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Some clarifications regarding moments of residence times with pharmacokinetic models

  • Pharmacometrics
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Abstract

The stochastic formulation of linear kinetic models is elaborated in order to introduce some new concepts and help clarify the meaning and role of residence time moments. Certain conditional moments are introduced. Multicompartment and steady-state dosing within the stochastic context are considered. A general model-independent formula for steady state volume of distribution and a new concept of steady-state moments are presented. A technique for constructing a model of a given topology from its moments is also given.

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References

  1. K. Yomaoka, T. Nakagawa, and T. Uno. Statistical moments in pharmacokinetics.J. Pharmacokin. Biopharm. 6:547–558 (1978).

    Article  Google Scholar 

  2. J. H. Matis, T. E. Wehrly, and C. M. Metzler. On some stochastic formulations and related statistical moments of pharmacokinetic models.J. Pharmacokin. biopharm. 11:77–92 (1983).

    Article  CAS  Google Scholar 

  3. L. Z. Benet and R. L. Galeazzi. Noncompartmental determination of the steady state volume of distribution.J. Pharmacol. Sci. 48:1071–1074 (1979).

    Article  Google Scholar 

  4. K. Pearson. Statistical fitting of curves to observations and measurements.Biometrika I:265–303;II:1–23 (1902).

    Article  Google Scholar 

  5. M. G. Kendall and A. Stuart.The Advanced Theory of Statistics, Vol. I, Hafner, New York, 1958.

    Google Scholar 

  6. N. Bailey.Stochastic Processes in Biological Applications, Wiley, New York, 1964, p. 79.

    Google Scholar 

  7. J. D. Kalbfleisch and R. L. Prentice.The Statistical Analysis of Failure Time Data, Wiley, New York, 1980, p. 8.

    Google Scholar 

  8. E. A. Nüesch. Noncompartmental approach in pharmacokinetics using moments.Drug Metab. Rev. 15:103–131 (1984).

    Article  PubMed  Google Scholar 

  9. C. Cobelli and G. Toffolo. Compartmental and noncompartmental models as candidate classes for kinetic modeling, theory and computational aspects. In J. Eisenfeld and C. Delisi (eds.),Mathematics and Computers in Biomedical Applications, Elsevier, 1985, pp. 219–236.

  10. J. Eisenfeld. Stochastic parameters in compartmental systems.Math. Biosci. 52:261–275 (1980).

    Article  Google Scholar 

  11. J. J. DiStefano III. Noncompartmental vs. compartmental analysis: Some bases for choice.Am. J. Physiol. 243 (Regulatory Integrative Comp. Physiol. 12):R1-R6 (1982).

    PubMed  Google Scholar 

  12. J. J. DiStefano III and E. M. Landaw. Multiexponential, multicompartmental, and noncompartmental modeling. I. Methodological limitations and physiological interpretations.Am. J. Physiol. 246 (Regulatory Integrative Comp. Phyisol. 15):R651-R664 (1984).

    PubMed  Google Scholar 

  13. P. S. Collier. Some considerations on the estimation of steady state apparent volume of distribution and the relationships between volume terms.J. Pharmacokin. Biopharm. 11:93–105 (1983).

    Article  CAS  Google Scholar 

  14. C. Cobelli and G. Toffolo. Compartmental vs. noncompartmental modeling for two accessible pools.Am. J. Physiol. 247(Regulatory Integrative Comp. Physiol. 16):R488-R496 (1984).

    CAS  PubMed  Google Scholar 

  15. IMSL Library: Problem-Solving Software System for Mathematical and Statistical FORTRAN Programming, IMSL, Houston, 1984.

  16. D. C. Murdoch.Linear Algebra, Wiley, New York, 1970, p. 134.

    Google Scholar 

  17. M. Gibaldi and D. Perrier.Pharmacokinetics, Marcel Dekker, New York, 1982, p. 410.

    Google Scholar 

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Authors and Affiliations

  1. Department of Laboratory Medicine, University of California, San Francisco, California

    Stuart L. Beal

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  1. Stuart L. Beal
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Beal, S.L. Some clarifications regarding moments of residence times with pharmacokinetic models. Journal of Pharmacokinetics and Biopharmaceutics 15, 75–92 (1987). https://doi.org/10.1007/BF01062940

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  • DOI: https://doi.org/10.1007/BF01062940

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