title: On the visualization of universal degeneracy in the IMRT problem.
abstract: BACKGROUND
  In general, the IMRT optimisation problem possesses many equivalent solutions. This makes it difficult to decide whether a result produced by an IMRT planning algorithm can be further improved, e.g. by adding more beams, or whether it is close to the globally best solution.
  
  
  RESULTS
  It is conjectured that the curvature properties of the objective function around any globally optimum dose distribution are universal. This allows an assessment of optimality of dose distributions that are generated by different beam arrangements in a complementary manner to the objective function value alone. A tool to visualize the curvature structure of the objective function is devised.
  
  
  CONCLUSIONS
  In an example case, it is demonstrated how the assessment of the curvature space can indicate the equivalence of rival beam configurations and their proximity to the global optimum.
authors.affiliation: Section for Biomedical Physics, Clinic for Radiooncology, University of Tübingen, Germany. markus.alber@med.uni-tuebingen.de
authors.forename: Markus L
authors.initials: ML
authors.lastname: Alber
authors.forename: Gustav
authors.initials: G
authors.lastname: Meedt
mesh_terms: D000465:Algorithms; D003196:Computer Graphics; D004307:Dose-Response Relationship, Radiation; D006801:Humans; D015233:Models, Statistical; D010255:Paranasal Sinus Neoplasms / Q000532:radiotherapy; D018787:Radiation Oncology / Q000379:methods; D011879:Radiotherapy Dosage; D011880:Radiotherapy Planning, Computer-Assisted / Q000379:methods*; D050397:Radiotherapy, Intensity-Modulated / Q000379:methods*; D012984:Software; D016896:Treatment Outcome