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Column generation for IMRT cancer therapy optimization with implementable segments

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  • Felisa Preciado-Walters
  • Mark Langer
  • Ronald Rardin
  • Van Thai

Abstract

A radiation beam passes through normal tissue to reach tumor. The latest devices for the radiotherapy of cancer provide intensity modulated radiation treatment, or IMRT. This method refines cancer treatment by varying the intensity profile across the face of a radiation beam. Intensity modulation is usually accomplished by partitioning each beam, distinguished by its angle of entry, into an array of smaller sized units, called beamlets, assigned different intensities. Planning treatment calls for an optimization over beamlet intensities to maximize the dose delivered to the targeted tumor while keeping the distribution of dose throughout the various organs within physician prescribed bounds. The choice of beam angles can be entered into the optimization as well. A common method to produce an intensity pattern is to block out different parts of the beam for different amounts of time. This can be done sliding narrow blocks (leafs) of unit width into the beam from either of two opposing sides to create different beam shapes called segments. A sequence of segments with their exposure times is superimposed to yield the dose distribution actually received in the patient. Current two stage treatment is derived in separate steps: optimization over independently considered beamlet intensities, and generation of a sequence of segments to approximate the planned intensity map. The approximation degrades the solution, and the separate search for segments adds to planning time. We present a mixed integer programming alternative employing column generation to optimize dose over segments themselves. Only segments that can be realized with delivery devices are generated, and adjustments made for the effects of block edges, so that the optimized plans are directly implementable. Preliminary testing demonstrates gains in both planning efficiency and quality of the plans produced. Copyright Springer Science + Business Media, LLC 2006

Suggested Citation

  • Felisa Preciado-Walters & Mark Langer & Ronald Rardin & Van Thai, 2006. "Column generation for IMRT cancer therapy optimization with implementable segments," Annals of Operations Research, Springer, vol. 148(1), pages 65-79, November.
    • Handle: RePEc:spr:annopr:v:148:y:2006:i:1:p:65-79:10.1007/s10479-006-0080-1
    DOI: 10.1007/s10479-006-0080-1
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    References listed on IDEAS

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    1. Y. Xiao & D. Michalski & J.M. Galvin & Y. Censor, 2003. "The Least-Intensity Feasible Solution for Aperture-Based Inverse Planning in Radiation Therapy," Annals of Operations Research, Springer, vol. 119(1), pages 183-203, March.
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    Cited by:

    1. Xuejiao Zeng & Hao Gao & Xunbin Wei, 2018. "Rapid direct aperture optimization via dose influence matrix based piecewise aperture dose model," PLOS ONE, Public Library of Science, vol. 13(5), pages 1-11, May.
    2. 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.
    3. 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.
    4. 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.
    5. Guillermo Cabrera-Guerrero & Matthias Ehrgott & Andrew J. Mason & Andrea Raith, 2022. "Bi-objective optimisation over a set of convex sub-problems," Annals of Operations Research, Springer, vol. 319(2), pages 1507-1532, December.
    6. 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.
    7. 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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