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

Abstract

This study compares the effectiveness of three fractionation schemes of equal fraction size, comprising five fractions of SBRT over 5 days, 10 days, or 15 days, respectively. Method: This comparative study is based on two tumor-control-probability (TCP) models that take into account tumor 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 one 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 favor of the fifteen-day regimen is theoretically possible. However, the fifteen-day 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.

The Impact of Different Timing Schedules on Prostate HDR-Mono-Brachytherapy. A TCP Modeling Investigation

“…We hypothesize that the better treatment outcome of the longer treatment schedule might be due to the initial existence of hypoxic (and hence, radio-resistant) region, which is fully re-sensitized during the longer treatment period. Therefore, we use in this study a modification of the linear-quadratic (LQ) cell kill model, where both radio-sensitivity parameters (α and β) of the LQ model are assumed to increase in time during treatment, as suggested in [7,9]. We developed in [9] a version of the LQ model where the cell radiosensitivity may increase in time according to the following function:…”

“…In a recent work [7], we assumed that β is related to α through the oxygen enhancement ratio (OER) [20,31] in the following way: OER = α m α 0 = β m β 0 , where β 0 is the initially low value of β and β m is its maximum value reached asymptotically in time. We assume that for intermediate times an analogous relation between α and β should also be valid, i.e.,…”

“…The probability of local control due to these modes of treatment is high [2][3][4][5][6]. In recent theoretical studies [7,8], the impact on the treatment outcome of prolonged hypo-fractionated schedules applied in SBRT is investigated. The investigations carried out in these works have indicated that it might be beneficial for the treatment outcome in terms of the local control if fractions of irradiations are delivered over a prolonged time interval.…”

“…For instance, in the terminology of Fisher, most of the TCP models which account for tumor resensitization are based on a combination of 'cell number-dependent' and 'non-secular time-dependent' mechanisms [10][11][12]20,21]. In this work, we use the Zaider-Minerbo TCP model, the derivation of which is based on the approach outlining the dynamics of birth and death processes, while the mechanism of re-oxygenation, which is incorporated in the linear-quadratic (LQ) model of radiation cell kill [7], follows the ideology of 'secular time-dependent' mechanism [19].…”

“…A similar cure rate (biochemical control) as in the group treated with three fractions is reported in [26] for prostate cancer patients treated with HDR brachytherapy of three fractions in 28 days. In the current study, we analyze the data reported in [25] using one of the TCP models, incorporating a possible increase in tumor radio-sensitivity developed in [7,9].…”