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On some Applications of the Eigenvector Decomposition Principle in Pharmacokinetic Analysis

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Mathematical Models in Medicine

Part of the book series: Lecture Notes in Biomathematics ((LNBM,volume 11))

Abstract

Pharmacokinetic analysis, as it is practised everywhere, is mainly a linear analysis /1/. Despite of wellknown nonlinear effects /2/ as protein-binding or active transport processes with their saturation phenomena, most authors apply models where all concentration versus time curves obey the superposition principle: i.e. all parts of a drug administered are assumed to travel independent of each other within the body.

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References

  1. Dost, F. H.: Grundlagen der Pharmakokinetik. 2nd edition, Thieme Stuttgart 1968.

    Google Scholar 

  2. Thron, C.D.: Linearity and superposition in pharmacokinetics. Pharmacol. Rev. 26, 3–31(1974).

    MathSciNet  Google Scholar 

  3. Müller-Schauenburg, W.: A new method for multi-compartment pharmacokinetic analysis: the eigenvector decomposition principle. Europ. J. Clin. Pharmacol. 6, 203–206(1973).

    Article  Google Scholar 

  4. Riggs, D. S.: The mathematical approach to physiological problems. M. I. T. Press paperback, Cambridge Mass., London 1970.

    Google Scholar 

  5. Rockoff, M.L.: Interpretation of the clearance curve of a diffusible tracer by blood flow in terms of a parallel-compartment model. p. 108–126 in Computer processing of dynamic images from an Anger scintillation camera. K.B. Larson and J. R. Cox ed. The society of nuclear medicine, Inc. New York 1974

    Google Scholar 

  6. Simon, W.: A method of exponential separation applicable to small computers. Phys.Med. Biol. 15,355–360(1970)

    Article  Google Scholar 

  7. Glass, H. I. and A. C. DeGarreta: The quantitative limitations of exponential curve fitting. Phys.Med. Biol. 16,119–130(1971)

    Article  Google Scholar 

  8. Feldmann, U.: Lecture notes in this volume.

    Google Scholar 

  9. Schneider, B.: Mathematical and statistical problems in pharmacokinetics. Advances in the Bioschiences. Schering Workshop on pharmacokintics, Berlin, May 8and 9, 1969. Pergamon Press — Vieweg 1970, p. 103–112.

    Google Scholar 

  10. Rescigno, A. and G. Segre: Drug and tracer kinetics. Blaisdell, Waltharn, Mass. 1966.

    Google Scholar 

  11. Gibaldi, M., R. Nagashima and G. Lewy: Relations between drug concentration in plasma or serum and amount of drug in the body. J. Pharm. Sci. 58, 193–197(1969).

    Article  Google Scholar 

  12. Lewi, P. J.: Pharmacokinetics and eigenvector decomposition. Two-compartment open system after rapid intravenous administration. Arch.int.de Pharmacodynamie et de Therapie 215, 283–300(1975).

    Google Scholar 

  13. Gladtke, E. und H.M. v. Hattingberg: Pharmakokinetik. Springer, Berlin Heidelberg NewYork 1973.

    Google Scholar 

  14. Dost, F.H.: Absorption, Transit, Occupancy und Availments als neue Begriffe in der Biopharmazeutik. Klin. Wschr. 50, 410–412(1972).

    Article  Google Scholar 

  15. Scholer, J. F. and C.F. Code: Rate of absorption of water from stomach and small bowel in human beings. Gastroenterology 27, 565–577(1954).

    Google Scholar 

  16. Wagner, J. G. and E. Nelson: Percent absorbed time plots derived from blood level andor urinary excretion data. J. Pharm. Sci. 52,610–611(1963).

    Article  Google Scholar 

  17. Loo, J. C. K. and S. Riegelman: New method for calculating the intrinsic absorption rate of drugs. J. Pharm. Sci. 57, 918–928(1968).

    Article  Google Scholar 

  18. Kwan, K. C. and A. E. Till: Novel method for bioavailability assessment. J.Pharm.Sci. 62,1494–1497(1973).

    Article  Google Scholar 

  19. Wagner, J.G.: Application of the Wagner-Nelson absorption method to two-compartment open model. J. Pharmacokinetics Biopharmaceutics 2,469–486 (1974).

    Article  Google Scholar 

  20. Wagner, J.G.: Application of the Loo-Riegelman absorption method. J. Pharmacokinetics Biopharmaceutics 3, 51–67(1975)

    Article  Google Scholar 

  21. Till, A. E., L. Z. Benet and K. C. Kwan: An integrated approach to the pharmacokinetic analysis of drug absorption. J. Pharmacokinetics Biopharmaceutics 2,525–544(1974)

    Article  Google Scholar 

  22. Gibaldi, M., R. N. Boyes and S. Feldman: Influence of first-pass effect on availability of drugs on oral administration. J. Pharm. Sci. 60, 1338–1340(1971).

    Article  Google Scholar 

  23. Rowland, M.: Influence of route of administraion on drug availability. J. Pharm. Sci. 61, 70–74(1972).

    Article  Google Scholar 

  24. Nüesch, E.: Proof of the general validity of Dost’s law of corresponding areas. Europ. J. clin. Pharmacol.6, 33–43(1973).

    Article  Google Scholar 

  25. Silverman, M. and A. S. V. Burgen: Application of analogue computer to measurement of intestinal absorption rates with tracers. J.Appl. Physiol. 16, 911–913(1961).

    Google Scholar 

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Author information

Authors and Affiliations

  1. Dep. of Nuclear Medicine, Medical Radiol. Institut, Röntgenweg 11, D-7400, Tübingen, Deutschland

    W. Müller-Schauenburg

Authors
  1. W. Müller-Schauenburg
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Editor information

Editors and Affiliations

  1. Fakultät für Klinische Medizin Mannheim, Universität Heidelberg, Theodor-Kutzer Ufer, 6200, Mannheim, Deutschland

    Jürgen Berger

  2. Fachbereich Mathematik, Johannes Gutenberg Universität, Saarstraße 21, 6500, Mainz, Deutschland

    Wolfgang J. Bühler

  3. Abt. Medizinische Statistik und Dokumentation, Theaterstraße 13, 5100, Aachen, Germany

    Rudolf Repges

  4. Institut für Dokumentation, Information und Statistik, Deutsches Krebsforschungszentrum, Im Neuenheimer Feld 280, 6900, Heidelberg 1, Germany

    Petre Tautu

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© 1976 Springer-Verlag Berlin · Heidelberg

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Müller-Schauenburg, W. (1976). On some Applications of the Eigenvector Decomposition Principle in Pharmacokinetic Analysis. In: Berger, J., Bühler, W.J., Repges, R., Tautu, P. (eds) Mathematical Models in Medicine. Lecture Notes in Biomathematics, vol 11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-93048-5_13

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  • DOI: https://doi.org/10.1007/978-3-642-93048-5_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07802-9

  • Online ISBN: 978-3-642-93048-5

  • eBook Packages: Springer Book Archive

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