Journal of Pharmacokinetics and Biopharmaceutics

, Volume 5, Issue 6, pp 625–653 | Cite as

Hepatic clearance of drugs. I. Theoretical considerations of a “well-stirred” model and a “parallel tube” model. Influence of hepatic blood flow, plasma and blood cell binding, and the hepatocellular enzymatic activity on hepatic drug clearance

  • K. Sandy Pang
  • Malcolm Rowland


Two commonly used models of hepatic drug clearance are examined. The “well-stirred” model (model I) views the liver as a well-stirred compartment with concentration of drug in the liver in equilibrium with that in the emergent blood. The “parallel tube” model (model II) regards the liver as a series of parallel tubes with enzymes distributed evenly around the tubes and the concentration of drug declines along the length of the tube. Both models are examined under steady-state considerations in the absence of diffusional limitations (cell membranes do not limit the movement of drug molecules). Equations involving the determinants of hepatic drug clearance (hepatic blood flow, fraction of drug in blood unbound, and the hepatocellular enzymatic activity) and various pharmacokinetic parameters are derived. Similarities and differences between the models are explored. Although both models predict similar hepatic drug clearances under a variety of conditions, marked differences between them become apparent in their predictions of the influence of changes in the determinants of drug clearance on various pharmacokinetic parameters.

Key words

hepatic drug clearance models blood flow drug binding hepatocelluSar enzymatic activity intrinsic clearance 



total area under the blood drug concentration-time profile


drug concentration


concentration of drug entering and leaving the liver, respectively


logarithmic average concentration of drug in hepatocyte,\(\hat C = \frac{{C_{In} - C_{Out} }}{{In({{C_{In} } \mathord{\left/ {\vphantom {{C_{In} } {C_{Out} }}} \right. \kern-\nulldelimiterspace} {C_{Out} }})}}\)


steady-state hepatic drug clearance


intrinsic hepatic drug clearance


intrinsic hepatic drug clearance when operating under linear conditions (C L,u K m,i )


steady-state hepatic extraction ratio


ratio of the unbound drug concentration in plasma water to the whole blood drug concentration


ratio of the unbound drug concentration in plasma water to the total plasma drug concentration


ratio of the unbound drug concentration in plasma water to the total drug concentration in blood cells


systemic availability of a drug given orally




Michaelis-Menten constant of the ith enzyme


rate of drug administration


elimination half-life of the drug


velocity of a reaction




hepatic blood flow


maximum velocity of the ith enzyme


interval between doses


L, B, BC, P, andR

liver, whole blood, blood cells, plasma, and reservoir, respectively


x and tube

pointx and the tube, respectively



unbound drug


oral, i.V., inf

oral and intravenous routes and constant intravenous infusion, respectively


l and ss

linear and steady-state conditions


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Copyright information

© Plenum Publishing Corporation 1977

Authors and Affiliations

  • K. Sandy Pang
    • 1
  • Malcolm Rowland
    • 1
  1. 1.School of PharmacyUniversity of CaliforniaSan Francisco

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