title: Evaluation of interpolation methods for TG-43 dosimetric parameters based on comparison with Monte Carlo data for high-energy brachytherapy sources.
abstract: OBJECTIVE
  The aim of this work was to determine dose distributions for high-energy brachytherapy sources at spatial locations not included in the radial dose functiongL(r) and 2D anisotropy functionF(r,θ) table entries for radial distancerand polar angleθ. The objectives of this study are as follows: 1) to evaluate interpolation methods in order to accurately derivegL(r) andF(r,θ) from the reported data; 2) to determine the minimum number of entries ingL(r) andF(r,θ) that allow reproduction of dose distributions with sufficient accuracy.
  
  
  METHODS
  Four high-energy photon-emitting brachytherapy sources were studied:60Co model Co0.A86,137Cs model CSM-3,192Ir model Ir2.A85-2, and169Yb hypothetical model. The mesh used forrwas: 0.25, 0.5, 0.75, 1, 1.5, 2-8 (integer steps) and 10 cm. Four different angular steps were evaluated forF(r,θ): 1°, 2°, 5° and 10°. Linear-linear and logarithmic-linear interpolation was evaluated forgL(r). Linear-linear interpolation was used to obtainF(r,θ) with resolution of 0.05 cm and 1°. Results were compared with values obtained from the Monte Carlo (MC) calculations for the four sources with the same grid.
  
  
  RESULTS
  Linear interpolation ofgL(r) provided differences ≤ 0.5% compared to MC for all four sources. Bilinear interpolation ofF(r,θ) using 1° and 2° angular steps resulted in agreement ≤ 0.5% with MC for60Co,192Ir, and169Yb, while137Cs agreement was ≤ 1.5% forθ< 15°.
  
  
  CONCLUSIONS
  The radial mesh studied was adequate for interpolatinggL(r) for high-energy brachytherapy sources, and was similar to commonly found examples in the published literature. ForF(r,θ) close to the source longitudinal-axis, polar angle step sizes of 1°-2° were sufficient to provide 2% accuracy for all sources.
authors.affiliation: Physics Section, Department of Radiation Oncology, La Fe University Hospital, Valencia, Spain.
authors.forename: Ma Carmen
authors.initials: MC
authors.lastname: Pujades-Claumarchirant
authors.affiliation: Department of Radiation Oncology, ERESA, Hospital General Universitario, Valencia, Spain.
authors.forename: Domingo
authors.initials: D
authors.lastname: Granero
authors.affiliation: Physics Section, Department of Radiation Oncology, La Fe University Hospital, Valencia, Spain.
authors.forename: Jose
authors.initials: J
authors.lastname: Perez-Calatayud
authors.affiliation: Department of Atomic, Molecular and Nuclear Physics, University of Valencia, Burjassot, Valencia, Spain.
authors.forename: Facundo
authors.initials: F
authors.lastname: Ballester
authors.affiliation: Department of Radiation Oncology, Tufts University School of Medicine, Boston, Massachusetts, USA.
authors.forename: Christopher
authors.initials: C
authors.lastname: Melhus
authors.affiliation: Department of Radiation Oncology, Tufts University School of Medicine, Boston, Massachusetts, USA.
authors.forename: Mark
authors.initials: M
authors.lastname: Rivard
keywords: 2D anisotropy function; TG-43; brachytherapy; dosimetry; interpolation; radial dose function