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

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  • Z. Taşkın
  • J. Smith
  • H. Romeijn

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. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Z. Taşkın & J. Smith & H. Romeijn, 2012. "Mixed-integer programming techniques for decomposing IMRT fluence maps using rectangular apertures," Annals of Operations Research, Springer, vol. 196(1), pages 799-818, July.
    • Handle: RePEc:spr:annopr:v:196:y:2012:i:1:p:799-818:10.1007/s10479-010-0767-1
    DOI: 10.1007/s10479-010-0767-1
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    References listed on IDEAS

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    1. H. Edwin Romeijn & Ravindra K. Ahuja & James F. Dempsey & Arvind Kumar, 2006. "A New Linear Programming Approach to Radiation Therapy Treatment Planning Problems," Operations Research, INFORMS, vol. 54(2), pages 201-216, April.
    2. Z. Caner Taşkın & J. Cole Smith & H. Edwin Romeijn & James F. Dempsey, 2010. "Optimal Multileaf Collimator Leaf Sequencing in IMRT Treatment Planning," Operations Research, INFORMS, vol. 58(3), pages 674-690, June.
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    Cited by:

    1. Ehsan Salari & H. Edwin Romeijn, 2012. "Quantifying the Trade-off Between IMRT Treatment Plan Quality and Delivery Efficiency Using Direct Aperture Optimization," INFORMS Journal on Computing, INFORMS, vol. 24(4), pages 518-533, November.
    2. Mustafa C. Camur & Thomas Sharkey & Chrysafis Vogiatzis, 2022. "The Star Degree Centrality Problem: A Decomposition Approach," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 93-112, January.

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