32 RADIOISOTOPES IN BIOLOGY AND AGRICULTURE 



imental observations are not difficult and that the application of the equa- 

 tions reciuires little more than algebraic manipulation. 



The procedures may perhaps best be explained by use of the data on 

 sodium and the equations as presented in the classic paper of Gellhorn, 

 Merrell, and Rankin (75). Experimental observations, as indicated later, 

 showed that labeled Na ions injected into man or dog were removed from 

 the plasma at two exponential rates to reach an equilibrium value. The 

 process is represented schematically in Fig. 1-7. By extension of the 

 reasoning used for Eq. (1-22) it can be shown that the change in plasma 

 of labeled sodium per unit time may be expressed (original notation used) 

 as 



^AT* AT* M* AT* AT* 



(1-30) 



in each area, 



rip, Ha, Ub = number of sodium ions in each area, respectively 

 Ta = number of sodium ions passing from plasma to 



area A and vice versa per unit time 

 Tb = as above, but from plasma to area B 

 By expressing Eq. (1-30) in terms of A'^* and concentration, the follow- 

 ing is derived by integration: 



Cp - Ce, = aie-^'' + 026-'=' (1-31) 



where Cp = plasma concentration of labeled Na at time t 



Ceq = plasma concentration of labeled Na at equilibrium 

 «i, 02 = concentration constants 



6i, 62 = rate constants for transfer to areas A and B, respectively 

 This equation is based on the assumptions that the volumes of the com- 

 partments remain constant, that there is no loss of labeled sodium during 

 the experiment, and that the rates of transfer in and out of the plasma are 

 equal for any one compartment. 



Before consideration of the physical meaning of Ec^. (1-31) it may be 

 helpful to go through the steps by means of which the numerical values 

 of the equation are derived from the data. The data are taken selectively 

 from the paper of Gellhorn et al. (75). Column 2 of Table 1-6 presents 

 the observed concentration of labeled Na in the plasma as a function of 

 time after injection. It may be noted by inspection that there was a 

 rapid initial drop with a leveling off at the equilibrium value after about 

 30 min. This gives a value of 1000 for Ceq, and column 3 gives the cal- 

 culated values of Cp — C,-„ for purposes of plotting. Figure 1-7 presents 

 the plot of Cp — Ceq on a log scale vs. i on a linear scale. Extrapolation of 



