IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v58y2010i3p674-690.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.1090.0759
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.1090.0759?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Matthias Ehrgott & Çiğdem Güler & Horst Hamacher & Lizhen Shao, 2010. "Mathematical optimization in intensity modulated radiation therapy," Annals of Operations Research, Springer, vol. 175(1), pages 309-365, March.
    3. Timothy C. Y. Chan & Tim Craig & Taewoo Lee & Michael B. Sharpe, 2014. "Generalized Inverse Multiobjective Optimization with Application to Cancer Therapy," Operations Research, INFORMS, vol. 62(3), pages 680-695, June.
    4. Dunbar, Michelle & O’Brien, Ricky & Froyland, Gary, 2020. "Optimising lung imaging for cancer radiation therapy," European Journal of Operational Research, Elsevier, vol. 282(3), pages 1038-1052.
    5. 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.
    6. Thomas Bortfeld & Timothy C. Y. Chan & Alexei Trofimov & John N. Tsitsiklis, 2008. "Robust Management of Motion Uncertainty in Intensity-Modulated Radiation Therapy," Operations Research, INFORMS, vol. 56(6), pages 1461-1473, December.
    7. Marc C. Robini & Feng Yang & Yuemin Zhu, 2020. "A stochastic approach to full inverse treatment planning for charged-particle therapy," Journal of Global Optimization, Springer, vol. 77(4), pages 853-893, August.
    8. Shabbir Ahmed & Ozan Gozbasi & Martin Savelsbergh & Ian Crocker & Tim Fox & Eduard Schreibmann, 2010. "An Automated Intensity-Modulated Radiation Therapy Planning System," INFORMS Journal on Computing, INFORMS, vol. 22(4), pages 568-583, November.
    9. Sera Kahruman & Elif Ulusal & Sergiy Butenko & Illya Hicks & Kathleen Diehl, 2012. "Scheduling the adjuvant endocrine therapy for early stage breast cancer," Annals of Operations Research, Springer, vol. 196(1), pages 683-705, July.
    10. 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.
    11. 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.
    12. Wei Chen & Yixin Lu & Liangfei Qiu & Subodha Kumar, 2021. "Designing Personalized Treatment Plans for Breast Cancer," Information Systems Research, INFORMS, vol. 32(3), pages 932-949, September.
    13. Eva K. Lee, 2004. "Generating Cutting Planes for Mixed Integer Programming Problems in a Parallel Computing Environment," INFORMS Journal on Computing, INFORMS, vol. 16(1), pages 3-26, February.
    14. Fabio Vitor & Todd Easton, 2018. "The double pivot simplex method," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(1), pages 109-137, February.
    15. Arkajyoti Roy & Shaunak S. Dabadghao & Ahmadreza Marandi, 2024. "Value of intermediate imaging in adaptive robust radiotherapy planning to manage radioresistance," Annals of Operations Research, Springer, vol. 339(3), pages 1307-1328, August.
    16. H. Rocha & J. Dias & B. Ferreira & M. Lopes, 2013. "Selection of intensity modulated radiation therapy treatment beam directions using radial basis functions within a pattern search methods framework," Journal of Global Optimization, Springer, vol. 57(4), pages 1065-1089, December.
    17. Ali Tuncel & Felisa Preciado & Ronald Rardin & Mark Langer & Jean-Philippe Richard, 2012. "Strong valid inequalities for fluence map optimization problem under dose-volume restrictions," Annals of Operations Research, Springer, vol. 196(1), pages 819-840, July.
    18. Gino J. Lim & Michael C. Ferris & Stephen J. Wright & David M. Shepard & Matthew A. Earl, 2007. "An Optimization Framework for Conformal Radiation Treatment Planning," INFORMS Journal on Computing, INFORMS, vol. 19(3), pages 366-380, August.
    19. Chan, Timothy C.Y. & Mišić, Velibor V., 2013. "Adaptive and robust radiation therapy optimization for lung cancer," European Journal of Operational Research, Elsevier, vol. 231(3), pages 745-756.
    20. Michael Ferris & Rikhardur Einarsson & Ziping Jiang & David Shepard, 2006. "Sampling issues for optimization in radiotherapy," Annals of Operations Research, Springer, vol. 148(1), pages 95-115, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:58:y:2010:i:3:p:674-690. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.