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Neighborhood search approaches to beam orientation optimization in intensity modulated radiation therapy treatment planning

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Abstract

The intensity modulated radiation therapy (IMRT) treatment planning problem consists of several subproblems which are typically solved sequentially. We seek to combine two of the subproblems: the beam orientation optimization (BOO) problem and the fluence map optimization (FMO) problem. The BOO problem is the problem of selecting the beam orientations to deliver radiation to the patient. The FMO problem is the problem of determining the amount of radiation intensity, or fluence, of each beamlet in each beam. The solution to the FMO problem measures the quality of a beam set, but the majority of previous BOO studies rely on heuristics and approximations to gauge the quality of the beam set. In contrast with these studies, we use an exact measure of the treatment plan quality attainable using a given beam set, which ensures convergence to a global optimum in the case of our simulated annealing algorithm and a local optimum in the case of our local search algorithm. We have also developed a new neighborhood structure that allows for faster convergence using our simulated annealing and local search algorithms, thus reducing the amount of time required to obtain a good solution. Finally, we show empirically that we can generate clinically acceptable treatment plans that require fewer beams than in current practice. This may reduce the length of treatment time, which is an important clinical consideration in IMRT.

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References

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

    Article  Google Scholar 

  2. Aleman, D.M., Romeijn, H.E., Dempsey, J.F.: Beam orientation optimization methods in intensity modulated radiation therapy treatment planning. IIE Conference Proceedings (2006)

  3. Aleman, D.M., Romeijn, H.E., Dempsey, J.F.: A response surface approach to beam orientation optimization in intensity modulated radiation therapy treatment planning. INFORMS J. Comput: Coumputat. Biol. Med. Appl. (2008, to appear)

  4. Aleman, D.M., Glaser, D., Romeijn, H.E., Dempsey, J.F.: A primal-dual interior point algorithm for fluence map optimization in intensity modulated radiation therapy treatment planning. Work in progress (2008)

  5. Bednarz, G., Michalski, D., Houser, C., Huq, M.S., Xiao, Y., Anne, P.R., Galvin, J.M.: The use of mixed-integer programming for inverse treatment planning with pre-defined field segments. Phys. Med. Biol. 47, 2235–2245 (2002)

    Article  Google Scholar 

  6. Bélisle, C.J.P.: Convergence theorems for a class of simulated annealing algorithms on \({\mathbb{R}^d}\) . J. Appl. Prob. 29, 885–895 (1992)

    Article  Google Scholar 

  7. Bélisle, C.J.P., Romeijn, H.E., Smith, R.L.: Hit-and-run algorithms for generating multivariate distributions. Math. Oper. Res. 18, 255–266 (1993)

    Article  Google Scholar 

  8. Bomze, I.: Fast simulated annealing. Phys. Lett. 122A, 157–162 (1987)

    Google Scholar 

  9. Bortfeld, T.: Optimized planning using physical objectives and constraints. Semin. Radiat. Oncol. 9, 20–34 (1999)

    Article  Google Scholar 

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

    Article  Google Scholar 

  11. Chen, G.T., Spelbring, D.R., Pelizzari, C.A., Balter, J.M., Myrianthopoulos, L.C., Vijayakumar, S., Halpern, H.: The use of beams eye view volumetrics in the selection of non-coplanar radiation portals. Int. J. Radiat. Oncol. Biol. Phys. 23, 153–163 (1992)

    Google Scholar 

  12. Cho, B.C.J., Roa, H.W., Robinson, D., Murray, B.: The development of target-eye-view maps for selection of coplanar or noncoplanar beams in conformal radiotherapy treatment planning. Med. Phys. 26, 2367–2372 (1999)

    Article  Google Scholar 

  13. Das, S.K., Marks, L.B.: Selection of coplanar or noncoplanar beams using three-dimensional optimization based on maximum beam separation and minimized nontarget irradiation. Int. J. Radiat. Oncol. Biol. Phys. 38, 643–655 (1997)

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  16. Gelfand, A.E., Smith, A.F.M.: Sampling based approaches to calculating marginal densities. J. Am. Stat. Assoc. 85, 398–409 (1990)

    Article  Google Scholar 

  17. Geman, S., Geman, D.: Stochastic relaxation, gibbs distributions, and the bayesian restoration of images. IEEE Trans. Pattern Analy. Mach. Intell. 6, 721–741 (1984)

