Skip to main content
SpringerLink
Log in

Pitfalls and valid approaches to pharmacokinetic analysis of mean concentration data following intravenous administration

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

Abstract

Pharmacokinetic analysis of arithmetic mean concentration data can lead to selection of an inappropriate deterministic compartmental model and biased pharmacokinetic parameter estimates. The terminal phase disposition rate constant estimated by fitting a deterministic model to mean data is in all cases an underestimate of the expected value of this rate constant. The area under the mean data curve calculated via the linear trapezoidal rule from time zero to the last detectable concentration sampling point is equal to the mean of the individual subject areas under the curve for the same time span. This equality supports the use of mean data for determination of model-independent pharmacokinetic parameters.

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

Abbreviations

AUC ∞Oi :

total area under the curve for theith subject

AUC ∞Oari :

total area under theC ari versus time curve

\(\overline {AUC} _0^\infty \) :

arithmetic mean of the total area under the individual subject's concentration versus time curve=

$$ = \frac{1}{n}\sum\limits_{i = 1}^n {AUC_{0_i }^\infty } $$
AUC ∞Oln :

total area under theC ln versus time curve

C ari :

arithmetic mean concentration

C O :

concentration at time zero

\(\bar C\) o :

arithmetic mean of the individual subject'sC O values

C Oari :

concentration at time zero extrapolated from theC ari versus time curve

C ln :

arithmetic mean of the logarithmic values of individual subject concentrations

\(\bar C\) ss :

average steady-state concentration

K i :

first-order elimination rate constant for theih subject

K ari :

arithmetic mean elimination rate constant

K har :

harmonic mean elimination rate constant

n :

number of subjects

V i :

apparent volume of distribution for theith subject

V geom :

geometric mean apparent volume of distribution

V har :

harmonic mean apparent volume of distribution

X O :

i.v. bolus dose

References

  1. A.B. Pritchard, P. A. Holmes, and J. C. Kirschman. The fate of FD & C Red No. 2 and its metabolite, naphthionic acid, after different routes of administration in the rat.Toxicol. Appl. Pharmacol. 35:1–10 (1976).

    Article  CAS  PubMed  Google Scholar 

  2. B. Gabard. Distribution and excretion of the mercury chelating agent sodium 2,3-dimercaptopropane-1-sulfonate in the rat.Arch. Toxicol. 39:289–298 (1978).

    Article  CAS  PubMed  Google Scholar 

  3. S. N. Giri, D. M. Siegel, and S. A. Peoples. Tissue distribution and binding of radioactivity in mouse after intravenous administration of14C-3-chloro-p-toluidine.Toxicology 11:153–165 (1978).

    Article  CAS  PubMed  Google Scholar 

  4. D. Reichert, H. W. Werner, M. Metzler, and D. Henschler. Molecular mechanism of 1,1-dichloroethylene toxicity: excreted metabolites reveal different pathways of reactive intermediates.Arch. Toxicol. 42:159–169 (1979).

    Article  CAS  PubMed  Google Scholar 

  5. S. H. Weinstein, M. Pfeffer, J. M. Schor, L. Franklin, M. Mintz, and E. R. Tutko. Absorption and distribution of naloxone in rats after oral and intravenous administration.J. Pharm. Sci. 62:1416–1419 (1973).

    Article  CAS  PubMed  Google Scholar 

  6. C. MacLeod, H. Rabin, R. Ogilvie, J. Ruedy, M. Caron, D. Zarowny, and R. O. Davies. Practical concepts of drug absorption, distribution and loss.CMA J. 111:341–346 (1974).

    CAS  Google Scholar 

  7. R. L. DeAngelis, M. F. Kearney, and R. M. Welch. Determination of triprolidine in human plasma by quantitative TLC.J. Pharm. Sci. 66:841–843 (1977).

    Article  CAS  PubMed  Google Scholar 

  8. D. C. Hobbs, T. M. Twomey, and R. F. Palmer. Pharmacokinetics of prazosin in man.J. Clin. Pharmacol. 18:402–405 (1978).

    Article  CAS  PubMed  Google Scholar 

  9. V. E. Ziegler, J. T. Biggs, L. T. Wylie, S. H. Rosen, D. J. Hawf, and W. H. Coryell. Doxepin kinetics.Clin. Pharmacol. Ther. 23:573–579 (1978).

    CAS  PubMed  Google Scholar 

  10. V. E. Ziegler, J. T. Biggs, L. T. Wylie, W. H. Coryell, K. M. Hanifl, D. J. Hawf, and S. H. Rosen. Protriptyline kinetics.Clin. Pharmacol. Ther. 23:580–584 (1978).

