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

Purpose. 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 pseudo-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