368 



ENERGY LOSS AND BIOLOGICAL EFFECTS 



Assume a given cell with a single, genie "site" to be affected by radiation, 

 mediated by a known intermediate ionization product P (for example, 

 OH, HO2, H2O2). Figure 6 will give a description of its path through 

 the cell medium. P will migrate through the fluid medium of the cell 

 along an irregular Brownian path until it has a chance to interact with 

 some cytoplasmic constituent R, forming a compound to be designated 

 PR; this will happen at a radial distance r from the point where the ion 



Sequence of Events Producing Biological Effects 

 ft — End product O 



Cytoplasmic constituent or gene 



Action radius, r 

 Mean action radius, 



Q 



^. 



Diffusion path 

 Mean free path, X 



intermediate (H2O2)- 

 Radical(OH) 



I 



Positive ion (H.^O"^)- 





Ray 



Fig. 6. Graphic presentation of the sequence of events in the diffusion model. Left 

 side: The positive ions, after their production by the ionizing rays, decompose into 

 radicals and other ions. The radicals chemically responsible for the radiation effect 

 diffuse through the medium of the cell along an irregular path. Their mean free path 

 for chemical interaction is X. Most of the time these radicals are annihilated in a 

 reaction with some extragenic molecule. Occasionally they interact with a genie 

 molecule. Right side: When densely ionizing beams are available, or in ion clusters, 

 different types of intermediates may be produced; for example, H2O2 is formed in 

 water. The intermediate molecules may then diffuse and act similarly to the radi- 

 cals. 



pair and shortly thereafter P were formed. According to procedures of 

 statistical mechanics the probability that P(r), the intermediate, will 

 diffuse at least to a distance r will be 



P(r) = e"'-'/"' 



(1) 



where p is a constant p^ = 45t; t is the mean life of the radical, and 8 is 

 its diffusion constant through the medium. 



Assuming a stationary sensitive site, a gene for example, it is easy to 

 calculate the mean number of intermediate ionization products to diffuse 

 to the site of the gene when ionization was produced at random in the 

 medium. If a dose of D ev per cm^ is given, and the energy per ion pair 

 is w ev, and if jS fraction of the ion pairs produces the intermediate P, 



