132 



RADIATION BIOLOGY 



5-3. "SIGMOID" DOSE-EFFECT CURVES 



Most dose-effect curves are of the "sigmoid" type shown in Fig. 1-81. 

 The initial flat portion of the curve indicates that no macroscopic bio- 

 logical effect is detected until a certain amount of latent action of radia- 

 tion has accumulated. The flattening of the curve at high doses means, 



100 200 



DOSE, arbitrary units 

 Fig. 1-81. Example of a sigmoid dose-action curve. 



more trivially, that the effect is approaching completion. (The same 

 flattening is observed also in exponential curves as shown in Fig. 1-77 

 where the ordinates are plotted in the opposite direction.) 



In principle a detailed analysis of the shape of sigmoid curves should 

 provide substantial information on the accumulation of latent action 

 which must precede a detectable effect. In practice such analyses have 

 not been successful. 



From the standpoint of the target theory, an effect which follows a 

 sigmoid curve is visualized as resulting from a definite number of latent 

 "single-hit" effects. This interpretation appears c^uite plausible in a few 

 instances in which there are good clues regarding these "single-hit" 

 effects. For example, certain rearrangements of chromosomes which 

 result from radiation treatments involve a breakage of two chromosomes. 

 The individual breakages appear to constitute "single-hit" phenomena 

 whose occurrence is a prerequisite for the completion of the rearrange- 

 ment. In some instances the frequency of single breaks has been 

 observed to follow a "single-hit" curve (see Sect. 5-2a) whereas the fre- 

 quency of rearrangements follows a sigmoid curve (see Sax, 1940). 



On the other hand, in the absence of clues regarding the nature of the 

 prerequisite "single-hit" effects the definite model suggested by the 

 target theory represents only a speculation of uncertain significance. 

 Some information on the mathematical development of the target theory 

 is given here for the purpose of orientation. 



Consider an observable event which results from the occurrence of a number n 

 of latent "single-hit" events. As long as the dose D remains low, each "single- 

 hit" event has a small probability of having occurred and this probability is 



