A different perception of the linear, nonthreshold hypothesis for low-dose irradiation.

Two equally useful dosimetric quantities, both of which are called dose, are used in toxicology. With radiation measurement, only one--the energy per unit mass D--is called dose. The other--the total energy in the irradiated system--is here distinguished from D by assigning it the name collective energy, epsilon. The collective energy is a more complete statement of dose because it is the product of the energy concentration D and the mass irradiated m. Especially in radioepidemiology, in which epsilon is the total energy imparted to all persons irradiated, the quantity m must be specified because it is situation specific and thus highly variable. At present, radioepidemiological dose-response curves are given only in terms of the toxicological model--i.e., the fraction (probability) of radiation-attributable cancers occurring as a function of D. Because this relation does not involve the number of persons at each value of D, it fosters the illusion that any dose, no matter how small, can result in cancer. However, we show that if the dose-response relationship is expressed in terms of the absolute number of attributable cancers as a function of epsilon, cancer occurs, on average, only if the collective energy exceeds a relatively large minimum value, the magnitude of which will be estimated. Therefore, we conclude that the nonthreshold aspect of the linear hypothesis is misleading and quite probably invalid. For example, in or around a facility in which exposure of humans to relatively low values of D occurs, attributable cancers are most unlikely to appear unless the epsilon to the irradiated population exceeds this minimum value.