During exposure to ionizing radiation, sub-lethal damage repair (SLDR) competes with DNA damage induction in cultured cells. By virtue of SLDR, cell survival increases with decrease of dose-rate, so-called dose-rate effects (DREs). Here, we focused on a wide dose-rate range and investigated the change of cell-cycle distribution during X-ray protracted exposure and dose-response curves via hybrid analysis with a combination of in vitro experiments and mathematical modelling. In the course of flow-cytometric cell-cycle analysis and clonogenic assays, we found the following responses in CHO-K1 cells: (1) The fraction of cells in S phase gradually increases during 6 h exposure at 3.0 Gy/h, which leads to radio-resistance. (2) Slight cell accumulation in S and G2/M phases is observed after exposure at 6.0 Gy/h for more than 10 hours. This suggests that an increase of SLDR rate for cells in S phase during irradiation may be a reproducible factor to describe changes in the dose-response curve at dose-rates of 3.0 and 6.0 Gy/h. By re-evaluating cell survival for various dose-rates of 0.186–60.0 Gy/h considering experimental-based DNA content and SLDR, it is suggested that the change of S phase fraction during irradiation modulates the dose-response curve and is possibly responsible for some inverse DREs.

DNA strand breaks are induced in cells mainly composed of liquid water along ionizing radiation tracks. For estimating DNA strand break yields, track structures for electrons in liquid water in Monte Carlo simulations are of great importance; however, detailed simulations to obtain both energy deposition and free radical reaction to DNA are time-consuming processes. Here, we present a simple model for estimating yields of single-and double-strand breaks (SSB, DSB, and DSB/SSB ratio) based only on spatial patterns of inelastic interactions (i.e., ionization and electronic excitation) generated by electrons, which are evaluated by the track structure mode of Particle and Heavy Ion Transport code System without analyzing the production and diffusion of free radicals. In the present model, the number of events per track and that of a pair composed of two events within 3.4 nm (10 base pairs) were stochastically sampled for calculating SSB and DSB yields. The results calculated by this model agree well with other simulations and experimental data on the DSB yield and the DSB/SSB ratio for monoenergetic electron irradiation. This model also demonstrates the relative biological effectiveness at the DSB endpoint for various photon irradiations, indicating that the spatial pattern composed of ionization and electronic excitation without physicochemical and chemical stages is sufficient to obtain the impact of electrons on the initial DNA strand break induction.

An improved biological weighting function (IBWF) is proposed to phenomenologically relate microdosimetric lineal energy probability density distributions with the relative biological effectiveness (RBE) for the in vitro clonogenic cell survival (surviving fraction = 10%) of the most commonly used mammalian cell line, i.e. the Chinese hamster lung fibroblasts (V79). The IBWF, intended as a simple and robust tool for a fast RBE assessment to compare different exposure conditions in particle therapy beams, was determined through an iterative global-fitting process aimed to minimize the average relative deviation between RBE calculations and literature in vitro data in case of exposure to various types of ions from 1H to 238U. By using a single particle- and energy- independent function, it was possible to establish an univocal correlation between lineal energy and clonogenic cell survival for particles spanning over an unrestricted linear energy transfer range of almost five orders of magnitude (0.2 keV µm−1 to 15 000 keV µm−1 in liquid water). The average deviation between IBWF-derived RBE values and the published in vitro data was ∼14%. The IBWF results were also compared with corresponding calculations (in vitro RBE10 for the V79 cell line) performed using the modified microdosimetric kinetic model (modified MKM). Furthermore, RBE values computed with the reference biological weighting function (BWF) for the in vivo early intestine tolerance in mice were included for comparison and to further explore potential correlations between the BWF results and the in vitro RBE as reported in previous studies. The results suggest that the modified MKM possess limitations in reproducing the experimental in vitro RBE10 for the V79 cell line in case of ions heavier than 20Ne. Furthermore, due to the different modelled endpoint, marked deviations were found between the RBE values assessed using the reference BWF and the IBWF for ions heavier than 2H. Finally, the IBWF was unchangingly applied to calculate RBE values by processing lineal energy density distributions experimentally measured with eight different microdosimeters in 19 1H and 12C beams at ten different facilities (eight clinical and two research ones). Despite the differences between the detectors, irradiation facilities, beam profiles (pristine or spread out Bragg peak), maximum beam energy, beam delivery (passive or active scanning), energy degradation system (water, PMMA, polyamide or low-density polyethylene), the obtained IBWF-based RBE trends were found to be in good agreement with the corresponding ones in case of computer-simulated microdosimetric spectra (average relative deviation equal to 0.8% and 5.7% for 1H and 12C ions respectively).

