Models of hepatic drug elimination

The liver is, by nature, heterogeneous. It contains a complex vascular network for blood flow and a stationary phase consisting of enzymes within parenchymal cells. Several physiological processes, therefore, may combine to give observed ranges in drug elimination. Net changes in concentration are a consequence of a series of steps: uptake of substrate into liver cells, enzymatic reactions within the cells, release of metabolites and unconverted substrate from the cells into the sinusoids, and the net flow of the perfusing medium in the vasculature. In addition, substrate binding to proteins in the blood and in the liver can influence hepatic elimination. An understanding of each of these processes is necessary to fully comprehend the overall process of drug elimination, and these processes must be accounted for, either individually or by grouping and approximation, if a model for drug elimination is to be developed. Existing models of hepatic elimination may be classified according to their treatment of mixing within the vasculature and whether or not the model explicitly accounts for mass transfer between the heterogeneous phases of the liver. Four major classes may be defined: 1. Nonparametric homogeneous models, which assume that either complete mixing or no mixing occurs within the vasculature of the organ. 2. Homogeneous mixing models, which allow for a range of mixing phenomena. 3. Heterogeneous micromixing models, which allow for mass transport between the cells and vasculature and describe mixing within the vasculature on a microscopic level. 4. Heterogeneous compartmental models, which also describe interphase mass transfer but assume complete mixing on a microscopic level, and therefore use a time and spatially averaged approach to model mixing. The utility of these models of hepatic elimination will be critically assessed based upon (1) their ability to account for the influence of the aforementioned physiological processes upon elimination; (2) the data requirements of the model, in addition to its mathematical complexity and ease of use; and (3) the range of compounds and metabolites which may be described using the model.