A column generation approach for evaluating delivery efficiencies of collimator technologies in IMRT treatment planning

Abstract

Intensity Modulated Radiation Therapy (IMRT) is a form of cancer treatment which delivers radiation beams to the patient from several directions by using a linear accelerator and a collimator. At the leaf sequencing optimization step of the IMRT treatment planning, the intensity matrices are decomposed into a set of deliverable apertures and their associated intensities. Collimator systems used in IMRT can form di erent geometric shapes of apertures depending on their physical capabilities. Hence, comparing the delivery e ciency of di erent collimator technologies is important to determine the value added by the di erent technologies. In this thesis, we compare the e ciency of using regular, rotating and dual multileaf collimator (MLC) systems under di erent combinations of consecutiveness, interdigitation and rectangular constraints and a virtual freeform collimator. We formulate the problem of minimizing total beam-on time (BOT) as a large-scale linear programming problem. To deal with its dimensionality, we propose a column generation approach. Although there exists a general master problem structure, subproblem depends on the used collimator system technology. Therefore, we model each subproblem individually and apply a di erent solution method to each of them. We test our approach on a set of clinical problem instances. Our results indicate that the dual MLC under consecutiveness constraint yields very similar beam-on time as a virtual freeform collimator which can form any possible segment shape by opening or closing each bixel independently. Our approach provides a ranking between other collimator technologies in terms of their delivery e ciencies.