108 THE SHORTER-TERM BIOLOGICAL HAZARDS OF A FALLOUT FIELD io? to b tT eT 100 Tee et T v 1000 Perret my T T TT 10,000 TTT Yy T TO rr Try QUANTITIVE ESTIMATION OF RADIATION INJURY AND LETHALITY sequences of the fundamental postulate that Wedefine the new variable radiation lethality is a consequence of physi- ologic injury. Therefore a correct, description i L |. of lethality can only follow from correct conceptions of the nature of physiologic injury and recovery. Despite the complexities that have been pointed out (and others that have not been considered) the prediction of lethal effects in man is possible if we can identify the “4 & 4 # tole ' C K4 c 7 = C 8 = c uf . thy L. ew As Z £ zE L s é ti L. al oo e Ao 4 /* J 4 oon T L£ T Ld 1 if o 4‘ £7 4° + si04 4 ar A ios 4 . lo 410° 10% r Pedi 10 Lredbdind tit 100 AFTER SURVIVAL, 1 . OOF ioé t a. L 10 i 7 10 100 lo days Frours 5.—Cumulant lethalily functions for several experimental species, based on all available data. DETERMINATION OF TILE CUMULANT LETHALITY FUNCTION FROM DATA ON TIME-DEPENDENT EXPOSURES In the previous gection, lethality functions for several species were obtained from data on 4 F 14 io" a + ‘ physiologic correlates of the various components of the lethality function. 4 /B SOE 1 . 3 bL. J Sk / a a 0 Wa, ‘fe - - ach at ie * TE 2 3 1? a 4 8 4 The curves are ever, the validity of the basic postulates of the exposure patterns, In this section it is shown that the cumulant lethality function may be deduced from data on time-dependent exposures. The comparison of the derived cumulant function with one determined directly permits a test of the consistency of the model. To simplify the derivation, the integral equation for injury will be solved for timedependent exposure on the assumption of linear effectiveness (Equation 12). The exposure intensity function, f(, will be written as a sum of exponentials ? platted on @ log-log grid. Note (a) lack of apectes differences in first 7 days, (b) existence of a plateau region indicating partial equilibration of the recoverable injury, (c) large species differences in the plateau level of injury, (d) appearance =P Aun of non-recoverable injury, aa indicated by final rising branch, after a latent period of several hundred days. The contribution of the empirical analysis presented thus far is to suggest that these parameters are independent and must be deter- mined separately. According to present evidence, the LDj is a poor predicter of the later phase of the recovering injury, and there is as yet no evidence that it has predictive value (16) with pal representation frome retained isotopes. + [1-40| (18) Equation 2 then becomes, with Y(é) 1, Z=f)DAc exp [—auctt~ | dr e = 3 de" f(oredr (19) (20) Thereis no need for the general solution because the limitations of the empirical data preclude the use of more than two exponential terms in Ff). The case that f() has two exponentials is nowconsidered. Let us define the new variable PaAef"ere"dr (21) The derivative of P, with respect to ¢* may be written DPy=aAef“pnedr+Awlt*) (22) 0 =PtAp where (23) _d p=t, (24) $=o(t*) (25) With 2=2, Equation 20 becomes Z=P,+P2 (26) Wealso obtain readily DZ=~—mP,\—mP2+¢ (27) D°Z=a/P\+07P2—(aArtorzd2¢+D¢ (28) for the true chronic injury, which is expressed in neoplasia and degenerative disease. There would appear to be only one methodologically sound approach to the problem of predicting lethality, that of pursuing the con- Zz duration-of-life exposure at a constant rate. It was possible to determine thereby some general properties of the injury process. Howlinear model was not tested thereby. The postulate of linearity of mechanism can be tested by using date from a numberofdifferent 109 t for the (17) se Otherclasses of exposure patterns (Hnear rise or (all, aquare wave, powerfunction, etc.) can also be solved. We can eliminate P, and P, between these to obtain (D+ (ay a) + 00)Z = (D-ronAy +aAa)e (29)