Advertisement

A Tutorial on Radiation Oncology and Optimization

  • Allen Holder
  • Bill Salter
Chapter
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 76)

Abstract

Designing radiotherapy treatments is a complicated and important task that affects patient care, and modern delivery systems enable a physician more flexibility than can be considered. Consequently, treatment design is increasingly automated by techniques of optimization, and many of the advances in the design process are accomplished by a collaboration among medical physicists, radiation oncologists, and experts in optimization. This tutorial is meant to aid those with a background in optimization in learning about treatment design. Besides discussing several optimization models, we include a clinical perspective so that readers understand the clinical issues that are often ignored in the optimization literature. Moreover, we discuss many new challenges so that new researchers can quickly begin to work on meaningful problems.

Keywords

Optimization Radiation Oncology Medical Physics Operations Research 

References

  1. [1]
    G. K. Bahr, J. G. Kereiakes. H. Horwitz, R. Finney, J. Galvin, and K. Goode. The method of linear programming applied to radiation treatment planning. Radiology, 91: 686–693, 1968.Google Scholar
  2. [2]
    F. Bartolozzi et al. Operational research techniques in medical treatment and diagnosis. a review. European Journal of Operations Research, 121(3): 435–466, 2000.zbMATHCrossRefGoogle Scholar
  3. [3]
    N. Boland, H. Hamacher, and F. Lenzen. Minimizing beam-on time in cancer radiation treatment using multileaf collimators. Technical Report Report Wirtschaftsmathematik, University Kaiserslautern, Mathematics, 2002.Google Scholar
  4. [4]
    T. Bortfeld and W. Schlegel. Optimization of beam orientations in radiation therapy: Some theoretical considerations. Physics in Medicine and Biology, 38: 291–304, 1993.CrossRefGoogle Scholar
  5. [5]
    Y. Censor, M. Altschuler, and W. Powlis. A computational solution of the inverse problem in radiation-therapy treatment planning. Applied Mathematics and Computation, 25: 57–87, 188.Google Scholar
  6. [6]
    D. Cheek, A. Holder, M. Fuss, and B. Salter. The relationship between the number of shots and the quality of gamma knife radiosurgeries. Technical Report 84, Trinity University Mathematics, San Antonio, TX, 2004.Google Scholar
  7. [7]
    J. Chinneck and H. Greenberg. Intelligent mathematical programming software: Past, present, and future. Canadian Operations Research Society Bulletin, 33(2): 14–28, 1999.Google Scholar
  8. [8]
    J. Chinneck. An effective polynomial-time heuristic for the minimum-cardinality iis setcovering problem. Annals of Mathematics and Artificial Intelligence, 17: 127–144, 1995.MathSciNetCrossRefGoogle Scholar
  9. [9]
    J. Chinneck. Finding a useful subset of constraints for analysis in an infeasible linear program. INFORMS Journal on Computing, 9(2): 164–174, 1997.zbMATHMathSciNetCrossRefGoogle Scholar
  10. [10]
    Consortium for Mathematics and Its Applications (COMAP), www.comap.com. Gamma Knife Treatment Planning, Problem B.Google Scholar
  11. [11]
    A. Drud. CONOPT: A GRG code for large sparse dynamic nonlinear optimization problems. Mathematical Programming, 31: 153–191, 1985.zbMATHMathSciNetGoogle Scholar
  12. [12]
    M. Ehrgott and J. Johnston. Optimisation of beam direction in intensity modulated radiation therapy planning. OR Spectrum, 25(2): 251–264, 2003.CrossRefzbMATHGoogle Scholar
  13. [13]
    K. Engel. A new algorithm for optimal multileaf collimator field segmentation. Technical report, Operations Research & Radiation Oncology Web Site, w.trinity.edu/aholder/HealthApp/oncology/, 2003.Google Scholar
  14. [14]
