Modeling for predicting survival fraction of cells after ultra-high dose rate irradiation

Objective. FLASH radiotherapy (FLASH-RT) with ultra-high dose rate (UHDR) irradiation (i.e. > 40 Gy s-1) spares the function of normal tissues while preserving antitumor efficacy, known as the FLASH effect. The biological effects after conventional dose rate-radiotherapy (CONV-RT) with ≤0.1 Gy s-1have been well modeled by considering microdosimetry and DNA repair processes, meanwhile modeling of radiosensitivities under UHDR irradiation is insufficient. Here, we developed anintegrated microdosimetric-kinetic(IMK)model for UHDR-irradiationenabling the prediction of surviving fraction after UHDR irradiation.Approach.TheIMK model for UHDR-irradiationconsiders the initial DNA damage yields by the modification of indirect effects under UHDR compared to CONV dose rate. The developed model is based on the linear-quadratic (LQ) nature with the dose and dose square coefficients, considering the reduction of DNA damage yields as a function of dose rate.Main results.The estimate by the developed model could successfully reproduce thein vitroexperimental dose-response curve for various cell line types and dose rates.Significance.The developed model would be useful for predicting the biological effects under the UHDR irradiation.

Markov chain Monte Carlo analysis for the selection of a cell-killing model under high-dose-rate irradiation

PURPOSE

High-dose-rate irradiation with 6 MV linac x rays is a wide-spread means to treat cancer tissue in radiotherapy. The treatment planning relies on a mathematical description of surviving fraction (SF), such as the linear-quadratic model (LQM) formula. However, even in the case of high-dose-rate treatment, the repair kinetics of DNA damage during dose-delivery time plays a function in predicting the dose-SF relation. This may call the SF model selection into question when considering the dose-delivery time or dose-rate effects (DREs) in radiotherapy and in vitro cell experiments. In this study, we demonstrate the importance of dose-delivery time at high-dose-rate irradiations used in radiotherapy by means of Bayesian estimation.

METHODS

To evaluate the model selection for SF, three types of models, the LQM and two microdosimetric-kinetic models with and without DREs (MKM_DR and MKM) were applied to describe in vitroSF data (our work and references). The parameters in each model were evaluated by a Markov chain Monte Carlo (MCMC) simulation.

RESULTS

The MCMC analysis shows that the cell survival curve by the MKM_DR fits the experimental data the best in terms of the deviance information criterion (DIC). In the fractionated regimen with 30 fractions to a total dose of 60 Gy, the final cell survival estimated by the MKM_DR was higher than that by the LQM. This suggests that additional fractions are required for attaining the total dose equivalent to yield the same effect as the conventional regimen using the LQM in fractionated radiotherapy.

CONCLUSIONS

Damage repair during dose-delivery time plays a key role in precisely estimating cell survival even at a high dose rate in radiotherapy. Consequently, it was suggested that the cell-killing model without repair factor during a short dose-delivery time may overestimate actual cell killing in fractionated radiotherapy.

Modeling cell survival and change in amount of DNA during protracted 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.

Quantitative estimation of DNA damage by photon irradiation based on the microdosimetric-kinetic model

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 (60)Co γ-rays, (137)Cs 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.