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Journal of Pharmacokinetics and Biopharmaceutics

, Volume 17, Issue 6, pp 687–719 | Cite as

Availability predictions by hepatic elimination models for Michaelis-Menten kinetics

  • Michael S. Roberts
  • John D. Donaldson
  • David Jackett
Article

Abstract

Numerical methods have been used to compare the availability predictions of a number of hepatic elimination models when Michaelis-Menten kinetics is operative. Propranolol and galactose were used as model compounds. Lower availabilities were predicted by the dispersion model than by a segregated distribution model for both compounds. The differences in the predictions were most pronounced for models corresponding to a large variation in solute residence times in the liver. The predictions of the tank-in-series, dispersion model with mixed boundary conditions and dispersion model with Dankwerts boundary conditions were similar over all concentrations studied. Changes in blood flow and protein binding provided little discrimination between the model predictions. It is concluded that micromixing of blood between sinusoids and the anatomical sites of mixing are important determinants of availability when liver eliminating enzymes are partially saturated.

Key words

propranolol dispersion model Dankwerts boundary conditions hepatic elimination models 

Notation

A

Cross-sectional area

C

Concentration

C

Concentration normalized to input concentration

CV2

Normalized variance

ĉ

Logarithmic mean concentration

CLint

Intrinsic clearance

DN

Dispersion number

f(t)

Output concentration-time profile after a bolus input

F

Availability

fu

Fraction unbound

g(L)

Distribution of tube lengths function

G(t)

Cumulative (total) fraction of dose leaving liver

k(c)

Rate estimation constant per unit volume

Km

Michaelis constant

L

Length of liver

n

Number of tanks

P

Permeability of hepatocyte to drug

Q

Blood flow rate

RN

Efficiency number

t

Time

¯t

Mean residence time

T

Dimensionless time (=t/¯t)

ν

Mean blood velocity

V

Volume or volume of distribution

Vmax

Maximum velocity

z

Distance within liver

Z

Fractional distance within liver (z/L)

Subscripts

b

based on measurement in blood

c

based on measurement in cell

in

input

out

exit

Greek Letters

o−2

Variance

ρ

Axial variation in enzyme activity

Partial derivative

Fraction of sinusoids in a given class

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Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • Michael S. Roberts
    • 1
  • John D. Donaldson
    • 2
  • David Jackett
    • 3
  1. 1.Department of PharmacyUniversity of Otago Medical SchoolDunedinNew Zealand
  2. 2.Department of MathematicsUniversity of TasmaniaHobartAustralia
  3. 3.CSIRO Division of Mathematics and StatisticsHobartAustralia

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