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 two phases. In the first phase, an optimal intensity profile (or fluence map) is determined that ensures that certain targets receive a required amount of dose while functional organs are spared. In order to deliver this intensity profile to the patient, a second phase must decompose it in to a collection of apertures and corresponding intensities. In this talk, we investigate this second phase problem. Formally, an intensity profile is represented as a nonnegative integer matrix; an aperture is represented as a binary matrix, each row of which obeys the so-called consecutive ones property (all ones appear consecutively in each row); and the aperture intensities must be integers. 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. In order 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 backtracking techniques. We demonstrate the efficacy of our approach on a set of 25 test instances derived from clinical data.
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Wilco van den Heuvel