Intercellular communication after ionizing radiation exposure, so-called non-targeted effects (NTEs), reduces cell survival. Here we describe an integrated cell-killing model considering NTEs and DNA damage along radiation particle tracks, known as DNA-targeted effects (TEs) based on repair kinetics of DNA damage. The proposed model was applied to a series of experimental data, i.e., signal concentration, DNA damage kinetics, cell survival curve and medium transfer bystander effects (MTBEs). To reproduce the experimental data, the model considers the following assumptions: (i) the linear-quadratic (LQ) function as absorbed dose to express the hit probability to emit cell-killing signals, (ii) the potentially repair of DNA lesions induced by NTEs, and (iii) lower efficiency of repair for the damage in NTEs than that in TEs. By comparing the model results with experimental data, we found that signal-induced DNA damage and lower repair efficiency in non-hit cells are responsible for NTE-related repair kinetics of DNA damage, cell survival curve with low-dose hyper-radiosensitivity (HRS) and MTBEs. From the standpoint of modelling, the integrated cell-killing model with the LQ relation and a different repair function for NTEs provide a reasonable signal-emission probability and a new estimation of low-dose HRS linked to DNA repair efficiency.

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.

In advanced radiotherapy, intensity modulated radiation fields and complex dose-delivery are utilized to prescribe higher doses to tumours. Here, we investigated the impact of modulated radiation fields on radio-sensitivity and cell recovery during dose delivery. We generated experimental survival data after single-dose, split-dose and fractionated irradiation in normal human skin fibroblast cells (AGO1522) and human prostate cancer cells (DU145). The dose was delivered to either 50% of the area of a T25 flask containing the cells (half-field) or 100% of the flask (uniform-field). We also modelled the impact of dose-rate effects and intercellular signalling on cell-killing. Applying the model to the survival data, it is found that (i) in-field cell survival under half-field exposure is higher than uniform-field exposure for the same delivered dose; (ii) the importance of sub-lethal damage repair (SLDR) in AGO1522 cells is reduced under half-field exposure; (iii) the yield of initial DNA lesions measured with half-field exposure is smaller than that with uniform-field exposure. These results suggest that increased cell survival under half-field exposure is predominantly attributed not to rescue effects (increased SLDR) but protective effects (reduced induction of initial DNA lesions). In support of these protective effects, the reduced DNA damage leads to modulation of cell-cycle dynamics, i.e., less G 1 arrest 6 h after irradiation. These findings provide a new understanding of the impact of dose-rate effects and protective effects measured after modulated field irradiation.

The microdosimetric-kinetic (MK) model is one of the models that can describe the fraction of cells surviving after exposure to ionizing radiation. In the MK model, there are specific parameters, k and yD, where k is an inherent parameter to represent the number of potentially lethal lesions (PLLs) and yD indicates the dose-mean lineal energy in keV/μm. Assuming the PLLs to be DNA double-strand breaks (DSBs), the rate equations are derived for evaluating the DSB number in the cell nucleus. In this study, we estimated the ratio of DSBs for two types of photon irradiation (6 MV and 200 kVp X-rays) in Chinese hamster ovary (CHO-K1) cells and human non-small cell lung cancer (H1299) cells by observing the surviving fraction. The estimated ratio was then compared with the ratio of γ-H2AX foci using immunofluorescent staining. For making a comparison of the number of DSBs among a variety of radiation energy cases, we next utilized the survival data in the literature for both cells exposed to other photon types, such as 60Co γ-rays, 137Cs γ-rays and 100 kVp X-rays. The ratio of DSBs based on the MK model with conventional data was consistent with the ratio of γ-H2AX foci numbers, confirming that the γ-H2AX focus is indicative of DSBs. It was also shown that the larger yD is, the larger the DSB number is. These results suggest that k and yD represent the characteristics of the surviving fraction and the biological effects for photon irradiation.

Hyper-radiosensitivity (HRS) is a well-known bioresponse under low-dose or low-dose-rate exposures. Although disorder of the DNA repair function, non-targeted effects and accumulation of cells in G2 have been experimentally observed, the mechanism for inducing HRS by long-term irradiation is still unclear. On the basis of biological experiments and a theoretical study, we have shown that change in the amount of DNA associated with accumulation of cells in G2 enhances radiosensitivity. To demonstrate continuous irradiation with 250 kVp X-rays, we adopted a fractionated regimen of 0.186 or 1.00 Gy per fraction at intervals of 1 h (i.e. 0.186 Gy/h, 1.00 Gy/h on average) to Chinese Hamster Ovary (CHO)-K1 cells. The change in the amount of DNA during irradiation was quantified by flow cytometric analysis with propidium iodide (PI). Concurrently, we attempted a theoretical evaluation of the DNA damage by using a microdosimetric-kinetic (MK) model that was modified to incorporate the change in the amount of DNA. Our experimental results showed that the fraction of the cells in G2/M phase increased by 6.7% with 0.186 Gy/h and by 22.1% with 1.00 Gy/h after the 12th irradiation. The MK model considering the change in amount of DNA during the irradiation exhibited a higher radiosensitivity at a high dose range, which could account for the experimental clonogenic survival. The theoretical results suggest that HRS in the high dose range is associated with an increase in the total amount of DNA during irradiation.