‡ Department of Mathematics, University of California, Berkeley, CA 94720, USA

Purpose. Radon risks derive from exposure of bronchio-epithelial cells to high-LET alpha particles. Alpha particle exposure can result in bystander effects, where irradiated cells emit signals resulting in damage to nearby unirradiated bystander cells. This can result in non-linear dose-response relations, and inverse dose-rate effects. Domestic radon risk estimates are currently extrapolated from miner data which are at both higher doses and higher dose rates, so bystander effects on unhit cells could play a large role the extrapolation of risks from mines to homes. We therefore extend an earlier quantitative mechanistic model of bystander effects to include protracted exposure, with the aim of quantifying the significance of the bystander effect for very prolonged exposures.

Methods. A model of high-LET bystander effects, originally developed to analyze oncogenic transformation in vitro, is extended to low dose rates. The model considers radiation response as a superposition of bystander and linear direct effects. It attributes bystander effects to a small subpopulation of hypersensitive cells, with the bystander contribution dominating the direct contribution at very low acute doses but saturating as the dose increases. Inverse dose-rate effects are attributed to replenishment of the hypersensitive subpopulation during prolonged irradiation.

Results. The model was fitted to dose- and dose-rate dependent radon-exposed miner data, suggesting that one directly-hit target bronchio-epithelial cell can send bystander signals to about 50 neighboring target cells. The model suggests that a naïve linear extrapolation of radon miner data to low doses, without accounting for dose rate, would result in an underestimation of domestic radon risks by about a factor of four, a value comparable to the empirical estimate applied in the recent BEIR-VI report on radon risk estimation.

Conclusions. Bystander effects represent a plausible quantitative and mechanistic explanation of inverse dose-rate effects by high-LET radiation, resulting in non-linear dose-response relations, and a complex interplay between the effects of dose and exposure time. The model presented here provides a potential mechanistic underpinning for the empirical exposure-time correction factors applied in the recent BEIR-VI for domestic radon risk estimation.

By far the largest component of the background radiation dose equivalent is from domestic radon exposure (NCRP 1987). For a variety of reasons, however, direct epidemiological assessment of the risks from domestic radon exposure is difficult, resulting in risk estimates with wide confidence intervals (Lubin et al. 1995). Consequently domestic radon risk estimates are currently based on extrapolation of data from miner studies, largely at considerably higher radon exposures and exposure rates. At present, a linear extrapolation of the risks from high to low radon exposures is generally considered to have the strongest biophysical rationale (NRC 1999).

At an average home radon concentration, few potential target cells in the bronchial epithelium of a home resident will be struck or traversed by an alpha particle in, say, one year (NRC 1999) - and this observation remains true even at high domestic radon levels (Fig. 1).

This inhomogeneous energy deposition by alpha particles is of potential relevance to the radon problem because there is convincing evidence, at least in vitro, that irradiated cells can send out signals that can result in damage to nearby unirradiated "bystander" cells. The evidence is particularly strong for high-LET radiation, with a broad variety of endpoints (summarized, for example, by Sawant et al., 2001) including chromosomal damage and oncogenic transformation. Some recent results suggest that bystander effects can be induced by high-LET radiation even when the bystander cells have been previously exposed to low doses of low-LET radiation (Sawant et al. 2001a).

In earlier work (Brenner et al. 2001), we suggested a model for acute exposure to high-LET particles, incorporating both bystander effects and the more classical "direct effects". The basic picture we proposed of the bystander effect was that:

1. it is a binary "all or nothing" phenomenon, in which a signal is sent out by cells whose nuclei are directly hit, but at high LET more hits to one cell nucleus do not lead to an increased bystander response in its neighbors;
2. the cell population contains, at any given time, a small subpopulation of cells which are hypersensitive in their response to the bystander signal;
3. a cell from this hypersensitive subpopulation is also very sensitive to direct particle traversals of the nucleus, such a traversal generally resulting in cell death.

This approach produced results consistent with data then available from in-vitro experiments designed to probe the bystander effect (e.g., Sawant et al. 2001, Miller et al. 1999) for oncogenic transformation, and also with data published since then (e.g., Belyakov et al. 2001). Broadly speaking it predicts dose-response curves for acute high-LET irradiation that rise rapidly to a plateau at low doses (due to the bystander effect) and then further increase at higher doses (due to "direct" effects). Thus at low doses, the curve is downwardly curving (Fig. 1a, solid curve), a pattern apparent for lung-cancer incidence in animals acutely exposed to radon (Cross 1992, Gilbert et al. 1996, Monchaux et al. 1999). This downward curvature for acute exposure is of potential significance for dose rate effects, as we now discuss.

The bystander model discussed above was for a single acute dose. By contrast domestic exposure to radon is protracted over a lifetime, and even miner exposure is typically protracted over several years (average 5.7 y (NRC 1999)). It is important, therefore, to extend models of bystander response from acute to protracted exposure when analyzing the extrapolation of radon risks from higher to lower exposures.

Before considering a specific model of bystander response to protracted exposures, it is useful to note that, with some limitations (see below), one can estimate the effect of protraction in a model-independent way. To take the simple example of splitting the dose into two fractions (see Fig. 2), one can picture the overall response to be the result of repeating the dose-response relation for each fraction (Rossi et al. 1982, Brenner and Sachs 2000). Then, if the acute dose-response relation has an upward curvature (as in, for example, the "classic" linear-quadratic relationship), protraction would be expected to decrease the response (Fig. 2a); a decrease of response with increasing dose protraction is often called a direct dose-rate effect. On the other hand, downward curvature in the acute dose-response relation, which appears to be the scenario relevant to bystander responses, would imply that protraction increases the response (Fig. 2a), giving an inverse dose-rate effect. Finally, a system whose dose-response relationship for acute irradiation is linear would be expected to show little protraction effect.