    CAS  PubMed  Google Scholar 

  11. L. B. Sheiner, B. Rosenberg, and V. V. Marathe. Estimation of population characteristics of pharmacokinetic parameters from routine clinical data.J. Pharmacokin. Biopharm. 5:445–479 (1977).

    Article  CAS  Google Scholar 

  12. M. Gibaldi and D. Perrier. In J. Swarbrick (ed.),Pharmacokinetics, Vol. I. Drugs and the Pharmaceutical Sciences. Marcel Dekker, New York, 1975.

    Google Scholar 

  13. J. G. Wagner,Biopharmaceutics and Relevant Pharmacokinetics, Drug Intelligence Publications, Hamilton, Ill., 1971.

    Google Scholar 

  14. J. G. Wagner,Fundamentals of Clinical Pharmacokinetics, Drug Intelligence Publications, Hamilton, Ill., 1975.

    Google Scholar 

  15. G. Levy and M. Gibaldi. Pharmacokinetics. In J. R. Gillette and J. R. Mitchell (eds.),Concepts in Biochemical Pharmacology. Handbook of Experimental Pharmacology, Volume 28, Springer-Verlag, Berlin, 1975, chap. 59.

    Google Scholar 

  16. G. Levy and L. E. Hollister. Inter- and intrasubject variations in drug absorption kinetics.J. Pharm. Sci. 53:1446–1452 (1964).

    Article  CAS  PubMed  Google Scholar 

  17. W. J. Westlake. Use of statistical methods in evaluation ofin vivo performance of dosage forms.J. Pharm. Sci. 62:1579–1589 (1973).

    Article  CAS  PubMed  Google Scholar 

  18. B. E. Rodda, C. B. Sampson, and D. W. Smith. The one-compartment open model: some statistical aspects of parameter estimation.Biometrics 28:1180 (1972).

    Google Scholar 

  19. J. H. Matis and T. E. Wehrly. Stochastic models of compartmental systems.Biometrics 35:199–220 (1979).

    Article  Google Scholar 

  20. J. H. Matis and H. D. Tolley. Compartmental models with multiple sources of stochastic variability: The one-compartment, time-invariant hazard rate case.Bull. Math. Biol. 41:491–516 (1979).

    Article  Google Scholar 

  21. J. H. Matis and H. D. Tolley. On the stochastic modeling of tracer kinetics.Fed. Proc. 39:104–109 (1980).

    CAS  PubMed  Google Scholar 

  22. W. L. Chiou. New calculation method for mean apparent drug volume of distribution and application to rational dosage regimens.J. Pharm. Sci. 68:1067–1069 (1979).

    Article  CAS  PubMed  Google Scholar 

  23. C. Lanczos.Applied Analysis, Prentice-Hall, Englewood Cliffs, N.J., 1956, pp. 272–280.

    Google Scholar 

  24. SAS User's Guide: 1976 Edition, SAS Institute Inc., SAS Version 76.6C, Raleigh, N.C.

  25. C. M. Metzler, G. L. Elfring, and A. J. McEwen. A package of computer programs for pharmacokinetic modeling.Biometrics 30:562 (1974).

    Article  Google Scholar 

  26. C. M. Metzler, G. L. Elfring, and A. J. McEwen.A User's Manual for NONLIN and Associated Programs, Upjohn Co., Kalamazoo, Mich., 1974.

    Google Scholar 

  27. B. H. Migdalof. Methods for obtaining drug time course data from individual small laboratory animals: serial microblood sampling and assay.Drug Metab. Rev. 5:295–310 (1976).

    Article  CAS  PubMed  Google Scholar 

  28. A. B. A. Jansen, Total radioactivity half-lives.Drug Metab. Dispos. 7:350 (1979).

    CAS  PubMed  Google Scholar 

  29. D. S. Riggs,The Mathematical Approach to Physiological Problems. MIT Press, Cambridge, Mass., 1963, p. 51.

    Google Scholar 

  30. R. S. Julius, The sensitivity of exponentials and other curves to their parameters.Comput. Biomed. Res. 5:473–478 (1972).

    Article  CAS  PubMed  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Division of Pharmaceutics, School of Pharmacy, University of North Carolina, 27514, Chapel Hill, NC

    David M. Cocchetto & William A. Wargin

  2. Department of Clinical Research, Medical Division, Burroughs Wellcome Co., 3030 Cornwallis Road, 27709, Research Triangle Park, NC

    David M. Cocchetto & James W. Crow

Authors
  1. David M. Cocchetto
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. William A. Wargin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. James W. Crow
    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

Cocchetto, D.M., Wargin, W.A. & Crow, J.W. Pitfalls and valid approaches to pharmacokinetic analysis of mean concentration data following intravenous administration. Journal of Pharmacokinetics and Biopharmaceutics 8, 539–552 (1980). https://doi.org/10.1007/BF01060052

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01060052

Key words

Search

Navigation