Examining the validity of Poissonian models against the birth and death TCP model for various radiotherapy fractionation schemes

Purpose: 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. Materials and 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. Fil: Horas, Jorge Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentina. Universidad Nacional de San Luis. Facultad de Ciencias Físico Matemáticas y Naturales. Departamento de Física; Argentina Fil: Olguín, Osvaldo Roberto. Universidad Nacional de San Luis. Facultad de Ciencias Físico Matemáticas y Naturales. Departamento de Física; Argentina