The applicability of this repeat rule - that the effect of protraction approximates repeated applications of the same initial part of the dose-response curve (Fig. 2) - depends on how a cell population changes during a protracted exposure. An acute exposure preferentially removes more radiosensitive cells from a heterogeneous population, and the repeat rule will then hold if, during the irradiation, there is continual restoration towards the pre-irradiation distribution of radiosensitivity. For the bystander model briefly outlined above, this rule would be expected to hold (Brenner et al. 2001). After an initial acute exposure, the small proportion of hypersensitive cells (sensitive both to bystander signals and to direct killing) would be decreased to still lower values due to direct cell killing or transformation, but over time this proportion should return to its pre-irradiation level due to normal redistribution effects (Hahnfeldt and Hlatky 1998). If the distribution of cellular sensitivities is restored on a time scale shorter than or comparable to the protraction time, then protraction would increase response relative to an acute exposure (Fig. 2b) – an inverse dose-rate effect.

In fact both laboratory and epidemiological evidence strongly suggest that increasing protraction of exposure to alpha particles increases the oncogenic risk. Of particular interest here is that inverse dose-rate effects have been demonstrated in miners exposed to radon-progeny alpha particles over differing periods of time: In comparisons between different epidemiological studies involving different average radon-progeny exposure rates, Howe et al. (1987) and Darby and Doll (1990) inferred inverse dose-rate effects. Within individual miner cohorts, inverse dose-rate effects were reported by Hornung and Meinhardt (1987), Hornung et al. (1998), Stram et al. (1999), Gilliland et al. (2000), Ševc et al. (1988), Tomášek et al. (1993), Lubin et al. (1990), and Xuan et al. (1993). In a joint analysis of 11 cohorts of miners exposed to radon, with data stratified both by exposure and exposure time, Lubin et al. (1995a) and BEIR VI (NRC 1999) clearly demonstrated the existence of a statistically-significant inverse dose-rate effect.

In parallel to these epidemiological studies, there have been many laboratory reports of inverse dose-rate effects for oncogenesis or oncogenic transformation induced by high-LET radiations (Hill et al. 1982, 1985, Yang et al. 1987, Miller et al. 1988, 1990, Bettega et al. 1992, Gilbert et al. 1996, Monchaux et al. 1999).

As discussed above, average domestic radon exposures are much lower than average miner exposures, to the extent that multiple alpha-particle traversals in target bronchial cell nuclei from domestic exposure will be much less common than for miners. The case where multiple traversals can occur in one target differs in an important way from the case where multiple traversals are very rare: Specifically, several authors (Barendsen 1985, Curtis 1989, Brenner 1993) have argued that, at low doses, a lack of multiple traversals may preclude any dose rate effects, inverse or direct. Subsequent studies, both epidemiological (Lubin et al. 1995a, Hornung et al. 1998, NRC 1999) and in animals (Gilbert et al. 1996, Monchaux et al. 1999) have indeed confirmed that inverse dose-rate effects do decrease as the dose decreases, essentially disappearing at fluences of around one alpha particle per target cell nucleus. We shall argue that when bystander effects are taken into account, a similar situation should hold, provided the concept of "one target" is appropriately enlarged to include all the bystander cells that can be signaled from a hit cell.

5. Modeling the influence of bystander effects on domestic radon risk

We are concerned with the extrapolation of radon risks from miners (comparatively high dose, significant numbers of multiple a-particle traversals per nucleus, relative short exposure time) to the domestic situation (low dose, almost no multiple nuclear a-particle traversals, long exposure time). The evidence we have discussed suggests that dose rate effects must be taken into account in such an extrapolation. In fact the most recent analysis of domestic radon risk, in the BEIR-VI report (NRC 1999), does make an empirical correction for dose rate effects, based on a phenomenological fit to miner data involving a range of exposure and exposure rates. For example, the BEIR-VI phenomenological model incorporates an increase in risk by a factor of about 4 for a radon exposure of more than 35 years, compared to typical miner exposure exposure of, say, 6 years.

Our goal in the current work is to provide a possible quantitative mechanistic underpinning for these empirical dose-rate-based correction factors – these being a central component of the extrapolation of radon risk from mines to homes. Specifically, we extend the bystander model which we reported earlier (Brenner et al. 2001) for high-LET acute exposure, to high-LET exposure at lower dose rates. The model is comparatively parsimonious, involving only four essential adjustable parameters. As discussed later, it is probably not appropriate to directly apply model parameters estimated in the analysis of in-vitro data, to the in-vivo situation. Therefore we provide some validation of this extended model by comparing it with the data provided by Lubin et al. (1995a) for lung-cancer mortality in miners, with data stratified both by exposure and by exposure time. Finally we use this extended model to draw some conclusions regarding the basis for the complex interplay of dose and dose rate (Brenner et al. 1994) in extrapolating radon risks from mines to homes, providing a mechanistic rationale for the phenomenologically-based dose-rate corrections adopted in the BEIR-VI report (NRC 1999).