Cell survival and radiosensitisation: modulation of the linear and quadratic parameters of the LQ model (Review)

The linear-quadratic model (LQ model) provides a biologically plausible and experimentally established method to quantitatively describe the dose-response to irradiation in terms of clonogenic survival. In the basic LQ formula, the clonogenic surviving fraction Sd/S₀ following a radiation dose d (Gy) is described by an inverse exponential approximation: Sd/S₀ = e-(αd+βd²), wherein α and β are experimentally derived parameters for the linear and quadratic terms, respectively. Radiation is often combined with other agents to achieve radiosensitisation. In this study, we reviewed radiation enhancement ratios of hyperthermia (HT), halogenated pyrimidines (HPs), various cytostatic drugs and poly(ADP-ribose) polymerase‑1 (PARP1) inhibitors expressed in the parameters α and β derived from cell survival curves of various mammalian cell cultures. A significant change in the α/β ratio is of direct clinical interest for the selection of optimal fractionation schedules in radiation oncology, influencing the dose per fraction, dose fractionation and dose rate in combined treatments. The α/β ratio may increase by a mutually independent increase of α or decrease of β. The results demonstrated that the different agents increased the values of both α and β. However, depending on culture conditions, both parameters can also be separately influenced. Moreover, it appeared that radiosensitisation was more effective in radioresistant cell lines than in radiosensitive cell lines. Furthermore, radiosensitisation is also dependent on the cell cycle stage, such as the plateau or exponentially growing phase, as well as on post-treatment plating conditions. The LQ model provides a useful tool in the quantification of the effects of radiosensitising agents. These insights will help optimize fractionation schedules in multimodality treatments.