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

Prediction of human pharmacokinetics—evaluation of methods for prediction of hepatic metabolic clearance

Methods for prediction of hepatic clearance (CLH) in man have been evaluated. A physiologically-based in-vitro to in-vivo (PB-IVIV) method with human unbound fraction in blood (fu,bl) and hepatocyte intrinsic clearance (CLint)-data has a good rationale and appears to give the best predictions (maximum ∼2-fold errors; < 25% errors for half of CL-predictions; appropriate ranking). Inclusion of an empirical scaling factor is, however, needed, and reasons include the use of cryopreserved hepatocytes with low activity, and inappropriate CLint- and fu,bl-estimation methods. Thus, an improvement of this methodology is possible and required. Neglect of fu,bl or incorporation of incubation binding does not seem appropriate. When microsome CLint-data are used with this approach, the CLH is underpredicted by 5- to 9-fold on average, and a 106-fold underprediction (attrition potential) has been observed. The poor performance could probably be related to permeation, binding and low metabolic activity. Inclusion of scaling factors and neglect of fu,bl for basic and neutral compounds improve microsome predictions. The performance is, however, still not satisfactory. Allometry incorrectly assumes that the determinants for CLH relate to body weight and overpredicts human liver blood flow rate. Consequently, allometric methods have poor predictability. Simple allometry has an average overprediction potential, > 2-fold errors for ∼1/3 of predictions, and 140-fold underprediction to 5800-fold overprediction (potential safety risk) range. In-silico methodologies are available, but these need further development. Acceptable prediction errors for compounds with low and high CLH should be ∼50 and ∼10%, respectively. In conclusion, it is recommended that PB-IVIV with human hepatocyte CLint and fu,bl is applied and improved, limits for acceptable errors are decreased, and that animal CLH-studies and allometry are avoided.

Reassessing models of hepatic extraction

The aim of this investigation is to compare different mathematical models of the liver in the context of in vitro-in vivo correlation. We reanalyze drugs from the Houston reviews [1, 2], and compare the mathematical models. For the well-stirred model, a particular form of the distributed tubes model, and the dispersion model, fits are done to in vitro and in vivo intrinsic clearance data from microsomal and hepatocyte experiments. The distributed and dispersion models have decreased residuals as compared to the well-stirred model, but neither is to be clearly preferred over theother. It seems likely that drug-specific factors have a major impact on the quality of IVIVC correlations. While new experiments are needed to validate IVIVC models, our results indicate that improved correlation of in vitroand in vivo data is possible for high clearance drugs by using either a dispersion or distributed tube model rather than a well-stirred model.

A compartmental model of hepatic disposition kinetics: 1. Model development and application to linear kinetics

The conventional convection-dispersion model is widely used to interrelate hepatic availability (F) and clearance (Cl) with the morphology and physiology of the liver and to predict effects such as changes in liver bloodflow on F and Cl. The extension of this model to include nonlinear kinetics and zonal heterogeneity of the liver is not straightforward and requires numerical solution of partial differential equation, which is not available in standard nonlinear regression analysis software. In this paper, we describe an alternative compartmental model representation of hepatic disposition (including elimination). The model allows the use of standard software for data analysis and accurately describes the outflow concentration-time profile for a vascular marker after bolus injection into the liver. In an evaluation of a number of different compartmental models, the most accurate model required eight vascular compartments, two of them with back mixing. In addition, the model includes two adjacent secondary vascular compartments to describe the tail section of the concentration-time profile for a reference marker. The model has the added flexibility of being easy to modify to model various enzyme distributions and nonlinear elimination. Model predictions of F, MTT, CV2, and concentration-time profile as well as parameter estimates for experimental data of an eliminated solute (palmitate) are comparable to those for the extended convection-dispersion model.

Commentary: using the convection-dispersion model and transit time density functions in the analysis of organ distribution kinetics

The convection-dispersion model and its extended form have been used to describe solute disposition in organs and to predict hepatic availabilities. A range of empirical transit-time density functions has also been used for a similar purpose. The use of the dispersion model with mixed boundary conditions and transit-time density functions has been queried recently by Hisaka and Sugiyama in this journal. We suggest that, consistent with soil science and chemical engineering literature, the mixed boundary conditions are appropriate providing concentrations are defined in terms of flux to ensure continuity at the boundaries and mass balance. It is suggested that the use of the inverse Gaussian or other functions as empirical transit-time densities is independent of any boundary condition consideration. The mixed boundary condition solutions of the convection-dispersion model are the easiest to use when linear kinetics applies. In contrast, the closed conditions are easier to apply in a numerical analysis of nonlinear disposition of solutes in organs. We therefore argue that the use of hepatic elimination models should be based on pragmatic considerations, giving emphasis to using the simplest or easiest solution that will give a sufficiently accurate prediction of hepatic pharmacokinetics for a particular application.