PRINCIPLES OF TRACER METHODOLOGY 29 



from one phase to another under steady-state conditions. This situation 

 is analogous to simple turnover as discussed above. However, it is 

 usually denoted as an exchange phenomenon. A relatively simple sys- 

 tem, the kinetics of which have been widely studied (70 to 73), is the 

 exchange of potassium between plasma and erythrocytes. Under ideal 

 experimental conditions this may be considered as a closed two-compart- 

 ment system in that the labeled potassium ions incubated with the blood 

 will leave the plasma for stoichiometric entry into the red cells. The 

 small net movement of potassium into the cells can be disregarded to a 

 first approximation. However, a mathematical correction for this effect 

 has been described (72). The process is represented schematically in 

 Fig. 1-6. 



Ai and A2 = concentration of potassium in plasma and cells, respec- 

 tively 

 A* and A* = concentration of labeled potassium in plasma and cells, 



respectively, at time t 

 A* = Af -\- Af = concentration of labeled potassium in plasma at 



zero time 



A* A* 



-j^ = Si and -j^ = *S2 are the specific activities in plasma and cells, 



respectively, at time t 



p = rate of movement of K from phase 1 to phase 2 and vice versa 



On the basis of the reasoning developed for Eq. (1-22), it can be seen 

 that the rate of movement of labeled K out of phase 1 will be —pAf/Ai, 

 and the rate of movement into phase 1 will be p^f/^2. Therefore the 

 net movement of labeled K nnay be represented as follows: 



rl A* A* A* 



This equation can be converted to terms of specific activity and becomes 



f = _ Jl (S, - S.) (1-27) 



Substituting for S2 in terms of Si and integrating, 



Si ^1 -^ yl2e-pn(i/.4.)+(i/A,)] 



.So A1 + A2 



where So = A*/Ai. The relationship between p and ti^ is 



(1-28) 



_ OmSAiA, 

 ^'UAi + A,) ^'^^^ 



