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

Abstract

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.

Keywords:

• tumour control probability (TCP)
• clonogenic cells distribution
• Poissonian and non-Poissonian TCP models
• protracted treatments

Acknowledgements

The authors are indebted to the referees for their help in improving the manuscript. This research was supported by Universidad Nacional de San Luis (UNSL) and Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET).

Declaration of interest: The authors report no conflicts of interest. The authors alone are responsible for the content and writing of the paper.