396 



ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 15 



but rather to consider the actual amount u of the eliminated (or accumulated) 



tracer. The rate of elimination (or of accumulation) can sometimes be 



represented by 



Am ,. . , , _,... . . . ,, 



• microcuries/day 



At 



= —a,\e k t t — • 



+ bxe-^ + 



The total amount eliminated during the interval of time to t is then 



u = —kidi(l — e~ klt ) — ' • • + b\hi(l — er hlt ) -+-••■ microcuries 

 A second example of accumulation sometimes occurs when an essentially 



100 



o 



< 



o 



o 



UJ 

 Q. 



10 



TIME 

 Fig. 111. Simple uptake curve. The uptake curve x(t) is subtracted from the constant a 

 to obtain c~ ki from which the parameter k can be determined by inspection. This method 

 presumes only one component to be present and that measurements are continued long 

 enough to enable a reasonable value of a to be estimated. 



foreign substance is introduced into the system. If it is introduced into 

 phase A from which it is transfered to phase B by a first-order reaction, the 

 amount accumulated and fixed in B is 



Mb = m (1 — e kt ) 



microcuries 



while the amount remaining in A is u a = u e~ kt . The specific activity of the 

 substance does not change; the substance is not normal to the system, and 

 the ratio of tagged to untagged molecules remains constant in any process. 



c. Constant Uptake Rate and Exponential Elimination. When the rate of 

 uptake of labeled molecules is maintained at a constant value of p micro- 



