Analogue tracers and lumped constant in capillary beds

The lumped constant is a proportionality factor for converting a tracer analogue's metabolic rate to that of its mother substance. In a uniform system, it is expressed as the ratio of the tracer analogue's extraction fraction (E*) to the extraction fraction of its mother substance (E). Here we show that, in capillary beds perfused by unidirectional blood flow, unequal concentration gradients of the tracer analogue and of the mother substance influence extraction fractions both locally and across the organ and that the direct proportionality of E* and E must be replaced by ln(1-E*)/ln(1-E) to yield Λ, i.e. the lumped constant derived from first principles of bi-substrate enzyme and membrane kinetics. In other words, at a given capillary blood flow (F), the ratio of systemic clearances (FE*/FE), often used in compartmental kinetic analysis, must be replaced by the ratio of the intrinsic clearances, [-F ln(1-E*)]/[-F ln(1-E)]. The conclusion is supported by 2-[(18)F]fluoro-2-deoxy-D-galactose removal kinetics in pig liver in vivo from previous publications by the dependence of E*/E and the independence of Λ, on blood galactose concentration. Moreover, our corrections to the results of compartmental kinetics are quantified for comparing extraction fractions in different regions of interest (e.g. by positron emission tomography) and for calculating Λ using whole-organ E* and E measured by arteriovenous concentration differences.