system and reduce the probability of repair of particular damage from a track (UNSCEAR 1993). However, there is no experimental evidence to support this model. As the dose is reduced, the β term becomes less important, and the dose-response relationship approaches linearity with a slope of α. For doses delivered in multiple fractions or at low dose rates, in which case the effects during the exposure period are independent and without additive or synergistic interactions, the dose-response relationship should also be linear with a slope of α. Theoretically, the value of α should be the same for high and low dose rates and for single or multiple doses, and there should be a limiting value, α1, so that reducing the dose rate further would not reduce the α term (see Figure 2-1 for an illustration of these concepts).

For extrapolating data from acute high-dose-rate experiments to results expected for low doses and low-dose-rate experiments, the dose and dose-rate effectiveness factor, DDREF, is estimated (see Figure 2-1). The DDREF is estimated by comparing the linear extrapolation (curve B) of the induced incidence for a set of acute dose points (curve A) with the linear curve (D) for low dose rate. The DDREF is equal to the slope αL for curve B divided by the slope α1 for curve D. If only acute high-dose data are available, the slope (α1) for the linear extrapolation of the data for acute doses that approach zero (tangent to curve A) is used. This is the dose effectiveness factor (DEF), which is assumed and shown (Cornforth and others 2002) to be equal to the dose-rate effectiveness factor (DREF). Therefore, the term DDREF is used to estimate effects for either low doses or low dose rates. This value for DDREF can be estimated from a fit of the acute data using the relationship described above (i.e., E = αD + βD2). Thus, the DDREF = [(αD + βD2)/D]/(αD/D)=(αD + βD2)/αD, which equals 1 + Dβ/α or 1 + D/(α/β). D is the dose at which the response for acute irradiation is divided by the response for low-dose-rate irradiation to obtain the DDREF, and the relationship shows that DDREF will increase with the dose at which the curves A and D are compared. Note, the contribution from the β term (βD2) equals the contribution from the α term (αD) (i.e., βD2 = αD, when D = α/β). For this dose equal to α/β, the incidence for curve D is equal to the difference between the incidence for curve A and the incidence for curve D; thus, curve A intersects the linear curve B at the dose equal to α/β. For example, if α/β equals 1 Gy, the DDREF for a dose of 1 Gy would theoretically equal (1 + 1/1) or 2; for a dose of 0.5 Gy, the DDREF would equal 1.5, and for a dose of 2 Gy, it would equal 3. If α/β equals 2 Gy, curves A and B would intersect at 2 Gy where the DDREF equals 2; at doses less than or greater than 2 Gy, the DDREF would be less than or greater than 2, respectively. This concept is illustrated with experimental data in Figure 2-8; for the induction of HPRT (hypoxanthine-guanine phosphoribosyl transferase) muta-

FIGURE 2-1 Schematic curves of incidence versus absorbed dose. The curved solid line for high absorbed doses and high dose rates (curve A) is the “true” curve. The linear, no-threshold dashed line (curve B) was fitted to the four indicated “experimental” points and the origin. Slope α1 indicates the essentially linear portion of curve A at low doses. The dashed curve C, marked “low dose rate,” slope αEx, represents experimental high-dose data obtained at low dose rates. SOURCE: Reproduced with permission of the National Council on Radiation Protection and Measurements, NCRP Report No. 64 (NCRP 1980).



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