DIFFUSION MODEL 369 



then the mean number of radicals M{D) diffusing to the sensitive site of 

 cross section a becomes 



M{D) = (2) 



w 



If a single molecule of the intermediate P is sufficient to inactivate a site 

 essential to cell division, then the number A^ of surviving cells is expressed 

 by the equation: 



N = Noe-^^"'^"" (3) 



The right side of Eq. 3 is a simple decaying exponential function of the 

 dose, resembling the single-hit survival curve of the target theory and 

 the monomolecular reactions in the intermediate theory. If there are 

 two kinds of intermediates with different ionic yields /Si, ^2 and mean 

 action radii pi, p2, the survival curve may be expressed as 



A/" __ A/" g--D/(/3i<ripi + /32<72P2)/"' (^\ 



Multiple-hit forms of the survival formula are also readily obtained. 

 Examination of Eq. 3 is worth while because this simple equation gives 

 precise and possibly measurable definition to certain quantities often 

 mentioned or described in radiobiology. 



The expression D^/iv is the number of ionization products formed per 

 unit volume in the medium, when exposed to D/iv ion pairs; jS is then the 

 "ionic" efficiency of formation of intermediates such as radicals H, OH, 

 O2H, molecules H2O2, H2S2, or other compounds capable of migration. 

 If the ions themselves are direct causes of the radiation effects, j3 may 

 be taken equal to 1. The ionic efficiency obviously depends on the 

 chemical composition of the medium and on the mean rate of energy 

 loss of the ionizing particles; /3 = ^{e). 



The product o- • p is analogous but not identical to the sensitive volume 

 of the target theory. In the diffusion model a is the "cross section" of 

 the sensitive site. If inactivation occurs every time an intermediate 

 finds itself at the sensitive site, then a corresponds to the true, geometri- 

 cal cross section. In other cases a will be smaller than the geometrical 

 cross section. The concept of o- is analogous to the term cross section as 

 it is used in nuclear physics, a may include the "cage factor," or even 

 conceivably a delayed recovery effect, p has the dimension of a distance ; 

 it expresses the mean radius to which the radicals diffuse from the site 

 of their formation before they disappear because of chemical interaction. 

 We have called p the "mean action radius" of an intermediate. Equation 

 1 shows the connection between the mean lifetime, the diffusion constant, 

 and p. As a rule, in wet tissues a -pis greater than V, the volume of the 

 "sensitive" site of the target theory. 



