Sec. 16.6] INTERNAL DOSIMETRY 433 



bT 



U = 



0.693 



1 0.693 U C 



microcurie sec/gm 



After a long interval compared to T the number of atoms that disintegrate 

 in the tissue, and hence the total dose, increases linearly with time. 



If instead of being fixed in the tissue the active material is eliminated 

 exponentially with a half-time T%, the formulas above are still valid when T 

 is replaced by TiT 2 /(Ti + T 2 ), where T x is now the radioactive decay 

 half-life. 



c. In many cases the active material is taken up and fixed in an organ or 

 certain kinds of tissue at a rate proportional to the activity remaining in a 

 reservoir such as blood when the material is given intravenously or perhaps 

 when given orally. Assuming that no activity is present initially in the 

 organ and no elimination occurs, the activity density at time t following 

 administration of n microcuries is 



u 

 * = n*n? g-°- 693 ' /r >(l - g-°- 693 '^) microcuries/gm 

 0.693m to 



where T\ = decay half-life 



To — uptake half-time 

 The accumulated activity reaches a maximum value when 



. Jj_, _Tj_ 



''max " f. /iCil o T" I T SeC 



U.OVO 1 i ~\- 1 2 



The disintegration function U for the interval to / following administration 

 is 



" r L_ a _ e -o,, m) Ln _ -a^(<*±*>v 



.693 K ' 0.693(7! - T 2 ) \ 



microcurie sec/gm 



When the entire quantity u decays, the disintegration function becomes 



U = — 



m 



U = Jn 0.6931^+ T % ) m ^rocurie sec/gm 



This formula, aside from the factor 3.7 X 10 4 , represents the number of dis- 

 integrations that actually occur in the organ during a long time compared 

 to T x . 



d. A more involved case is encountered when part of the administered 

 active substance is taken up in the tissue under consideration at one rate and 

 removed at another rate. Part of the administered substance may also be 

 taken up in other tissues or eliminated directly. All such processes tend to 

 decrease the concentration in the reservoir, and if the removal is exponential 



