Optimal Multileaf Collimator Leaf Sequencing in IMRT Treatment Planning

Z. Caner Taşkın (), J. Cole Smith (), H. Edwin Romeijn () and James F. Dempsey ()
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Z. Caner Taşkın: Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida 32611
J. Cole Smith: Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida 32611
H. Edwin Romeijn: Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan 48109
James F. Dempsey: Department of Radiation Oncology, University of Florida, Gainesville, Florida 32610, and ViewRay Inc., Village of Oakwood, Ohio 44146

Operations Research, 2010, vol. 58, issue 3, 674-690

Abstract: 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. 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 ones appear consecutively in each row. A feasible decomposition is one in which the original desired intensity profile is equal to the sum of a number of feasible binary matrices multiplied by corresponding intensity values. To most efficiently treat a patient, we wish to minimize a measure of total treatment time, which is given as a weighted sum of the number of apertures and the sum of the aperture intensities used in the decomposition. We develop the first exact algorithm capable of solving real-world problem instances to optimality within practicable computational limits, using a combination of integer programming decomposition and combinatorial search techniques. We demonstrate the efficacy of our approach on a set of 25 test instances derived from actual clinical data and on 100 randomly generated instances.

Keywords: health care; treatment; programming; integer; algorithms; applications; Benders decomposition (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (5)

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