title: Reporting and analyzing statistical uncertainties in Monte Carlo-based treatment planning.
abstract: OBJECTIVE
  To investigate methods of reporting and analyzing statistical uncertainties in doses to targets and normal tissues in Monte Carlo (MC)-based treatment planning.
  
  
  METHODS
  Methods for quantifying statistical uncertainties in dose, such as uncertainty specification to specific dose points, or to volume-based regions, were analyzed in MC-based treatment planning for 5 lung cancer patients. The effect of statistical uncertainties on target and normal tissue dose indices was evaluated. The concept of uncertainty volume histograms for targets and organs at risk was examined, along with its utility, in conjunction with dose volume histograms, in assessing the acceptability of the statistical precision in dose distributions. The uncertainty evaluation tools were extended to four-dimensional planning for application on multiple instances of the patient geometry. All calculations were performed using the Dose Planning Method MC code.
  
  
  RESULTS
  For targets, generalized equivalent uniform doses and mean target doses converged at 150 million simulated histories, corresponding to relative uncertainties of less than 2% in the mean target doses. For the normal lung tissue (a volume-effect organ), mean lung dose and normal tissue complication probability converged at 150 million histories despite the large range in the relative organ uncertainty volume histograms. For "serial" normal tissues such as the spinal cord, large fluctuations exist in point dose relative uncertainties.
  
  
  CONCLUSIONS
  The tools presented here provide useful means for evaluating statistical precision in MC-based dose distributions. Tradeoffs between uncertainties in doses to targets, volume-effect organs, and "serial" normal tissues must be considered carefully in determining acceptable levels of statistical precision in MC-computed dose distributions.
authors.affiliation: Department of Radiation Oncology, The University of Michigan, Ann Arbor, MI 48109-0010, USA. indrin@med.umich.edu
authors.forename: Indrin J
authors.initials: IJ
authors.lastname: Chetty
authors.forename: Mihaela
authors.initials: M
authors.lastname: Rosu
authors.forename: Marc L
authors.initials: ML
authors.lastname: Kessler
authors.forename: Benedick A
authors.initials: BA
authors.lastname: Fraass
authors.forename: Randall K
authors.initials: RK
authors.lastname: Ten Haken
authors.forename: Feng-Ming Spring
authors.initials: FM
authors.lastname: Kong
authors.forename: Daniel L
authors.initials: DL
authors.lastname: McShan
mesh_terms: D004947:Esophagus / Q000000981:diagnostic imaging; D008168:Lung / Q000528:radiation effects; D008175:Lung Neoplasms / Q000000981:diagnostic imaging / Q000532:radiotherapy*; D009010:Monte Carlo Method; D011879:Radiotherapy Dosage; D011880:Radiotherapy Planning, Computer-Assisted / Q000379:methods*; D012189:Retrospective Studies; D013116:Spinal Cord / Q000000981:diagnostic imaging; D014057:Tomography, X-Ray Computed; D035501:Uncertainty