title: Bi- and tri-exponential fitting to TG-43 radial dose functions of brachytherapy sources based on a genetic algorithm.
abstract: OBJECTIVE
  To find the coefficients for bi- and tri-exponential fitting functions to represent the radial dose functions of 16 commercially available brachytherapy sources.
  
  
  METHODS
  The search for the coefficients was done using a genetic algorithm. Coefficients were encoded into chromosomes, which were subjected to crossover and mutation. After each operation, chromosomes were evaluated according to their fitness and the better ones were chosen with higher probability for the next generation. The best chromosomes obtained after 2000 operations were used for the coefficients.
  
  
  RESULTS
  For all brachytherapy sources, tri-exponential dose functions agreed with the respective input data within 1.4%. The mean deviation, obtained by averaging absolute deviations of all sources and input data, was <1.0%. For 8 of the 16 sources, the fit offered by bi-exponential functions was virtually identical to that of tri-exponential ones.
  
  
  CONCLUSIONS
  Tri-exponential functions can accurately represent the radial dose functions of all commercially available brachytherapy sources. For the eight sources where bi-exponential functions provide nearly equally accurate fits, their continued usage is recommended.
authors.affiliation: Department of Radiation Oncology, University of Alabama at Birmingham, 35249, USA. xnwu@uabmc.edu
authors.forename: Xingen
authors.initials: X
authors.lastname: Wu
authors.forename: Ivan A
authors.initials: IA
authors.lastname: Brezovich
authors.forename: John B
authors.initials: JB
authors.lastname: Fiveash
mesh_terms: D000465:Algorithms; D001918:Brachytherapy / Q000295:instrumentation*; D004307:Dose-Response Relationship, Radiation; D006801:Humans; D008954:Models, Biological; D011879:Radiotherapy Dosage; D011880:Radiotherapy Planning, Computer-Assisted