    Google Scholar 

  18. Glaser, D.: A primal-dual interior-point method for convex Fluence Map Optimization problems. Master’s thesis, Royal Institute of Technology (2005)

  19. Goitein, M., Abrams, M., Rowell, D., Pollari, H., Wiles, J.: Multi-dimensional treatment planning: Ii. beams eye-view, back projection, and projection through CT sections. Int. J. Radiat. Oncol. Biol. Phys. 9, 789–797 (1983)

    Google Scholar 

  20. Gokhale, P., Hussein, E.M., Kulkarni, N.: The use of beams eye view volumetrics in the selection of non-coplanar radiation portals. Med. Phys. 23, 153–163 (1994)

    Google Scholar 

  21. Haas, O.C., Burnham, K.J., Mills, J.: Optimization of beam orientation in radiotherapy using planar geometry. Phys. Med. Biol. 43, 2179–2193 (1998)

    Article  Google Scholar 

  22. Hamacher, H.W., Küfer, K.-H.: Inverse radiation therapy planning a multiple objective optimization approach. Discr. Appl. Math. 118, 145–161 (2002)

    Article  Google Scholar 

  23. Jones, L.C., Hoban, P.W.: Treatment plan comparison using equivalent uniform biologically effective dose (eubed). Phys. Med. Biol. 45, 159–170 (2000)

    Article  Google Scholar 

  24. Kallman, P., Lind, B.K., Brahme, A.: An algorithm for maximizing the probability of complication–free tumor–control in radiation-therapy. Phys. Med. Biol. 37, 871–890 (1992)

    Article  Google Scholar 

  25. Kirkpatrick, S., Gelatt, C.D.: Optimization by simulated annealing. Science 220, 671–680 (1983)

    Article  Google Scholar 

  26. Kumar, A.: Novel methods for intensity-modulated radiation therapy treatment planning. PhD thesis, University of Florida (2005)

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

    Google Scholar 

  28. Langer, M., Morrill, S., Brown, R., Lee, O., Lane, R.: A comparison of mixed integer programming and fast simulated annealing for optimizing beam weights in radiation therapy. Med. Phys. 23, 957–964 (1996)

    Article  Google Scholar 

  29. Lee, E.K., Fox, T., Crocker, I.: Simultaneous beam geometry and intensity map optimization in intensity-modulated radiation therapy treatment planning. Ann. Oper. Res. 119, 165–181 (2003)

    Article  Google Scholar 

  30. Lee, E.K., Fox, T., Crocker, I.: Integer programming applied to intensity-modulated radiation therapy treatment planning. Int. J. Radiat. Oncol. Biol. Phys. 64, 301–320 (2006)

    Google Scholar 

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

    Article  Google Scholar 

  32. Li, Y., Yao, J., Yao, D., Chen, W.: A particle swarm optimization algorithm for beam angle selection in intensity-modulated radiotherapy planning. Phys. Med. Biol. 50, 3491–3514 (2005)

    Article  Google Scholar 

  33. 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)

    Article  Google Scholar 

  34. Lu, H.M., Kooy, H.M., Leber, Z.H., Ledoux, R.J.: Optimized beam planning for linear accelerator-based stereotactic radiosurgery. Int. J. Radiat. Oncol. Biol. Phys. 39, 1183–1189 (1997)

    Google Scholar 

  35. Mavroidis, P., Lind, B.K., Brahme, A.: Biologically effective uniform dose for specification, report and comparison of dose response relations and treatment plans. Phys. Med. Biol. 46, 2607–2630 (2001)

    Article  Google Scholar 

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

    Article  Google Scholar 

  37. Niemierko, A.: Reporting and analyzing dose distributions: a concept of equivalent uniform dose. Med. Phys. 24, 103–110 (1997)

    Article  Google Scholar 

  38. Niemierko, A., Urie, M., Goitein, M.: Optimization of 3d radiation-therapy with both physical and biological end-points and constraints. Int. J. Radiat. Oncol. Biol. Phys. 23, 99–108 (1992)

