Calculation of substrate flux using stable isotopes.

The use of stable isotope tracers to calculate substrate kinetics in humans is favored over the use of radioactive isotopes because of their greater safety and versatility. However, potential complications not met when dealing with radioactive tracers are caused by 1) the natural occurrence of the stable isotope used as a tracer and 2) the necessity to administer the tracer in an amount that cannot be treated as "massless." We therefore found it desirable to derive a theoretically valid equation for calculating the rate of appearance, Ra, of a substrate under steady-state conditions using a stable isotope tracer. This theoretically valid equation yields results that differ from those of the equations conventionally used to calculate (endogenous) Ra in steady state. Quantitative determination of the error in one of these equations revealed that for tracers commonly used in metabolic studies the error is negligible, whereas the error made in the other equation is likely to be quite high in commonly encountered situations. Finally, to allow for proper use of different definitions of isotopic enrichment that have arisen from practical considerations, we use the results derived above to determine valid equations for Ra appropriate to the two prevalent definitions.