Sec. 16.5] 



INTERNAL DOSIMETRY 



423 



di 



I Au{R,t)e-» R 



dV 



Jv R 2 



and the accumulated dose received in an interval of time T is 



r/sec 



A-/ r * 



A 



The subscript i indicates the dose delivered by one monoenergetic gamma- 

 ray component. It will, however, be dropped with the understanding that 

 the formulas refer only to one component. The factor / is a constant for 

 conversion to roentgens, assuming that the tissue is uniform in density and 

 composition, and A is a constant giving the number of gamma rays of a 

 particular energy emitted per microcurie of active substance. If gamma rays 

 of more than one energy are present, the actual dose is the sum of the doses 



delivered by the components d = > di and D = > Di. 



i i 



In practice, evaluation of the dose integral above is possible only after 

 the most extreme geometrical and 

 physical simplifications are introduced. 

 The volume V can take only the most 

 elementary geometrical forms such 

 as spheres, cylinders, disks, and ellip- 

 soids. These shapes may, however, 

 often be used to approximate a given 

 organ or animal. Formulas for dose 

 calculations with these forms are given 

 in Sec. 16.7. The density u(R,t) of 

 radiative material, in microcuries per 

 gram of tissue, may sometimes be 



regarded as a point source, as in the case of radium needles, but usually it is 

 assumed to be constant throughout the tissue within a certain region or 

 organ; nevertheless, because of metabolic processes and radioactive decay, 

 the activity density is, in general, dependent on time. Only in the single 

 instance of a long-lived isotope that remains fixed in the tissue can u be 

 considered a constant. In other cases, when the rates of accumulation and 

 elimination are known, u may be estimated with formulas given in Sec. 16.6. 



Assuming the active material to be distributed uniformly in a particular 

 region, organ, or entire animal that is essentially constant in tissue density 

 and composition, the dosage rate and total dose at one point due to gamma 

 rays of a particular energy can be computed from the somewhat simpler 

 formulas 



d = IAu{t)g r/sec 



D = I A U(t)g r 



Fig. 117 



