RADIATION INJURY AND LETHALITY 



453 



point, which may be the mean or median animal of the population. 

 We postulate that there exists a single-dose injury function, or impulse 

 injury function, which has the value (f)(t - t) at time t after a unit 

 impulse dose delivered at the earlier time t. If exposure is administered 

 as a function of time, /(r), the course of injury will be described by the 

 integral equation 



X{t) = 0t- f I{T)4>{t - t) dr (1) 



where the term ^t describes approximately the accumulation of injury 

 due to natural aging (see above, p. 446). We further postulate the exist- 



100 150 



Time, days 



Fig. 7. Cumulant lethality function for ABC male mice, exposed at dose rates rang- 

 ing from 20 to 1000 r/day. For exposure at a constant rate for the duration of life, 

 the cumulant lethaUty function is given by (33) : 



Cl 



^\i}-t) 



where ti and /o are mean or median survival times for the exposed and the control group, 

 respectively. The major characteristics of the Cl as determined by the mean survival 

 times of treatment groups may be observed in the mortality rates witliin single popu- 

 lations exposed at constant dose rates (37). 



ence of a lethal bound of injury M, such that X{t) = M at the time 

 when the representative animal succumbs. For the special case that 

 7(0 = constant, this equation can be solved simply, giving 



1 r'^ 1/ ti\ 



MJo I\ to/ 



(2) 



where the term on the left is the integral of the impulse lethality func- 



