Skip to main content
Log in

Comparison of four basic models of indirect pharmacodynamic responses

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

Abstract

Four basic models for characterizing indirect pharmacodynamic responses after drug administration have been developed and compared. The models are based on drug effects (inhibition or stimulation) on the factors controlling either the input or the dissipation of drug response. Pharmacokinetic parameters of methylprednisolone were used to generate plasma concentration and response-time profiles using computer simulations. It was found that the responses produced showed a slow onset and a slow return to baseline. The time of maximal response was dependent on the model and dose. In each case, hysteresis plots showed that drug concentrations preceded the response. When the responses were fitted with pharmacodynamic models based on distribution to a hypothetical effect compartment, the resulting parameters were dose-dependent and inferred biological implausibility. Indirect response models must be treated as distinct from conventional pharmacodynamic models which assume direct action of drugs. The assumptions, equations, and data patterns for the four basic indirect response models provide a starting point for evaluation of pharmacologie effects where the site of action precedes or follows the measured response variable.

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

Abbreviations

C e :

Drug concentration at the hypothetical effect site

C p :

Plasma concentration of drug

C p(Tmax):

Plasma concentration of drug at the time of maximal response

D :

Dose

EC 50 :

Drug concentration producing 50% of maximum stimulation at effect site

E max :

Maximum effect attributed to drug

E o :

Baseline effect prior to drug administration

IC 50 :

Drug concentration producing 50% of maximum inhibition at effect site

K el :

First-order rate constant for drug elimination

K eo :

First-order rate constant for drug loss from effect site

K in :

Zero-order rate constant for production of drug response

K out :

First-order rate constant for loss of drug response

n :

Sigmoidicity factor of the sigmoid Emax equation

R :

Response variable

Rmax :

Maximal (or minimal) response

Ro :

Initial response (time zero) prior to drug administration

t :

time after drug administration

T :

Infusion time

Tmax :

Time to reach maximum effect following drug administration

V :

Volume of distribution

References

  1. N. H. G. Holford and L. B. Sheiner. Understanding the dose-effect relationship: Clinical application of pharmacokinetic-pharmacodynamic models.cin Pharmacokin. 6:429–453 (1981).

    Article  CAS  Google Scholar 

  2. L. B. Sheiner, D. R. Stanski, S. Vozeh, R. D. Miller, and J. Ham. Simultaneous modeling of pharmacokinetics and pharmacodynamics: Application to d-tubocurarine.Clin Pharmacol Ther. 25:358–371 (1979).

    CAS  PubMed  Google Scholar 

  3. D. Verotta, S. L. Beal, and L. B. Sheiner. Semiparametric approach to pharmacokinetic-pharmacodynamic data.Am. J. Physiol. 256:R1005-R1010 (1989).

    CAS  PubMed  Google Scholar 

  4. N. H. G. Holford and L. B. Sheiner. Pharmacokinetic and pharmacodynamic modeling in vivo.CRC Crit. Rev. Bioeng. 5:273–322 (1981).

    CAS  Google Scholar 

  5. R. L. Lalonde. In W. E. Evans, J. J. Schentag, and W. J. Jusko (eds.),Applied Pharmacokinetics, 3rd ed., Applied Therapeutics, Vancouver, 1992, pp. 4–33.

    Google Scholar 

  6. R. Nagashima, R. A. O'Reilly, and G. Levy. Kinetics of pharmacologie effects in man: The anticoagulant action of warfarin.Clin. Pharmacol. Ther. 10:22–35 (1969).

    CAS  PubMed  Google Scholar 

  7. P. H. Abbrecht, T. J. O'Leary, and D. M. Behrendt. Evaluation of a computer-assisted method for individualized anticoagulation: Retrospective and prospective studies with a pharmacodynamic model.Clin. Pharmacol. Ther. 32:129–136 (1982).

    Article  CAS  PubMed  Google Scholar 

  8. A.-N. Kong, E. A. Ludwig, R. L. Slaughter, P. M. Distefano, J. Demasi, E. Middleton Jr., and W. J. Jusko. Pharmacokinetics and pharmacodynamic modeling of direct suppression effects of methylprednisolone on serum cortisol and blood histamine in human subjects.Clin. Pharmacol. Ther. 46:616–628 (1989).

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  9. J. A. Wald, D. E. Salazar, H. Cheng, and W. J. Jusko. Two-compartment basophil cell trafficking model for methylprednisolone pharmacodynamics.J. Pharmacokm. Biopharm. 19:521–536 (1991).

