Magae, J., Hoshi, Y., Furukawa, C., Kawakami, Y. and Ogata, H. Quantitative Analysis of Biological Responses to Ionizing Radiation, Including Dose, Irradiation Time, and Dose Rate. Radiat. Res. 160, 543–548 (2003).
Because biological responses to radiation are complex processes that depend on both irradiation time and total dose, consideration of both dose and dose rate is necessary to predict the risk from long-term irradiations at low dose rates. Here we mathematically and statistically analyzed the quantitative relationships between dose, dose rate and irradiation time using micronucleus formation and inhibition of proliferation of human osteosarcoma cells as indicators of biological response. While the dose–response curves did not change with exposure times of less than 20 h, at a given dose, both biological responses clearly were reduced as exposure time increased to more than 8 days. These responses became dependent on dose rate rather than on total dose when cells were irradiated for 20 to 27 days. Mathematical analysis demonstrates that the relationship between effective dose and dose rate is well described by an exponential function when the logarithm of effective dose is plotted as a function of the logarithm of dose rate. These results suggest that our model, the modified exponential (ME) model, can be applied to predict the risk from exposure to low-dose/low-dose-rate radiation.