PRINCIPLES OF RADIOLOGICAL PHYSICS 



125 



be found in Table 1 of a paper by Carlson (1941). The total frequency of 

 breaks per cell, /, may well become larger than 1; in fact, it increases 

 steadily in direct proportion to the radiation dose: 



f(D) = aD 



(50) 



2 

 o 



I- 

 o 

 < 



u. 



o 



2 



> 



q: 

 to 



0.01 



0.001 



The probabilities v and /i pertaining to the passage of particles and 

 X rays through matter have a primitive significance, as explained in 

 Sect. 2, and do not represent the net statistical result of complex back- 

 ground phenomena. On the contrary, the probability a is introduced in 

 Eqs. (49), (49'), or (49") as a purely empirical constant, which character- 

 izes the slope of semilogarithmic plots such as the one in Fig. l-77b. 



A more substantial understanding of the significance of a requires an 

 understanding of the mechanism through which the observed "events" 

 arise from the action of radiation. This question is also often raised in 

 the opposite way by asking: What clues does the simple law (49) give 

 regarding the mechanism of action? 

 How can the rate of action, a, be 

 defined in a most significant way? 



5-2b. Range of Validity of Exponen- 

 tial Curves. In order to evaluate the 

 significance of the simple exponential 

 dose-effect curves, consideration should 

 first be given to whether the mathe- 

 matical expression (49) describes the 

 observed facts over a limited range of 

 doses only or over a very wide range. 



Some experimental survival curves 

 of unicellular organisms follow an ex- 

 ponential curve quite closely down to a 

 very minute fraction of survival (see 

 Fig. l-77b). In other instances the 

 semilogarithmic survival plot flattens 

 out at a low level, as in Fig. 1-78, indi- 

 cating that a small proportion of the initial cell population displays a 

 special resistance to radiation. 



It may be asked, in general, what is to be expected if the different 

 organisms of the population tested are not homogeneous with respect to 

 radiation resistance. This implies that the probability a of a biological 

 event has different values for different groups of the population. If so, 

 the survival curve has a trend similar to that of a narrow-beam absorption 

 curve of non-monochromatic X rays (see Sect. 4-3b) whose absorption 

 coefficients have different values for different monochromatic components. 

 This trend shows an upward curvature in the semilogarithmic plot of Fig. 

 1-66, and a corresponding curvature should appear in Fig. l-77b. The 



0.0001 



40 60 80 



DOSE, kr 

 Fig. 1-78. Exponential dose-action 

 curve (killing of E. coli) flattened at 

 the end, thus showing the existence 

 of a more resistant component 

 strain. This strain, after isolation, 

 yields the dotted dose-action curve 

 {Witkin 1947.) 



