Interconnected-tubes model of hepatic elimination: steady-state considerations

In the interconnected-tubes model of hepatic transport and elimination, intermixing between sinusoids was modelled by the continuous interchange of solutes between a set of parallel tubes. In the case of strongly interconnected tubes and for bolus input of solute, a zeroth-order approximation led to the governing equation of the dispersion model. The dispersion number was expressed for the first time in terms of its main physiological determinants: heterogeneity of flow and density of interconnections. The interconnected-tubes model is now applied to steady-state hepatic extraction. In the limit of strong interconnections, the expression for output concentrations is predicted to be similar in form to those predicted by the distributed model for a narrow distribution of elimination rates over sinusoids, and by the dispersion model in the limit of a small dispersion number D(N). More generally, the equations for the predicted output concentrations can be expressed in terms of a dimensionless 'heterogeneity number'H(N), which characterizes the combined effects of variations in enzyme distribution and flow rates between different sinusoids, together with the effects of interconnections between sinusoids. A comparative analysis of the equations for the dispersion and heterogeneity numbers shows that the value of H(N)can be less than, greater than or equal to the value of D(N)for a correlation between distributions of velocities and elimination rates over sinusoids, anticorrelation between them, and when all sinusoids have the same elimination rate, respectively. Simple model systems are used to illustrate the determinants of H(N)and D(N).