Compatibility of the repairable-conditionally repairable, multi-target and linear-quadratic models in converting hypofractionated radiation doses to single doses

摘要

The experimental data used in this study are derived from our previous experiments [6]. Briefly, EMT6 mouse mammary sarcoma cells were used for single cell experiments, and V79 Chinese hamster lung fibroblasts were used for single cell and spheroid experiments, as described in detail previously [6]. V79 spheroids were used, grown to approximately 0.8 mm in diameter 14–18 days after spinner culture. Irradiation was carried out using a 210-kVp X-ray machine (10 mA with 2-mm Al filter; Chubu Medical Co., Matsusaka, Japan) at a dose rate of 1.8 Gy/min. In both experiments for single cells and spheroids, irradiation was given at appropriate intervals to allow potentially lethal damage repair (PLDR) and sublethal damage repair (SLDR) [6, 13, 14]. A standard colony assay was also used to determine cell survival. Both V79 and EMT6 single cells received single doses of 0–12 Gy or 2 or 3 fractions of 4 or 5 Gy each at 4-h intervals. V79 spheroids received single doses of 0–26 Gy or 2–5 fractions of 4–12 Gy at 2–4-h intervals. A colony assay was used to determine cell survival. Dose-survival curves were obtained for single doses of 0–12 Gy in single cell experiments and 0–26 Gy in spheroid experiments. In the single cell experiments, single doses used in the experiments, and surviving fractions at those doses, were substituted into equations of the RCR models (where Sis the surviving fraction, Dis the dose in Gy, d₁and d₀are parameters that determine the initial and final slope of the survival curve, respectively, and nis the y-intercept of the asymptote) in the calculation software Mathematica. Then, each parameter coefficient was computed by carrying out the optimum convergence to approximate the survival curves. The software employs the minimum chi-square model to fit the curves. Cell surviving fractions after hypofractionated doses were superimposed on each dose-survival curve after single–fraction irradiation, and actually-determined equivalent single doses for the hypofractionated doses (measured doses), were estimated for these three models. The method is shown in Figs 1 and 2, the symbol X representing the measured equivalent single doses for the hypofractionated doses using the LQ model. Thereafter, cell survival data after hypofractionated doses were assigned to these three models with the parameter coefficients, and equivalent single doses for the hypofractionated doses were calculated (calculated doses). The calculated doses were then compared with the measured doses. In V79 spheroid experiments, the α/β ratio and parameter coefficients for single cells were used because there were no appropriate models to estimate the α/β ratio or parameter coefficients for spheroid cells [6, 15]. Moreover, since the surviving fractions in the high dose range for the V79 spheroid cells could be approximated by a linear line, the measured doses for these three models were calculated using the linear equations: for 2- or 3-fraction experiments and for 4- or 5-fraction experiments. Statistical analyses were carried out with StatView version 5 (SAS Institute Inc., Cary, NC, USA) and SPSS 11.0J (SPSS Japan Inc., Tokyo, Japan).