Revision 1
March 19, 1998
by Radiation, Science, and Health, Inc.,
Edited by J. Muckerheide

1.6
Biological Models

"Lung cancer risk estimates of indoor radon exposure (mean Rn-levels <100 Bq/m3) have been obtained by linear extrapolation of data on highly exposed underground miners (104-105 Bq/m3), since epidemiological case-control studies have either yielded statistically insignificant results for Rn-levels <200 Bq/m3, or conflicting results for higher Rn-levels. Recently, data have been presented by Cohen, showing a significant negative correlation between average indoor Rn-level and lung cancer incidence in US counties (Cohen 1995). Being a geographical study, it has attracted serious criticism, probably also because its results do not agree with the generally accepted idea of linear extrapolation.

"Biologically based mathematical models of carcinogenesis describe the kinetics of cell transformation events leading to cancer, and can be useful in evaluating the effects of low level irradiation that are too small to be assessed directly in experimental or epidemiological studies. A widely accepted model is the two-stage clonal expansion model of cancer induction (Moolgavkar 1978). This model has been shown to explain the exponential behaviour of age-specific incidence of many human cancers, and it has been used to analyse data on lung cancer induction in rats after radon exposure, where both the mutagenic and cell killing potential of a-particles had been incorporated."

Figure 1

"It has been suggested that, in a multi-stage model, a cell may need to acquire several mutations before entering the next stage, their total number for two stages probably being three. Therefore, a three-mutation model has been developed, see Fig 1. Normal pulmonary stem cells in compartment C1 may switch over to C2, C3 and C4 by spontaneous or radon induced mutations. The rate of spontaneous mutations is equal to m [y-1], the radiation induced rate equals r [Gy-1] times dose rate dD/dt [Gy?y-1]...Cells in C2 are assumed to behave normally. C3 is the stage of clonal expansion, where cells have become pre-malignant and divide spontaneously at a rate H [y-1] to form an exponentially expanding clone. The net rate of clonal expansion is affected by radon-induced cell kill, determined by K [Gy-1]. Malignant transformation is described by transition of pre-malignant cells to C4, where, with a lag time, a detectable tumor develops...

"An initial value of l07 was selected for the number of normal lung epithelial stem cells (literature value: 106 - 109). A value of 2.0 Gy-1 was selected for parameter K, as cell survival studies in vitro have yielded estimates for the cell kill probability of a-particles of 1.1 - 2.8 Gy-1."

"Numerical values for m and H were obtained by fitting the model to several data sets on age-specific human lung cancer incidence (setting R=0 Bq?m3 for simplicity). Male populations from different countries all yielded excellent fits, with values of m that varied from 3-6x106 y-1. This order of magnitude can be considered realistic, regarding the broad range of values that have been reported in the literature for spontaneous mutation rates in vitro. The value of H was almost constant for all data sets (0.22 - 0.24 y-1), suggesting that clonal expansion may be a process that, among different populations, takes place at a relatively constant rate. In all further calculations, parameter H was kept constant at a value of 0.23 y-1.

Figure 2

"Values for r and d have been estimated by fitting the model to data on radon exposed miners (Lubin et al 1995). ..The model fitted the data quite well, see Fig 2. For m, a value of 5x10-6 y-1 resulted, which is within the range found above. A value of 2x10-4 Gy-1 was found for r, which is in agreement with literature values reported for radiation induced mutations. For d [the dose conversion factor], a value of 0.2 mGy?y-1?Bq-1?m3 was obtained. From reported values for dose per WLM and WLM per Bq/m3, a literature value for d may be derived in the range 0.01 - 1 mGy?y-1?Bq-1?m3, which is in agreement with the value obtained presently.

Figure 3

"Finally, the model was applied to radon related lung cancer among males in US counties (Cohen 1995). The parameters m, r and H were fixed at the values obtained from the miners data, but d has been used as a fit parameter, since it has been suggested that the dose conversion factor could be higher for the general population, as compared with underground miners...The results can be found in Fig 3. The model fits the data quite well, and it may be shown that the negative initial slope of the curve is caused by pre-malignant cell kill due to radiation. A value of 1 mGy?y-1?Bq-1?m3 was obtained for d, which indeed is higher than the value obtained from the miners data."

"It may be concluded that the results of the study by Cohen (1995), as well as the data on underground miners (Lubin et al 1995), may be quantitatively described by a very simple model of lung cancer induction, with realistic numerical values of input parameters. It is thus suggested that, in the low dose region, the dose-response relationship may be highly non-linear, and a negative initial slope may be possible."