Generalizations in linear pharmacokinetics using properties of certain classes of residence time distributions. II. Log-concave concentration-time curves following oral administration

  • Michael Weiss
Article
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Abstract

The present approach enables a noncompartmental assessment of log-concave plasma concentration-time profiles following oral drug administration. Observed log-concavity corresponds to a nonparametric class of residence time distributions with the following properties: (1) The fractional rate of elimination kB(t) (failure rate of the distribution) increases monolonically until reaching the terminal exponential coefficient kB,Z.(2) The relative dispersion of body residence times CV B 2 (ratio of variance to the squared mean , VBRT/MBRT2,)acts as a shape parameter of the curve. The role of the input process in determining the shape of the concentration profile is discussed. In this connection evidence is provided for the importance of log-concave percent undissolved versus time plots, introducing the general concept of a time-varying fractional rate of dissolution. The governing factor for the appearance of log-concavity is the ratio of mean absorption time to mean disposition residence time (MAT/MDRT);this factor exceeds a particular threshold value which depends on the distributional properties of the drug. Generalizing previous approaches which are valid for first-order input processes, the “flipflop” phenomenon and the problem of “vanishing of exponential terms” are explained using fewer assumptions. Upper bounds for the elimination time (more than 90% eliminated) and the cutoff error in AUCdetermination are presented. The concept of logconcavity reveals general features of the pharmacokinetic behavior of oral dosage forms exhibiting a dominating influence of the absorption/dissolution process.

Key words

Pharmacokinetics oral administration noncompartmental approach log-concavity dissolution profile reliability theory 
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References

  1. 1.
    M. Weiss. Generalizations in linear pharmacokinetics using properties of certain classes of residence time distributions. I. Log-convex drug disposition curves.J. Pharmacokin. Biopharm. 14:635–657 (1986).CrossRefGoogle Scholar
  2. 2.
    K. K. H. Chan and M. Gibaldi. Assessment of drug absorption after oral administrtation.J. Pharm. Sci 74:388–393 (1985).PubMedCrossRefGoogle Scholar
  3. 3.
    M. Weiss. Theorems on log-convex disposition curves in drug and tracer kinetics.J. Theor. Biol. 116:355–368 (1985).PubMedCrossRefGoogle Scholar
  4. 4.
    R. E. Barlow and F. Proschan.Mathematical Theory of Reliability, Wiley, New York, 1965.Google Scholar
  5. 5.
    L. Nyberg, K.-E. Anderson, and A. Bertler. Biovailability of digoxin from tablets. III. Availability of digoxin in man from preparations with different dissolution rate.Acta Pharm. Suecica 11:471–492 (1974).Google Scholar
  6. 6.
    D. Brockmeier, H. J. Dengler, and D. Voegele.In vitro-in vivo correlation a time scaling problem? Transformation ofin vitro results to thein vivo situation, using theophylline as a practical example.Eur. J. Clin. Pharmacol. 28:291–300 (1985).PubMedCrossRefGoogle Scholar
  7. 7.
    J. Keilson.Markov Chain Models—Rarity and Exponentiality, Springer, New York, 1979.CrossRefGoogle Scholar
  8. 8.
    P. R. Byron and R. E. Notari. Critical analysis of “flip-flop” phenomenon in twocompartment pharmacokinetic model.J. Pharm. Sci. 65:1140–1144 (1976).PubMedCrossRefGoogle Scholar
  9. 9.
    R. H. Guy, J. Hadgraft, I. W. Kellaway, and M. J. Taylor. Calculations of drug release rates from spherical particles.Int. J. Pharm. 11:199–207 (1982).CrossRefGoogle Scholar
  10. 10.
    J. R. Leary and S. D. Ross. Mathematical expression of tablet dissolution profiles.Int. J. Pharm. 17:193–201 (1983).CrossRefGoogle Scholar
  11. 11.
    N. Watari and N. Kaneniwa. Prediction of blood levels following oral administration of weakly acidic drug particles such as sulfa drugs in rabbits from thein vitro dissolution behavior.J. Pharmacobiodyn. 7:351–365 (1984).PubMedCrossRefGoogle Scholar
  12. 12.
    J. M. van Rossum and C. A. M. van Ginneken. Pharmacokinetic system dynamics. In E. Gladtke and H. Heimann (eds.),Pharmacokinetics, Fischer, Stuttgart, 1980, pp. 53–73.Google Scholar
  13. 13.
    M. Weiss. Use of gamma distributed residence times in pharmacokinetics,Eur. J. Clin. Pharmacol. 25:695–702 (1983).PubMedCrossRefGoogle Scholar
  14. 14.
    N. Watari, T. Funaki, K. Aizawa, and N. Kaneniwa. A flip-flop model for nitrofurantoin disposition in the rabbit following oral administration.Int. J. Pharm. 21:85–98 (1984).CrossRefGoogle Scholar
  15. 15.
    R. E. Barlow and F. Proschan.Statistical Theory of Reliability and Life Testing, Holt, Rinehart and Winston, New York, 1975.Google Scholar
  16. 16.
    M. Weiss. A general model of metabolite kinetics following intravenous and oral administration of the precursor drug.Biopharm. Drug Dispos., in press.Google Scholar

Copyright information

© Plenum Publishing Corporation 1987

Authors and Affiliations

  • Michael Weiss
    • 1
  1. 1.Department of Pharmacology and ToxicologyMartin Luther UniversityHalleGerman Democratic Republic

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