Sec. 16.5] INTERNAL DOSIMETRY 429 



dose at the center of the trunk of an average man to whom 0.1 mc of Na 24 

 is administered. 



Tracer investigations have shown [20] that Na 24 given intravenously 

 comes to equilibrium in the interstitial fluids throughout the body within the 

 first 10 min. Following the initial 10-min mixing period, about 27 per cent 

 of the original Na 24 is accumulated in the bones at two different rates for 

 which the corresponding half-times are 10 to 15 min and 1 to 3 hr. Finally, 

 elimination of the Na 24 from the body is found to occur exponentially with 

 a half-time of 12 to 14 days. 



The uptake in the bone structure of 27 per cent of the Na 24 does not appre- 

 ciably alter the gamma-ray dose at various points in the body. The dose 

 may therefore be calculated on the basis of a fixed, uniform distribution of 

 the Na 24 . The justification for this is evident from the fact that the half- 

 value thickness of tissue for the gamma rays from Na 24 is about 25 cm, and 

 consequently within distances of this magnitude the bone structure can also 

 be regarded as uniformly distributed. It should be borne in mind, however, 

 that calculations of the dose delivered by the beta particles to bone and to 

 soft tissue must take into account the uptake of Na 24 in bone. 



Finally, the data and approximations required for computing the gamma- 

 ray dosage rate and accumulated dose in this example may be listed in detail: 



1. Point in the body for which the dose is to be determined. The trunk may 

 be approximated geometrically by a cylinder of tissue 60 cm long and 40 cm 

 in diameter. The point under consideration then lies on the axis midway 

 between the ends of the cylinder and represents the region in the body 

 receiving the maximum gamma-ray dose. The total body weight is assumed 

 to be 60,000 gm. 



2. Effective half-time of Na 24 . The elimination half-time of Na 24 is long 

 compared to the decay half-life of 14.8 hr, hence only the latter need be 

 considered in the accumulated dose calculation. 



3. Gamma rays. Two gamma rays are emitted with energies of 1.38 and 

 2.76 mev in each disintegration (see Sec. 7.10). 



4. Absorption coefficient. The absorption coefficients for the 1.38 and 2.76 

 mev gamma rays are about 0.03 and 0.024 cm 2 per gm respectively. 



5. Distribution of Na 24 . The total quantity of 0.1 mc Na 24 is assumed to 

 be uniformly distributed throughout the cylindrical volume. 



The dosage rate at the center of the trunk may now be calculated from 

 the formula d = I Aug for each gamma-ray component and for any time 

 following administration of Na 24 . For the 1.38-mev gamma ray, the factors 

 in the formula takes the following form and values: 



1 = 4tt (S amma - ra y energy) (absorption coefficient) ( ^) y e ™™ tissue ) 



