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.

In the history of medicine, different treatments for cancer have been developed, such as radiotherapy, surgery and chemotherapy. However, nowadays more than 50% of the people diagnosed with cancer, undergo a radiotherapy treatment. One of the devices used for the treatment is the CyberKnife: a robotic radiodurgery system that can move around the patient using 102 virtually placed nodes. For the treatment of a patient, usually around 25 nodes are used, which result in a certain plan quality for the patient. The aim of this project is to find shorter paths than the existing ones, without significantly degrading the plan quality. This is done by using Dijkstra’s Algorithm, as well as incorporating Hamiltonian paths and the Traveling Salesman Problem. With these techniques, we developed the OPA (Optimal Path Algorithm): an algorithm that finds Hamiltonian paths through the nodes, combined with the iterated process of interchanging nodes with adjacent ones. With OPA, the traveltimes for the CyberKnife have been brought down by 38.6% on average without degrading the plan quality.