114 



RADIOBIOLOGY 



equately approximated by the first two terms: 1 — np. Thus the sur- 

 viving fraction of cells becomes 



N_ 

 N 



= 1 - (1 ■ - np) 



lip. 



That is, the surviving fraction is n times what it would have been 

 for a mononucleated cell. This is entirely understandable, because n 

 times as much radiation is required to hit n times as many targets. 



Since p is the survival probability corresponding to a dose D, if we 

 express D in terms of the average number of ionizations produced in 

 the target, we can at once write the expression for p, for p is the fraction 

 of cells having no hits, if the aver- 

 age is D hits. This is just the zero 

 class of the Poisson distribution 

 again, so 



-D 



p = e 



Thus for mononucleate cells the 

 surviving fraction is 



N_ 

 No 



= p = e 



-D 



or 



i N 

 l ° g N- = 



D. 



For multinucleate cells, we had 



N_ 

 No 



np 



ne 



-D 



so that 



log 



N_ 



Nn 



log n - D. 



Both of these expressions have a 

 slope of —I). As shown in Fig. 53, 

 where log N/N is plotted against 

 D for several values of n, the 

 asymptotic slopes are parallel and 

 are n times higher than the value 

 for the mononucleate cell. Thus, if 



2 4 6 8 10 

 Dose in units of 37% survival dose 



Fk;. 53. Theoretical survival curves 



where there are n equally radiosensitive 

 nuclei per cell. The curves are plots 

 of the expression in the text: 1 — 

 (1 — e~ D ) n , where // is the number of 

 nuclei and D is the radiation dose in 

 units of the 37% survival dose. The 

 dashed-line extrapolations of the 

 straight portions of the curves give 

 the number of nuclei as the intercepts 

 on the zero dose axis. 



