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Optimal Multileaf Collimator Leaf Sequencing in IMRT Treatment Planning

Author

Listed:
  • 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)

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.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:58:y:2010:i:3:p:674-690
    DOI: 10.1287/opre.1090.0759
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    References listed on IDEAS

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    1. Matthias Ehrgott & Horst W. Hamacher & Marc Nußbaum, 2008. "Decomposition of matrices and static multileaf collimators: a survey," Springer Optimization and Its Applications, in: Carlos J. S. Alves & Panos M. Pardalos & Luis Nunes Vicente (ed.), Optimization in Medicine, pages 25-46, Springer.
    2. Eva Lee & Tim Fox & Ian Crocker, 2003. "Integer Programming Applied to Intensity-Modulated Radiation Therapy Treatment Planning," Annals of Operations Research, Springer, vol. 119(1), pages 165-181, March.
    3. Andreas T. Ernst & Vicky H. Mak & Luke R. Mason, 2009. "An Exact Method for the Minimum Cardinality Problem in the Treatment Planning of Intensity-Modulated Radiotherapy," INFORMS Journal on Computing, INFORMS, vol. 21(4), pages 562-574, November.
    4. 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.
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    Cited by:

    1. Luke Mason & Vicky Mak-Hau & Andreas Ernst, 2015. "A parallel optimisation approach for the realisation problem in intensity modulated radiotherapy treatment planning," Computational Optimization and Applications, Springer, vol. 60(2), pages 441-477, March.
    2. 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.
    3. Danielle A. Ripsman & Thomas G. Purdie & Timothy C. Y. Chan & Houra Mahmoudzadeh, 2022. "Robust Direct Aperture Optimization for Radiation Therapy Treatment Planning," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 2017-2038, July.
    4. Turgay Ayer & Can Zhang & Anthony Bonifonte & Anne C. Spaulding & Jagpreet Chhatwal, 2019. "Prioritizing Hepatitis C Treatment in U.S. Prisons," Operations Research, INFORMS, vol. 67(3), pages 853-873, May.
    5. Dursun, Pınar & Taşkın, Z. Caner & Altınel, İ. Kuban, 2019. "The determination of optimal treatment plans for Volumetric Modulated Arc Therapy (VMAT)," European Journal of Operational Research, Elsevier, vol. 272(1), pages 372-388.

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