Binary Level-Set Shape Optimization Model and Algorithm for Volumetric Modulated Arc Therapy in Cancer Radiotherapy

Radiation therapy is one of the most commonly used treatment modalities for cancer. Its purpose is to deliver prescribed radiation doses to cancerous targets using high energy radiation beams while sparing nearby healthy organs. The treatment planning process of radiotherapy is an optimization problem, where beam parameters, such as directions, shapes, and intensities, can be adjusted in simulations to yield desired dose distributions. This can be applied under the recently developed volumetric modulated arc therapy (VMAT) setup which involves the use of a full-rotation trajectory of the beam about the patient along with a multi-leaf collimator for beam shape sculpting, with notable advantages in shortened treatment time. Treatment plan optimization in this setting, however, can be quite complicated due to constraints arising from the equipment involved. We introduce a variational model in the VMAT setup for the optimization of ∗Department of Mathematics, University of California, San Diego, 9500 Gilman Drive, Mail code: 0112, La Jolla, CA 92093-0112, Email: [email protected] †Department of Mathematics, University of Arizona, 617 N. Santa Rita Ave, Tucson, AZ, 85721-0089, Email: [email protected] ‡Center for Advanced Radiotherapy Technologies and Department of Radiation Medicine and Applied Sciences, University of California, San Diego, 3855 Health Sciences Drive, Mail code: 0843, La Jolla, CA 92093-0843, Email: {cmen, xunjia, sbjiang}@ucsd.edu