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Sampling issues for optimization in radiotherapy

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Abstract

A wide variety of optimization problems and techniques are used in radiation treatment planning. The problems typically involve large amounts of data, derived from simulations of patient anatomy and the properties of the delivery device. We investigate a three phase approach for their solution based on sampling of the underlying data that determines optimal beam angles, wedge orientations and delivery intensities in patient examples. Phase I uses multiple coarse samplings of the data and linear programming to adapt the sampling and determine a collection of promising angles to use. Phase II solves the adapted sample problems as mixed integer programs using only the promising angles. Phase III refines the sampling further, and fixes most of the discrete decision variables to reduce computation times. Particular emphasis will be given to general principles that are applicable to large classes of treatment planning problems. Specific examples show enormous increase in speed of planning, without detriment to the solution quality.

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References

  • Bortfeld, Th., A.L. Boyer, W. Schlegel, D.L. Kahler, and T.J. Waldron. (1994). “Realization and Verification of Three-Dimensional Conformal Radiotherapy with Modulated Fields.” International Journal of Radiation Oncology: Biology, Physics, 30(4), 899–908.

    Google Scholar 

  • Bortfeld, Th., J. Burkelbach, R. Boesecke, and W. Schlegel. (1990). “Methods of Image Reconstruction from Projections Applied to Conformation Radiotherapy.” Physics in Medicine and Biology, 25(10), 1423–1434.

    Article  Google Scholar 

  • Bortfeld, Th. and W. Schlegel. (1993). “Optimization of Beam Orientations in Radiation Therapy: Some Theoretical Considerations.” Physics in Medicine and Biology, 38(2), 291–304.

    Article  Google Scholar 

  • Bortfeld, Th.R., D.L. Kahler, T.J. Waldron, and A.L. Boyer. (1994). “X-ray Field Compensation with Multileaf Collimators.” International Journal of Radiation Oncology, Biology and Physics, 28(3), 723–730.

    Google Scholar 

  • Brahme, A. (1993). “Optimization of Radiation Therapy and the Development of Multileaf Collimation.” International Journal of Radiation Oncology, Biology and Physics, 25, 373–375.

    Google Scholar 

  • Brewster, L., R. Mohan, G. Mageras, C. Burman, S. Leibel, and Z. Fuks. (1995). “Three Dimensional Conformal Treatment Planning with Multileaf Collimators.” International Journal of Radiation Oncology, Biology and Physics, 33(5), 1081–1089.

    Article  Google Scholar 

  • Chen, Y., D. Michalski, C. Houser, and J.M. Galvin. (2002). “A Deterministic Iterative Least-Squares Algorithm for Beam Weight Optimization in Conformal Radiotherapy.” Physics in Medicine and Biology, 47, 1647–1658.

    Article  Google Scholar 

  • Du, M.N., C.X. Yu, M. Symons, D. Yan, R. Taylor, R.C. Matter, G. Gustafson, A. Martinez, and J.W. Wong. (1994). “A Multileaf Collimator Field Prescription Preparation System for Conventional Radiotherapy.” International Journal of Radiation Oncology, Biology and Physics, 30(3), 707–714.

    Google Scholar 

  • Holder, A. (2004). “Radiotherapy Treatment design and linear programming. In M.L. Brandeau, F. Sainfort, and W.P. Pierskalla (eds.), Operations Research and Health Care: A Handbook of Methods and Applications. Kluwer Academic Publishers, Boston, pp. 741–774.

  • Intensity Modulated Radiation Therapy Collaborative Working Group (2001). “Intensity-modulated Radiotherapy: Current Status and Issues of Interest.” International Journal of Radiation Oncology: Biology, Physics, 51(4), 880–914.

    Google Scholar 

  • Jordan, T.J. and P.C. Williams. (1994). “The Design and Performance Characteristics of a Multileaf Collimator. Physics in Medicine and Biology, 39, 231–251.

    Article  Google Scholar 

  • Langer, M., R. Brown, M. Urie, J. Leong, M. Stracher, and J. Shapiro. (1990). “Large Scale Optimization of Beam Weights Under Dose-Volume Restrictions.” International Journal of Radiation Oncology, Biology and Physics, 18, 887–893.

    Google Scholar 

  • Leavitt, D.D., M. Martin, J.H. Moeller, and W.L. Lee. (1990). “Dynamic Wedge Field Techniques Through Computer-Controlled Collimator Motion and Dose Delivery.” Medical Physics, 17(1), 87–92.

    Article  Google Scholar 

  • Lim, J. H., M.C. Ferris, S.J. Wright, D.M. Shepard, and M.A. Earl. (2006). “An Optimization Framework for Conformal Radiation Treatment Planning.” INFORMS Journal on Computing, forthcoming.

