title: Technical note: Extension of Van Herk's treatment margin model for anisotropic systematic positioning errors in cartesian coordinate systema.
abstract: OBJECTIVE
  A coefficient of a treatment margin model for anisotropic systematic positioning errors has been calculated in Cartesian coordinate system based on van Herk's analytical formulation.
  
  
  METHODS
  Three-dimensional (3D) patient population distribution was formulated in Cartesian coordinate system to model anisotropic systematic positioning errors. Analytical 3D integration with anisotropic standard deviations Sigma's and the following Newton's method yielded the coefficient of van Herk's systematic positioning error model in Cartesian coordinate system.
  
  
  RESULTS
  The treatment margins for the anisotropic systematic errors in Cartesian coordinate system were 2.1 Sigma for 90% patient population coverage and 2.4 Sigma for 95% patient population coverage.
  
  
  CONCLUSIONS
  It was found that the treatment margins for anisotropic systematic positioning errors in Cartesian coordinate system were smaller than those for the isotropic model in spherical coordinate system for a given patient population coverage probability.
authors.affiliation: Kiyoshi.Yoda@elekta.com
authors.forename: Kiyoshi
authors.initials: K
authors.lastname: Yoda
authors.forename: Keiichi
authors.initials: K
authors.lastname: Nakagawa
mesh_terms: D000818:Animals; D016880:Anisotropy; D003198:Computer Simulation; D006801:Humans; D008954:Models, Biological; D011874:Radiometry / Q000379:methods*; D011880:Radiotherapy Planning, Computer-Assisted / Q000379:methods*; D020266:Radiotherapy, Conformal / Q000379:methods*; D015203:Reproducibility of Results; D012542:Scattering, Radiation; D012680:Sensitivity and Specificity