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Iterative solution methods for beam angle and fluence map optimization in intensity modulated radiation therapy planning

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Abstract

We present computational approaches for optimizing beam angles and fluence maps in Intensity Modulated Radiation Therapy (IMRT) planning. We assume that the number of angles to be used for the treatment is given by the treatment planner. A mixed integer programming (MIP) model and a linear programming (LP) model are used to find an optimal set of beam angles and their corresponding fluence maps. The MIP model is solved using the branch-and-bound method while the LP model is solved using the interior point method. In order to reduce the computational burden for solving the optimization models, we introduce iterative beam angle elimination algorithms in which an insignificant beam angle is eliminated in each iteration. Other techniques are also explored including feasible set reduction for LP and data reduction. Experiments are made to show the computational advantage of the iterative methods for optimizing angles using real patient cases.

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References

  • Alber M, Nusslin F (1999) An objective function for radiation treatment optimization based on local biological measures. Phys Med Biol 44:479–493

    Article  Google Scholar 

  • American Cancer Society. Cancer Facts & Figures (2005) http://www.cancer.org/downloads/STT/ CAFF2005f4PWSecured.pdf

  • Bevilacqua V, Mastronardi G, Piscopo G (2003) Full beam configuration for coplanar radiotherapy inverse planning: a genetic algorithm-based framework. In: Hamza MH (ed) Proceedings of Artificial intelligence and applications, Track 403-022. ACTA Press, Benalmádena, Spain

  • Bortfeld T, Schlegel W (1993) Optimization of beam orientations in radiation therapy: some theoretical considerations. Phys Med Biol 38:291–304

    Article  Google Scholar 

  • Brook A, Kendrick D, Meeraus A, Raman R (2002) GAMS: A User’s Guide, GAMS Development Corporation. http://www.gams.com/

  • Djajaputra D, Wu Q, Wu Y, Mohan R (2003) Algorithm and performance of a clinical IMRT beam-angle optimization system. Phys Med Biol 48:3191–3212

    Article  Google Scholar 

  • D’Souza WD, Meyer RR, Shi L (2004) Selection of beam orientations in intensity-modulated radiation therapy using single-beam indices and integer programming. Phys Med Biol 49:3465–3481

    Article  Google Scholar 

  • Ehrgott M, Burjony M (2001) Radiation therapy planning by multicriteria optimization. In: Proceedings of the 36th Annual Conference of the Oper. Res. Soc. of New Zealand, vol 27, pp 244–253

  • Ehrgott M, Johnston R (2003) Optimisation of beam directions in intensity modulated radiation therapy planning. OR Spectr 25:251–264

    Article  Google Scholar 

  • Ezzell GA (1996) Genetic and geometric optimization of three-dimensional radiation therapy treatment planning. Med Phys 23:293–305

    Article  Google Scholar 

  • Ferris MC, Lim J, Shepard DM (2003a) Optimization approaches for treatment planning on a Gamma Knife. SIAM J Optim 13:921–937

    Article  Google Scholar 

  • Ferris MC, Lim J, Shepard DM (2003b) Radiosurgery treatment planning via nonlinear programming. Ann Oper Res 119:247–260

    Article  Google Scholar 

  • Ferris MC, Meyer RR, D’Souza W (2005) Radiation treatment planning: mixed integer programming formulations and approaches. In: Williams HP, Appa G, Pitsoulis L (eds) Handbook on modelling for discrete optim. Kluwer, Boston

    Google Scholar 

  • The General Algebraic Modeling System (GAMS), http://www.gams.com

  • Haas OCL, Burnham KJ, Mills JA (1998) Optimization of beam orientation in radiotherapy using planar geometry. Phys Med Biol 43:2179–2193

    Article  Google Scholar 

  • Hamacher HW, K”ufer K-H (2002) Inverse radiation therapy planning—a multiple objective optimization approach. Discret Appl Math 118:145–161

    Article  Google Scholar 

  • Holder A (2003) Designing radiotherapy plans with elastic constraints and interior point methods. Health Care Manage Sci 6:5–16

    Article  Google Scholar 

  • Holder A (2004) Radiotherapy treatment design and linear programming. In: Brandeau ML, Sainfort F, Pierskalla WP (eds) Operations research and health care: a handbook of methods and applications. Kluwer, Boston, pp 741–774

  • ILOG CPLEX 10.0, http://www.ilog.com

  • Intensity Modulated Radiation Therapy Collaborative Working Group (2001) Intensity modulated radiotherapy: current status and issues of interest. Int J Radiat Oncol Biol Phys 51:880–914

    Google Scholar 

  • Johnston LA (2002) Optimisation of irradiation directions in IMRT treatment. In: Proceedings of the 37th Annual Conference of the Oper. Res. Soc. Of New Zealand

  • Langer M, Brown R, Urie M, Leong J, Stracher M, Shapiro J (1990) Large scale optimization of beam weights under dose-volume restrictions. Int J Radiat Oncol Biol Phys 18:887–893

    Google Scholar 

  • Lee EK, Fox T, Crocker I (2000) Optimization of radiosurgery treatment planning via mixed integer programming. Med Phys 27:995–1004

