ANALOGIES WITH TARGET THEORY 345 



of s targets can be changed by a sufficiently large group of decisive proc- 

 esses, n/s is the number of such groups of targets which must be trans- 

 formed into decisive entities to produce the decisive state. 



Now it is a fact that experimental survival curves frequently have 

 shapes very similar to those of the theoretical ones, such as shown in Fig. 

 4. The question arises : how much information can we extract from this 

 comparison of experimental and theoretical curves? If in our experi- 

 ments we could measure both the effect and the dose to any desired 

 precision, we could determine in/r and 7i/s forthwith. This, of course, 

 would be a great help. However, in most cases our experimental ac- 

 curacy is far too low to permit unequivocal determination of these quan- 

 tities. Let us consider those curves in Fig. 4 which represent the survival 

 function of Eq. 1 for the two simple cases where m/r = 1, n/s = 2 

 (curve 2) and m/r = 2, n/s = 1 (curve 3), the value of h being constant. 

 When we adjust the abscissae to make the 50 per cent survival points 

 coincide, we find that these simple curves have surprisingly similar 

 shapes. In fact, they are so similar that currently available experi- 

 mental techniques are entirely too inaccurate to enable us to distinguish 

 between them on the basis of shape alone. If h were known, they could 

 be distinguished by the difference in slopes of curves 2 and 3, but un- 

 fortunately the evaluation of h involves additional data which almost 

 always are lacking. 



The foregoing difficulties are enhanced when we consider that the 

 radiobiological properties of a given cell species may vary quantitatively 

 from individual to individual. In fact, many persons have maintained 

 that the exponential and sigmoid shapes of experimental survival curves 

 are entirely due to such biological variation, that is to a frequency dis- 

 tribution of radiosensitivities. Some notion of the validity of this claim 

 can be gained from consideration of the frequency distributions necessary 

 to account for the shapes of the experimental curves. For convenience 

 let us consider experimental data which fit simple theoretical curves such 

 as shown in Fig. 4. Then the corresponding frequency distributions are 

 readily calculated, since each is the negative derivative of the appropriate 

 special case of the survival function : 



d{N/No) d 



dD dDl 



i-a-Y) 



njs 



(4) 



where Y is defined by Eq. 2. In Fig. 5 are shown the frequency-distribu- 

 tion curves which result from assigning various small integral values to 

 m/r and n/s. It will be noted that, whenever m/r times n/s is greater 

 than 2, the pertinent frequency distribution has a shape which corre- 

 sponds reasonably with general observations of variations in biological 



