Skip to main content
SpringerLink
Log in

Optimal Experimental Design for Precise Estimation of the Parameters of the Axial Dispersion Model of Hepatic Elimination

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

Abstract

The axial dispersion model of hepatic drug elimination is characterized by two dimensionless parameters, the dispersion number, DN , and the efficiency number, RN , corresponding to the relative dispersion of material on transit through the organ and the relative efficiency of elimination of drug by the organ, respectively. Optimal design theory was applied to the estimation of these two parameters based on changes in availability (F) of drug at steady state for the closed boundary condition model, with particular attention to variations in the fraction of drug unbound in the perfusate (fuB ). Sensitivity analysis indicates that precision in parameter estimation is greatest when F is low and that correlation between RN and DN is high, which is desirable for parameter estimation, when DN lies between 0.1 and 100. Optimal design points were obtained using D-optimization, taking into account the error variance model. If the error variance model is unknown, it is shown that choosing Poisson error model is reasonable. Furthermore, although not optimal, geometric spacing of fuB values is often reasonable and definitively superior to a uniform spacing strategy. In practice, the range of fuB available for selection may be limited by such practical considerations as assay sensitivity and acceptable concentration range of binding protein. Notwithstanding, optimal design theory provides a rational approach to precise parameter estimation.

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

Access this article

Log in via an institution

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. D. J. Morgan and R. A. Smallwood. Clinical significance of pharmacokinetic models of hepatic elimination. Clin. Pharmacokin. 18:61–70 (1990).

    Article  CAS  Google Scholar 

  2. G. R. Wilkinson. Clearance concepts in pharmacology. Pharmacol. Rev. 39:1–47 (1987).

    CAS  PubMed  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  5. L. Bass. Models of hepatic drug elimination. J. Pharm. Sci. 72:1229 (1983).

    Article  CAS  PubMed  Google Scholar 

  6. W. A. Colburn. Albumin binding and hepatic uptake: The importance of model selection-A response. J. Pharm. Sci. 72:1233 (1983).

    Article  Google Scholar 

  7. E. L. Forker and B. A. Luxon. Albumin binding and hepatic uptake: The importance of model selection. J. Pharm. Sci. 72:1232–1233 (1983).

    Article  CAS  PubMed  Google Scholar 

  8. D. J. Morgan. Models of hepatic drug elimination: A response. J. Pharm. Sci. 72:1230 (1983).

    Article  Google Scholar 

  9. D. J. Morgan, D. B. Jones, and R. A. Smallwood. Modeling of substrate elimination by the liver: has the albumin receptor model superseded the well-stirred model? Hepatology 5:1231–1235 (1985).

    Article  CAS  PubMed  Google Scholar 

  10. S. Keiding and E. Steiness. Flow dependence of propranolol elimination in perfused rat liver. J. Pharmacol. Exp. Ther. 230:474–477 (1984).

    CAS  PubMed  Google Scholar 

  11. D. B. Jones, D. J. Morgan, G. W. Mihaly, L. K. Webster, and R. A. Smallwood. Discrimination between the venous equilibrium and sinusoidal models of hepatic drug elimination in the isolated perfused rat liver by perturbation of propranolol protein binding. J. Pharmacol. Exp. Ther. 229:522–526 (1984).

    CAS  PubMed  Google Scholar 

  12. D. B. Jones, M. S. Ching, R. A. Smallwood, and D. J. Morgan. A carrier-protein receptor is not a prerequisite for avid hepatic elimination of highly bound compounds: A study of propranolol elimination by the isolated perfused rat liver. Hepatology 5:590–593 (1985).

    Article  CAS  PubMed  Google Scholar 

  13. R. H. Smallwood, G. W. Mihaly, R. A. Smallwood, and D. J. Morgan. Propranolol elimination as described by the venous equilibrium model using flow perturbations in the isolated perfused rat liver. J. Pharm. Sci. 77:330–333 (1988).

    Article  CAS  PubMed  Google Scholar 

  14. 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 

  15. M. S. Ching, D. J. Morgan, and R. A. Smallwood. Models of hepatic elimination: Implications from studies of the simultaneous elimination of taurocholate and diazepam by isolated rat liver under varying conditions of binding. J. Pharmacol. Exp. Ther. 250:1048–1054 (1989).

    CAS  PubMed  Google Scholar 

  16. R. H. Smallwood, D. J. Morgan, G. W. Mihaly, D. B. Jones, and R. A. Smallwood. Effect of plasma protein binding on elimination of taurocholate by isolated perfused rat liver: Comparison of venous equilibrium, undistributed and distributed, sinusoidal and dispersion models. J. Pharmacokin. Biopharm. 16:377–396 (1988).

    Article  CAS  Google Scholar 

  17. R. H. Smallwood, D. J. Morgan, G. W. Mihaly, and R. A. Smallwood. Lack of linear correlation between hepatic ligan uptake rate and unbound ligand concentration does not necessarily imply receptor-mediated uptake. J. Pharmacokin. Biopharm. 16:397–412 (1988).

