Pharmaceutical Research

, Volume 22, Issue 10, pp 1589–1596 | Cite as

Quasi-Equilibrium Pharmacokinetic Model for Drugs Exhibiting Target-Mediated Drug Disposition

  • Donald E. Mager
  • Wojciech KrzyzanskiEmail author
Research Paper


The aim of this study is to derive and evaluate an equilibrium model of a previously developed general pharmacokinetic model for drugs exhibiting target-mediated drug disposition (TMDD).


A quasi-equilibrium solution to the system of ordinary differential equations that describe the kinetics of TMDD was obtained. Computer simulations of the equilibrium model were carried out to generate plasma concentration-time profiles resulting from a large range of intravenous bolus doses. Additionally, the final model was fitted to previously published pharmacokinetic profiles of leukemia inhibitory factor (LIF), a cytokine that seems to exhibit TMDD, following intravenous administration of 12.5, 25, 100, 250, 500, or 750 μg/kg in sheep.


Simulations show that pharmacokinetic profiles display steeper distribution phases for lower doses and similar terminal disposition phases, but with slight underestimation at early time points as theoretically expected. The final model well-described LIF pharmacokinetics, and the final parameters, which were estimated with relatively good precision, were in good agreement with literature values.


An equilibrium model of TMDD is developed that recapitulates the essential features of the full general model and eliminates the need for estimating drug-binding microconstants that are often difficult or impossible to identify from typical in vivo pharmacokinetic data.

Key Words

leukemia inhibitory factor mathematical model nonlinear pharmacokinetics target-mediated drug disposition 



The authors would like to thank Dr. S. A. Charman, Dr. C. J. H. Porter, and Dr. A. M. Segrave for providing the LIF PK data. This study was funded in part by Grant 57980 from the National Institute of General Medical Sciences, National Institutes of Health (for W. K.) and start-up funds (to D. E. M.) from the University at Buffalo, State University of New York.


  1. 1.
    Mager, D. E., Wyska, E., Jusko, W. J. 2003Diversity of mechanism-based pharmacodynamic modelsDrug Metab. Dispos.31510518CrossRefPubMedGoogle Scholar
  2. 2.
    Derendorf, H., Meibohm, B. 1999Modeling of pharmacokinetic/pharmacodynamic (PK/PD) relationships: concepts and perspectivesPharm. Res.16176185CrossRefPubMedGoogle Scholar
  3. 3.
    Levy, G. 1994Pharmacologic target-mediated drug dispositionClin. Pharmacol. Ther.56248252PubMedGoogle Scholar
  4. 4.
    Lobo, E. D., Hansen, R. J., Balthasar, J. P. 2004Antibody pharmacokinetics and pharmacodynamicsJ. Pharm. Sci.9326452668CrossRefPubMedGoogle Scholar
  5. 5.
    Mager, D. E., Jusko, W. J. 2001General pharmacokinetic model for drugs exhibiting target-mediated drug dispositionJ. Pharmacokinet. Pharmacodyn.28507532CrossRefPubMedGoogle Scholar
  6. 6.
    Mager, D. E., Jusko, W. J. 2002Receptor-mediated pharmacokinetic/pharmacodynamic model of interferon-beta 1a in humansPharm. Res.1915371543CrossRefPubMedGoogle Scholar
  7. 7.
    Mager, D. E., Neuteboom, B., Efthymiopoulos, C., Munafo, A., Jusko, W. J. 2003Receptor-mediated pharmacokinetics and pharmacodynamics of interferon-beta1a in monkeysJ. Pharmacol. Exp. Ther.306262270CrossRefPubMedGoogle Scholar
  8. 8.
    Eppler, S. M., Combs, D. L., Henry, T. D., Lopez, J. J., Ellis, S. G., Yi, J.H., Annex, B. H., McCluskey, E. R., Zioncheck, T. F. 2002A target-mediated model to describe the pharmacokinetics and hemodynamic effects of recombinant human vascular endothelial growth factor in humansClin. Pharmacol. Ther.722032CrossRefPubMedGoogle Scholar
  9. 9.
    Levy, G., Mager, D. E., Cheung, W. K., Jusko, W. J. 2003Comparative pharmacokinetics of coumarin anticoagulants L: physiologic modeling of S-warfarin in rats and pharmacologic target-mediated warfarin disposition in manJ. Pharm. Sci.92985994CrossRefPubMedGoogle Scholar
  10. 10.
    Jin, F., Krzyzanski, W. 2004Pharmacokinetic model of target-mediated disposition of thrombopoietinAAPS Pharm Sci6E9CrossRefGoogle Scholar
  11. 11.
    Segrave, A. M., Mager, D. E., Charman, S. A., Edwards, G. A., Porter, C. J. 2004Pharmacokinetics of recombinant human leukemia inhibitory factor in sheepJ. Pharmacol. Exp. Ther.30910851092CrossRefPubMedGoogle Scholar
  12. 12.
    Mager, D. E., Mascelli, M. A., Kleiman, N. S., Fitzgerald, D. J., Abernethy, D. R. 2004Nonlinear binding models suggest that abciximab pharmacokinetics and pharmacodynamics are target-mediatedClin. Pharmacol. Ther.7588(Abstract)CrossRefGoogle Scholar
  13. 13.
    Mager, D. E., Mascelli, M. A., Kleiman, N. S., Fitzgerald, D. J., Abernethy, D. R. 2003Simultaneous modeling of abciximab plasma concentrations and ex vivo pharmacodynamics in patients undergoing coronary angioplastyJ. Pharmacol. Exp. Ther.307969976CrossRefPubMedGoogle Scholar
  14. 14.
    Wagner, J. G. (1971)A new generalized nonlinear pharmacokinetic model and its implicationsWagner, J. G. eds. Biopharmaceutics and Relevant PharmacokineticsDrug Intelligence PublicationsHamilton, IL302317Google Scholar
  15. 15.
    Segel, I. H. 1975Enzyme Kinetics. Behavior and Analysis of Rapid Equilibrium and Steady-State Enzyme SystemsJohn Wiley & SonsNew YorkGoogle Scholar
  16. 16.
    Murray, J. D. 2002Mathematical BiologySpringerNew YorkGoogle Scholar
  17. 17.
    Linand, C. C., Segel, L. A. 1974Mathematics Applied to Deterministic Problems in the Natural SciencesMacmillan Publishing Co., Inc.New YorkGoogle Scholar
  18. 18.
    D'Argenio, D. Z., Schumitzky, A. 1997ADAPT II User's GuideBiomedical Simulations ResourceLos AngelesGoogle Scholar
  19. 19.
    Gibaldi, M., Perrier, D. 1982PharmacokineticsMarcel Dekker, Inc.New YorkGoogle Scholar
  20. 20.
    Kemme, M. J., Schoemaker, R. C., Burggraaf, J., Linden, M., Noordzij, M., Moerland, M., Kluft, C., Cohen, A. F. 2003Endothelial binding of recombinant tissue plasminogen activator: quantification in vivo using a recirculatory modelJ. Pharmacokinet. Pharmacodyn.30322CrossRefPubMedGoogle Scholar

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of Pharmaceutical SciencesUniversity at Buffalo, State University of New YorkBuffaloUSA

Personalised recommendations