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The Least-Intensity Feasible Solution for Aperture-Based Inverse Planning in Radiation Therapy

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  • Y. Xiao
  • D. Michalski
  • J.M. Galvin
  • Y. Censor

Abstract

Aperture-based inverse planning (ABIP) for intensity modulated radiation therapy (IMRT) treatment planning starts with external radiation fields (beams) that fully conform to the target(s) and then superimposes sub-fields called segments to achieve complex shaping of 3D dose distributions. The segments' intensities are determined by solving a feasibility problem. The least-intensity feasible (LIF) solution, proposed and studied here, seeks a feasible solution closest to the origin, thus being of least intensity or least energy. We present a new iterative, primal–dual, algorithm for finding the LIF solution and explain our experimental observation that Cimmino's algorithm for feasibility actually converges to a close approximation of the LIF solution. Comparison with linear programming shows that Cimmino's algorithm has the additional advantage of generating much smoother solutions. Copyright Kluwer Academic Publishers 2003

Suggested Citation

  • Y. Xiao & D. Michalski & J.M. Galvin & Y. Censor, 2003. "The Least-Intensity Feasible Solution for Aperture-Based Inverse Planning in Radiation Therapy," Annals of Operations Research, Springer, vol. 119(1), pages 183-203, March.
    • Handle: RePEc:spr:annopr:v:119:y:2003:i:1:p:183-203:10.1023/a:1022990724772
    DOI: 10.1023/A:1022990724772
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    Cited by:

    1. Gino J. Lim & Michael C. Ferris & Stephen J. Wright & David M. Shepard & Matthew A. Earl, 2007. "An Optimization Framework for Conformal Radiation Treatment Planning," INFORMS Journal on Computing, INFORMS, vol. 19(3), pages 366-380, August.
    2. Michael Ferris & Rikhardur Einarsson & Ziping Jiang & David Shepard, 2006. "Sampling issues for optimization in radiotherapy," Annals of Operations Research, Springer, vol. 148(1), pages 95-115, November.
    3. Matthias Ehrgott & Çiğdem Güler & Horst Hamacher & Lizhen Shao, 2010. "Mathematical optimization in intensity modulated radiation therapy," Annals of Operations Research, Springer, vol. 175(1), pages 309-365, March.
    4. Felisa Preciado-Walters & Mark Langer & Ronald Rardin & Van Thai, 2006. "Column generation for IMRT cancer therapy optimization with implementable segments," Annals of Operations Research, Springer, vol. 148(1), pages 65-79, November.
    5. Noha Hamza & Ruhul Sarker & Daryl Essam, 2013. "Differential evolution with multi-constraint consensus methods for constrained optimization," Journal of Global Optimization, Springer, vol. 57(2), pages 583-611, October.
    6. John W. Chinneck, 2004. "The Constraint Consensus Method for Finding Approximately Feasible Points in Nonlinear Programs," INFORMS Journal on Computing, INFORMS, vol. 16(3), pages 255-265, August.

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