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Mixed-integer programming techniques for decomposing IMRT fluence maps using rectangular apertures

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Abstract

We consider a matrix decomposition problem arising in Intensity Modulated Radiation Therapy (IMRT). The problem input is a matrix of intensity values that are to be delivered to a patient via IMRT from some given angle, under the condition that the IMRT device can only deliver radiation in rectangular shapes. This paper studies the problem of minimizing the number of rectangles (and their associated intensities) necessary to decompose such a matrix. We propose an integer programming-based methodology for providing lower and upper bounds on the optimal solution, and demonstrate the efficacy of our approach on clinical data.

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Authors and Affiliations

  1. Department of Industrial Engineering, Boğaziçi University, 34342, Bebek, İstanbul, Turkey

    Z. Caner Taşkın

  2. Department of Industrial and Systems Engineering, University of Florida, 303 Weil Hall, P.O. Box 116595, Gainesville, FL, 32611-6595, USA

    J. Cole Smith

  3. Department of Industrial and Operations Engineering, University of Michigan, 1205 Beal Avenue, Ann Arbor, MI, 48109-2117, USA

    H. Edwin Romeijn

Authors
  1. Z. Caner Taşkın
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  2. J. Cole Smith
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  3. H. Edwin Romeijn
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Correspondence to H. Edwin Romeijn.

Additional information

The work of H. Edwin Romeijn was supported by the National Science Foundation under grant No. DMI-0457394/CMMI-0852727.

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Taşkın, Z.C., Smith, J.C. & Romeijn, H.E. Mixed-integer programming techniques for decomposing IMRT fluence maps using rectangular apertures. Ann Oper Res 196, 799–818 (2012). https://doi.org/10.1007/s10479-010-0767-1

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  • DOI: https://doi.org/10.1007/s10479-010-0767-1

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