Solid tumor risks after high doses of ionizing radiation

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   Fig. 1.

   Excess relative risks for radiation-induced lung cancer (A) and female breast cancer (B). The data points from A-bomb survivors (19, 20) are at moderate doses (<4 Gy). The data points at high doses are from studies of second cancers after radiotherapy of Hodgkin's disease patients: lung cancer, median age at exposure 45, median age at second cancer 58 (18); and breast cancer, median age at exposure 23, median age at second cancer 42 (16, 17). In the published reports, the breast cancer risks for Hodgkin's disease patients were internally normalized to the lowest-dose group [mean dose 3.2 Gy for Travis et al. (16) and 3.6 Gy for van Leeuwen et al. (17)]; these breast cancer data (B) have here been renormalized based on the estimated A-bomb excess relative risks for breast cancer (19) at 3.2 and 3.6 Gy, respectively, adjusted for the different demographics and background risks of the Hodgkin's breast cancer patients vs. the A-bomb survivors. The data points for lung cancer (B) are taken directly from the published data (18). The dashed curves represent fits to the A-bomb data using the standard “initiation + killing” model (refs. 6 and 7 and see Supporting Text), which involves a balance solely between induction of premalignant cells and cell killing, without considering cellular repopulation. As discussed in the text, it is clear that the predictions of this standard model are inconsistent with the high-dose data.

   
   
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   Fig. 2.

   Normal and premalignant stem cell numbers as a function of time during and after irradiation. (A) The predictions of Eqs. 1 and 3 for the number, n, of normal stem cells as a function of time for 20 daily fractions of d = 2 Gy each, with cell killing parameter α = 0.18 per Gy and repopulation rate λ = 0.4 per day. Initially, n has its setpoint value N, so the ratio shown is 1. At each fraction, n is decreased by killing, then some repopulation occurs between fractions. The repopulation is accelerated; in this logarithmic plot, the acceleration is manifested by the fact that the vertical height of the repopulation is larger between later fractions than near the start of irradiation. After irradiation stops, n gradually returns to its set point value N, here effectively reaching N at about day 40. Similar patterns hold if there is no treatment on weekends (see Supporting Text). (B) The number, m, of radiogenic premalignant cells (Eqs. 2 and 4). Parameters are those used for n in A and the following: setpoint N = 10⁶, initiation parameter γ = 10^–6 per Gy, and repopulation ratio r = 0.96. Each fraction produces some new premalignant cells as well as killing some premalignant cells already present. Between fractions, there is repopulation of premalignant cells, essentially tracking the repopulation of normal stem cells (Eq. 4). After irradiation stops, m continues to track n until at 40 days it has almost reached a plateau value M (Eq. 5). The models of this paper do not explicitly consider cell proliferation patterns for longer time scales, which may differ, both for normal and for premalignant cells.

   
   
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   Fig. 3.

   Measured and predicted excess relative risks for lung cancer (A) and female breast cancer (B) induced by high doses of ionizing radiation. The data points are from studies of second cancers after radiotherapy of Hodgkin's disease patients (16–18), as in Fig. 1. The dashed lines are the predictions of the simplified repopulation model (Eq. 13), which has no free parameters: its single relevant parameter, the slope at low doses, is derived from the excess relative risks of the A-bomb survivors for lung and breast, respectively, adjusted for the different demographic variables of the Hodgkin's patients vs. the A-bomb survivors [after adjustment (ERR/D)_lung = 0.18/Gy, (ERR/D)_breast = 1.2/Gy]. In B, that the points near 3.5 Gy (shown without error bars) fall exactly on the dashed line is automatic, given our renormalization procedure described in Fig. 1, but the approximate fit for the other points is an intrinsic property of the data. The solid curves are the predictions of the repopulation model (Eqs. 1–4), which allows different repopulation rates for normal vs. premalignant stem cells. For these curves, the initial slope was fixed as above; the cell killing parameter α (see Eq. 1) was fixed at 0.18/Gy (39). The other two free parameters, obtained by adjusting to the data shown, are the ratio of the per cell growth rates, r (see Eq. 4, r _lung = 0.96, r _breast = 0.76), and the repopulation rate parameter λT (see Eq. 3, λT = 0.4 for both lung and breast).