Mathematical Optimization Models for Treatment Planning of Spatially Fractionated Radiation Therapy

Abstract

Spatially Fractionated Radiation Therapy (SFRT) is an emerging approach in radiationoncology that has gained interest in recent years as an effective method for the treatment of large and bulky tumors. Rather than prescribing a consistent, high dose of radiation to the entire tumor volume, SFRT prescribes delivery of high doses of radiation to discrete spheres within the tumor. While clinical guidelines exist regarding sphere size and separation, currently there is no rigorously defined method that places these spheres within the tumor. Instead, treatment planners rely on their own experience to determine sphere locations, aiming to maximize the number of spheres while satisfying clinical constraints. This step is typically followed by fluence map optimization, the primary task in radiation therapy planning, where the intensity of the radiation “beamlets” is computed. This manual sphere placement process introduces variation in both the number of spheres placed and the locations of these spheres, which can result in inconsistent and suboptimal treatment plans with potentially unfavorable patient outcomes. In this thesis, we propose a novel mathematical optimization model that computes the optimal SFRT treatment plan that places the maximum number of spheres within the tumor by integrating an instance of the maximum independent set (MIS) problem within fluence map optimization. Our model places spheres within the tumor in the configuration that maximizes radiation dose to the tumor and minimizes radiation dose to healthy tissues. We conduct an experimental evaluation of our model using real imaging data provided by the National Cancer Institute through The Cancer Imaging Archive (TCIA). Our results demonstrate the effectiveness and flexibility of the proposed framework and its potential to assist clinicians in making more informed decisions that improve patient outcomes.