Optimization approaches for planning external beam radiotherapy

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Gozbasi, Halil Ozan
Ahmed, Shabbir
Savelsbergh, Martin W. P.
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External beam radiotherapy is delivered from outside the body 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 tissues unless carefully planned. Therefore, the goal of treatment plan optimization is to find the best system configuration to deliver sufficient dose to target structures while avoiding damage to healthy tissues. 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 an automated treatment planning technology for IMRT which generates several high-quality treatment plans satisfying the provided requirements in a single invocation and without human guidance. Our approach is based on an existing linear programming-based fluence map optimization model that approximates dose-volume requirements using conditional value-at-risk (C-VaR) constraints. We show how the parameters of the C-VaR constraints can be used to control various metrics of treatment plan quality. A novel bi-criteria scoring based beam selection algorithm is developed which finds the best beam configuration at least ten times faster for real-life brain, prostate, and head and neck cases as compared to an exact mixed integer programming model. Patient anatomy changes due to breathing during the treatment of lung cancer need to be considered in treatment planning. To date, a single phase of the breathing cycle is typically selected for treatment and radiation is shut-off in other phases. We investigate optimization technology that finds optimal fluence maps for each phase of the breathing cycle by considering the overall dose delivered to a patient using image registration algorithms to track target structures and organs at risk. Because the optimization exploits the opportunities provided in each phase, better treatment plans are obtained. The improvements are shown on a real-life lung case. VMAT is a recent radiation treatment technology which has the potential to provide treatments in less time compared to other delivery techniques. This enhances patient comfort and allows for the treatment of more patients. We build a large-scale mixed-integer programming model for VMAT treatment plan optimization. The solution of this model is computationally prohibitive. Therefore, we develop an iterative MIP-based heuristic algorithm which solves the model multiple times on a reduced set of decision variables. We introduce valid inequalities that decrease solution times, and, more importantly, that identify higher quality integer solutions within specified time limits. Computational studies on a spinal tumor and a prostate tumor case produce clinically acceptable results.
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