On the relation between extended forms of the sinusoidal perfusion and of the convection-dispersion models of hepatic elimination.

Two models of hepatic elimination, the distributed sinusoidal perfusion model, and the convection-dispersion model, are extended and then compared for first order kinetics in the steady-state. The sinusoidal perfusion model is extended by the inclusion of intrahepatic sites of mixing between sinusoids. The degree of such mixing is estimated for taurocholate elimination by isolated perfused rat livers by a comparison of anatomical and kinetic estimates of uptake heterogeneity, using previously published data. The dispersion model is generalized by the inclusion of distributions of enzyme activity along the flow. Direct comparison of the two models in the limit in which the degree of dispersion is small, allows the flow-dependence of the dispersion coefficient to be determined, thereby greatly extending the explanatory power of the convection-dispersion model. Finally, the effect of intrahepatic mixing sites on uptake by Michaelis-Menten kinetics is quantified in terms of the distributed sinusoidal perfusion model, with results which may be applicable to capillary beds in general.