The multiple indicator-dilution method for the study of enzyme heterogeneity in liver: theoretical basis

The theoretical basis of the use of the multiple indicator dilution technique to account for the heterogeneous distribution (or zonation) of enzymes in the liver was explored. The microcirculation was assumed to consist of identical capillaries perfused in parallel, with enzymatic activities for drug metabolism being distributed uniformly over the upstream half (periportal or pp) or the downstream half (perivenous or pv) of the flow path, whereas all other transport/removal processes were assumed to be homogeneously distributed. Outflow dilution profiles for parent drug and metabolite were estimated by inversion of Laplace transforms or by a finite difference method. The areas under the curves for parent and metabolite, the mean transit times of parent (MTT) and metabolite (MTTM, mean time from injection of parent to exit of metabolite from organ), and their relative dispersions (CV2 or CVM2) were estimated from analytical expressions. When the influx-efflux ratio (or cellular-sinusoidal distribution ratio) for metabolite was equal to or smaller than that of the parent, the MTTM ranking was: pp < homogeneous < pv. The ranking was reversed when the influx-efflux ratio for metabolite greatly exceeded that for the parent. The presence of elimination pathways for the metabolite reduced its MTTM and CVM2, more for pp than for homogeneous and pv cases. The theory can be applied to determine enzyme zonation in multiple indicator dilution studies with use of the area under the curve for the metabolite and MTTM during prograde (from portal vein to hepatic vein) and retrograde (from hepatic vein to portal vein) perfusion.