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Mathematical optimization in intensity modulated radiation therapy

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  • Matthias Ehrgott
  • Çiğdem Güler
  • Horst Hamacher
  • Lizhen Shao

Abstract

The design of an intensity modulated radiotherapy treatment includes the selection of beam angles (geometry problem), the computation of an intensity map for each selected beam angle (intensity problem), and finding a sequence of configurations of a multileaf collimator to deliver the treatment (realization problem). Until the end of the last century research on radiotherapy treatment design has been published almost exclusively in the medical physics literature. However, since then, the attention of researchers in mathematical optimization has been drawn to the area and important progress has been made. In this paper we survey the use of optimization models, methods, and theories in intensity modulated radiotherapy treatment design. Copyright Springer Science+Business Media, LLC 2010

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:175:y:2010:i:1:p:309-365:10.1007/s10479-009-0659-4
    DOI: 10.1007/s10479-009-0659-4
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    6. 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.
    7. 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.
    8. Lizhen Shao & Matthias Ehrgott, 2008. "Approximately solving multiobjective linear programmes in objective space and an application in radiotherapy treatment planning," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(2), pages 257-276, October.
    9. Davaatseren Baatar & Natashia Boland & Robert Johnston & Horst W. Hamacher, 2009. "A New Sequential Extraction Heuristic for Optimizing the Delivery of Cancer Radiation Treatment Using Multileaf Collimators," INFORMS Journal on Computing, INFORMS, vol. 21(2), pages 224-241, May.
    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. Fredrik Carlsson & Anders Forsgren & Henrik Rehbinder & Kjell Eriksson, 2006. "Using eigenstructure of the Hessian to reduce the dimension of the intensity modulated radiation therapy optimization problem," Annals of Operations Research, Springer, vol. 148(1), pages 81-94, November.
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    2. Kelsey Maass & Minsun Kim & Aleksandr Aravkin, 2022. "A Nonconvex Optimization Approach to IMRT Planning with Dose–Volume Constraints," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1366-1386, May.
    3. 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.
    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. Oylum S¸eker & Mucahit Cevik & Merve Bodur & Young Lee & Mark Ruschin, 2023. "A Multiobjective Approach for Sector Duration Optimization in Stereotactic Radiosurgery Treatment Planning," INFORMS Journal on Computing, INFORMS, vol. 35(1), pages 248-264, January.
    6. Raith, Andrea & Ehrgott, Matthias & Fauzi, Fariza & Lin, Kuan-Min & Macann, Andrew & Rouse, Paul & Simpson, John, 2022. "Integrating Data Envelopment Analysis into radiotherapy treatment planning for head and neck cancer patients," European Journal of Operational Research, Elsevier, vol. 296(1), pages 289-303.
    7. Salazar-González, Juan-José, 2021. "Designing optimal masks for a multi-object spectrometer," Omega, Elsevier, vol. 103(C).
    8. Jason Xu & Eric C. Chi & Meng Yang & Kenneth Lange, 2018. "A majorization–minimization algorithm for split feasibility problems," Computational Optimization and Applications, Springer, vol. 71(3), pages 795-828, December.
    9. Lim, Gino J. & Cao, Wenhua, 2012. "A two-phase method for selecting IMRT treatment beam angles: Branch-and-Prune and local neighborhood search," European Journal of Operational Research, Elsevier, vol. 217(3), pages 609-618.
    10. Shraddha Ghatkar, 2019. "Optimization of fractionation schemes and beamlet intensities in intensity-modulated radiation therapy with changing cancer tumor properties," DECISION: Official Journal of the Indian Institute of Management Calcutta, Springer;Indian Institute of Management Calcutta, vol. 46(4), pages 385-407, December.
    11. 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.
    12. 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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