Skip to main content
Log in

Statistical moments in pharmacokinetics

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

Abstract

Statistical moments are parameters that describe the characteristics of the time courses of plasma concentration (area, mean residence time, and variance of residence time) and of the urinary excretion rate that follow administration of a single dose of a drug. The relationship between the moments of a time-course curve and pharmacokinetic profiles of drug disposition, i.e., absorption, distribution, metabolism, and excretion, is described. The moments are related to the extent and rate of bioavailability, and it is shown that they can be effectively applied to the deconvolution operation.

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.

Similar content being viewed by others

References

  1. T. Teorell. Kinetics of distribution of substances administered to body. I. The extravascular modes of administration.Arch. Int. Pharmacodyn. Ther. 57:205–225 (1937).

    CAS  Google Scholar 

  2. T. Teorell. Kinetics of distribution of substances administered to the body. II. The intravascular modes of administration.Arch. Int. Pharmacodyn. Ther. 57:226–240 (1937).

    CAS  Google Scholar 

  3. R. Dominguez and E. Pomerene. Calculation of the rate of absorption of exogeneous creatinine.Proc. Soc. Exp. Biol. Med. 60:173–181 (1945).

    Article  CAS  PubMed  Google Scholar 

  4. E. Nelson. Urinary excretion kinetics for evaluation of drug absorption I.J. Am. Pharm. Assoc. 48:489–495 (1945).

    Article  Google Scholar 

  5. J. G. Wagner and E. Nelson. Per cent absorbed time plots derived from blood level and/or urinary excretion data.J. Pharm. Sci. 52:610–611 (1963).

    Article  CAS  PubMed  Google Scholar 

  6. J. G. Wagner and E. Nelson. Kinetics analysis of blood levels and urinary excretion in the absorptive phase after single doses of drug.J. Pharm. Sci. 53:1392–1403 (1964).

    Article  CAS  PubMed  Google Scholar 

  7. J. G. Wagner and J. I. Northam. Estimation of volume of distribution and half-life of a compound after rapid intravenous injection.J. Pharm. Sci. 56:529–531 (1967).

    Article  CAS  PubMed  Google Scholar 

  8. H. Nogami, M. Hanano, S. Awazu, and H. H. Moon. Pharmacokinetic analysis on the disappearance of ethoxybenzamide from plasma: Statistical treatment of data of two compartment model by digital computer.Chem. Pharm. Bull. 17:2097–2104 (1969).

    Article  CAS  PubMed  Google Scholar 

  9. R. E. Wiegant and P. G. Sanders. Calculation of kinetic constants from blood levels of drugs.J. Pharmacol. Exp. Ther. 146:271–275 (1964).

    Google Scholar 

  10. J. F. Borzelleca and W. Lowenthal. Drug absorption from the rectum. II.J. Pharm. Sci. 55:151–154 (1966).

    Article  CAS  PubMed  Google Scholar 

  11. W. Lowenthal and B. L. Vitsky. Computer program from a double exponential equation to determine biological constants.J. Pharm. Sci. 56:169–173 (1967).

    Article  CAS  PubMed  Google Scholar 

  12. D. G. Gardner, J. G. Gardner, G. Laush, and W. W. Meinke. Method for the analysis of multicomponent exponential decay curves.J. Chem. Phys. 31:978–986 (1959).

    Article  CAS  Google Scholar 

  13. S. D. Foss. A method of exponential curve fitting by numerical integration.Biometrics 26:815–821 (1970).

    Article  Google Scholar 

  14. R. G. Cornell. A method for fitting linear combinations of exponentials.Biometrics 18:104–113 (1962).

    Article  Google Scholar 

  15. R. Aris. On the dispersion of a solute in a fluid flowing through a tube.Proc. Roy. Soc. A235:67–77 (1956).

    Article  Google Scholar 

  16. D. M. Himmelblau and K. B. Bischoff. Process analysis and simulation. InDeterministic Systems, Wiley, New York, 1968.

    Google Scholar 

  17. J. X. Hearon. Theorems of linear systems.Ann. N.Y. Acad. Sci. 108:36–68 (1963).

    Article  CAS  PubMed  Google Scholar 

  18. C. D. Thron. Linearity of superposition in pharmacokinetics.Pharmacol. Rev. 26:3–31 (1974).

    CAS  PubMed  Google Scholar 

  19. L. Z. Benet. General treatment of linear mammillary models with elimination from any compartment as used in pharmacokinetics.J. Pharm. Sci. 61:536–541 (1972).