    Google Scholar 

  39. Nocedal, J., Wright, S.: Numerical Optimization. Springer-Verlag, Inc., New York (1999)

    Google Scholar 

  40. Pugachev, A., Xing, L.: Computer-assisted selection of coplanar beam orientations in intensity-modulated radiation therapy. Phys. Med. Biol. 46, 2467–2476 (2001)

    Article  Google Scholar 

  41. Pugachev, A., Xing, L.: Pseudo beam’s-eye-view as applied to beam orientation selection in intensity-modulated radiation therapy. Int. J. Radiat. Oncol. Biol. Phys. 51, 1361–1370 (2001)

    Google Scholar 

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

    Google Scholar 

  43. Romeijn, H.E., Ahuja, R.K., Dempsey, J.F., Kumar, A., Li, J.G.: A novel linear programming approach to fluence map optimization for intensity modulated radiation therapy treatment planning. Phys. Med. Biol. 38, 3521–3542 (2003)

    Article  Google Scholar 

  44. Romeijn, H.E., Dempsey, J.F., Li, J.G.: A unifying framework for multi-criteria fluence map optimization models. Phys. Med. Biol. 49, 1991–2013 (2004)

    Article  Google Scholar 

  45. Romeijn, H.E., Ahuja, R.K., Dempsey, J.F., Kumar, A., Li, J.G.: A column generation approach to radiation therapy treatment planning using aperature modulation. SIAM J. Optim. 15, 838–862 (2005)

    Article  Google Scholar 

  46. Romeijn, H.E., Ahuja, R.K., Dempsey, J.F., Kumar, A.: A new linear programming approach to radiation therapy treatment planning problems. Oper. Res. 54, 201–216 (2006)

    Article  Google Scholar 

  47. Rowbottom, C.G., Oldham, M., Webb, S.: Constrained customization of non-coplanar beam orientations in radiotherapy of brain tumours. Phys. Med. Biol. 44, 383–399 (1999)

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  50. Shepard, D.M., Ferris, M.C., Olivera, G.H., Mackie, T.R.: Optimizing the delivery of radiation therapy to cancer patients. SIAM Rev. 41, 721–744 (1999)

    Article  Google Scholar 

  51. Smith, R.L.: A monte carlo procedure for the random generation of feasible solutions to mathematical programming problems. Bulletin of the TIMS/ORSA Joint National Meeting, p. 101 (1980)

  52. Söderstrom, S., Brahme, A.: Selection of suitable beam orientations in radiation therapy using entropy and fourier transform measures. Phys. Med. Biol. 37, 911–924 (1992)

    Article  Google Scholar 

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

    Article  Google Scholar 

  54. Wu, Q.W., Mohan, R., Niemierko, A., Schmidt-Ullrich, R.: Optimization of intensity-modulated radiotherapy plans based on the equivalent uniform dose. Int. J. Radiat. Oncol. Biol. Phys. 52, 224–235 (2002)

    Google Scholar 

  55. Wu, Q.W., Djajaputra, D., Wu, Y., Zhou, J.N., Liu, H.H., Mohan, R.: Intensity-modulated radiotherapy optimization with geud-guided dose-volume objectives. Phys. Med. Biol. 48, 279–291 (2003)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Industrial and Systems Engineering, University of Florida, 303 Weil Hall, P.O. Box 116595, Gainesville, FL, 32611-6595, USA

    Dionne M. Aleman, Ravindra K. Ahuja & H. Edwin Romeijn

  2. Innovative Scheduling, Gainesville Technology Enterprise Center (GTEC), 2153 Hawthorne Road, Suite 128, Gainesville, FL, 32641, USA

    Arvind Kumar

  3. Department of Radiation Oncology, University of Florida, P.O. Box 100385, Gainesville, FL, 32610-0385, USA

    James F. Dempsey

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  1. Dionne M. Aleman
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  2. Arvind Kumar
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  3. Ravindra K. Ahuja
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  4. H. Edwin Romeijn
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  5. James F. Dempsey
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Correspondence to Dionne M. Aleman.

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Aleman, D.M., Kumar, A., Ahuja, R.K. et al. Neighborhood search approaches to beam orientation optimization in intensity modulated radiation therapy treatment planning. J Glob Optim 42, 587–607 (2008). https://doi.org/10.1007/s10898-008-9286-x

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  • DOI: https://doi.org/10.1007/s10898-008-9286-x

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