Uncertainty incorporated beam angle optimization for IMPT treatment planning

Wenhua Cao, Gino J. Lim, Andrew Lee, Yupeng Li, Wei Liu, X. Ronald Zhu, Xiaodong Zhang

Research output: Contribution to journalArticlepeer-review

35 Scopus citations


Purpose: Beam angle optimization (BAO) by far remains an important and challenging problem in external beam radiation therapy treatment planning. Conventional BAO algorithms discussed in previous studies all focused on photon-based therapies. Impact of BAO on proton therapy is important while proton therapy increasingly receives great interests. This study focuses on potential benefits of BAO on intensity-modulated proton therapy (IMPT) that recently began available to clinical cancer treatment. Methods: The authors have developed a novel uncertainty incorporated BAO algorithm for IMPT treatment planning in that IMPT plan quality is highly sensitive to uncertainties such as proton range and setup errors. A linear programming was used to optimize robust intensity maps to scenario-based uncertainties for an incident beam angle configuration. Unlike conventional intensity-modulated radiation therapy with photons (IMXT), the search space for IMPT treatment beam angles may be relatively small but optimizing an IMPT plan may require higher computational costs due to larger data size. Therefore, a deterministic local neighborhood search algorithm that only needs a very limited number of plan objective evaluations was used to optimize beam angles in IMPT treatment planning. Results: Three prostate cancer cases and two skull base chordoma cases were studied to demonstrate the dosimetric advantages and robustness of optimized beam angles from the proposed BAO algorithm. Two- to four-beam plans were optimized for prostate cases, and two- and three-beam plans were optimized for skull base cases. By comparing plans with conventional two parallel-opposed angles, all plans with optimized angles consistently improved sparing at organs at risks, i.e., rectum and femoral heads for prostate, brainstem for skull base, in either nominal dose distribution or uncertainty-based dose distributions. The efficiency of the BAO algorithm was demonstrated by comparing it with alternative methods including simulated annealing and genetic algorithm. The numbers of IMPT plan objective evaluations required were reduced by up to a factor of 5 while the same optimal angle plans were converged in selected comparisons. Conclusions: Uncertainty incorporated BAO may introduce pronounced improvement of IMPT plan quality including dosimetric benefits and robustness over uncertainties, based on the five clinical studies in this paper. In addition, local search algorithms may be more efficient in finding optimal beam angles than global optimization approaches for IMPT BAO.

Original languageEnglish (US)
Pages (from-to)5248-5256
Number of pages9
JournalMedical physics
Issue number8
StatePublished - Aug 2012


  • IMPT
  • beam angle optimization
  • uncertainty

ASJC Scopus subject areas

  • Biophysics
  • Radiology Nuclear Medicine and imaging


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