Saturation kinetics in hepatic drug removal: a statistical approach to functional heterogeneity

Extraction of drugs and other substrates from blood passing through the intact liver (or other capillary beds), inferred from samples taken at the organ inlet and outlet, is influenced by two kinds of heterogeneity of capillaries: transverse and longitudinal with respect to the direction of blood flow. The transverse heterogeneity is exemplified by arteriovenous shunts of the extracting system; the longitudinal one by zones of liver function. These two clinically interesting examples are among transverse and longitudinal distributions of capillary properties that can be inferred from the way the organ transforms the influx of a substance (or of a pair of substances interacting via liver cells) into the outflux over a range of input concentrations or of rates of blood flow. Mathematical and statistical ideas recently developed to implement this program in terms of saturation kinetics of uptake are reviewed and elucidated in relation to key experiments, data analysis, and statistical hypothesis testing.