On the validity of the dispersion model of hepatic drug elimination when intravascular transit time densities are long-tailed

Bull Math Biol. 1997 Sep;59(5):911-29. doi: 10.1007/BF02459999.


The dispersion model with mixed boundary conditions uses a single parameter, the dispersion number, to describe the hepatic elimination of xenobiotics and endogenous substances. An implicit a priori assumption of the model is that the transit time density of intravascular indicators is approximately by an inverse Gaussian distribution. This approximation is limited in that the model poorly describes the tail part of the hepatic outflow curves of vascular indicators. A sum of two inverse Gaussian functions is proposed as an alternative, more flexible empirical model for transit time densities of vascular references. This model suggests that a more accurate description of the tail portion of vascular reference curves yields an elimination rate constant (or intrinsic clearance) which is 40% less than predicted by the dispersion model with mixed boundary conditions. The results emphasize the need to accurately describe outflow curves in using them as a basis for determining pharmacokinetic parameters using hepatic elimination models.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Animals
  • Enalapril / pharmacokinetics
  • Lidocaine / pharmacokinetics
  • Liver / blood supply
  • Liver / metabolism*
  • Mathematics
  • Metabolic Clearance Rate
  • Models, Biological
  • Normal Distribution
  • Pharmacokinetics*
  • Tissue Distribution


  • Enalapril
  • Lidocaine