THE SHORTER-TERM BIOLOGICAL HAZARDS OF A FALLOUT FIELD the weight effect in groups of male Sprague-Dawleyrats given 4,3, or 16r 6 days per week beginning at 53 days of age [16]. Weight effect, H(#), is defined as E(Q =log CQ log RY —log Cotlog Ry where logarithms are in several physiologic systems, and the degree of lethal injuryis a sum of these. 2. Injury from other causes, and in par- ticular accumulatedinjury due to ageing processes, also contributes additively to the lethal injury Figure 24 givea the result of a graphical differentiation of the H(® curve in Figure } ‘nypotheses1s limited, as is discssed balow. DIST r/day Wp ()- 025) 20 WEIGHT EFFECT Ete} he 685 r/doy |_——> > 3 A E0G We )] ° 3 0.1 i These are postulated properties of the model system, They are Aypotheses about the properties of reel blological systems, Their value as DERIVATIVE OF DAILY DOSE RESPONSE 1. Radiation in general produces injury Figure 28, the same measure of effect is applied to the at 53 days of age. g (14, 17, 18]. to base 10, C(f) is control weight at time t, R(t) is weight of irradiated animals at time t, and Cy and Ro are mean Weights over the pretreatment period. In eight response of male rats given a single dose of 200 r 7O) ° a 3° Figure 1 shows The properties of the lincar model may be expressed in the following set of postulates nl An example of an experimental test of the additivity hypothesis is given in Figures land 2. OTS, with the size of the dose, 6 pendent of the effects of the other incremenis. 1.002 232 3 3 about the combined effect: of a sequence of dosages is the additive hypothesis which states that the effect produced at a given time is the sum at that time of the effects of the dosages given separately in their proper positions in the sequence. This implies that every incremeni of dose produces an effect that is inde- 1.003 loos depth of the minimum and alse with respect to the W, an injury response with a characteristic amplitude and time-course. The simplest hypothesis stable vatue reached after 60 days postirraciation, This comparison is not quantitative, because of the difficulty in obtaining reproducibility of weight responser after siugle doses of 200 r or less, However, the comparison of hematologic respouses to single and daily doses yields results of a similar nature, It is concluded (171 Ghat the responses to simall dases may be additive, but the departure from additivity inereases 0.005 Wo (tH them. We knowthat a single dose produces 0.006 2 increments and of the time intervals between C.007 °° When several increments of exposure are given sufficiently close together, the physiologic response is some function of all the dose for rais given 161 daily. The daily dose weight curve van be accounted for on the busis that each daily dose produces by itself a weight response as in Figure 2A, Uf the enurves in Figure 24 and 2H agres, the additivity hypothesis is upheld. There is agreement in overall amplitude of the firsé peak, and in the presence of two peaks of effect separated by a minimum at about 14 days, There is disagreement with iespect to the eo A GENERAL LINEAR MODEL OF RADIA. TION LETHALITY 103 QUANTITIVE ESTIMATION OF RADIATION INJURY AND LETHALITY SINGLE DOSE RESPONSE—L5 OG 102 100 110 120 130 uo 1 TIME - DAYS Froure 1.—Effect of daily X-ray exposure on weight of growing rats, expressed ag the difference of logarithms of etperimental and control weights. Upward displacement signifies weight loss in treated groups. O15) 010) Osi TIME (DAYS) Ficurn 2.—Observed and calculated response of growth curve following single exposure to X-rays. Lower observed effect of a single dose of 200 7. Upper curve is a graphical differentiation of the curve for daily 13.7 r/day in Figure 1. curve ia the exposure at