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.

In intensity modulated proton therapy (IMPT), patients are irradiated with small spots, that deliver a local dose to the tumor. The number of possible spots to choose from is virtually infinite, but practically limited, which requires a spot selection. This spot selection should result in an optimal treatment plan, i.e., to deliver a sufficient dose to the tumor, while sparing the healthy surrounding tissue. These trade-offs make treatment planning in radiotherapy a multi-criteria optimization problem. The current approach for this spot selection by the Erasmus Medical Center (MC) is an iterative resampling method which uses a trial and error principal. A random sampled spot selection is made, bad spots are removed, and new spots are randomly added. The research goal of this project is to improve the current spot selection method, by inducing sparsity on spot selections with the L1-norm, without decreasing the plan quality of the current solution. Sparse solutions are beneficial for optimization problems since they reduce the problem size and have higher probability of producing qualitative solutions. To achieve these goals, the Sparsity-Induced-Spot-Selection (SISS) method was developed. Contrary to the iterative resampling approach, the SISS method uses a top-down approach. Starting with a large spot coverage, it selects as little relevant spots as possible through the use of the L1-norm to induce sparsity, until an acceptable treatment plan using as little spots as possible is made. The developed method was validated on a test set consisting of 10 head and neck patients. Using the SISS method, an average spot selection of 1159 spots was produced, compared to a solution of 1074 spots for the resampling method. For the average patient, 6 out of 10 Organs-at-risk (OAR) received a lower dose with the SISS method than with the resampling method. The remaining OARs all received a marginal dose surplus of 0.6 Gy, with a maximum of 2.6 Gy. The target volumes in the tumor also received a similar dose to the resampling method, with the near-minimum dose of the tumor receiving a dose shortage of 0.2 Gy, and the near-maximum dose of the tumor receiving a dose surplus of 0.5 Gy, both being considered as marginal differences. The SISS method produces a comparable spot selection and shows no decline in plan quality of the dose distributions. Using the L1-norm to induce sparsity on spot selections in treatment planning is feasible. The computation time of the SISS method could be reduced using a voxel reduction, although this reduction in computation time is not guaranteed in practice due to robust optimization being applied.

Cancer is a disease that one of every three people will get in The Netherlands. One of the treatment methods for this disease is radiotherapy. Approximately half of all cancer patients will get radiotherapy at some point of their treatment. During radiotherapy cancer cells are destroyed with ionizing radiation, but healthy cells get destroyed too. When a patient gets treated with radiotherapy, the goal is to find a treatment plan which will destroy all of the cancer cells and as few healthy cells as possible. To reach this goal we want to make a unique treatment plan for every patient, because every patient is anatomical unique. We use a wish-list to generate this unique optimal treatment plan. This wish-list contains all of the demands of the physician. All of the demands can be written into cost-functions. We will use inverse multicriteria optimisation to find the most relevant cost-functions for every organ and the tumour (planning target volume (PTV)). The relevance of a cost-function can be obtained by determining the weight of a cost-function. We start with a non-linear problem and we use the Karush-Kuhn-Tucker conditions. We did not receive the desired solutions.Afterwards, we tried to find the optimal weights for a linear problem by writing it in the form of an absolute duality gap minimization problem. This gave the results we were hoping for.

In Intensity Modified Proton Therapy, the number of energy layers and the number of beamlets determine the radiation time and the plan calculation time. The purpose of this research project is to test sparsity inducing terms to reduce both the energy layers and the beamlets.

Purpose - To develop and evaluate a fast and automated multi-criterial treatment planning strategy for High-Dose-Rate (HDR) brachytherapy (BT) for patients with locally advanced cervical cancer. This automated strategy avoids suboptimal and slow manual treatment planning and results in reproducible and conformal treatment plans with a clinically favorable trade-off between multiple treatment objectives. Methods and Materials - An automated treatment planning approach was developed using the Erasmus- iCycle framework. A wish-list containing hard constraints and prioritized objectives is required as input was configured according to the clinical protocol using 22 single-fraction training plans. Special at- tention was paid to establishing the clinically desired ‘pear-shaped’ dose distribution. To evaluate the dwell time optimization approach, 66 automatically generated single-fraction plans (PLANauto) were compared against the clinically delivered plans (PLANref ), both by blind-pairwise comparison carried out by an expert clinician and by the analysis of dosimetric plan parameters. Subsequently, for 17 complete fractioned BT treatments each consisting of 3 single-fraction BT plans, automatically generated plans (TREATMENTauto) were compared against the clinically delivered plans (TREATMENTref) to evaluate dosimetric plan parameters according to the clinical protocol. The possibility of extending the algorithm with a needle selection objective was also explored on 13 test cases and its performance was evaluated by studying the number of needles selected in the optimized plans and its effect on the remaining treatment objectives.Results - All PLANauto were considered clinically acceptable by the clinician. The clinician’s plan comparison pointed strongly at an overall preference for the automated plans: in 62/66 cases the clincian preferred PLANauto over PLANref , in three cases the overall quality was considered equal and for one case the clinical plan was preferred. For PLANauto, the mean HR-CTV D90% improved while also the rectum was spared compared to PLANref . The average optimization time was 19.5 seconds (range [4.4 – 106.4] s). The mean D90% for TREATMENTauto improved by + 3.0 Gy (in EQD2) (p<0.005) over the whole radiotherapy treatment with differences ranging from -4.3 to +6.0 Gy, while the bladder and rectum were spared similarly (p=0.01, p=0.02 respectively). In 6/13 of the plans, the number of needles that were implanted could be reduced while still establishing sufficient plan quality. Conclusions - Fast automated multi-criterial treatment planning for locally advanced cervical cancer HDR-BT is feasible. High-quality treatment plans are automatically generated within a clinically acceptable time frame and treatment plans have a clinically preferable trade-off between all treat- ment objectives. The observed improvement in dosimetric parameters, mainly the improvement of the dose to the HR-CTV, is clinically relevant. The algorithm can be extended with an approach for the optimization of the implant geometry, which could allow interactive intra-operative treatment planning.