    M. Ferris, J. Lim, and D. Shepard. An optimization approach for the radiosurgery treatment planning. SIAM Journal on Optimization, 13(3): 921–937, 2003.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    M. Ferris, J. Lim, and D. Shepard. Radiosurgery optimization via nonlinear programming. Annals of Operations Research, 119: 247–260, 2003.CrossRefzbMATHGoogle Scholar
  16. [16]
    M. Ferris and M. Voelker. Neuro-dynamic programming for radiation treatment planning. Technical Report Numerical Analysis Group Research Report NA-02/06, Oxford University Computing Laboratory, 2002.Google Scholar
  17. [17]
    S. Gaede, E. Wong, and H. Rasmussen. An algorithm for systematic selection of beam directions for imrt. Medical Physics, 31(2): 376–388, 2004.CrossRefGoogle Scholar
  18. [18]
    A. Gersho and M. Gray. Vector Quantization and Signal Processing. Kluwer Academic Publishers, Boston, MA, 1992.Google Scholar
  19. [19]
    M. Goitein and A Niemierko. Biologically based models for scoring treatment plans. Scandanavian Symposium on Future Directions of Computer-Aided Radiotherapy, 1988.Google Scholar
  20. [20]
    H. Greenberg. A Computer-Assisted Analysis System for Mathematical Programming Models and Solutions: A User’s Guide for ANALYZE. Kluwer Academic Publishers, Boston, MA, 1993.zbMATHGoogle Scholar
  21. [21]
    H. Greenberg. Consistency, redundancy and implied equalities in linear systems. Annals of Mathematics and Artificial Intelligence, 17: 37–83, 1996.zbMATHMathSciNetCrossRefGoogle Scholar
  22. [22]
    L. Hodes. Semiautomatic optimization of external beam radiation treatment planning. Radiology, 110: 191–196, 1974.Google Scholar
  23. [23]
    A. Holder. Partitioning Multiple Objective Solutions with Applications in Radiotherapy Design. Technical Report 54, Trinity University Mathematics, 2001.Google Scholar
  24. [24]
    A. Holder. Radiotherapy treatment design and linear programming. Technical Report 70, Trinity University Mathematics, San Antonio, TX, 2002. to appear in the Handbook of Operations Research/Management Science Applications in Health Care.Google Scholar
  25. [25]
    A. Holder. Designing radiotherapy plans with elastic constraints and interior point methods. Health Care and Management Science, 6(1): 5–16, 2003.CrossRefGoogle Scholar
  26. [26]
    T. Kalinowski. An algorithm for optimal collimator field segmentation with interleaf collision constraint 2. Technical report, Operations Research & Radiation Oncology Web Site, w.trinity.edu/aholder/HealthApp/oncology/, 2003.Google Scholar
  27. [27]
    T. Kalinowski. An algorithm for optimal multileaf collimator field segmentation with interleaf collision constraint. Technical report, Operations Research & Radiation Oncology Web Site, w.trinity.edu/aholder/HealthApp/oncology/, 2003.Google Scholar
  28. [28]
    G. Kutcher and C. Burman. Calculation of complication probability factors for non uniform normal tissue irradiation. International Journal of Radiation Oncology Biology and Physics, 16: 1623–30, 1989.Google Scholar
  29. [29]
    M. Langer, R. Brown, M. Urie, J. Leong, M. Stracher, and J. Shapiro. Large scale optimization of beam weights under dose-volume restrictions. International Journal of Radiation Oncology, Biology, Physics, 18: 887–893, 1990.Google Scholar
  30. [30]
    E. Lee, T. Fox, and I. Crocker. Optimization of radiosurgery treatment planning via mixed integer programming. Medical Physics, 27(5): 995–1004, 2000.CrossRefGoogle Scholar
  31. [31]
    E. Lee. T. Fox, and I. Crocker. Optimization of radiosurgery treatment planning via mixed integer programming. Medical Physics, 27(5): 995–1004, 2000.CrossRefGoogle Scholar
  32. [32]
    E. Lee, T Fox, and I Crocker. Integer Programming Applied to Intensity-Modulated Radiation Treatment Planning. To appear in Annals of Operations Research, Optimization in Medicine.Google Scholar
