title: Examining the validity of Poissonian models against the birth and death TCP model for various radiotherapy fractionation schemes.
abstract: OBJECTIVE
  To compare the results obtained for tumour control probability (TCP) in protracted treatments, we used two models which apply Poisson statistics for clonogenic cell distribution and a non-Poissonian model, emphasising the conditions for the validity of Poissonian models. Previously published results on two cell lines growing as megacolonies in vitro irradiated with conventional and accelerated dose fractionation schemes were used.
  
  
  METHODS
  The expressions of TCP for three models are described and conclusions are drawn on the applicability of each model, and their usefulness for different fractionations.
  
  
  RESULTS
  The fits to experimental data are shown and the parameter values for both Poissonian and non-Poissonian models are given. We also determined if differences exist in repopulation rate and other related parameters, for different protocols of treatment.
  
  
  CONCLUSIONS
  Both the Poissonian models, when they satisfied the required conditions, and the non-Poissonian model, gave acceptable fits. We observed no significant differences in repopulation for different irradiation protocols.
authors.affiliation: Universidad Nacional de San Luis, Departamento de Física, Instituto de Matemática Aplicada San Luis (IMASL), Consejo Nacional de Investigaciones Científicas y Técnicas, San Luis, Argentina. jhoras@unsl.edu.ar
authors.forename: Jorge A
authors.initials: JA
authors.lastname: Horas
authors.forename: Osvaldo R
authors.initials: OR
authors.lastname: Olguín
authors.forename: Marcos G
authors.initials: MG
authors.lastname: Rizzotto
mesh_terms: D019583:Dose Fractionation, Radiation; D006801:Humans; D015233:Models, Statistical; D009369:Neoplasms / Q000401:mortality / Q000532:radiotherapy*; D016012:Poisson Distribution; D011336:Probability