Theoretical investigation of the impact of different timing schemes in hypofractionated radiotherapy.

PURPOSE This study compares the effectiveness of three fractionation schemes of equal fraction size, comprising five fractions of SBRT over five days, ten days, or fifteen days respectively. METHOD This comparative study is based on two tumour-control-probability (TCP) models that take into account tumour cell re-sensitization and repopulation during treatment; the Zaider-Minerbo-Stavreva (ZMS) and the Ruggieri-Nahum (RN) models. The ZMS model is further modified to include also re-sensitization according to the β mechanism of the linear-quadratic (LQ) model of cell killing. The modified version of the ZMS model is verified through fitting to the experimental data set of Fisher and Moulder. The study applies an idea used in a plan ranking methodology developed for the case when the specific values of the model parameters are not known. RESULTS The TCPs of the compared regimens are calculated for various values of the model parameters and for two different values of the dose per fraction. The TCPs are presented as 2-D functions of two of the model parameters for each model correspondingly. The differences between the TCPs of each of the prolonged regimens and the TCP of the every week day regimen are also calculated for each model. CONCLUSIONS Both models predict that the prolonged regimens are superior in terms of TCP to the every week-day ones for most of the studied cases; however this is shown to exist to a different degree by the two models. It is shown again to a different degree that reversed situations where the every week day schedule is better than the prolonged regimens are also possible. It is concluded that a 30% TCP difference observed in a clinical study in favour of the fifteen-days regimen is theoretically possible. However, the fifteen-days regimen is outperformed in terms of TCP by the every week day regimen in more cases than the regimen lasting ten days. Therefore the choice of a prolongation in time must be made with care.