    Article  CAS  Google Scholar 

  10. L. E. Fisher, E. A. Ludig, and W. J. Jusko. Pharmacoimmunodynamics of methylprednisolone: Trafficking of helper T lymphocytes.J. Pharmacokin. Biopharm. 20:319–331 (1992).

    Article  CAS  Google Scholar 

  11. Z.-X. Xu and W. J. Jusko. Pharmacodynamic modeling of prednisolone effects on natural killer cell trafficking, (submitted for publication)

  12. P. Francheteau, J.-L. Steimer, C. Dubray, and D. Lavene. Mathematical model for in vivo pharmacodynamics integrating fluctuation of the response: Application to the prolactin suppressant effect of the dopaminomimetic drug DCN 203-922.J. Pharmacokin. Biopham. 19:287–309 (1991).

    Article  CAS  Google Scholar 

  13. J. A. Wald and W. J. Jusko. Corticosteroid pharmacodynamic modeling: Osteocalcin suppression by prednisolone.Pharm. Res. 9:1096–1098 (1992).

    Article  CAS  PubMed  Google Scholar 

  14. F. D. Boudinot, R. D'Ambrosio, and W. J. Jusko. Receptor-mediated pharmacodynamics of prednisolone in the rat.J. Pharmacokin. Biopharm. 14:469–493 (1986).

    Article  CAS  Google Scholar 

  15. B. Oosterhuis, R. J. M. Ten Berge, H. P. Sauerwein E. Endert, P. T. A. Schellekens, and C. J. Van Boxtel. Pharmacokinetic-pharmacodynamic modeling of prednisolone-induced lymphocytopenia in man.J. Pharmacol. Exp. Ther. 229:539–546 (1984).

    CAS  PubMed  Google Scholar 

  16. H. Derendorf, H. Mollmann, M. Krieg, S. Tunn, C. Mollmann, J. Barth, and H.-J. Bothig. Pharmacodynamics of methylprednisolone phosphate after single intravenous administration to healthy volunteers.Pharm. Res. 8:263–268 (1991).

    Article  CAS  PubMed  Google Scholar 

  17. S. K. Gupta, J. C. Ritchie, E. G. Ellinwood, K. Wiedemann, and F. Holsboer. Modeling the pharmacokinetics and pharmacodynamics of dexamethasone in depressed patients.Eur. J. Clin. Pharmacol. 43:51–55 (1992).

    Article  CAS  PubMed  Google Scholar 

  18. J. H. Lin. Pharmacokinetic and pharmacodynamic properties of histamine H2-receptor antagonists—relationship between intrinsic potency and effective plasma concentrations.Clin. Pharmacokin. 20:218–236 (1991).

    Article  CAS  Google Scholar 

  19. O. P. Ganda, C. B. Kahn, J. S. Soeldner, and R. E. Gleason. Dynamics of tolbutamide, glucose, and insulin: Interrelationships following varying doses of intravenous tolbutamide in normal subjects.Diabetes.24:354–361 (1975).

    Article  CAS  PubMed  Google Scholar 

  20. G. G. Belz, W. Kirch, and C. H. Kleinbloesem. Angiotensin-converting enzyme inhibitors: relationship between pharmacodynamics and pharmacokinetics.Clin. Pharmacokin. 15:295–318 (1988).

    Article  CAS  Google Scholar 

  21. M. Averbuch, M. Weintraub, J. C. Liao, R. K. Brazzell, and R. E. Dobbs. Red blood cell sorbitol lowering effects and tolerance of single doses of AL 1576 (HOE 843) in diabetic patients.J. Clin. Pharmacol. 28:757–761 (1988).

    Article  CAS  PubMed  Google Scholar 

  22. G. Movin-Osswald and M. Hammarlund-Udenaes. Remoxipride: pharmacokinetics and effect on plasma prolactin.Br. J. Clin. Pharmacol. 32:355–360 (1991).

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  23. G. Alvan, L. Helleday, A. Lindholm, E. Sanz, and T. Villen. Diuretic effect and diuretic efficiency after intravenous dosage of frusemide.Br. J. Clin. Pharmacol. 29:215–219 (1990).

    Article  CAS  PubMed Central  PubMed  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Supported in part by Grant No. 24211 from the National Institutes of General Medical Sciences, National Institutes of Health.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dayneka, N.L., Garg, V. & Jusko, W.J. Comparison of four basic models of indirect pharmacodynamic responses. Journal of Pharmacokinetics and Biopharmaceutics 21, 457–478 (1993). https://doi.org/10.1007/BF01061691

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01061691

Key words

Navigation