title: Projections onto the Pareto surface in multicriteria radiation therapy optimization.
abstract: OBJECTIVE
  To eliminate or reduce the error to Pareto optimality that arises in Pareto surface navigation when the Pareto surface is approximated by a small number of plans.
  
  
  METHODS
  The authors propose to project the navigated plan onto the Pareto surface as a postprocessing step to the navigation. The projection attempts to find a Pareto optimal plan that is at least as good as or better than the initial navigated plan with respect to all objective functions. An augmented form of projection is also suggested where dose-volume histogram constraints are used to prevent that the projection causes a violation of some clinical goal. The projections were evaluated with respect to planning for intensity modulated radiation therapy delivered by step-and-shoot and sliding window and spot-scanned intensity modulated proton therapy. Retrospective plans were generated for a prostate and a head and neck case.
  
  
  RESULTS
  The projections led to improved dose conformity and better sparing of organs at risk (OARs) for all three delivery techniques and both patient cases. The mean dose to OARs decreased by 3.1 Gy on average for the unconstrained form of the projection and by 2.0 Gy on average when dose-volume histogram constraints were used. No consistent improvements in target homogeneity were observed.
  
  
  CONCLUSIONS
  There are situations when Pareto navigation leaves room for improvement in OAR sparing and dose conformity, for example, if the approximation of the Pareto surface is coarse or the problem formulation has too permissive constraints. A projection onto the Pareto surface can identify an inaccurate Pareto surface representation and, if necessary, improve the quality of the navigated plan.
authors.affiliation: Optimization and Systems Theory, Department of Mathematics, KTH Royal Institute of Technology, Stockholm SE-100 44, Sweden and RaySearch Laboratories, Sveavägen 44, Stockholm SE-103 65, Sweden.
authors.forename: Rasmus
authors.initials: R
authors.lastname: Bokrantz
authors.affiliation: Optimization and Systems Theory, Department of Mathematics, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden and University of Jyvaskyla, Department of Mathematical Information Technology, FI-400 14 University of Jyvaskyla, Finland.
authors.forename: Kaisa
authors.initials: K
authors.lastname: Miettinen
mesh_terms: D006258:Head and Neck Neoplasms / Q000532:radiotherapy; D006801:Humans; D008297:Male; D011471:Prostatic Neoplasms / Q000532:radiotherapy; D061766:Proton Therapy; D011879:Radiotherapy Dosage; D011880:Radiotherapy Planning, Computer-Assisted / Q000379:methods*; D050397:Radiotherapy, Intensity-Modulated