Sec. 15.2] THEORY OF TRACER METHODS 391 



procedures, its particular usefulness is to be found in problems where the 

 total quantity of a substance must be ascertained without at the same time 

 disturbing the system in which it occurs, such as determinations of total body 

 water, or of certain amino acids in humans in vivo, or in problems where 

 quantitative recovery together with a high order of purity is otherwise 

 impossible. 



In principle the method consists in adding to the system containing the 

 substance to be analyzed a small quantity of the same substance that has been 

 tagged with a radioactive or rare stable isotope. After complete mixing has 

 taken place, a sample of the substance is isolated with the requisite purity 

 and analyzed for its content of the tracer isotope. The dilution of the isotope 

 is then directly related to the total quantity of the substance with which 

 mixing can occur. In practice the major difficulty sometimes lies in syn- 

 thesizing with a labeling agent the compound to be used. Furthermore, for 

 measurements in vivo it is necessary that the substance is neither eliminated 

 nor produced in appreciable quantity during the course of the experiment; i.e., 

 the system must be in static or quasi-statie equilibrium during the experi- 

 ment. In simple solutions and mixtures this difficulty usually does not exist, 

 but in metabolizing systems some caution must be exercised. 



When the labeling agent is a radioactive isotope, computation of the total 

 initial quantity of substance in the system from the observed dilution is 

 simple. Denoting the specific activity of the material introduced by X\ and 

 that of the sample afterward taken from the system by X2, the total quantity 

 of diluent [1,2] is 



6H 



Q = q [— — 1) gm or cc 



where q is the quantity of labeled material added. 



The situation with regard to stable isotopic tracers is somewhat more 

 involved so far as measuring the isotopic concentrations is concerned. Both 

 diluent and labeled material contain the two isotopic species; the former 

 contains both isotopes in their normal abundance, and in the latter the rare 

 isotope is enriched by an arbitrary but accurately known amount. For 

 this reason it is more convenient to express isotopic concentrations in atom 

 per cent excess (per cent in excess of normal abundance) rather than atom per 

 cent. In most applications of the dilution method there is only a single dilu- 

 ent and carrier (labeled substance), and only two isotopes to consider. The 

 total quantity of diluent [1,2] is then 



(a - ■) 



<2 = <7^M^-1) gmorcc 