    Article  CAS  Google Scholar 

  18. G. E. P. Box, and H. L. Lucas. Design of experiments in non-linear situations. Biometrika 46:77–90 (1959).

    Article  Google Scholar 

  19. A. C. Atkinson and W. G. Hunter. The design of experiments for parameter estimation. Technometrics 10:271–289 (1968).

    Article  Google Scholar 

  20. R. C. St. John and N. R. Draper. D-optimality for regression design. A review. Technometrics 17:15–23 (1975).

    Article  Google Scholar 

  21. D. Z. D'Argenio. Optimal sampling times for pharmacokinetics experiments. J. Pharmacokin. Biopharm. 9:739–755 (1981).

    Article  Google Scholar 

  22. J. J. Distefano III. Design and optimization of tracer experiments in physiology and medicine. Fed. Proc. 39:84–90 (1980).

    PubMed  Google Scholar 

  23. L. Endrenyi. Design of experiments for estimating enzyme and pharmacokinetic parameters. In L. Endrenyi (ed.), Kinetic Data Analysis: Design and Analysis of Enzyme and Pharmacokinetic Experiments, Plenum Press, New York, 1981, pp. 137–167.

    Chapter  Google Scholar 

  24. L. Endrenyi and F.-Y. Chan. Optimal design of experiments for the estimation of precise hyperbolic kinetic and binding parameters. J. Theoret. Biol. 90:241–263 (1981).

    Article  CAS  Google Scholar 

  25. A. Z. Khan and L. Aarons. Design and analysis of protein binding experiments. J. Theoret. Biol. 140:145–166 (1989).

    Article  CAS  Google Scholar 

  26. E. M. Landaw. Optimal design for individual parameter estimation in pharmacokinetics. In M. Rowland, L. B. Sheiner, and J. L. Steiner (eds.), Variability in Drug Therapy: Description, Estimation and Control, Raven Press, New York, 1985, pp. 187–200.

    Google Scholar 

  27. E. D. Morris, M. Saidel, and G. M. Chisolm III. Optimal design of experiments to estimate LDL transport parameters in arterial wall. Am. J. Physiol. 261:H929–H949 (1991).

    CAS  PubMed  Google Scholar 

  28. M. H. Nathanson and G. M. Saidel. Multiple-objective criteria for optimal experimental design: application to ferrokinetics. Am. J. Physiol. 248:R378–R386 (1985).

    CAS  PubMed  Google Scholar 

  29. C. C. Peck, L. B. Sheiner, and A. I. Nichols. The problem of choosing weights in nonlinear regression analysis of pharmacokinetic data. Drug Metab. Rev. 15:133–148 (1984).

    Article  CAS  PubMed  Google Scholar 

  30. Y. Bard. Nonlinear Parameter Estimation, Academic Press, New York, 1974, pp. 258–286.

    Google Scholar 

  31. V. V. Fedorov. Theory of Optimal Experiments, Academic Press, New York, 1972.

    Google Scholar 

  32. M. J. Box. Some experience with a nonlinear experimental design criterion. Technometrics 12:569–589 (1970).

    Article  Google Scholar 

  33. C. M. Metzler, G. L. Elfring, and A. J. McEwea. A User's Manual for NONLIN and Associated Programs, The Upjohn Company, Kalamazoo, MI, 1974.

    Google Scholar 

  34. N. R. Draper and H. Smith. Applied Regressions Analysis, Wiley, New York, 1966.

    Google Scholar 

  35. D. A. Ratowsky, Nonlinear Regression Modeling: A Unified Practical Approach, Marcel Dekker, New York, 1983.

    Google Scholar 

  36. D. J. Pritchard and D. W. Bacon. Prospects for reducing correlations among parameter estimates in kinetic models. Chem. Eng. Sci. 33:1539–1543 (1978).

    Article  CAS  Google Scholar 

  37. M. Bezeau and L. Endrenyi. Design of experiments for the precise estimation of dose-response parameters: the Hill equation. J. Theoret. Biol. 123:415–430 (1986).

    Article  CAS  Google Scholar 

  38. Z. Hussein, A. M. Evans, and M. Rowland. Physiologic models of hepatic drug clearance. Influence of altered protein binding on the elimination of diclofenac in the isolated perfused rat liver. J. Pharm. Sci. 82:880–885 (1993).

    Article  CAS  PubMed  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Pharmacy and Pharmaceutical Sciences, University of Manchester, Manchester, M13 9PL, United Kingdom

    Chen-Hsi Chou, Leon Aarons & Malcolm Rowland

  2. Department of Clinical Pharmacy, National Cheng Kung University, 1 University Road, Tainan, Taiwan

    Chen-Hsi Chou

Authors
  1. Chen-Hsi Chou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Leon Aarons
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Malcolm Rowland
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chou, CH., Aarons, L. & Rowland, M. Optimal Experimental Design for Precise Estimation of the Parameters of the Axial Dispersion Model of Hepatic Elimination. J Pharmacokinet Pharmacodyn 26, 595–615 (1998). https://doi.org/10.1023/A:1023229318017

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1023229318017

Search

Navigation