Optimal Multileaf Collimator Leaf Sequencing in IMRT Treatment Planning

We consider a problem dealing with the efficient delivery of Intensity Modulated Radiation Therapy (IMRT) to individual patients. IMRT treatment planning is usually performed in three phases. The first phase determines a set of beam angles through which radiation is delivered, followed by a second phase that determines an optimal radiation intensity profile (or fluence map). This intensity profile is selected to ensure that certain targets receive a required amount of dose while functional organs are spared. In order to deliver these intensity profiles to the patient, a third phase must decompose them into a collection of apertures and corresponding intensities. In this paper, we investigate this last problem. Formally, an intensity profile is represented as a nonnegative integer matrix; an aperture is represented as a binary matrix whose ∗Department of Industrial and Systems Engineering, University of Florida, 303 Weil Hall, P.O. Box 116595, Gainesville, Florida 32611-6595; e-mail: [email protected]. †Department of Industrial and Systems Engineering, University of Florida, 303 Weil Hall, P.O. Box 116595, Gainesville, Florida 32611-6595; e-mail: [email protected]. ‡Department of Industrial and Operations Engineering, The University of Michigan, 1205 Beal Avenue, Ann Arbor, Michigan 48109-2117; e-mail: [email protected]. The work of this author was supported by the National Science Foundation under grant no. DMI-0457394. §ViewRay Inc., 2 Thermo Fisher Way, Village of Oakwood, Ohio 44146; e-mail: [email protected]. The work of this author was supported by the National Science Foundation under grant no. DMI-0457394.