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Integer Programming Applied to Intensity-Modulated Radiation Therapy Treatment Planning

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Listed:
  • Eva Lee
  • Tim Fox
  • Ian Crocker

Abstract

In intensity-modulated radiation therapy (IMRT) not only is the shape of the beam controlled, but combinations of open and closed multileaf collimators modulate the intensity as well. In this paper, we offer a mixed integer programming approach which allows optimization over beamlet fluence weights as well as beam and couch angles. Computational strategies, including a constraint and column generator, a specialized set-based branching scheme, a geometric heuristic procedure, and the use of disjunctive cuts, are described. Our algorithmic design thus far has been motivated by clinical cases. Numerical tests on real patient cases reveal that good treatment plans are returned within 30 minutes. The MIP plans consistently provide superior tumor coverage and conformity, as well as dose homogeneity within the tumor region while maintaining a low irradiation to important critical and normal tissues. Copyright Kluwer Academic Publishers 2003

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:119:y:2003:i:1:p:165-181:10.1023/a:1022938707934
    DOI: 10.1023/A:1022938707934
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Dionne M. Aleman & H. Edwin Romeijn & James F. Dempsey, 2009. "A Response Surface Approach to Beam Orientation Optimization in Intensity-Modulated Radiation Therapy Treatment Planning," INFORMS Journal on Computing, INFORMS, vol. 21(1), pages 62-76, February.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Mustafa Sir & Marina Epelman & Stephen Pollock, 2012. "Stochastic programming for off-line adaptive radiotherapy," Annals of Operations Research, Springer, vol. 196(1), pages 767-797, July.
    13. 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.
    14. Gino Lim & Laleh Kardar & Wenhua Cao, 2014. "A hybrid framework for optimizing beam angles in radiation therapy planning," Annals of Operations Research, Springer, vol. 217(1), pages 357-383, June.
    15. 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.
    16. Joana Dias & Humberto Rocha & Brígida Ferreira & Maria Lopes, 2014. "A genetic algorithm with neural network fitness function evaluation for IMRT beam angle optimization," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 22(3), pages 431-455, September.
    17. 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.
    18. 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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