An Approach for Treatment Programming in Intensity Modulated Radiation Therapy (IMRT)

Document Type: Research Paper


Department of Industrial Engineering, Sharif University of Technology, Tehran, Iran


Intensity modulated radiation therapy is one of the most commonly procedures used for delivering radiation to cancerous tissues. It aims to deliver the prescribed dose in the target volume while minimizing damage to the nearby healthy organs. In this procedure, two decisions being very important are selecting the beam angles and calculating the beam intensities. Although beam angle selection (beam angle optimization) is one of the most important decisions in this procedure, it is often be made manually and based on radio therapist experience and intuition. In order to overcome this drawback, this paper proposes a hybrid approach for automated beam angle selection and intensity computation. The proposed approach first finds a good feasible solution, and then use this solution as a starting point in local neighborhood search to find the local optimal solution. As the results of numerical experiments demonstrate, the proposed hybrid-approach, compared to its corresponding stand-alone methods, finds a better solution quickly and consistently.


1. Lee, E.K., T. Fox, and I. Crocker. (2000). Optimization of radiosurgery treatment planning via mixed integer programming, Medical physics, Vol. 27, No. 5, PP. 995-1004.

2. Cho, P.S. et al. (1998). Optimization of intensity modulated beams with volume constraints using two methods: Cost function minimization and projections onto convex sets, Medical Physics, Vol. 25, No. 4, PP. 435-443.

3. Romeijn, H.E. et al. (2003). A novel linear programming approach to fluence map optimization for intensity modulated radiation therapy treatment planning, Physics in Medicine and Biology,Vol.48, No.21, P. 3521.

4. Saka, B., R.L. Rardin, and M.P. Langer. (2014). Biologically guided intensity modulated radiation therapy planning optimization with fraction-size dose constraints, Journal of the OperationalResearch Society, Vol. 65, No. 4, PP. 557-571.

5. Holder, A. (2003). Designing radiotherapy plans with elastic constraints and interior point methods, Health care management science, Vol. 6, No. 1, PP. 5-16.

6. Spirou, S.V. and C.-S. Chui. (1998). A gradient inverse planning algorithm with dose-volume constraints. Medical physics, Vol. 25, No. 3, PP. 321-333.

7. Bednarz, G. et al. (2004). Inverse treatment planning using volume-based objective functions, Physics in Medicine and Biology, Vol. 49, No. 12, P. 2503.

8. Langer, M. et al. (1990). Largescale optimization of beam weights under dose-volume restrictions, Vol. 18, No. 4, PP. 887-893.

9. Lee, E.K., T. Fox, and I. Crocker, (2003), Integer programming applied to intensity-modulated radiation therapy treatment planning. Annals of Operations Research, Vol. 119, No. 1-4, PP. 165-181.

10. Romeijn, H.E., Dempsey. J.F and J.G. Li. (2004). A unifying framework for multi-criteria fluence map optimization models, Physics in Medicine and Biology, Vol. 49, No. 10, P. 1991.

11. D D'Souza, W., Meyer, R.R., and Shi, L. (2004). Selection of beam orientations in intensity-modulated radiation therapy using single-beam indices and integer programming, Physics in Medicine and Biology, Vol. 49, No. 15, PP. 34-65.

12. Kirkpatrick, S., Gelatt, C.D., and Vecchi, M.P. (1983). Optimization by simmulated annealing, science, Vol. 220, No. 4598, PP. 671-680.

13. Li, Y., Yao, J., and. Yao, D. (2004). Automatic beam angle selection in IMRT planning using genetic algorithm, Physics in medicine and biology, Vol. 49, No. 10, P. 1915.

14. Price, S. et al. (2014). Data mining to aid beam angle selection for intensity-modulated radiation therapy. in Proceedings of the 5th ACM conference on bioinformatics, computational biology, and health informatics, ACM.

15. Aleman, D.M. et al. (2008). Neighborhood search approaches to beam orientation optimization in intensity modulated radiation therapy treatment planning, Journal of Global Optimization, Vol. 42, No. 4, PP. 587-607.

16. Kirkpatrick, S. (1984). Optimization by simulated annealing: Quantitative studies, Journal of statistical physics, Vol. 34, No. 5-6, PP. 975-986.

17. Bertsimas, D. et al. (2013). A hybrid approach to beam angle optimization in intensity-modulated radiation therapy, Computers and Operations Research, Vol. 40, No. 9, PP. 2187-2197.

18. Lin, S., Lim, G.J., and J.F. (2016). Bard, Benders decomposition and an IP-based heuristic for selecting IMRT treatment beam angles, European Journal of Operational Research, Vol. 251, No. 3, PP. 715-726.

19. Lim, G.J., Choi, J., and Mohan, (R. 2008). Iterative solution methods for beamangle and fluence map optimization in intensity modulated radiation therapy planning, OR Spectrum, Vol. 30, No. 2, PP. 289-309.

20. Lim, G.J., and Cao, W. (2012), A two-phase method for selecting IMRT treatment beam angles: Branch-and-Prune and local neighborhood search, European Journal of Operational Research, Vol. 217, No. 3, PP. 609-618.

21. Zhang, H.H. et al. (2009). Solving beam-angle selection and dose optimization simultaneously via high-throughput computing, INFORMS Journal on Computing, Vol. 21, No. 3, PP. 427-444.

22. Li, Y. et al. (2005). A particle swarm optimization algorithm for beam angle selection in intensity-modulated radiotherapy planning, Physics in medicine and biology, Vol. 50, No. 15, P. 3491.

23. Ahnesjö, A., Saxner, M., and Trepp, A. (1992). A pencil beam model for photondose calculation, Medical physics, Vol. 19, No. 2, PP. 263-273.

24. Deasy, J.O., Blanco, A.I., and Clark, V.H. (2003). CERR: A computational environment for radiotherapy research, Medical Physics, Vol. 30, No. 5, PP. 979-985.

25. Group, I.M.R.T.C.W., (2001), Intensity-modulated radiotherapy: current status and issues of interest, International Journal of Radiation Oncology* Biology* Physics, Vol. 51, No. 4, PP. 880-914.