Skip to main content
Log in

Modeling of Hepatic Elimination and Organ Distribution Kinetics with the Extended Convection-Dispersion Model

  • Published:
Journal of Pharmacokinetics and Biopharmaceutics Aims and scope Submit manuscript

Abstract

The conventional convection-dispersion (also called axial dispersion) model is widely used to interrelate hepatic availability (F) and clearance (Cl) with the morphology and physiology of the liver and to predict effects such as changes in liver blood flow on F and Cl. An extended form of the convection-dispersion model has been developed to adequately describe the outflow concentration–time profiles for vascular markers at both short and long times after bolus injections into perfused livers. The model, based on flux concentration and a convolution of catheters and large vessels, assumes that solute elimination in hepatocytes follows either fast distribution into or radial diffusion in hepatocytes. The model includes a secondary vascular compartment, postulated to be interconnecting sinusoids. Analysis of the mean hepatic transit time (MTT) and normalized variance (CV2) of solutes with extraction showed that the discrepancy between the predictions of MTT and CV2 for the extended and unweighted conventional convection-dispersion models decreases as hepatic extraction increases. A correspondence of more than 95% in F and Cl exists for all solute extractions. In addition, the analysis showed that the outflow concentration–time profiles for both the extended and conventional models are essentially identical irrespective of the magnitude of rate constants representing permeability, volume, and clearance parameters, providing that there is significant hepatic extraction. In conclusion, the application of a newly developed extended convection-dispersion model has shown that the unweighted conventional convection-dispersion model can be used to describe the disposition of extracted solutes and, in particular, to estimate hepatic availability and clearance in both experimental and clinical situations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. M. Rowland, L. Z. Benet, and G. G. Graham. Clearance concepts in pharmacokinetics. J. Pharmacokin. Biopharm. 1:123–136 (1973).

    Article  CAS  Google Scholar 

  2. K. Winkler, L. Bass, S. Keiding, and N. Tygstrup. The effect of hepatic perfusion on the assessment of kinetic constants in regulation of hepatic metabolism. In F. Lundquist and N. Tygstrup (eds.), A. Benzon Symposium VI, Munksgaard, Copenhagen, 1974, pp. 797–807.

  3. J. Burggraaf, H. C. Schoemaker, and A. F. Cohen. Assessment of changes in liver blood flow after food intake-comparison of ICG clearance and echo-Doppler. Br. J. Clin. Pharmacol. 42:499–502 (1996).

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  4. J. Burggraaf, R. C. Schoemaker, J. M. Kroon, and A. F. Cohen. The influence of nifedipine and captopril on liver blood flow in healthy subjects. Br. J. Clin. Pharmacol. 45:447–451 (1998).

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  5. G. R. Wilkinson and D. G. Shand. Commentary: a physiological approach to hepatic drug clearance. Clin. Pharmacol. Ther. 18:377–390 (1975).

    CAS  PubMed  Google Scholar 

  6. M. S. Roberts and M. Rowland. Hepatic elimination—dispersion model. J. Pharm. Sci. 74:585–587 (1985).

    Article  CAS  PubMed  Google Scholar 

  7. M. S. Roberts and M. Rowland. A dispersion model of hepatic elimination: 1. Formulation of the model and bolus considerations. J. Pharmacokin. Biopharm. 14:227–260 (1986).

    Article  CAS  Google Scholar 

  8. M. S. Roberts, J. D. Donaldson, and M. Rowland. 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. J. Pharmacokin. Biopharm. 16:41–83 (1988).

    Article  CAS  Google Scholar 

  9. M. S. Roberts and M. Rowland. A dispersion model of hepatic elimination: 2. Steady-state considerations. Influence of blood flow, protein binding and hepatocellular enzymatic activity. J. Pharmacokin. Biopharm. 14:261–288 (1986).

    Article  CAS  Google Scholar 

  10. M. S. Roberts and M. Rowland. A dispersion model of hepatic elimination: 3. Application to metabolite formation and elimination kinetics. J. Pharmacokin. Biopharm. 14:289–307 (1986).

