Fig. 1.

Model scheme describing the hepatobiliary disposition of TVP and metabolites in rat isolated perfused livers. The rate of change in the amount of TVP in perfusate flowing into the first sinusoidal compartment with respect to time, , was determined by multiplying the inflow concentration (C_in) by the perfusate flow rate (Q). The rate of change in the amount of TVP in the outflow perfusate from the final sinusoidal compartment with respect to time, , was determined by multiplying the outflow concentration (C_out) by Q. Based on the well-stirred model (Pang and Rowland, 1977a,b,c), C_out was assumed to be equal to the concentration in the final sinusoidal compartment, C_EC,5. The uptake clearance of TVP from the sinusoidal space to the hepatocellular space was described by CL_UP, whereas CL_BL described the efflux clearance from the hepatocellular space to the sinusoidal space and CL_Bile described the clearance of TVP from the hepatocellular space to bile. The biliary excretion rate, , was determined by multiplying the intracellular concentration of TVP (C_IC) by the biliary clearance CL_Bile, as detailed in the differential equations. In the case of polycystic kidney rats, the biliary excretion rates of TVP and DM-4103 + DM-4107 were best described by including transit compartments (X_Bile,1–5 and X_{03,07,Bile,1–5}, respectively) and transit rate constants (K_Lag,Bile and K_{Lag,Bile,03,07}, respectively) following the excretion of these compounds into bile (denoted by the gray shading). Cytochrome P450–mediated biotransformation of TVP into DM-4103 + DM-4107 and other metabolites occurs in the hepatocellular space, and the formation of these metabolites was described by the clearance parameters CL_03,07 and CL_Met, respectively. Once DM-4103 and DM-4107 were formed in the hepatocellular space, the hepatobiliary disposition of these metabolites was described with similar clearance parameters as those for TVP, while an uptake clearance parameter for DM-4103 + DM-4107 was not necessary to describe the metabolite profiles. The hepatobiliary disposition of other TVP metabolites could not be assessed directly because only TVP, DM-4103, and DM-4107 concentrations were quantified. Here, X_EC and X_IC denote the amount of TVP in the extracellular and intracellular space, respectively, and X_03,07,EC and X_03,07,IC denote the amount of DM-4103 + DM-4107 in the extracellular and intracellular space, respectively. Likewise, V_EC, V_IC, V_03,07,EC, and V_03,07,IC denote the volumes of the extracellular and intracellular space for TVP and metabolites, respectively. V_EC and V_03,07,EC were assumed to be equal; likewise, V_IC and V_03,07,IC were assumed to be equal. The term C_IC,n represents the concentration in the nth liver compartment.