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Availability predictions by hepatic elimination models for Michaelis-Menten kinetics

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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.

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Abbreviations

A:

Cross-sectional area

C:

Concentration

C :

Concentration normalized to input concentration

CV 2 :

Normalized variance

ĉ :

Logarithmic mean concentration

CL int :

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

K m :

Michaelis constant

L :

Length of liver

n :

Number of tanks

P:

Permeability of hepatocyte to drug

Q:

Blood flow rate

R N :

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)

b :

based on measurement in blood

c:

based on measurement in cell

in:

input

out:

exit

o −2 :

Variance

ρ :

Axial variation in enzyme activity

∂:

Partial derivative

∝ :

Fraction of sinusoids in a given class

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Authors and Affiliations

  1. Department of Pharmacy, University of Otago Medical School, P.O. Box 913, Dunedin, New Zealand

    Michael S. Roberts

  2. Department of Mathematics, University of Tasmania, GPO Box 252C, 7001, Hobart, Australia

    John D. Donaldson

  3. CSIRO Division of Mathematics and Statistics, GPO Box 1538, Hobart, Australia

    David Jackett

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  1. Michael S. Roberts
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  2. John D. Donaldson
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  3. David Jackett
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Additional information

One of us (M.S.R.) wishes to thank the National Health and Medical Research Council of Australia (NHMRC) and the Dean's Fund (MRC, NZ).

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Roberts, M.S., Donaldson, J.D. & Jackett, D. Availability predictions by hepatic elimination models for Michaelis-Menten kinetics. Journal of Pharmacokinetics and Biopharmaceutics 17, 687–719 (1989). https://doi.org/10.1007/BF01062125

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  • DOI: https://doi.org/10.1007/BF01062125

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