Optimization approaches for planning external beam radiotherapy

Cancer begins when cells grow out of control as a result of damage to their DNA. These abnormal cells can invade healthy tissue and form tumors in various parts of the body. Chemotherapy, immunotherapy, surgery and radiotherapy are the most common treatment methods for cancer. According to American Cancer Society about half of the cancer patients receive a form of radiation therapy at some stage. External beam radiotherapy is delivered from outside the body and aimed at cancer cells to damage their DNA making them unable to divide and reproduce. The beams travel through the body and may damage nearby healthy tissue unless carefully planned. Therefore, the goal of treatment plan optimization is to find the best system parameters to deliver sufficient dose to target structures while avoiding damage to healthy tissue. This thesis investigates optimization approaches for two external beam radiation therapy techniques: Intensity-Modulated Radiation Therapy (IMRT) and Volumetric-Modulated Arc Therapy (VMAT).;We develop automated treatment planning technology for IMRT that produces several high-quality treatment plans satisfying provided clinical requirements in a single invocation and without human guidance. A novel bi-criteria scoring based beam selection algorithm is part of the planning system and produces better plans compared to those produced using a well-known scoring-based algorithm. Our algorithm is very efficient and finds the beam configuration at least ten times faster than an exact integer programming approach. Solution times range from 2 minutes to 15 minutes which is clinically acceptable.;With certain cancers, especially lung cancer, a patient's anatomy changes during treatment. These anatomical changes need to be considered in treatment planning. Fortunately, recent advances in imaging technology can provide multiple images of the treatment region taken at different points of the breathing cycle, and deformable image registration algorithms can accurately link these images making it possible to track an individual voxel during the entire breathing cycle. This allows the development of optimization models that generate treatment plans that deliver radiation in multiple phases. Our model finds optimal fluence maps for each phase of the breathing cycle simultaneously by considering the overall dose delivered to patient. Because the optimization exploits the specific opportunities provided in each of the phases, better treatment plans are obtained. A computational study of a real lung case shows that the tumor coverage can be improved from only 51% using single-phase gating to 96% using five-phase gating.;VMAT is a recent radiation treatment technology which is based on continuous rotation of the radiation source around the patient. VMAT has the potential to provide treatments in less time compared to other delivery techniques which enhances patient comfort and allows for the treatment of more patients. A treatment planning system has to decide how the beam shapes and dose rates change during the rotation of the radiation source. We develop two treatment planning approaches for VMAT. The first approach finds shapes and dose rates separately in a two-stage algorithm. Although this approach produces treatment plans extremely fast their quality is not clinically acceptable. The second approach is based on a large-scale mixed-integer programming model that optimizes shapes and dose rates simultaneously. As solving the model directly is computationally prohibitive, we develop a heuristic approach which solves the model multiple times on a reduced set of decision variables. We derive valid inequalities that not only decrease the solution times but also allows us to get better integer solutions within specified time limits. Computational studies on a spinal tumor and a prostate tumor case produce clinically acceptable results.