logical Indicators 1S and leukemia numberof aberrations per exposed cell, is a measure of the severity of effect that has prognostic value for any individual exposed person. Furthermore. the sensitivity of the methodis low: Excess leukemia cases/10,000 PY F 10 27 Bond differences cease to be significant below perhaps 0.1 or .15 Gy. Thus these approaches cannotbe used to provide significantly more information than does dose, with respect to the probable fate of any given irradiated individual. Nonetheless, Figure 7 doesillustrate clearly the important point that a “biological dosimeter” does not require conversion to dose to be useful in predicting excess in the incidence of cancer in an exposed population. One can, if the system is appropriately calculated, readily determine the expected excess incidence directiy from the biological indicator of the severity of effect. Thus, for the present, and no doubt for some 2 fraction of cells *excess leukemia bomb survivors, about 1.5 Gy. time in the future when the situation may be changed entirely by increased knowledge gained through molecular biology and related approaches, potential cancer cannot be approached on a medical basis, i.e., from the standpoint of determining the severity of effect on an individual as indicated by a causative biological marker. and taking some course of action with respect to advising or treating the individual. Rather, the presence or absenceof cancer in individuals must be regarded as a public health problem. With respect to Figure 1 , this meansthat the biologicalentity of interest must be a defined human population which has been exposed to a carcinogen such as radiation, and the system elements ofinterest are those individuals who have been exposed and who may develop, or actually have developed, a cancer. ‘nship is essen- ‘e and shape of However, this ot in any way “ecision use, disease. The mosome aber- ‘NA changes, 2 proportional ges may be a given can7h at least one nor the total Again, it is useful to use a specific example and chromosome ained) such as the atomic bombsurvivors. In Figure 9 is showna dose response curvefor a selected group of survivors, some 40,000 total [3]. Shownis the excess incidence of cancer as a function of absorbed dose (Fig. 1, system-element pair B). This function is often assumed to be “linear and withoutthreshold.” It is on the basis of functions such as this. coupled with the fact that individual cell systems, whenirradiated either at tow doses or at higher doses, but at markedly reduced dose rates, also are often linear, that gives rise to the so called “linear, nonthreshold hypothesis.” The hypothesis states that what happensat low doses —_—, “| 2 #.2 39) can be deduced from what is observed at high ‘hep between aberrations Ors. »& ae UI ey f i Kae doses, and that “any amountof radiation, however smali, can be harmful, perhaps lethally so (from induced cancer).” 5i ib ‘i qd However, there are serious problems with plotting the data as it has been in Figure 9. which has the same coordinates as does the typ- ical sigmoid-shaped toxicological dose response curve for noncancer effects shown in Figure 2. In medicine, it is only the ordinate. the fraction responding quantally. that must be additive (up to saturation at 1.0). while the denominator, defined as the mean agent concentration. is not additive. The abscissa must be in this form because, in chemical toxicology. as 1s quite generally understood. the mass of the subject ts taken into account. e.g.. the subject is weighed, and the quantity e/m is multiplied by m in order to obtain the absolute amountof agent. €. to be administered (i.e.. €/m is the mean “quality” of the agent, which must be multiplied by the “quantity” in terms of mass). Only then can the responseindicated on the ordinate be observed. However, for absorbed dose on the abscissa of the curve shownin Figure 9. no indication is given that the absorbed dose, e/m. is to be muluphied by the mass. Furthermore, it is necessary to keep in mind that the ultimate aim of dealing with any dose response curves for cancer is radiation protec- tion. Here “film badges” are issued to a number of individuals. and these readings must be provided in a collective or cumulative form in order to obtain the total physical insult to the population of interest. Thus, for this reason also, the abscissa in Figure 9 cannot be the nonadditive absorbed dose. e/m in Gy. but must rather be the additive quantity, €. Such a function is shown in Figure 10. An added advantageof a plot such as that in Figure 10 is that the inverse of the slope 0.06 5 a? a6 00 oS 10 15 20 25 36 35 Absorbed Dose, D (Gy} Fig.9. The fraction of dosed atomic bomb survivors with a solid cancer, as a function of absorbed dose.