Turnover with nonidentical sources of labelled and unlabelled substance

The rate of appearance or production of a metabolite in steady state in an intact animal (e.g., the number of moles per minute of glucose or lactate which are released into the blood) is measured by infusing a tracer into the system at a constant rate. Often one can regard both the unlabelled metabolite and the labelled metabolite (tracer) as entering the system in the same fluid pool, so that as equilibrium is approached, specific activity (the ratio of the concentration of labelled to unlabelled substance) becomes constant throughout the organism. The method for calculating the rate of appearance for this case is well known. When it is not possible to infuse the tracer in such a manner, gradients in specific activity must appear. This necessitates a change in the method of calculation. The rate at which the unlabelled metabolite enters the body is now given by the rate of infusion of tracer, multiplied by the ratio of the concentration of the unlabelled substance in the pool of entry of the tracer, to the concentration of the tracer in the pool of entry of the unlabelled metabolite. Violation of this rule can produce appreciable errors in the calculation of the rate of appearance. This new rule suggests a generalization of the concept of specific activity.