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ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 15 



the tracer concentration, are plotted on semilog paper with a linear time axis. 

 The separate exponential component of the resulting curve may then be 

 subtracted out as straight lines. From the analyzed curve the coefficients 

 dj are obtained by extrapolating each component back to zero time. The 

 parameters kj are also obtained from the component curves by their relation 

 to the half-times, kj = 0.693/Tj. For most purposes the half-times Tj are 

 determined with sufficient accuracy by inspection. However, unless the 



1000 



TIME 

 Fig. 110. Reduction of elimination curves of the type x = aie~*i' + atf - ** 1 + • • • into 

 separate components. Three components are shown in the diagram together with the 

 curve from which they are'reduced. The longest component is taken out first by approxi- 

 mating the straight line to which the curve is asymptotic. The remaining components are 

 obtained by successive subtractions. 



parameters kj differ in magnitude by a factor of two or more, it is often diffi- 

 cult to evaluate them, and also a,-, with accuracy or even to assign uniquely 

 the number of components that appear to be present. This becomes espe- 

 cially difficult when the number of terms exceeds three or four. In any event, 

 whether one or several components are present the physical and physiological 

 significance of the constants may not always be obvious until other phases 

 of the system are also investigated. 



A number of simple processes frequently encountered in tracer studies of 

 biological systems are described in greater detail below. It must be kept in 

 mind, however, that the expressions are valid only for systems possessing the 

 following physical characteristics: (1) only first-order reactions occur; (2) the 

 system cannot distinguish between labeled and unlabeled substance of the 

 same chemical and physical form; (3) the system, except for the tagged 

 molecules, remains in a steady state; (4) the mixing time of tagged molecules 



