Evaluation of the cell survival curve under radiation exposure based on the kinetics of lesions in relation to dose-delivery time

Abstract

We have investigated the dose rate effects on cell damage caused by photon-beam irradiation. During a relatively long dose-delivery time with a low dose rate, lesions created in cells may undergo some reactions, such as DNA repair. In order to investigate these reactions quantitatively, we adopted the microdosimetric-kinetic (MK) model and deduced a cell surviving fraction (SF) formula for continuous irradiation. This model enabled us to estimate the SF from dose and dose rate. The parameters in the MK model were determined so as to generate the SF, and we attempted to evaluate the dose rate effects on the SF. To deduce the cell-specific parameters in the SF formula, including the dose rate, we performed a split-dose experiment and a single-dose experiment with a constant dose-delivery time (10 min) (to retain the condition for equivalent behavior of cell lesions) by means of a clonogenic assay. Then, using the MK model parameters, the SFs were reproduced for a variety of dose rates (1.0, 0.31, 0.18, 0.025 and 0.0031 Gy/min) and were compared with reported experimental data. The SF curves predicted by the MK model agreed well with the experimental data, suggesting that the dose rate effects appear in the kinetics of cell lesions during the dose-delivery time. From fitting the analysis of the model formula to the experimental data, it was shown that the MK model could illustrate the characteristics of log-SF in a rectilinear form at a high dose range with a relatively low dose rate.

Keywords: continuous irradiation; dose rate effects; linearity of high dose region; microdosimetric–kinetic model.

Fig. 1.

Two cases of single-continuous irradiation: (a) T < t_r and (b) t_r ≤ T. PLLs = potentially lethal lesions.

Fig. 2.

Schematic of the irradiation geometry for 250-kVp X-rays. The dose rates in water were measured using ionization chamber NE2751. We confirmed that these dose rates followed the inverse square law of the distance.

Fig. 3.

Surviving fraction obtained to deduce the MK parameters: (a) the result using a split-dose experiment with an equal dose condition: D₁ = D₂ = 3.0 Gy (5 min dose delivery time) for the interval (τ) from 0 to 4 h to determine (a + c) according to Eq. (26), (b) the result using a single-dose experiment in the case of 10 min (our) dose-delivery time to determine α₀ and β₀ using the value of (a + c) and Eqs (48) and (49). In Fig. 3a, S(0) and S(∞) represent the surviving fraction with an interval time (τ) with a split-dose exposure equalling zero and a limit of τ equalling infinity, respectively. The limit of dS/dτ was calculated as the gradient of three experimental points via spline interpolation.

Fig. 4.

Results of γ-H2AX foci assay: (a) for foci observed in control cells and irradiated (1.0 Gy) cells, (b) for the number of foci. Each red point represents a γ-H2AX focus that is assumed to be a DNA double-strand break, and the blue area highlights the cell nucleus stained with DAPI. In Fig. 4b, the double asterisk signs indicate significant difference between foci number in the control cell nucleus and that in the irradiated one using the analysis of variance (ANOVA) test (P = 4.244 × 10⁻⁴³).

Fig. 5.

Cell survival curves and experimental data reported by Metting et al. [23]: (a)–(e) for the cell survival curves predicted by the MK model for various dose rates in comparison with the LQ curve according to Eq. (8) for an extremely high dose rate, (f) for the curves predicted by the MK model with experimental data for a dose up to ∼15 Gy.

Fig. 6.

Cell survival curves for a variety of (a + c) values in the MK model. The shape has the tendency to become rectilinear above 10 Gy or more. In this figure, we used the MK parameters α₀ and β₀ indicated in Table 1.