Skip to main content

A model-independent proof of Dost's law of corresponding areas


Provided that the body is regarded as a linear system and the response to a unit impulse input is Riemann integrable in the interval [0, ∞), the validity of Dost's law of corresponding areas is demonstrated. No other restrictions are placed on the nature of the blood drug concentration-time curve. The derivation is independent of any drug distribution models. However, the specification of a drug input point is essential for the application of the area relationship. A limit theorem for the improper integration of a convolution integral is presented.

This is a preview of subscription content, access via your institution.


  1. Guidelines for biopharmaceutical studies in man, APhA Academy of Pharmaceutical Sciences, February 10–11 (1972).

  2. F. H. Dost.Grundlagen der Pharmakokinetic, 2nd ed., Thieme, Stuttgart, 1968, pp. 155–161.

    Google Scholar 

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

    CAS  PubMed  Article  Google Scholar 

  4. D. P. Vaughan and A. Trainor. A general equation for the ratio of the areas below the blood or plasma concentration time-curves following intravenous and oral drug administration and its application to inter-subject variations in drug elimination.Br. J. Clin. Pharmacol. 1:239–250 (1975).

    Article  Google Scholar 

  5. E. Nuesch. Proof of the general validity of Dost's law of corresponding areas.Eur. J. Clin. Pharmacol. 6:33–43 (1973).

    CAS  PubMed  Article  Google Scholar 

  6. J. G. Wagner. Do you need a pharmacokinetic model, and if so, which one?J. Pharmacokin. Biopharm. 3:457–478 (1975).

    CAS  Article  Google Scholar 

  7. D.P. Vaughan and G. T. Tucker. General theory for rapidly establishing steady state drug concentrations using two consecutive constant rate intravenous infusions.Eur. J. Clin. Pharmacol. 9:235–238 (1975).

    CAS  PubMed  Article  Google Scholar 

  8. D. P. Vaughan and G. T. Tucker. General derivation of the ideal intravenous drug input required to achieve and maintain a constant plasma drug concentration: Theoretical applications to lignocaine therapy.eur. J. Clin. Pharmacol. 10:433–440 (1976).

    CAS  PubMed  Article  Google Scholar 

  9. D. P. Vaughan. A general method for estimating thein vivo release rate constant of a drug from its oral formulation.J. Pharm. Pharmacol. 28:505–507 (1976).

    CAS  PubMed  Article  Google Scholar 

  10. R. V. Churchill.Operational Mathematics, McGraw-Hill, New York, 1958.

    Google Scholar 

  11. B. M. Brown.The Mathematical Theory of Linear Systems, Chapman and Hall, London, 1961.

    Google Scholar 

  12. D. S. Riggs.Control Theory and Physiological Feedback Mechanisms, Williams and Wilkins, Baltimore, 1970.

    Google Scholar 

  13. M. G. Smith.Laplace Transform Theory, Van Nostrand, London, 1966.

    Google Scholar 

  14. G. Doetsch.Guide to the Application of Laplace Transforms, Van Nostrand, London, 1961.

    Google Scholar 

Download references

Author information

Authors and Affiliations


Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Vaughan, D.P. A model-independent proof of Dost's law of corresponding areas. Journal of Pharmacokinetics and Biopharmaceutics 5, 271–276 (1977).

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI:

Key words

  • law of corresponding areas
  • Dost's law
  • convolution integral