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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

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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.

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Abbreviations

AUC:

total area under the blood drug concentration-time profile

C :

drug concentration

In C Out :

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 (C L,u K m,i )

E :

steady-state hepatic extraction ratio

f B :

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

f P :

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

f bc :

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

K m,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

L, B, BC, P, andR :

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

x and tube:

pointx and the tube, respectively

u :

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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Supported in part by National Institutes of Health Grant GM 16496 and the Patent Fund, School of Pharmacy, University of California, San Francisco.

Abstracted in part from a dissertation submitted by K. Sandy Pang to the Graduate Division, University of California, San Francisco, California, in partial fulfillment of the Doctor of Philosophy degree requirement.

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Pang, K.S., Rowland, M. 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. Journal of Pharmacokinetics and Biopharmaceutics 5, 625–653 (1977). https://doi.org/10.1007/BF01059688

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  • DOI: https://doi.org/10.1007/BF01059688

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