  33. [33]
    J. Legras, B. Legras, and J. Lambert. Software for linear and non-linear optimization in external radiotherapy. Computer Programs in Biomedicine, 15: 233–242, 1982.CrossRefGoogle Scholar
  34. [34]
    G. Leichtman, A. Aita, and H. Goldman. Automated gamma knife dose planning using polygon clipping and adaptive simulated annealing. Medical Physics, 27(1): 154–162, 2000.CrossRefGoogle Scholar
  35. [35]
    L. Leksell. The stereotactic method and radiosurgery of the brain. Ada Chirurgica Scandinavica, 102:316–319, 1951.Google Scholar
  36. [36]
    W. Lodwick, S. McCourt, F. Newman, and S. Humphries. Optimization methods for radiation therapy plans. In C. Borgers and F. Natterer, editors, IMA Series in Applied Mathematics-Computational, Radiology and Imaging: Therapy and Diagnosis. Springer-Verlag, 1998.Google Scholar
  37. [37]
    N. Lomax and S. Scheib. Quantifying the degree of conformality in radiosurgery treatment planning. International Journal of Radiation Oncology, Biology, and Physics, 55(5): 1409–1419, 2003.CrossRefGoogle Scholar
  38. [38]
    L. Luo, H. Shu, W. Yu, Y. Yan, X. Bao, and Y. Fu. Optimizing computerized treatment planning for the gamma knife by source culling. International Journal of Radiation Oncology Biology and Physics, 45(5): 1339–1346, 1999.CrossRefGoogle Scholar
  39. [39]
    J. Lyman and A. Wolbarst. Optimization of radiation therapy iii: A method of assessing complication probabilities from dose-volume histograms. International Journal of Radiation Oncology Biology and Phsyics, 13: 103–109, 1987.CrossRefGoogle Scholar
  40. [40]
    J. Lyman and A. Wolbarst. Optimization of radiation therapy iv: A dose-volume histogram reduction algorithm. International Journal of Radiation Oncology Biology and Phsyics, 17: 433–436, 1989.Google Scholar
  41. [41]
    J. Lyman. Complication probability as assessed from dose-volume histrograms. Radiation Research, 104: S 13–19, 1985.Google Scholar
  42. [42]
    S. McDonald and P. Rubin. Optimization of external beam radiation therapy. International Journal of Radiation Oncology, Biology, Physics, 2: 307–317, 1977.Google Scholar
  43. [43]
    S. Morrill, R. Lane, G. Jacobson, and I. Rosen. Treatment planning optimization using constrained simulated annealing. Physics in Medicine & Biology, 36(10): 1341–1361, 1991.CrossRefGoogle Scholar
  44. [44]
    S. Morrill, I. Rosen, R. Lane, and J. Belli. The influence of dose constraint point placement on optimized radiation therapy treatment planning. International Journal of Radiation Oncology, Biology, Physics, 19: 129–141, 1990.Google Scholar
  45. [45]
    J. Leong M. Langer. Optimization of beam weights under dose-volume restrictions. International Journal of Radiation Oncology, Biology, Physics, 13: 1255–1260, 1987.Google Scholar
  46. [46]
    A. Niemierko and M. Goitein. Calculation of normal tissue complication probability and dose-volume histogram reduction schemes for tissues with critical element architecture. Radiation Oncology, 20:20, 1991.Google Scholar
  47. [47]
    I. Paddick. A simple scoring ratio to index the conformality of radiosurgical treatment plans. Journal of Neurosurgery, 93(3): 219–222, 2000.Google Scholar
  48. [48]
    W. Powlis, M. Altschuler, Y. Censor, and E. Buhle. Semi-automatic radiotherapy treatment planning with a mathematical model to satisfy treatment goals. International Journal of Radiation Oncology, Biology, Physics, 16: 271–276, 1989.Google Scholar
  49. [49]
    F. Preciado-Walters, M. Langer, R. Rardin, and V. Thai. Column generation for imrtcancer therapy optimization with implementable segments. Technical report, Purdue University, 2004.Google Scholar
  50. [50]
