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.

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.