434 JS0T0P1C TRACERS AND NUCLEAR RADIATIONS [Chap. 16 



the tissues that take up most activity are those with the shortest uptake 

 half-times. In any one tissue the activity density following administration 

 of u microcuries of substance is 



u = — _ Z lTz n, v 0-°- 693 ' /r ' - g-o.693 < /r 3 )g-o.693 < /r m i C rocuries/gm 

 m 1 2 {i i — I 3) 



where T = radioactive decay half-life 



T\ = half-time for removal of active substance by all processes from 

 blood, reservoir, site of injection, or precursor 



T<t = uptake half-time of activity in given tissue 



T z = elimination half-time for same tissue 

 If, as it frequently happens, the metabolic half-times are much shorter than 

 the decay half-life, the last factor, containing T, can be omitted. Under 

 this condition the maximum activity occurs when 



T X T Z T\ 



' max " 0.693(7\ - T z ) 10g T z SCC 



The disintegration function for the interval to t following administration 

 is 



0.693 (T+Ti) 



tj __ ffs TTiT 3 



m 0.693 TziTi - T z ) 



T, 



Tx + T 



(e TT > - 1) 



rr, 0.693 (T+Tz) 



1 S 



->] 



(e TTl — 1) microcurie sec/gm 



T z + T 

 as before, if T y> Ti,T 2 ,T z , then 



U = - o f. Q xJ(T Z ^m [Ti{e~™™' T * - 1) - T z (e- -™» T > - 1)] 



m 0.693r 2 (i i — Tz) 



microcurie sec/gm 



16.7. Geometrical Factor. The dosage rate in roentgens per second at a 

 certain point in an organ or animal due to a known volume distribution of u 

 microcuries of active material per gram of tissue was shown in Sec. 16.5 

 to be given by the expression 



d = IAu(i)g 



The geometrical factor g gives the contributions of all parts of the volume 

 distribution of active material to the dose at the point under consideration. 

 Assuming a uniform distribution of radioisotope and a constant tissue density 

 and composition within the volume V, then 



g = / e ~w dV cm 