    F. Preciado-Walters, M. Langer, R. Rardin, and V. Thai. A coupled column generation, mixed-integer approach to optimal planning of intensity modulated radiation therapy for cancer. Technical report, Purdue University, 2004. to appear in Mathematical Programming.Google Scholar
  51. [51]
    A. Pugachev, A. Boyer, and L. Xing. Beam orientation optimization in intensity-modulated radiation treatment planning. Medical Physics, 27(6): 1238–1245, 2000.CrossRefGoogle Scholar
  52. [52]
    A. Pugachev and L. Xing. Computer-assisted selection of coplaner beam orientations in intensity-modulated radiation therapy. Physics in Medicine and Biology, 46: 2467–2476, 2001.CrossRefGoogle Scholar
  53. [53]
    C. Raphael. Mathematical modeling of objectives in radiation therapy treatment planning. Physics in Medicine & Biology, 37(6): 1293–1311, 1992.CrossRefGoogle Scholar
  54. [54]
    H. Romeijn, R. Ahuja, J.F. Dempsey, and A. Kumar. A column generation approach to radiation therapy treatment planning using aperture modulation. Technical Report Research Report 2003-13, Department of Industrial and Systems Engineering, University of Florida, 2003.Google Scholar
  55. [55]
    I. Rosen, R. Lane, S. Morrill, and J. Belli. Treatment plan optimization using linear programming. Medical Physics, 18(2): 141–152, 1991.CrossRefGoogle Scholar
  56. [56]
    D. Shepard, M. Ferris, G. Olivera, and T. Mackie. Optimizing the delivery of radiation therapy to cancer patients. SIAM Review, 41(4): 721–744, 1999.CrossRefzbMATHGoogle Scholar
  57. [57]
    D. Shepard, M. Ferris, R. Ove, and L. Ma. Inverse treatment planning for gamma knife radios urgery. Medical Physics, 27(12): 2748–2756, 2000.CrossRefGoogle Scholar
  58. [58]
    H. Shu, Y. Yan, X. Bao, Y. Fu, and L. Luo. Treatment planning optimization by quasinewton and simulated annealing methods for gamma unit treatment system. Physics in Medicine and Biology, 43(10): 2795–2805, 1998.CrossRefGoogle Scholar
  59. [59]
    H. Shu, Y. Yan, L. Luo, and X. Bao. Three-dimensional optimization of treatment planning for gamma unit treatment system. Medical Physics, 25(12): 2352–2357, 1998.CrossRefGoogle Scholar
  60. [60]
    G. Starkshcall. A constrained least-squares optimization method for external beam radiation therapy treatment planning. Medical Physics, 11(5): 659–665, 1984.CrossRefGoogle Scholar
  61. [61]
    J. Stein et al. Number and orientations of beams in intensity-modulated radiation treatments. Medical Physics, 24(2): 149–160, 1997.CrossRefGoogle Scholar
  62. [62]
    S. Söderström and A. Brahme. Selection of suitable beam orientations in radiation therapy using entropy and fourier transform measures. Physics in Medicine and Biology, 37(4): 911–924, 1992.CrossRefGoogle Scholar
  63. [63]
    H. Withers, J. Taylor, and B. Maciejewski. Treatment volume and tissue tolerance. International Journal of Radiation Oncology, Biology, Physics, 14: 751–759, 1987.Google Scholar
  64. [64]
    A. Wolbarst. Optimization of radiation therapy II: The critical-voxel model. International Journal of Radiation Oncology, Biology, Physics, 10: 741–745, 1984.Google Scholar
  65. [65]
    Q. Wu and J. Bourland. Morphology-guided radiosurgery treatment planning and optimization for multiple isocenters. Medical Physics, 26(10): 2151–2160, 1999.CrossRefGoogle Scholar
  66. [66]
    P. Zhang, D. Dean, A. Metzger, and C. Sibata. Optimization o gamma knife treatment planning via guided evolutionary simulated annealing. Medical Physics, 28(8):1746–17521746.CrossRefGoogle Scholar

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  • Allen Holder
    • 1
  • Bill Salter
    • 2
  1. 1.Department of MathematicsTrinity UniversityUSA
  2. 2.Radiation Oncology Department and Cancer Therapy and Research CenterUniversity of Texas Health Science CenterSan AntonioUSA

Personalised recommendations