Journal of Pharmacokinetics and Biopharmaceutics

, Volume 5, Issue 6, pp 625–653

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
Article

DOI: 10.1007/BF01059688

Cite this article as:
Pang, K.S. & Rowland, M. Journal of Pharmacokinetics and Biopharmaceutics (1977) 5: 625. doi:10.1007/BF01059688

Abstract

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 clearancemodelsblood flowdrug bindinghepatocelluSar enzymatic activityintrinsic clearance

Glossary

AUC

total area under the blood drug concentration-time profile

C

drug concentration

InCOut

concentration of drug entering and leaving the liver, respectively

Ĉ

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

CL

steady-state hepatic drug clearance

CLint

intrinsic hepatic drug clearance

CLin,t

intrinsic hepatic drug clearance when operating under linear conditions (CL,uKm,i)

E

steady-state hepatic extraction ratio

fB

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

fP

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

fbc

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

F

systemic availability of a drug given orally

H

hematocrit

Km,i

Michaelis-Menten constant of the ith enzyme

R

rate of drug administration

t1/2

elimination half-life of the drug

v

velocity of a reaction

V

volume

Q

hepatic blood flow

Vmax,i

maximum velocity of the ith enzyme

τ

interval between doses

subscripts

L, B, BC, P, andR

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

subscripts

x and tube

pointx and the tube, respectively

subscript

u

unbound drug

subscripts

oral, i.V., inf

oral and intravenous routes and constant intravenous infusion, respectively

subscripts

l and ss

linear and steady-state conditions

Copyright information

© Plenum Publishing Corporation 1977

Authors and Affiliations

  • K. Sandy Pang
    • 1
  • Malcolm Rowland
    • 1
  1. 1.School of PharmacyUniversity of CaliforniaSan Francisco
  2. 2.Laboratory of Chemical Pharmacology, National Heart, Lung, and Blood InstituteNational Institutes of HealthBethesda
  3. 3.Department of PharmacyUniversity of ManchesterManchesterEngland