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An Optimization-Based Approach to the Multiple Static Delivery Technique in Radiation Therapy

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Abstract

The paper considers the intensity modulated radiation therapy (inverse) treatment planning. An approach to determine the trajectories of the leaves of the multileaf collimator (MLC) in order to produce the prescribed intensity distribution is developed. The paper concentrates on the multiple static delivery technique. A mathematical model for calculating the intensity distribution with the help of locations of the leafheads of subsequent subfields is constructed. Furthermore, an optimization model in which the decision variables are the locations of leafheads is developed. The relevant constraints are considered as well. The optimization problem is a large dimensional constrained nonlinear global extremum problem. It is solved by the LGO (Lipschitz (Continuous) Global Optimizer) program system. Comparisons with other optimization method (Hooke–Jeeves iteration) are included. Numerical experiments are presented to confirm the functionality of the method.

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References

  1. C. Börgers, The radiation therapy planning problem, in: Computational Radiology and Imaging: Therapy and Diagnostic, eds. C. Börgers and F. Natterer (Springer, Berlin, 1997).

    Google Scholar 

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

    Google Scholar 

  3. T. Bortfeld, D. Kahler, T.J. Waldron and A.L. Boyer, X-ray field compensation with multileaf compensators, Int. J. Radiat. Oncol. 28 (1994) 723–730.

    Google Scholar 

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

    Google Scholar 

  5. A.T. Boyer and C.X. Yu, Intensity-modulated radiation therapy with dynamic multileaf collimators. Semin. Radiat. Oncol. 9 (1999) 48–59.

    Google Scholar 

  6. A. Brahme, Treatment optimization using physical and radiological objective functions, in: Radiation Therapy Physics, ed. A. Smith (Springer, Berlin, 1995).

    Google Scholar 

  7. Y. Censor and S.A. Zenios, Parallel Optimization: Theory, Algorithms and Applications (Oxford Univ. Press, Oxford, 1997) Chapter 11.

    Google Scholar 

  8. P.S. Cho and R.J. Marks II, Hardware-sensitive optimization for intensity modulated radiotherapy, Phys. Med. Biol. 45 (2000) 429–440.

    Google Scholar 

  9. D.J. Convery and M.E. Rosenbloom, The generation of intensity-modulated fields for conformal radiotherapy by dynamic collimation, Phys. Med. Biol. 37(6) (1992) 1359–1374.

    Google Scholar 

  10. D.J. Convery and S. Webb, Generation of discrete beam-intensity modulation by dynamic multileaf collimation under minimum leaf separation constraints, Phys. Med. Biol. 43 (1998) 2521–2538.

    Google Scholar 

  11. J.O. Deasy, Multiple local minima in radiotherapy optimization problems with dose-volume constraints, Med. Phys. 24(7) (1997) 1157–1161.

    Google Scholar 

  12. F.C. Difilippo, Forward and adjoint methods for radiotherapy planning, Med. Phys. 25(9) (1998) 1702–1710.

    Google Scholar 

  13. P.M. Evans, N.H. Vibeke and W. Swindell, The optimum intensities for multiple static collimator field compensation, Med. Phys. 24(7) (1997) 1147–1156.

    Google Scholar 

  14. J.M. Galvin, X.G. Chen and R.M. Smith, Combining multileaf fields to modulate fluence distribution, Int. J. Radiat. Oncol. Biol. Phys. 27 (1993) 697–705.

    Google Scholar 

  15. P. Geis and L. Bojer, Use of multileaf collimator as a dynamic missing-tissue compensator, Med. Phys. 23 (1996) 1199–1205.

    Google Scholar 

  16. O. Haas, Radiotherapy Treatment Planning: New System Approaches (Springer, London, UK, 1999).

    Google Scholar 

  17. T. Holmes and T.R. Mackie, A comparison of three inverse treatment planning algorithms, Phys.Med. Biol. 39 (1994) 91–106.

    Google Scholar 

  18. R. Horst and P.M. Pardalos, eds., Handbook of Global Optimization, Vol. 1 (Kluwer Academic, Dordrecht, 1995).

    Google Scholar 

  19. D.H. Hristov and B.G. Fallone, An active set algorithm for treatment planning optimization, Med. Phys. 24(9) (1997) 1455–1464.

