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A hybrid framework for optimizing beam angles in radiation therapy planning

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Abstract

The purpose of this paper is twofold: (1) to examine strengths and weaknesses of recently developed optimization methods for selecting radiation treatment beam angles and (2) to propose a simple and easy-to-use hybrid framework that overcomes some of the weaknesses observed with these methods. Six optimization methods—branch and bound (BB), simulated annealing (SA), genetic algorithms (GA), nested partitions (NP), branch and prune (BP), and local neighborhood search (LNS)—were evaluated. Our preliminary test results revealed that (1) one of the major drawbacks of the reported algorithms was the limited ability to find a good solution within a reasonable amount of time in a clinical setting, (2) all heuristic methods require selecting appropriate parameter values, which is a difficult chore, and (3) the LNS algorithm has the ability to identify good solutions only if provided with a good starting point. On the basis of these findings, we propose a unified beam angle selection framework that, through two sequential phases, consistently finds clinically relevant locally optimal solutions. Considering that different users may use different optimization approaches among those mentioned above, the first phase aims to quickly find a good feasible solution using SA, GA, NP, or BP. This solution is then used as a starting point for LNS to find a locally optimal solution. Experimental results using this unified method on five clinical cases show that it not only produces consistently good-quality treatment solutions but also alleviates the effort of selecting an initial set of appropriate parameter values that is required by all of the existing optimization methods.

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Authors and Affiliations

  1. Department of Industrial Engineering, University of Houston, Houston, TX, USA

    Gino J. Lim, Laleh Kardar & Wenhua Cao

Authors
  1. Gino J. Lim
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  2. Laleh Kardar
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  3. Wenhua Cao
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Corresponding author

Correspondence to Gino J. Lim.

Appendix

Appendix

See Appendix Figs. 5, 6

Fig. 5
figure 5

LNS objective value comparison for the IMRT prostate case with 12 candidate angles. The upper black boxes are the objective values of the starting points obtained from SA, GA, NP, and BP, and the lower gray boxes are the objective values obtained from LNS. Numbers in parentheses are the percentages of objective function deterioration with respect to optimal value

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Fig. 6
figure 6

LNS Objective value comparison for the IMRT pancreas case with 12 candidate angles. The upper black boxes are the objective values of the starting points obtained from SA, GA, NP, and BP and the lower lines are the objective values obtained from LNS. Numbers in parentheses show the percentage of objective function deterioration with respect to optimal value

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Lim, G.J., Kardar, L. & Cao, W. A hybrid framework for optimizing beam angles in radiation therapy planning. Ann Oper Res 217, 357–383 (2014). https://doi.org/10.1007/s10479-014-1564-z

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