ULTRAVIOLET RADIATION AND CANCER 



547 



they double in volume in as little as 2 or 3 days. Curves illustrating 

 certain aspects of progressively accelerated growth are shown in Fig. 

 14-46. Curve I is an accelerated growth curve following Eq. (14-12) in 

 which Vd/Vo is taken as 10** and td as 150 days. The value 10** represents 

 the change from a single cell of volume 10~^ mm'^ to a tumor of 100 mm^, 

 that is, Vd- As the curve shows, such a tumor would first be grossly 

 detectable about 20 days before it reached 100 mm* volume. This agrees 

 in general with observation, since, as a rule, these tumors are not grossly 

 manifest for more than two or three weeks before thev reach this volume. 



3 4 5 6 7 



DOSE PER EXPOSURE, D 



Fig. 14-7. Relation between dose D and development time td for three different 

 intervals i. The drawn curves follow the theory of progressive acceleration of tumor 

 growth discussed in the text. The data and curves are the same as those plotted in a 

 different manner in Fig. 14-6. (From Bhini, 1950.) 



To illustrate another aspect of the problem, let us assume for purposes 

 of discussion that every tumor develops from foci of cells, the growth of 

 which foci is progressively accelerated by successive doses of radiation. 

 Let us imagine that there are two foci, one growing thus at a "fast" rate 

 and the other at a "slow" rate. If the growth rate of the fast focus 

 exceeds that of the slow focus by only a very little, the ultimate tumor 

 would arise almost exclusively from the fast focus. As shown in Fig. 

 14-46, the broken curve IV is based on the same value of Vd/Vo as is curve 

 I, but is calculated for a slightly lower acceleration. At 150 days, when 

 curve I arrives at volume 100 mm'*, curve IV is only about 10 per cent as 

 high, yet curve IV if continued reaches 100 mm* only 10 days later than I. 

 The slow focus represented by curve IV would contribute only 10 per cent 

 to the total tumor volume at time td- If it is assumed that there is some 



