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The residence time distribution of noneliminated solutes in the liver can be represented by a variety of stochastic models. The dispersion model (closed and mixed boundary conditions), gamma distribution, log normal distribution and normal distribution models were used to describe output concentration-time profiles after bolus injections into the liver of labeled erythrocytes and albumin. The dispersion model and log normal distribution model provide the best representation of the data and give similar estimates of relative dispersion and availability for varying hepatocellular enzyme activity. The availability of solutes eliminated from the liver by first-order kinetics is determined by the residence time distribution of the solute in the liver and not on events occurring in the liver when a uniform enzyme distribution is assumed. Both enzyme heterogeneity (axial or transverse) and hepatocyte permeability may affect solute availability. A more complex model accounting for enzyme distribution and the micromixing of solute within the liver is required for solutes undergoing saturable kinetics.

Numerical methods have been used to compare the availability predictions of a number of hepatic elimination models when Michaelis-Menten kinetics is operative. Propranolol and galactose were used as model compounds. Lower availabilities were predicted by the dispersion model than by a segregated distribution model for both compounds. The differences in the predictions were most pronounced for models corresponding to a large variation in solute residence times in the liver. The predictions of the tank-in-series, dispersion model with mixed boundary conditions and dispersion model with Dankwerts boundary conditions were similar over all concentrations studied. Changes in blood flow and protein binding provided little discrimination between the model predictions. It is concluded that micromixing of blood between sinusoids and the anatomical sites of mixing are important determinants of availability when liver eliminating enzymes are partially saturated.

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