A multicompartment geometric model of the liver in relation to regional induction of cytochrome P450s

A geometric, multicompartment model of the liver was developed to examine regional protein induction and to provide model output suitable for predicting the degree of induction in both the whole liver and in specific regions. The model was based on functional hexagonal arrays within the liver. A geometric representation was used to divide these functional units into five zones: a concentric periportal zone, a fenestrated periportal region that interconnects among multiple functional units, and three concentric centrilobular areas, referred to, respectively, as zones 1 through 5. The surface areas (and volumes for hexagonal cylinders) of these five zones were, respectively, 13.5, 25.2, 33.9, 20.3, and 6.8% of the total liver. The pharmacokinetic model for induction had dissociation constants (K(d)) and Hill constants (n) for interactions of transcriptional activator-ligand complexes with response elements on DNA. Estimates of regional induction were converted to color intensities to 'paint' the two-dimensional liver for a visual comparison with immunohistochemical observations. To obtain sharp moving boundaries of induced areas with increasing dose (as noted in various experiments),n values in each subcompartment must be large. To create realistic total induction curves that are relatively smooth, the differences in K(d) values between adjacent subcompartments must be less than fivefold. Because of the high n values, the low-dose induction characteristics predicted with the multicompartment liver model differ significantly from those predicted with a model that considers the liver as a single homogeneous compartment.