    Article  CAS  Google Scholar 

  11. M. S. Roberts and M. Rowland. Correlation between in-vitro microsomal enzyme activity and whole organ hepatic elimination kinetics: Analysis with a dispersion model. J. Pharm. Pharmacol. 38:117–181 (1986).

    Article  Google Scholar 

  12. M. S. Roberts, J. D. Donaldson, and D. Jackett. Availability predictions by hepatic elimination models for Michaelis-Menten kinetics. J. Pharmacokin. Biopharm. 17:687–719 (1989).

    Article  CAS  Google Scholar 

  13. L. Bass, M. S. Roberts, and P. J. Robinson. On the relation between extended forms of the sinusoidal perfusion and of the convection-dispersion models of hepatic elimination. J. Theoret. Biol. 126:457–482 (1987).

    Article  CAS  Google Scholar 

  14. P. J. Robinson, L. Bass, S. M. Pond, M. S. Roberts, and J. G. Wagner. Clinical applicability of current pharmacokinetic models: splanchnic elimination of 5-fluorouracil in cancer patients. J. Pharmacokin. Biopharm. 16:229–249 (1988).

    Article  CAS  Google Scholar 

  15. T. Iwatsubo, H. Suzuki, N. Shimada, K. Chiba, T. Ishizaki, C. E. Green, C. A. Tyson, T. Yokoi, T. Kamataki, and Y. Sugiyama. Prediction of in vivo hepatic metabolic clearance of YM796 from in vitro data by use of human liver microsomes and recombinant P-450 isozymes. J. Pharmacol. Exp. Ther. 282:909–919 (1997).

    CAS  PubMed  Google Scholar 

  16. Y. Yano, K. Yamaoka, Y. Aoyama, and H. Tanaka. Two-compartment dispersion model for analysis of organ perfusion system of drugs by fast inverse Laplace transform (FILT). J. Pharmacokin. Biopharm. 17:179–202 (1989).

    Article  CAS  Google Scholar 

  17. A. M. Evans, Z. Hussein, and M. Rowland. A two-compartment dispersion model describes the hepatic outflow profile of diclofenac in the presence of its binding protein. J. Pharm. Pharmacol. 43:709–714 (1991).

    Article  CAS  PubMed  Google Scholar 

  18. M. S. Roberts, S. Fraser, A. Wagner, and L. McLeod. Residence time distributions of solutes in the perfused rat liver using a dispersion model of hepatic elimination: 1. Effect of changes in perfusate flow and albumin concentration on sucrose and taurocholate. J. Pharmacokin. Biopharm. 18:209–234 (1990).

    Article  CAS  Google Scholar 

  19. L. N. Ballinger, S. E. Cross, and M. S. Roberts. Availability and mean transit times of phenol and its metabolites in the isolated perfused rat liver: normal and retrograde studies using tracer concentrations of phenol. J. Pharm. Pharmacol. 47:949–956 (1995).

    Article  CAS  PubMed  Google Scholar 

  20. B. A. Luxon and R. A. Weisiger. Extending the multiple indicator dilution method to include slow intracellular diffusion. Math. Biosci. 113:211–230 (1993).

    Article  CAS  PubMed  Google Scholar 

  21. L. P. Rivory, M. S. Roberts, and S. M. Pond. Axial tissue diffusion can account for the disparity between current models of hepatic elimination for lipophilic drugs. J. Pharmacokin. Biopharm. 20:19–61 (1992).

    Article  CAS  Google Scholar 

  22. G. D. Mellick, Y. G. Anissimov, A. J. Bracken, and M. S. Roberts. Metabolite mean transit times in the liver as predicted by various models of hepatic elimination. J. Pharmacokin. Biopharm. 25:477–505 (1997).

    Article  CAS  Google Scholar 

  23. D. Y. Hung, G. D. Mellick, Y. G. Anissimov, M. Weiss, and M. S. Roberts. Hepatic structure-pharmacokinetic relationships: the hepatic disposition and metabolite kinetics of a homologous series of O-acyl derivatives of salicylic acid. Br. J. Pharmacol. 124:1475–1483 (1998).

