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

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 different geometric shapes of apertures depending on their physical capabilities. Hence, comparing the delivery efficiency of different collimator technologies is important to determine the value added by the different technologies. In this thesis, we compare the efficiency of using regular, rotating and dual multileaf collimator (MLC) systems under different 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 different 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 efficiencies. %Our results indicate a ranking between collimator technologies in terms of their treatment BOT values. The minimum BOT results are obtained by freeform collimator as expected. The dual MLC under consecutiveness constraint acts almost as well as the freeform collimator. On the other hand, collimators that can only form rectangular shapes yield very high BOT results.