A stochastic two-stage cancer model with clonal expansion was used to investigate the potential impact on human lung cancer incidence of some aspects of the hormesis mechanisms suggested by Feinendegen (Health Phys. 52 663–669, 1987). The model was applied to low doses of low-LET radiation delivered at low dose rates. Non-linear responses arise in the model because radiologically induced adaptations in radical scavenging and DNA repair may reduce the biological consequences of DNA damage formed by endogenous processes and ionizing radiation. Sensitivity studies were conducted to identify critical model inputs and to help define the changes in cellular defense mechanisms necessary to produce a lifetime probability for lung cancer that deviates from a linear no-threshold (LNT) type of response. Our studies suggest that lung cancer risk predictions may be very sensitive to the induction of DNA damage by endogenous processes. For doses comparable to background radiation levels, endogenous DNA damage may account for as much as 50 to 80% of the predicted lung cancers. For an additional lifetime dose of 1 Gy from low-LET radiation, endogenous processes may still account for as much as 20% of the predicted cancers (Fig. 2). When both repair and scavengers are considered as inducible, radiation must enhance DNA repair and radical scavenging in excess of 30 to 40% of the baseline values to produce lifetime probabilities for lung cancer outside the range expected for endogenous processes and background radiation. FIGURE 2 Contribution to the lifetime probability for lung cancer of DNA damage formed by endogenous processes and ionizing radiation. Protective effects are not included in this set of calculations (i.e., F = G = const. = 1). Solid curve: stochastic cancer model ... Keywords: radioprotective mechanisms, low-LET, lung cancer, LNT, threshold, hormesis, endogenous damage INTRODUCTION There are biological responses to a variety of chemical and radiological agents that may be U-shaped rather than LNT (Calabrese and Baldwin 2003). Azzam et al. (1996) demonstrated that low doses (1–100 mGy) of γ-rays, when delivered at 2.4 mGy min−1, reduced the neoplastic transformation frequency in C3H 10T1/2 cells to a rate three- to four-fold below the spontaneous transformation frequency. This has been confirmed in human-hybrid cell systems (Redpath and Antoniono 1998, Redpath et al. 2001, 2003a, 2003b). In animals in vivo, low doses have been shown to reduce tumor frequency (Ishii et al. 1996) and increased both radiation-induced and spontaneous tumor latency (Mitchel et al. 1999, 2003). These results demonstrate that low-dose exposures may induce processes, such as adaptations in DNA repair processes (Le et al. 1998, Ye et al. 1999), radical scavenging (Yamaoka et al. 1991, Yukawa et al. 1999) or apoptosis (Bauer 1995, 1996, 2000) that reduce the overall rate of cell transformation. In addition to the in vitro and animal in vivo studies, a review of human epidemiological studies suggests that protracted exposure to low doses of low-LET radiation does not appear to cause lung cancer and a reduction of the natural cancer incidence level may even be evident (Rossi and Zaider 1997). In an earlier study (Schollnberger et al. 2004), the concept of radiologically induced adaptations that also prevent and repair endogenous (oxidative) DNA damage was developed using a deterministic 3-stage lung cancer model. In this work, we develop methods of incorporating these mechanisms into a stochastic two-stage cancer model. In a deterministic model the hazard rate increases indefinitely while in a stochastic cancer model it levels off at advanced ages (Heidenreich and Hoogenveen 2001, Chen 1993). The trends predicted by stochastic models are consistent with observations suggesting that lung cancer incidence and mortality rates increase with age, but start to level off at advanced age and (for many cancers) decline at very high ages (see e.g., Benson 1996, Herrero-Jimenez et al. 2000). The aim of the current study is to define the magnitude of the changes in DNA damage repair and enzymatic radical scavengers that would be required to produce a lifetime probability for lung cancer that deviates from a linear no-threshold (LNT) type of response. Studies are presented for hypothetical exposure scenarios in which individuals are exposed to low doses rates of low-LET radiation in addition to natural background radiation. The reported studies are most appropriate when high-LET radiations, such as α particles from radon progeny, are a minor component of the natural background radiation. Although continuous exposure to low dose rates of low-LET radiation are not typical of many environmental exposure settings, this type of exposure setting is a reasonable facsimile of the types of exposures that may be encountered by workers in nuclear power plants or other radiation facilities. The reported studies are the first to consider the effects that radiation-induced adaptations in cellular defense mechanisms have on predictions of lung cancer incidence made with a stochastic multistage model. The approach developed in this work is an important first step in developing new models and methods to describe dose-response relations that deviate from the LNT response models that are widely used for radiation protection purposes.