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  24. D. Y. Hung, G. D. Mellick, Y. G. Anissimov, M. Weiss, and M. S. Roberts. Hepatic disposition and metabolite kinetics of a homologous series of diflunisal esters. J. Pharm. Sci. 87:943–951 (1998).

    Article  CAS  PubMed  Google Scholar 

  25. C. H. Chou and M. Rowland. Effect of altered tissue binding on the disposition of barbital in the isolated perfused rat liver: application of the axial dispersion model. J. Pharm. Sci. 86:1310–1314 (1997).

    Article  CAS  PubMed  Google Scholar 

  26. M. Weiss, C. Stedtler, and M. S. Roberts. On the validity of the dispersion model of hepatic drug elimination when intravascular transit time densities are long-tailed. Bull. Math. Biol. 59:911–929 (1997).

    Article  CAS  PubMed  Google Scholar 

  27. M. Weiss and M. S. Roberts. Tissue distribution kinetics as determinant of transit time dispersion of drugs in organs: application of a stochastic model to the rat hindlimb. J. Pharmacokin. Biopharm. 24:173–196 (1996).

    Article  CAS  Google Scholar 

  28. R. E. Oliver, A. C. Heatherington, A. F. Jones, and M. Rowland. A physiologically based pharmacokinetic model incorporating dispersion principles to describe solute distribution in the perfused rat hindlimb preparation. J. Pharmacokin. Biopharm. 25:389–412 (1997).

    Article  CAS  Google Scholar 

  29. A. J. Schwab, W. Geng, and K. S. Pang. Application of the dispersion model for description of the outflow dilution profiles of noneliminated reference indicators in rat liver perfusion studies. J. Pharmacokin. Biopharm. 26:163–181 (1998).

    Article  CAS  Google Scholar 

  30. C. A. Goresky, G. C. Bach, and B. E. Nadeau. On the uptake of materials by the intact liver. The transport and net removal of galactose. J. Clin. Invest. 52:991–1009 (1973).

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  31. B. A. Luxon, D. C. Holly, M. T. Milliano, and R. A. Weisiger. Sex differences in multiple steps in hepatic transport of palmitate support a balanced uptake mechanism. Am. J. Physiol. 274:G51–61 (1998).

    Google Scholar 

  32. A. Kreft and A. Zuber. On the physical meaning of the dispersion equation and its solutions for different initial and boundary conditions. Chem. Eng. Sci. 33:1471–1480 (1978).

    Article  CAS  Google Scholar 

  33. G. F. Froment and K. B. Bischoff. Chemical Reactor Analysis and Design, John Wiley, New York, 1989.

    Google Scholar 

  34. P. V. Danckwerts. Continuous flow systems: distribution of residence times. Chem. Eng. Sci. 2:1–13 (1953).

    Article  CAS  Google Scholar 

  35. Y. S. Choe, I. S. Kang, and K. S. Chang. A study of the dynamic behaviour of the dispersion-type tubular reactor models. Korean J. Chem. Eng. 15:95–98 (1998).

    Article  CAS  Google Scholar 

  36. M. T. van Genuchten and J. C. Parker. Boundary conditions for displacement experiments through short laboratory soil columns. Soil Sci. Soc. Am. J. 48:703–708 (1984).

    Article  Google Scholar 

  37. R. D. Purves. Accuracy of numerical inversion of Laplace transforms for pharmacokinetic parameter estimation. J. Pharm. Sci. 84:71–74 (1995).

    Article  CAS  PubMed  Google Scholar 

  38. A. Koo, I. Y. Liang, and K. K. Cheng. The terminal hepatic microcirculation in the rat. Quart. J. Exp. Physiol. Cogn. Med. Sci. 60:261–266 (1975).

    CAS  Google Scholar 

  39. W. Geng, A. J. Schwab, T. Horie, C. A. Goresky, and K. S. Pang. Hepatic uptake of bromosulfophthalein-glutathione in perfused Eisai hyperbilirubinemic mutant rat liver: a multiple-indicator dilution study. J. Pharmacol. Exp. Ther. 284:480–492 (1998).

