After fifty years of hepatic clearance models, where should we go from here? Improvements and implications for PBPK modeling

There is overwhelming preference for application of the unphysiologic, well-stirred model (WSM) over the parallel tube (PTM) and dispersion (DM) models to predict hepatic drug clearance, CLH, despite that liver blood flow is dispersive and closer to the DM in nature. The reasoning is the ease in computation relating the hepatic intrinsic clearance (CL_int), hepatic blood flow (Q_H), unbound fraction in blood (fu_b) and the transmembrane clearances (CL_in and CL_ef) to CL_H for the WSM. However, the WSM, being the least efficient liver model, predicts a lower E_H that is associated with the in vitro CL_int (V_max/K_m), therefore requiring scale-up to predict CL_H in vivo. By contrast, the miniPTM, a 3-subcompartment tanks-in-series model of uniform enzymes, closely mimics the DM and yielded similar patterns for CL_int vs. E_H, substrate concentration [S], and K_L/B, the tissue to outflow blood concentration ratio. We placed these liver models nested within PBPK models to describe the kinetics of the flow-limited, phenolic substrate, harmol, using the WSM (single compartment) and the miniPTM and ZLM (zonal liver) models of evenly- and unevenly-distributed glucuronidation and sulfation activities, respectively, to predicted CL_H. For the same, given CL_int (V_max and K_m), the WSM again furnished the lowest extraction ratio (E_H,WSM = 0.5) compared to the miniPTM and ZLM (>0.68). Values of E_H,WSM were elevated to those for E_H,PTM and E_H,ZLM when the V_maxs for sulfation and glucuronidation were raised 5.7 to 1.15-fold. The miniPTM is easily manageable mathematically and should be the new normal for liver/physiological modeling.