Models of hepatic elimination: Comparison of stochastic models to describe residence time distributions and to predict the influence of drug distribution, enzyme heterogeneity, and systemic recycling on hepatic elimination

  • Michael S. Roberts
  • John D. Donaldson
  • Malcolm Rowland


The residence time distribution of noneliminated solutes in the liver can be represented by a variety of stochastic models. The dispersion model (closed and mixed boundary conditions), gamma distribution, log normal distribution and normal distribution models were used to describe output concentration-time profiles after bolus injections into the liver of labeled erythrocytes and albumin. The dispersion model and log normal distribution model provide the best representation of the data and give similar estimates of relative dispersion and availability for varying hepatocellular enzyme activity. The availability of solutes eliminated from the liver by first-order kinetics is determined by the residence time distribution of the solute in the liver and not on events occurring in the liver when a uniform enzyme distribution is assumed. Both enzyme heterogeneity (axial or transverse) and hepatocyte permeability may affect solute availability. A more complex model accounting for enzyme distribution and the micromixing of solute within the liver is required for solutes undergoing saturable kinetics.

Key words

hepatic extraction stochastic models dispersion gamma distribution log normal distribution enzyme heterogeneity drug distribution 


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Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • Michael S. Roberts
    • 1
  • John D. Donaldson
    • 2
  • Malcolm Rowland
    • 3
  1. 1.School of PharmacyUniversity of TasmaniaHobartAustralia
  2. 2.Department of MathematicsUniversity of TasmaniaHobartAustralia
  3. 3.Department of PharmacyUniversity of ManchesterManchesterEngland

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