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

Abstract

Collimator systems used in Intensity Modulated Radiation Therapy can form different geometric aperture shapes depending on their physical capabilities. We compare the efficiency of using regular, rotating and dual multileaf collimator (MLC) systems under different combinations of consecutiveness, interdigitation and rectangular constraints. We also create a virtual freeform collimator, which can form any possible segment shape by opening or closing each bixel independently, to provide a basis for comparison. We formulate the problem of minimizing beam-on time as a large-scale linear programming problem. To deal with its dimensionality, we propose a column generation approach. We demonstrate the efficacy of 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 to a virtual freeform collimator. Our approach also provides a ranking between other collimator technologies in terms of their delivery efficiencies.