DIFFUSION MODEL 373 



We should now define relative biological effectiveness $ of a radiation 

 with REL e in terms of that of a standard radiation, for example 200-kv 

 x-rays with REL eq. The same biological effect is caused by dose D of 

 e, and dose -Do of eo- 



<!> = — (5) 



D 



In the simplest case, and neglecting the distribution of ions in tracks, 

 the criterion might be the survival of a given fraction of cells having a 

 single sensitive site. For this case from Eq. 3 



$ = 



or, with cr = o-Q, 





<!> = ^ (6) 



/3oPo 



The mathematical considerations involved in predicting the RBE with 

 radiations of different REL become involved, since one should remember 

 at this point that ionizing radiations produce entire tracks of ions 

 simultaneous^, not single ion pairs as it was assumed up to the present. 

 It is necessary to calculate the probability of diffusion of intermediates 

 to a certain distance from the center of the track. This can be done, 

 however. It turns out that, if a sensitive site is close to densely ionizing 

 tracks, then there is a high probability of its becoming inactivated. 

 However, if the ion density becomes very high, some of the ions in the 

 track will be wasted, since a single track cannot be responsible for more 

 than the inactivation of a single cell. 



It is possible to obtain approximate mathematical expressions for the 

 relative biological effectiveness, using the diffusion model and assuming 

 values for the ionic yield of different intermediates that are likely to be 

 present; further, one has to consider the heterogeneous distribution of 

 the ionization along the tracks. 



If intermediates due to formation of single ion pairs only are con- 

 sidered, the diffusion model does not explain a rise in biological effective- 

 ness of radiations when the rate of energy loss is increased. In order to 

 account for the numerous older and for the present experimental findings, 

 one is forced to assume the action of intermediates, the yield of which 

 increases with specific ionization. In the example under discussion at 

 present, since the water content of the cell is important one might draw 

 a cautious analogy with the example of decomposition of water. At low 

 REL the ionic yield of peroxide in pure unoxygenated water is low. At 

 high REL the ionic yield of peroxide is high. 