    CAS  PubMed  Google Scholar 

  40. A. J. Schwab, F. D. Barker, C. A. Goresky, and K. S. Pang. Transfer of enalaprilat across rat liver cell membranes is barrier limited. Am. J. Physiol. 258:G461–475 (1990).

    CAS  PubMed  Google Scholar 

  41. K. S. Pang, and M. Rowland. Hepatic clearance of drugs. I. Theoretical considerations of a “well-stirred” model and a “parallel tube” model. Influence of hepatic blood flow, plasma and blood cell binding, and the hepatocellular enzymatic activity on hepatic drug clearance. J. Pharmacokin. Biopharm. 5:625–653 (1977).

    Article  CAS  Google Scholar 

  42. A. W. Wolkoff, C. A. Goresky, J. Sellin, Z. Gatmaitan, and I. M. Arias. Role of ligandin in transfer of bilirubin from plasma into liver. Am. J. Physiol. 236:E638–648 (1979).

    CAS  PubMed  Google Scholar 

  43. Z. Hussein, A. J. McLachlan, and M. Rowland. Distribution kinetics of salicylic acid in the isolated perfused rat liver assessed using moment analysis and the two-compartment axial dispersion model. Pharm. Res. 11:1337–1345 (1994).

    Article  CAS  PubMed  Google Scholar 

  44. C. H. Chou, A. M. Evans, G. Fornasini, and M. Rowland. Relationship between lipophilicity and hepatic dispersion and distribution for a homologous series of barbiturates in the isolated perfused in situ rat liver. Drug Metab. Dispos. 21:933–938 (1993).

    CAS  PubMed  Google Scholar 

  45. A. M. Evans, Z. Hussein, and M. Rowland. Influence of albumin on the distribution and elimination kinetics of diclofenac in the isolated perfused rat liver: analysis by the impulse-response technique and the dispersion model. J. Pharm. Sci. 82:421–428 (1993).

    Article  CAS  PubMed  Google Scholar 

  46. J. M. Diaz-Garcia, A. M. Evans, and M. Rowland. Application of the axial dispersion model of hepatic drug elimination to the kinetics of diazepam in the isolated perfused rat liver. J. Pharmacokin. Biopharm. 20:171–193 (1992).

    Article  CAS  Google Scholar 

  47. R. G. Tirona, A. J. Schwab, W. Geng, and K. S. Pang. Hepatic clearance models: comparison of the dispersion and Goresky models in outflow profiles from multiple indicator dilution rat liver studies. Drug Metab. Dispos. 26:465–475 (1998).

    CAS  PubMed  Google Scholar 

  48. J.-Y. Parlange, J. L. Starr, M. T. van Genuchten, D. A. Barry, and J. C. Parker. Exit condition for miscible displacement experiments. Soil Sci. 153:165–171 (1992).

    Article  CAS  Google Scholar 

  49. J. C. Parker. Analysis of solute transport in column tracer studies. Soil Sci. Soc. Am. J. 48:719–724 (1984).

    Article  CAS  Google Scholar 

  50. Y. G. Anissimov, A. J. Bracken, and M. S. Roberts. Interconnected-tubes model of hepatic elimination. J. Theoret. Biol. 188:89–101 (1997).

    Article  CAS  Google Scholar 

  51. C. A. Goresky. A linear method for determining liver sinusoidal and extravascular volumes. Am. J. Physiol. 204:626–640 (1963).

    CAS  PubMed  Google Scholar 

  52. C. A. Goresky. Kinetic interpretation of hepatic multiple-indicator dilution studies. Am. J. Physiol. 245:G1–12 (1983).

    CAS  PubMed  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Michael S. Roberts.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Roberts, M.S., Anissimov, Y.G. Modeling of Hepatic Elimination and Organ Distribution Kinetics with the Extended Convection-Dispersion Model. J Pharmacokinet Pharmacodyn 27, 343–382 (1999). https://doi.org/10.1023/A:1020992421184

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1020992421184

Navigation