Measuring tracee turnover from tracer specific activity in the steady state.

When a substrate appears in and disappears from an unmeasured (tissue) compartment, the proper sites for tracer infusion and sampling to measure tracee turnover become controversial. We analyze a three-compartment model representing arterial blood, tissue, and venous blood. The desired quantity, tracee turnover, is the ratio of the steady-state infusion rate to tissue specific activity. However, specific activity in the tissue compartment is unknown. We assume infusion of tracer into the arterial pool at a constant rate and consider sampling of specific activity of either blood compartment in the steady state. We obtain estimates of tissue specific activity from measurement of concentrations of tracer and tracee in blood samples in two extreme cases. In case I, tracee is assumed to appear in the venous compartment but to disappear from the tissue pool. Then tissue specific activity is equal to arterial specific activity. In case II, both appearance and disappearance are from the tissue pool. Tissue specific activity is then less than arterial or venous specific activity. We give formulas for the difference in each case. We discuss the relationship of our models to actual tracer experiments and define physiological locations for our three compartments. Appearance of substrates is probably intermediate between our extreme cases. A numerical estimate of turnover for the substrate lactate in resting humans reveals an error bound of approximately 30%. We discuss sites of infusion and sampling consistent with our model, the effects of relaxing some of our modeling constraints, and experimental necessities for getting beyond the steady state.