title: Application of constrained least-squares techniques to IMRT treatment planning.
abstract: OBJECTIVE
  The purpose of this work was to apply the method of constrained least-squares to inverse treatment planning and to explore its potential for providing a fast interactive planning environment for intensity-modulated radiation therapy (IMRT).
  
  
  METHODS
  The description of the dose inside a patient is a linear matrix transformation of beamlet weights. The constrained least-squares method adds additional matrix operators and produces beamlet weights by a direct linear transformation. These matrix operators contain a priori knowledge about the radiation distribution. The constrained least-squares technique was applied to obtain IMRT plans for prostate and paraspinal cancer patients and compared with the corresponding plans optimized using the CORVUS inverse planning system.
  
  
  RESULTS
  It was demonstrated that a constrained least-squares technique is suitable for IMRT plan optimization with significantly increased computing speed. For the two cases we have tested, the constrained least-squares method was an order of magnitude faster than conventional iterative techniques because of the avoidance of the iterative calculations. We also found that the constrained least-squares method is capable of generating clinically acceptable treatment plans with less trial-and-error adjustments of system variables, and with improved target volume coverage as well as sensitive structure sparing in comparison with that obtained using CORVUS.
  
  
  CONCLUSIONS
  The constrained least-squares method has the advantage that it does not require iterative calculation and thus significantly speeds up the therapeutic plan optimization process. Besides shedding important insight into the inverse planning problem, the technique has strong potential to provide a fast and interactive environment for IMRT treatment planning.
authors.affiliation: Department of Radiation Oncology, Stanford University School of Medicine, 300 Pasteur Drive, Stanford, CA 94305-5304, USA.
authors.forename: S M
authors.initials: SM
authors.lastname: Crooks
authors.forename: L
authors.initials: L
authors.lastname: Xing
mesh_terms: D000465:Algorithms; D006801:Humans; D016018:Least-Squares Analysis; D008297:Male; D011471:Prostatic Neoplasms / Q000532:radiotherapy; D011880:Radiotherapy Planning, Computer-Assisted / Q000379:methods*