124 



RADIATION BIOLOGY 



The plots of these equations are identical with the plots of Fig. l-46a and 

 b. Figure 1-77 shows some corresponding plots of experimental data 

 which appear to follow the equation well. The coefficient a indicates the 

 rate of action of the radiation and its value is given by the slope of the 

 plot in Fig. l-77b. 



25 50 75 100 12 3 4 5 6 



DOSE, kr DOSE, kr 



ia) Cb) 



Fig. 1-77. Example of an exponential dose-action curve, (a) Linear plot; {b) semi- 

 logarithmic plot. 



In the exponential laws (27) and (40), which are similar to Eq. (49), the 

 coefficients v and ^u represent the probability of a particle collision or, 

 respectively, of photon absorption per unit distance of penetration in a 

 material. Similarly the coefficient a in Eq. (49) represents the probabil- 

 ity of occurrence of the "event" under consideration in an organism per 

 unit amount of radiation treatment. This significance is particularly 

 apparent in the differential form of Eq. (49), which is analogous to Eq. 

 (26): 



dN{D) 



N{D) 



a 



dD 



(49") 



The ratio —dN(D)/N{D) indicates the frequency of events which results 

 from the infinitesimal dose dD among the population still unaffected. 



In certain experiments the occurrence of a number of similar events 

 may be observed in the same organism. For example, many unrelated 

 chromosome breaks may appear in a single cell. In this example the 

 fraction of cells which show no chromosome break may follow an exponen- 

 tial function of the dose. If so, the occurrence of cells showing 1, 2, 3, 

 . . . breaks should relate to the occurrence of no breaks in the same way 

 as the occurrence of 1, 2, 3, . . . collisions along a length of track of a 

 particle relates to the occurrence of no collisions (see Sect. 3-6a). An 

 example of a case in which this expectation obtains outstandingly may 



