540 



RADIATION BIOLOGY 



poses of ilhistration /,/ will be taken as 150 days, a value which is ronsistent 

 with experiment. We may assume any given volume I'l, for the tuuKjr at 

 the time (he first dose of ultraviolet radiation is applied, and calculate the 

 shape the growth curve would take throughout the course of the develop- 

 ment of the tumor if the growth rate remained constant. This is done for 

 values of I'n in Fig. 14-4a, using E(i. (14-3). In this figure curve I is based 

 on an initial volume of 10"" mm-', the approximate volume of a single cell. 

 On casual examination of this curve it seems that there is a long period of 

 time during which nothing happens, but this is only because the volume 

 diH'ing this period is too small to show on the graph. The volume at the 



50 



100 



100 



150 



150 50 



TIME OF GROWTH, days 



Fig. 14-4. Hypothetical growth curves, (a) Growth following the simple equation of 

 relative growth. Curve I, T% = IQ-s mni^; II, T^o = 10 ^ mm^; III, Fo = 1 mm^. 

 (6) Progressively accelerated growth curves. Curve I, T'o = 10~^mm2;II, Fo = 10"- 

 mm^; III, Fo = 1 nim^; IV, Fo = lO"'' mm^ but rate slightly less than for curve I. 

 {From Bhim, 1950.) 



end of 100 days is 0.2 mm^ A tumor of this size would be too small to be 

 detected grossly in the living animal. Suppose, then, that a tumor origi- 

 nated as a single cell and grew at a constant rate. No tumor w'ould be 

 grossly observable until at least 100 days after the advent of the first 

 tumor cell. We see at once that a gross fallacy is possible in those theories 

 which assume that the period previous to the actual appearance of the 

 tumor is occupied in the "induction" of the first tumor cells. The fact 

 that a tumor appears quite suddenly at a time long after application of a 

 carcinogenic agent cannot, without other evidence, be taken to mean that 

 the tumor has not been growing ever since the first application of the 

 agent. Curve II in Fig. 14-4a is based on the assumption that the tumor 

 has a volume of 10~^ mm^ at the begiiuiing of the curve, corresponding 

 approximately to 10,000 tumor cells. In this case the tumor would not 

 reach an observable volume until after 50 days. In the case of curve III, 



