title: Ultrafast treatment plan optimization for volumetric modulated arc therapy (VMAT).
abstract: OBJECTIVE
  To develop a novel aperture-based algorithm for volumetric modulated are therapy (VMAT) treatment plan optimization with high quality and high efficiency.
  
  
  METHODS
  The VMAT optimization problem is formulated as a large-scale convex programming problem solved by a column generation approach. The authors consider a cost function consisting two terms, the first enforcing a desired dose distribution and the second guaranteeing a smooth dose rate variation between successive gantry angles. A gantry rotation is discretized into 180 beam angles and for each beam angle, only one MLC aperture is allowed. The apertures are generated one by one in a sequential way. At each iteration of the column generation method, a deliverable MLC aperture is generated for one of the unoccupied beam angles by solving a subproblem with the consideration of MLC mechanic constraints. A subsequent master problem is then solved to determine the dose rate at all currently generated apertures by minimizing the cost function. When all 180 beam angles are occupied, the optimization completes, yielding a set of deliverable apertures and associated dose rates that produce a high quality plan.
  
  
  RESULTS
  The algorithm was preliminarily tested on five prostate and five head-and-neck clinical cases, each with one full gantry rotation without any couch/collimator rotations. High quality VMAT plans have been generated for all ten cases with extremely high efficiency. It takes only 5-8 min on CPU (MATLAB code on an Intel Xeon 2.27 GHz CPU) and 18-31 s on GPU (CUDA code on an NVIDIA Tesla C1060 GPU card) to generate such plans.
  
  
  CONCLUSIONS
  The authors have developed an aperture-based VMAT optimization algorithm which can generate clinically deliverable high quality treatment plans at very high efficiency.
authors.forename: Chunhua
authors.initials: C
authors.lastname: Men
authors.forename: H Edwin
authors.initials: HE
authors.lastname: Romeijn
authors.forename: Xun
authors.initials: X
authors.lastname: Jia
authors.forename: Steve B
authors.initials: SB
authors.lastname: Jiang
mesh_terms: D000465:Algorithms; D003196:Computer Graphics; D003198:Computer Simulation; D003201:Computers; D004307:Dose-Response Relationship, Radiation; D006258:Head and Neck Neoplasms / Q000532:radiotherapy*; D006801:Humans; D008297:Male; D015233:Models, Statistical; D011471:Prostatic Neoplasms / Q000532:radiotherapy*; D011879:Radiotherapy Dosage; D011880:Radiotherapy Planning, Computer-Assisted / Q000379:methods*; D015203:Reproducibility of Results; D013997:Time Factors