548 



RADIATION BIOLOGY 



sort of distribution of the rates of growth of the tumor cells, only those 

 growiii{>; near the maximum rate would contribute appreciai)ly to the total 

 tumor volume. If there were many foci of tumor cells in close proximity, 

 those which proliferated most rapidly might so far outstrip the others that 

 the tumor when finally formed would be composed almost entirely of cells 

 arising from fast-growing foci. 



We have not yet accounted for the maximum limit of growth rate repre- 

 sented in the curves by the failure of increase in dose to decrease the time 

 to appearance of tumors after a certain value D„, is reached (see Figs. 14-0 

 and 7). It must be obvious that there is a maximum rate of growth which 



otioo r 



o 



s 



5 80 



o 



O 



UJ 



o 



< 



60 



UJ 



u 



UJ 



a. 



UJ 



> 



< 



_j 



o 

 u 



40 



20 



END OF 

 - EXPOSURES 

 CD CE CF 



1,9 



2.0 2.1 2.2 2.3 2.4 



TUMOR DEVELOPMENT TIME fi'^j, log days 



Fig. 14-8. Effect on development time of discontinuation of dose. In series CF, CE, 

 and CD the exposures were discontinued at the times indicated. In series CH the 

 dosage continued until the appearance of tumors. {From Blum, 1950.) 



a tumor cannot exceed. Physiological factors, for example, the rate at 

 which materials for growth can be supplied, must set an upper limit. So 

 progressive acceleration of growth, which is the essence of this theory, 

 could be pushed only to a certain point, and, acceleration being directly 

 related to dose, a maximum should be reached beyond which increase in 

 dose would not increase the rate of development. This is what appears 

 to happen. It seems probable that the minimum value of ta in the three 

 curves in the figures corresponds to a common maximum rate of prolifer- 

 ation which cannot for physiological reasons be exceeded. Numerically 

 this condition is satisfied. 



According to the model illustrated in Fig. 14-5, if the exposures were 

 stopped, a tumor should continue to grow at the rate that was established 

 at the time the exposures ceased. In a certain number of experiments the 

 doses of ultraviolet radiation were stopped before tumors appeared, with 

 a resultant increase in /,/. This is illustrated in Fig. 14-8, where it is shown 

 that the earlier the doses were discontinued, the longer was td. In Table 