    Google Scholar 

  20. C.T. Kelley, Iterative Methods for Optimization (SIAM, Philadelphia, PA, 1999).

    Google Scholar 

  21. P. Kolmonen, J. Tervo and T. Lahtinen, Use of the Cimmino algorithm and continuous approximation for the dose deposition kernel in the inverse problem of radiation treatment planning, Phys.Med. Biol. 43 (1998) 2539–2554.

    Google Scholar 

  22. S. Lee, P.S. Cho, R.J. Marks and S. Oh, Conformal radiotherapy computation by the method of alternating projections onto convex sets, Phys. Med. Biol. 42 (1997) 1065–1086.

    Google Scholar 

  23. P.M. Pardalos and H.E. Romeijn, eds., Handbook of Global Optimization, Vol. 2 (Kluwer Academic, Dordrecht, 2002).

    Google Scholar 

  24. J.D. Pintér, Global Optimization in Action (Kluwer Academic, Dordrecht, 1996).

    Google Scholar 

  25. J.D. Pintér, A model development system for global optimization, in: High Performance Algorithms and Software in Nonlinear Optimization, eds. R. DeLeone et al. (Kluwer Academic, Dordrecht, 1998).

    Google Scholar 

  26. J.D. Pintér, Computational Global Optimization in Nonlinear Systems – An Interactive Turorial (Lionheart Publishing Inc., Atlanta, GA, 2001).

    Google Scholar 

  27. J.D. Pintér, LGO – A Model Development System for Continuous Global Optimization, User Guide (Pintér Consulting Services, Halifax, NS, 2002).

    Google Scholar 

  28. S.V. Spirou and C.-S. Chui, Generation of arbitrary intensity profiles by combining the scanning beam with dynamic multileaf collimation, Med. Phys. 23(1) (1996) 1–8.

    Google Scholar 

  29. S.V. Spirou and C.-S. Chui, A gradient inverse planning algorithm with dose-volume constraints, Med. Phys. 25(3) (1998) 321–333.

    Google Scholar 

  30. J. Stein, Dynamic X-ray compensation for conformal radiotherapy by means of multi-leaf collimation, Radiother. Oncol. 32 (1994) 163–173.

    Google Scholar 

  31. R. Svensson, P. Källman and A. Brahme, An analytical solution for the dynamic control of multileaf collimators, Phys. Med. Biol. 39 (1994) 37–61.

    Google Scholar 

  32. J. Tervo and P. Kolmonen, A model for the control of multileaf collimator in radiation therapy treatment planning, Inv. Probl. 16 (2000) 1875–1895.

    Google Scholar 

  33. J. Tervo, P. Kolmonen, M. Vauhkonen, L.M. Heikkinen and J.P. Kaipio, A finite element model of electron transport in radiation therapy and related inverse problem, Inv. Probl. 15 (1999) 1345–1361.

    Google Scholar 

  34. J. Tervo, T. Lyyra-Laitinen, P. Kolmonen and E. Boman, An inverse treatment planning model for intensity modulated radiation therapy with dynamic MLC, Appl. Math. Comput. (2002) to appear.

  35. S. Webb, The Physics of Three-Dimensional Radiation Therapy (Institute of Physics Publishing, Bristol, UK, 1993).

    Google Scholar 

  36. S. Webb, Configuration options for intensity-modulated radiation therapy using multiple static fields shaped by a multileaf collimator, Phys. Med. Biol. 43 (1998) 241–260.

    Google Scholar 

  37. S. Webb, Intensity-Modulated Radiation Therapy (Institute of Physics Publishing, Bristol, UK, 2001).

    Google Scholar 

  38. S. Webb, T. Bortfeld, J. Stein and D. Convery, The effect of stair-step leaf transmission on the ‘tongueand-groove problem’ in dynamic radiotherapy with a multileaf collimator, Phys.Med. Biol. 42 (1997) 595–602.

    Google Scholar 

  39. P. Xia and L.J. Verhey, Multileaf collimator leaf sequencing algorithm for intensity modulated beams with multiple static segments, Med. Phys. 25(8) (1998) 1424–1434.

    Google Scholar 

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Tervo, J., Kolmonen, P., Lyyra-Laitinen, T. et al. An Optimization-Based Approach to the Multiple Static Delivery Technique in Radiation Therapy. Annals of Operations Research 119, 205–227 (2003). https://doi.org/10.1023/A:1022942825680

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