Hepatic drug elimination is a major PK process contributing to loss of drug concentration in the body. The prediction of hepatic clearance (and hence drug concentrations in the body) requires an understanding of the physiology and mechanisms of the hepatic elimination process and their compilation into a mechanistic model. Several physiological models including well-stirred model, parallel tube model and dispersion model have been developed to describe the hepatic elimination process and to determine how physiological variables such as blood flow, unbound fraction and enzyme activity may influence the hepatic clearance. However, each model has distinguishing advantages and limitations, which lead sometimes to very disparate prediction outcomes. Although hepatic drug elimination has been mathematically described by different physiological models, the mass transfer phenomena in the liver has not been described from a porous media viewpoint using local volume averaging method. The inherently porous structure of the liver allows us to describe the hepatic drug elimination process based on a porous media approach such that structural properties of the liver tissue, physico-chemical properties of the drug as well as transport properties associated with the hepatic blood perfusion are included in the model.
Applying local volume averaging method and local equilibrium to the liver as a porous medium, a governing partial differential equation which takes into account liver porosity, tortuosity, permeability, unbound drug fraction and hepatic tissue partition coefficient, drug-plasma diffusivity, axial/radial dispersion and hepatocellular metabolism parameters was developed. The governing equation was numerically solved using implicit finite difference and Gauss-Seidel iterative method in order to describe changes in dug concentration with time and position across the liver following an intravenous drug administration. The model was used to predict hepatic clearance and bioavailability, which were then compared to reported observations.
The predicted values of hepatic clearance and bioavailability had good agreement with the reported observations for high and low clearance drugs. As well, the model was able to successfully predict an unsteady state of hepatic drug elimination with concentration dependent intrinsic clearance. When statistically compared to the well-stirred, parallel tube and dispersion models the proposed model suggested a smaller mean squared prediction error and very good agreement to reported observations for eight drugs. A sensitivity analysis revealed that an increase in liver porosity results in a slight decrease in the drug concentration gradient across the liver while higher tissue partition coefficient values increase the concentration gradient. The model also suggested that the bioavailability was sensitive to the interaction between unbound fraction and intrinsic clearance. This study indicates that the liver and hepatic drug elimination can be successfully explored from a porous media viewpoint and may provide better mechanistic predictions of drug elimination processes by the liver
