PRINCIPLES or RADIOLOGICAL PHYSICS ' 123 



5-2. SIMPLE DOSE-EFFECT RELATIONS 



The relation between the amount of energy dissipated in a material 

 and the magnitude of the resulting effects has been the object of much 

 study. The interpretation of this relation depends on the following line 

 of argument : If the exposure of a material to successive equal amounts of 

 radiation contributes equal increments to the over-all effect, each sep- 

 arate amount of radiation appears to act independently of the others. 

 This is the simplest situation. 



On the other hand, if successive equal doses contribute increasingly to 

 the macroscopic effect, the action of each portion of the treatment appears 

 to combine with some latent effect of earlier exposure. An attempt is 

 then made to obtain additional evidence on the combined effect of differ- 

 ent partial exposures from more detailed features of the dose-effect 

 relation. Most chemical effects and a large number of biological effects 

 of radiation follow simple dose-effect relationships. 



For example, radiation induces a delay of cell division of corneal epithe- 

 lium (Friedenwald, 1951) which varies in proportion to the radiation dose 

 from 50 to 4000 r. This and other earlier similar discoveries of simple 

 effects on time delays and other variables have not led to fully successful 

 interpretations. As mentioned before, attention has centered partic- 

 ularly on other types of effects. 



5-2a. Exponential Curves. When a macroscopic effect of radiation is 

 measured by the frequency of occurrence of a certain event within a pop- 

 ulation, the rule of "equal effect for equal dose" leads to the following 

 result. Suppose that a certain amount of radiation produces the event 

 under consideration in 10 per cent of the population. Then an additional 

 equal dose would produce the event in another 10 per cent of the remain- 

 ing 90 per cent of the population, which were still unaffected. A third 

 additional equal dose would produce the event in the 81 per cent which 

 remained unaffected after the second dose, and so on. 



This situation presents a complete formal analogy with the statistical 

 occurrence of collisions along the tracks of particles, which was discussed 

 in Sect. 3-6a. It is described by the same mathematical law as Eq. (27). 

 Here we indicate by iVo the number of organisms exposed to the radiation 

 treatment and by N{D) the number of organisms in which the event has 

 not yet occurred after exposure to a dose D of radiation. The frequency 

 of nonoccurrence of the event varies as a function of the dose according 

 to the law 



mm - .-«. 



(49) 



or 



In NiB) = In iVo - aD (49') 