  • Lodwick, W., S. McCourt, F. Newman, and S. Humphries. (1998). “Optimization Methods for Radiation Therapy Plans.” In C. Borgers and F. Natterer (eds.), Computational Radiology and Imaging: Therapy and Diagnosis, IMA Series in Applied Mathematics. Springer-Verlag, Berlin, Germany, pp. 229–250.

  • Mackie, T.R., T. Holmes, S. Swerdloff, P. Reckwerdt, J.O. Deasy, J. Yang, B. Paliwal, and T. Kinsella. (1993). “Tomotherapy: A New Concept for the Delivery of Dynamic Conformal Radiotherapy.” Medical Physics, 20(6), 1709–1719.

    Article  Google Scholar 

  • Mohan, R. (1995). “Field Shaping for Three-Dimensional Conformal Radiation Therapy and Multileaf Collimation.” Seminars in Radiation Oncology, 5(2), 86–99.

    Article  Google Scholar 

  • Olafsson, A. and S.J. Wright. (2006). “Linear Programming Formulations and Algorithms for Radiotherapy Treatment Planning.” Optimization Methods and Software, 21, 201–232.

    Article  Google Scholar 

  • Olivera, G.H., D.M. Shepard, K.J. Ruchala, J.S. Aldridge, J.M. Kapatoes, E.E. Fitchard, P.J. Reckwerdt, G. Fang, J. Balog, J. Zachman, and T.R. Mackie. (1999). “Tomotherapy.” In Dyk, J. Van (ed.), Modern Technology of Radiation Oncology. Medical Physics Publishing, Madison, Wisconsin, pp. 521–587.

  • Romeijn, H.E., R.K. Ahuja, J.F. Dempsey, and A. Kumar. (2006). “A New Linear Programming Approach to Radiation Therapy Treatment Planning Problems.” Operations Research, 54, 201–216.

    Article  Google Scholar 

  • Rosen, I., R. Lane, S. Morrill, and J. Belli. (1990). “Treatment Plan Optimization Using Linear Programming.” Medical Physics, 18(2), 141–152.

    Article  Google Scholar 

  • Shepard, D.M., M.C. Ferris, G. Olivera, and T.R. Mackie. (1999a). “Optimizing the Delivery of Radiation to Cancer Patients.” SIAM Review, 41, 721–744.

    Article  Google Scholar 

  • Shepard, D.M., G.H. Olivera, L. Angelos, O.A. Sauer, P.J. Reckwerdt, and T.R. Mackie. (1999b). “A Simple Model for Examining Issues in Radiotherapy Optimization.” Medical Physics, 26.

  • Tervo, J. and P. Kolmonen. (2000). “A Model for the Control of a Multileaf Collimator in Radiation Therapy Treatment Planning.” Inverse Problems, 16, 1875–1895.

    Article  Google Scholar 

  • Webb, S. (1998). “Configuration Options for Intensity-Modulated Radiation Therapy Using Multiple Static Fields Shaped by a Multileaf Collimator.” Physics in Medicine and Biology, 43, 241–260.

    Article  Google Scholar 

  • Wu, X. and Y. Zhu. (2001). “A Global Optimization Method for Three-Dimensional Conformal Radiotherapy Treatment Planning.” Physics in Medicine and Biology, 46, 109–119.

    Google Scholar 

  • Xiao, Y., Y. Censor, D. Michalski, and J.M. Galvin. (2003). “The Least-Intensity Feasible Solution for Aperture-Based Inverse Planning in Radiation Therapy.” Annals of Operations Research, 119, 183–203.

    Article  Google Scholar 

  • Yu, C.X. (1995). “Intensity-Modulated Arc Therapy with Dynamic Multileaf Collimation: An Alternative to Tomotherapy.” Physics in Medicine and Biology, 40(9), 1435–1449.

    Article  Google Scholar 

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Authors and Affiliations

  1. Computer Sciences Department, University of Wisconsin, 1210 West Dayton Street, Madison, WI, 53706, USA

    Michael C. Ferris

  2. Industrial Engineering Department, University of Wisconsin, 1513 University Ave, Madison, WI, 53706, USA

    Rikhardur Einarsson

  3. Department of Radiation Oncology, University of Maryland School of Medicine, 22 South Greene St, Baltimore, MD, 21201, USA

    Ziping Jiang

  4. Director of Medical Physics, Swedish Cancer Institute, 1221 Madison St., 1st Floor, Seattle, WA, 98104, USA

    David Shepard

Authors
  1. Michael C. Ferris
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  2. Rikhardur Einarsson
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  3. Ziping Jiang
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  4. David Shepard
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Corresponding author

Correspondence to Michael C. Ferris.

Additional information

This material is based on research supported by the National Science Foundation Grant ACI-0113051 and the Air Force Office of Scientific Research Grant FA9550-04-1-0192.

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Ferris, M.C., Einarsson, R., Jiang, Z. et al. Sampling issues for optimization in radiotherapy. Ann Oper Res 148, 95–115 (2006). https://doi.org/10.1007/s10479-006-0083-y

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