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: [Figure: see text] 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.

Radiobiological model comparison of 3D conformal radiotherapy and IMRT plans for the treatment of prostate cancer

The main aim of radiotherapy is to deliver a dose of radiation that is high enough to destroy the tumour cells while at the same time minimising the damage to normal healthy tissues. Clinically, this has been achieved by assigning a prescription dose to the tumour volume and a set of dose constraints on critical structures. Once an optimal treatment plan has been achieved the dosimetry is assessed using the physical parameters of dose and volume. There has been an interest in using radiobiological parameters to evaluate and predict the outcome of a treatment plan in terms of both a tumour control probability (TCP) and a normal tissue complication probability (NTCP). In this study, simple radiobiological models that are available in a commercial treatment planning system were used to compare three dimensional conformal radiotherapy treatments (3D-CRT) and intensity modulated radiotherapy (IMRT) treatments of the prostate. Initially both 3D-CRT and IMRT were planned for 2 Gy/fraction to a total dose of 60 Gy to the prostate. The sensitivity of the TCP and the NTCP to both conventional dose escalation and hypo-fractionation was investigated. The biological responses were calculated using the Källman S-model. The complication free tumour control probability (P+) is generated from the combined NTCP and TCP response values. It has been suggested that the alpha/beta ratio for prostate carcinoma cells may be lower than for most other tumour cell types. The effect of this on the modelled biological response for the different fractionation schedules was also investigated.