Population TCP estimators in case of heterogeneous irradiation: A new discussion of an old problem

Author: Stavrev Pavel   Schinkel Colleen   Stavreva Nadia   Warkentin Brad   Carlone Marco   Fallone B. Gino  

Publisher: Informa Healthcare

ISSN: 0284-186X

Source: Acta Oncologica, Vol.49, Iss.8, 2010-11, pp. : 1293-1303

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Abstract

AbstractPurpose. To investigate the capacity of two phenomenological expressions to describe the population tumor response in case of a heterogeneous irradiation of the tumor. The generalization of the individual tumor control probability (TCP) models to include the case of a heterogeneous irradiation is a trivial problem. However, an analytical solution that results in a closed form population TCP formula for the heterogeneous case is, unfortunately, a very complex mathematical problem. Therefore we applied a numerical approach to the problem. Method. Pseudo-experimental data sets are constructed through the generation of dose distributions and population TCP data obtained by a numerical solution of a multi-dimensional integral over an individual TCP model. The capacity of the following two phenomenological – Poisson and equivalent uniform dose (EUD) based – TCP expressions: to describe the population tumor response in case of heterogeneous irradiation is investigated through their fitting to the psuedo-experimental data sets. Results and conclusions. While both expressions produce statistically acceptable fits to the pseudo-experimental data within 2% TCP error band, the use of the second expression is preferable since it produces considerably better fits to the data sets.