Optimal multileaf collimator leaf sequencing in IMRT treatment planning

Z. Caner Taskin, J. Cole Smith, H. Edwin Romeijn, James F. Dempsey

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


We considera problem dealing with the efficient delivery of intensity modulated radiation therapy (IMRT) to individualpatients. 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.

Original languageEnglish (US)
Pages (from-to)674-690
Number of pages17
JournalOperations Research
Issue number3
StatePublished - May 2010
Externally publishedYes

ASJC Scopus subject areas

  • Computer Science Applications
  • Management Science and Operations Research


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