with 116 MeV protons. The aim was (1) to measure the effect, and (2) if the effect were significant, see whether it depended on the oxygen concentration in the tissue, as the oxygen depletion hypothesis (a popular theory on the underlying mechanics of the FLASH effect) predicts. We irradiated embryos with either FLASH or CONV, where a possible FLASH effect would reduce toxicity of the FLASH radiation. We did the same for zebrafish which were deliberately put in a hypoxic condition prior to irradiation. In that case, the depletion hypothesis would predict that the difference between FLASH and CONV disappears. Our biomarkers for radiobiological damage were the survival rate and γ­H2AX foci formation. In our experimental conditions, the radiation effect on the survival rate was
eclipsed by other factors which could not be isolated. We did confirm the possibility of using γ­H2AX foci formation as a marker for radiobiological damage in full­body irradiated zebrafish embryos. There were individual samples that showed clear and localised specific γ­H2AX signal, but these were too
scarce and the signal was too inconsistent across samples to gather meaningful statistics. This was most often caused by limited antibody penetration in the embryo. We were therefore unable to draw conclusions about the FLASH effect. Better and more consistent antibody penetration, e.g. by longer digestion in collagenase before antibody staining, could change this in the future. We further custom­built and validated a hypoxic aquarium to produce hypoxic zebrafish tissue, as well as a computational model of the irradiation setup to simulate the dose distribution in the zebrafish container. We found the dose distribution to be sufficiently homogeneous for our experiment, at least 91.47% uniform for CONV and 90.72% uniform for FLASH.

Cancer is a disease that causes almost 10 million deaths each year. Currently, there is no perfect treatment for it. However, there is a promising treatment called proton radiotherapy. This works almost the same as one of the older cancer treatments called photon radiotherapy. However, radiotherapy with protons has an advantage in comparison with radiotherapy with photons. This advantage lies in the way the protons lose their energy when going through tissue. The protons deliver most of their dose in a very small region. Cause of this advantage, proton radiotherapy can deliver a lot of dose into the tumour while minimizing the dose delivered into healthy tissue. But this advantage can change into a disadvantage when the location of the tumour moves a few millimeters.
Therefore ideally a scan is taken each time the patient comes in, so the location of the tumour is known very accurately. After the scan it is best to immediately create a treatment plan and do the treatment session. But creating a treatment plan takes to much time to be able to do that. Mainly, this is because the calculation of the dose distribution is not fast enough. This report studies a faster method for the calculation of the dose distribution. The method is derived by the Medical Physics \& Technology group from TU Delft. This method is currently not accurate enough to use for treatment planning. The problem of the method is that the dose due to nuclear interactions is not included correctly. The goal of this report is to make the method more accurate by adding the nuclear dose caused by secondary particles formed due to inelastic nuclear interactions to the dose calculated by the existing method.
The nuclear dose is calculated using a convolution of a kernel with the proton flux. The nuclear dose of the following secondary particles is calculated: alpha particles, deuteron particles and secondary protons. Adding the nuclear dose caused by these three secondary particles increased the accuracy of the model by 0.36 percent. However adding the nuclear dose calculation increased the time needed to calculate the dose distribution with 18625 percent. By calculating the convolution using the fast Fourier transform this could be decreased by a factor of 11. However adding the nuclear dose calculation to the fast method increases the time needed to calculate the dose distribution too much. Therefore the calculation of the dose distribution is not fast enough to scan a patient and immediately start with the best possible treatment plan using the fast method with the nuclear dose calculation added.

Proton therapy is a great way to treat cancer, since protons can concentrate energy on one single spot, which minimises the irradiated healthy tissue. Because of this property protons are sensitive to uncertainties. Since the tumour is not stationary throughout the treatment, multiple scans are essential. With the current dose calculation technique (Monte Carlo simulations) this is not possible, since the simulations take too much time. This report therefore proposes a new deep learning algorithm to calculate accurate proton dose distributions much faster than the currently used methods.

The developed deep learning model consists of a convolutional encoder, two transformer encoder blocks and a convolutional decoder. Slices of a Computed Tomography (CT) image are processed through the model to output a corresponding dose distribution. The model is trained using gradient descent with a mean squared error loss function. The total dataset used to train, validate and test the model consists of 9,940 samples which are created using slices of a patient's CT scan and Monte Carlo simulations. Only a proton beam energy of 134 MeV is evaluated.

The model yielded a mean gamma-analysis index pass rate of 99.87 +/- 0.16 \%, which is much higher than any other model or method available. The model struggles most with predicting complex dose distributions but is excellent at predicting the general beam shape and the Bragg-peak location of the dose distribution. The average run-time of the model lies around 75 ms, which is much faster than Monte Carlo simulations and is even faster than the Pencil Beam method. The run-time is roughly equal to the fastest deep learning alternative when considering image dimensions.

For future researches it is suggested to train the model with more data to improve the accuracy, train the model with different proton beam energies to see if it generalises well and find the optimal convolutional encoder and decoder parameters to decrease run-time.

Cancer remains one of the leading causes of death in today's world. Radiation is a widely used in the treatment of cancer. One of the relatively newer methods is proton therapy, which can spare healthy tissues better than traditional photon treatments due to the unique Bragg peak of protons. A promising improvement is FLASH proton therapy, which utilises ultra-high dose rates (40-100x higher than conventionally used). However, a lot is still unknown about this method. This research took first steps towards experimentally investigating FLASH proton radiation in living tissues. To achieve this, three types of experiments were performed. The first consisted of simulation with proton radiation, the second used proton to irradiation zebrafish, and the last experiment irradiated zebrafish with a gamma source. First, a virtual model of the irradiation conditions was built with TopasMC, using an 140 MeV proton beam propagating in a water tank containing model cells. The flux and number of protons were tallied at various positions. A new beam was created for each positing using the tallied data resembling the original beam. The new beam was used for small scale irradiation of a model cell. The damage was assessed by calculating DNA strand breaks.
The simulation showed a Bragg peak for dose measurements, in accordance with literature. The damages to DNA significantly increased as the LET increased, as expected. This forms a basis for future simulation into FLASH. Next an experimental setup was realised and a first experiment was preformed. The setup showed a field homogeneity with a maximum difference of 3\%, as well as a maximum dose difference of 2\% in the region of interest. This provided a solid foundation for accurate measurements of the experiment with living samples. Subsequently, zebrafish embryos were irradiated with protons with either 5 Gy or 20 Gy and a dose rate of approximately 1 Gy/min. A different batch of zebrafish embryos received gamma radiation with a dose rate of around 10 Gy/min, also to 5 Gy and 20 Gy dosages. The damage to the embryos was estimated via the detection of heart beats, and their length, directly after receiving radiation and after a day of growth. The results of the proton irradiation of the embryos showed no significant differences between the separate groups. For the gamma irradiation also no significant difference were found, either for the 0-day measurements. After a day of growth, a tangible difference was found, but this was with a control group that was not transported. Therefore, no direct link could be made to radiation as a sole source of the influence. Additionally, temperature had a large effect on the development of the embryos. The simulations showed the difference in biological effect of different LET coefficients of protons. The practical irradiation's do appear to reveal some discrepancy between the different samples, but the samples sizes are too small to draw definitive conclusions from, especially went comparing the results after a day of growth. Nevertheless, a solid base has has been build for future research into FLASH. A simulation capable of doing physical and biological measurement was constructed. Also, an accurate physical setup for proton irradiation was made. In addition, a design for the containment of the zebrafish during transport, irradiation, and processing was devised. Lastly, protocols for the transportation, handling, processing, and analysis of the samples were created.