title: Evaluating target cold spots by the use of tail EUDs.
abstract: OBJECTIVE
  To propose a new measure of target underdose that can be used in the evaluation and optimization of radiotherapy dose distributions.
  
  
  METHODS
  We compare various formulations of the equivalent uniform dose (EUD) and introduce a modification of existing EUD definitions, which we call tail EUD. Tail EUD is a measure of "cold spots" below the prescription dose in the target dose distribution, using units of gray (Gy). We investigate the mathematical properties of various target EUD concepts, including tail EUD. We apply the tail EUD measure retrospectively to intensity modulated radiation therapy (IMRT) treatment plans from our plan database. We also use tail EUD as an optimization objective in the optimization of prostate, pancreas, and head-and-neck plans.
  
  
  RESULTS
  Tail EUD has desirable mathematical properties. In particular, it is convex and it leads to convex level sets (i.e., no local minima) if the EUD from which it is derived is concave. The tail EUD value is correlated with the subjective degree of target coverage. Constraining tail EUDs to a certain level in plan optimization leads to comparable target coverage in different plans and treatment sites.
  
  
  CONCLUSIONS
  The newly introduced concept of tail EUD appears to be useful for both plan evaluation and optimization. In addition it can potentially be applied in the design of new clinical protocols.
authors.affiliation: Department of Radiation Oncology, Massachusetts General Hospital and Harvard Medical School, Boston, MA 02114, USA. tbortfeld@partners.org
authors.forename: Thomas
authors.initials: T
authors.lastname: Bortfeld
authors.forename: David
authors.initials: D
authors.lastname: Craft
authors.forename: James F
authors.initials: JF
authors.lastname: Dempsey
authors.forename: Tarek
authors.initials: T
authors.lastname: Halabi
authors.forename: H Edwin
authors.initials: HE
authors.lastname: Romeijn
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D006801:Humans; D008954:Models, Biological; D011874:Radiometry / Q000379:methods*; D011879:Radiotherapy Dosage; D011880:Radiotherapy Planning, Computer-Assisted / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity