A new column-generation-based algorithm for VMAT treatment plan optimization

Fei Peng, Xun Jia, Xuejun Gu, Marina A. Epelman, H. Edwin Romeijn, Steve B. Jiang

Research output: Contribution to journalArticlepeer-review

44 Scopus citations


We study the treatment plan optimization problem for volumetric modulated arc therapy (VMAT). We propose a new column-generation-based algorithm that takes into account bounds on the gantry speed and dose rate, as well as an upper bound on the rate of change of the gantry speed, in addition to MLC constraints. The algorithm iteratively adds one aperture at each control point along the treatment arc. In each iteration, a restricted problem optimizing intensities at previously selected apertures is solved, and its solution is used to formulate a pricing problem, which selects an aperture at another control point that is compatible with previously selected apertures and leads to the largest rate of improvement in the objective function value of the restricted problem. Once a complete set of apertures is obtained, their intensities are optimized and the gantry speeds and dose rates are adjusted to minimize treatment time while satisfying all machine restrictions. Comparisons of treatment plans obtained by our algorithm to idealized IMRT plans of 177 beams on five clinical prostate cancer cases demonstrate high quality with respect to clinical dose-volume criteria. For all cases, our algorithm yields treatment plans that can be delivered in around 2min. Implementation on a graphic processing unit enables us to finish the optimization of a VMAT plan in 25-55s.

Original languageEnglish (US)
Pages (from-to)4569-4588
Number of pages20
JournalPhysics in medicine and biology
Issue number14
StatePublished - Jul 21 2012

ASJC Scopus subject areas

  • Radiological and Ultrasound Technology
  • Radiology Nuclear Medicine and imaging


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