    Article  Google Scholar 

  • Lee EK, Fox T, Crocker I (2003) Integer programming applied to intensity-modulated radiation therapy treatment planning. Ann Oper Res 119:165–181

    Article  Google Scholar 

  • Li Y, Yao J, Yao D (2004) Automatic beam angle selection in IMRT planning using genetic algorithm. Phys Med Biol 49:1915–1932

    Article  Google Scholar 

  • Lim J (2002) Optimization in radiation treatment planning. Ph.D. dissertation, University of Wisconsin-Madison, Madison, Wisconsin

  • Lim GJ, Ferris MC, Shepard DM (2004) Optimization tools for radiation treatment planning in matlab. In: Brandeau ML, Saintfort F, Pierskalla WP (eds) Operations research and health care: a handbook of methods and applications. Kluwer, Boston, pp 775–806

    Google Scholar 

  • Lim GJ, Ferris MC, Wright SJ, Shepard DM, Earl MA (2007) An optimization framework for conformal radiation treatment planning. INFORMS J Comput (in press)

  • Meedt G, Alber M, Nusslin F (2003) Non-coplanar beam direction optimization for intensity-modulated radiotherapy. Phys Med Biol 48:2999–3019

    Article  Google Scholar 

  • Preciado-Walters F, Rardin R, Langer M, Thai V (2004) A coupled column generation, mixed-integer approach to optimal planning of intensity modulated radiation therapy for cancer. Math Program 101:319–338

    Article  Google Scholar 

  • Price RA, Hanks GE, McNeeley SW, Horwitz EM, Pinover WH (2002) Advantages of using noncoplanar vs. axial beam arrangements treating prostate cancer with intensity-modulated radiation therapy and the step-and-shoot delivery method. Int J Radiat Oncol Biol Phys 53:236–243

    Google Scholar 

  • Pugachev A, Li JG, Boyer AL, Hancock SL, Le QT, Donaldson SS, Xing L (2001) Role of beam orientation optimization in intensity-modulated radiation therapy. Int J Radiat Oncol Biol Phys 50:551–560

    Article  Google Scholar 

  • Pugachev A, Lei X (2002) Incorporating prior knowledge into beam orientation optimization in IMRT. Int J Radiat Oncol Biol Phys 54:1565–1574

    Google Scholar 

  • Rowbottom CG, Khoo VS, Webb S (2001) Simultaneous optimization of beam orientations and beam weights in conformal radiotherapy. Med Phys 28(8):1696–1702

    Article  Google Scholar 

  • Rowbottom CG, Webb S, Oldham M (1998) Improvements in prostate radiotherapy from the customization of beam directions. Med Phys 25:1171–1179

    Article  Google Scholar 

  • Rowbottom CG, Webb S, Oldham M (1999) Beam-orientation customization using an artificial neural network. Phys Med Biol 44:2251–2262

    Article  Google Scholar 

  • Schreibmann E, Xing L (2004a) Feasibility study of beam orientation class-solutions for prostate IMRT. Med Phys 31:2863–2870

    Article  Google Scholar 

  • Schreibmann E, Lahanas M, Xing L, Baltas D (2004b) Multi-objective evolutionary optimization of the number of beams, their orientations and weights for intensity modulated radiation therapy. Phys Med Biol 49:747–770

    Article  Google Scholar 

  • Shepard DM, Ferris MC, Olivera G, Mackie TR (1999) Optimizing the delivery of radiation to cancer patients. SIAM Rev 41:721–744

    Article  Google Scholar 

  • Soderstrom S, Gustafsson A, Brahme A (1995) Few-field radiation-therapy optimization in the phase-space of complication-free tumor central. Int J Image Syst Technol 6(1):91–103

    Article  Google Scholar 

  • Stein J, Mohan R, Wang XH, Bortfeld T, Wu Q, Preiser K, Ling CC, Schlegel W (1997) Number and orientations for beams in intensity-modulated radiation treatments. Med Phys 24:149–160

    Article  Google Scholar 

  • Webb S (2001) Intensity-modulated radiation therapy. In: Orton CG, Spaan JAE, Webster JG (eds) Institute of physics, Series in medical physics, IOP Publishing Ltd

  • Wolsey LA (1998) Integer programming. Wiley-Interscience Series in Discrete Mathematics and Optimization. Wiley, New York

    Google Scholar 

  • Xia P (2005) Fundamental Issues in IMRT treatment planning, AAPM 47 the Annual meeting, course MO-B-T-6E

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Authors and Affiliations

  1. Department of Industrial Engineering, University of Houston, 4800 Calhoun Road, Houston, TX, 77204, USA

    Gino J. Lim & Jaewon Choi

  2. Department of Radiation Physics, University of Texas, MD Anderson Cancer Center, Houston, TX, USA

    Radhe Mohan

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  1. Gino J. Lim
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  2. Jaewon Choi
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  3. Radhe Mohan
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Correspondence to Gino J. Lim.

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Lim, G.J., Choi, J. & Mohan, R. Iterative solution methods for beam angle and fluence map optimization in intensity modulated radiation therapy planning. OR Spectrum 30, 289–309 (2008). https://doi.org/10.1007/s00291-007-0096-1

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