    Article  CAS  PubMed  Google Scholar 

  20. R. L. Schoenfeld. Linear network theory and tracer analysis.Ann. N.Y. Acad. Sci. 108:69–91 (1963).

    Article  CAS  PubMed  Google Scholar 

  21. V. F. Smolen, B. D. Turrie, and W. A. Wiegand. Drug input optimization: Bioavailabilityeffected time-optimal control of multiple, simultaneous, pharmacological effects and their interrelationships.J. Pharm. Sci. 61:1941–1952 (1972).

    Article  CAS  PubMed  Google Scholar 

  22. K. Yamaoka and T. Nakagawa. Application of numerical Laplace transformation to Chromatographic peak analysis.J. Chromatog. 92:213–222 (1974).

    Article  CAS  Google Scholar 

  23. O. Lievenspiel and W. K. Smith. Notes on the diffusion-type model for the longitudinal mixing flow.Chem. Eng. Sci. 7:187–191 (1957).

    Google Scholar 

  24. D. A. McQuarrie. On the stochastic theory of chromatography.J. Chem. Phys. 38:437–445 (1963).

    Article  CAS  Google Scholar 

  25. J. G. Wagner. An overview of the analysis and interpretation of bioavailability studies in man.Arzneim. Forsch. 26:105–108 (1976).

    CAS  Google Scholar 

  26. A. Rescigno and G. Segre.Drug and Tracer Kinetics, Blaisdell, Waltham, Mass., 1966, p. 102.

    Google Scholar 

  27. H. Kiwada, K. Morita, M. Hayashi, S. Awazu, and M. Hanano. A new numerical calculation method for deconvolution in linear compartment analysis for pharmacokinetics.Chem. Pharm. Bull. 25:1312–1318 (1977).

    Article  CAS  PubMed  Google Scholar 

  28. K. C. Kwan, E. L. Foltz, G. O. Breault, J. E. Baer, and J. A. Totaro. Pharmacokinetics of methyldopa in man.J. Pharmacol. Exp. Ther. 198:264–277 (1976).

    CAS  PubMed  Google Scholar 

  29. D. L. Smith, J. G. Wagner, and G. C. Gerritsen. Absorption, metabolism, and excretion of 5-methylpyrazole-3-carboxylic acid in the rat, dog, and human.J. Pharm. Sci. 56:1150–1157 (1967).

    Article  CAS  PubMed  Google Scholar 

  30. E. Krüger-Thiemer and S. P. Eriksen. Mathematical model of sustained-release preparations and its analysis.J. Pharm. Sci. 55:1249–1253 (1966).

    Article  Google Scholar 

  31. P. N. Maurice, W. Reiss, W. Welke, and K. Amson. Cephacetril (C36278-Ba), eines neues Antibioticum aus der Cephalosporinreihe.Arzneim. Forsch. 24:1497–1501 (1974).

    CAS  Google Scholar 

  32. K. Dvoraček, Z. Modr, O. Schmidt, and A. Necaskova. Contribution to the pharmacokinetics of a new cephalosporin derivative.Arzneim. Forsch. 24:1467–1501 (1974).

    Google Scholar 

  33. P. E. Gower, C. H. Dash, and C. H. O'Collaghan. Serum and blood concentration of sodium cephalexin in man given single intramuscular and intravenous injection.J. Pharm. Pharmacol. 25:376–381 (1973).

    Article  CAS  PubMed  Google Scholar 

  34. A. R. Disanto and J. G. Wagner. Pharmacokinetics of highly ionized drug. III. Methylene blue-blood levels in the dog and tissue levels in the rat following intravenous administration.J. Pharm. Sci. 61:1090–1094 (1972).

    Article  CAS  PubMed  Google Scholar 

  35. J. G. Wagner. Linear pharmacokinetic models and vanishing exponential terms: Implication in pharmacokinetics.J. Pharmacokin. Biopharm. 4:395–425 (1976).

    Article  CAS  Google Scholar 

  36. J. G. Wagner. A modern review of pharmacokinetics.J. Pharmacokin. Biopharm. 1:363–401 (1973).

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yamaoka, K., Nakagawa, T. & Uno, T. Statistical moments in pharmacokinetics. Journal of Pharmacokinetics and Biopharmaceutics 6, 547–558 (1978). https://doi.org/10.1007/BF01062109

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01062109

Key words

Navigation