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


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 



Cross-sectional area




Concentration normalized to input concentration


Normalized variance


Logarithmic mean concentration


Intrinsic clearance


Dispersion number


Output concentration-time profile after a bolus input




Fraction unbound


Distribution of tube lengths function


Cumulative (total) fraction of dose leaving liver


Rate estimation constant per unit volume


Michaelis constant


Length of liver


Number of tanks


Permeability of hepatocyte to drug


Blood flow rate


Efficiency number




Mean residence time


Dimensionless time (=t/¯t)


Mean blood velocity


Volume or volume of distribution


Maximum velocity


Distance within liver


Fractional distance within liver (z/L)



based on measurement in blood


based on measurement in cell





Greek Letters




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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