Critical evaluation of the potential error in pharmacokinetic studies of using the linear trapezoidal rule method for the calculation of the area under the plasma level-time curve


The linear trapezoidal rule method is commonly used for the estimation of the area under the plasma level-time curve. Error analyses are performed when the method is used in first-order absorption and first-order elimination kinetics in the one-compartment system. It is found that significant underestimations and overestimations in area during the absorption phase and postabsorption phase, respectively, can occur when the method is improperly used. During the exponential postabsorption phase the relative error is only a function of the ratio (n)of the time interval over the half-life of the two plasma data points in the interval. The error from the linear trapezoidal rule method at n=0.5 is about 1%. The error increases to 15.5% and 57.1 % when nis increased to 2 and 4, respectively. It is recommended that for most absorption studies the linear trapezoidal method be used for prepeak and plateau plasma data and the logarithmic trapezoidal method for postpeak plasma data.

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  1. 1.

    S. A. Kaplan. Biopharmaceutics in the pre-formulation stages of drug development. In J. Swarbrick (ed.),Current Concepts in the Pharmaceutical Sciences: Dosage Form Design and Bioavailability, Lea and Febiger, Philadelphia, 1973, Chap. 1.

    Google Scholar 

  2. 2.

    M. Gibaldi and D. Perrier.Pharmacokinetics, Dekker, 1975, pp. 67, 132, and 293.

  3. 3.

    D.S. Riggs.The Mathematical Approach to Physiological Problems, Williams and Wilkins, Baltimore, 1967.

    Google Scholar 

  4. 4.

    W. L. Chiou, M. A. F. Gadalla, and G. W. Peng. Method for the rapid estimation of the total body drug clearance and adjustment of dosage regimens in patients during a constant-rate intravenous infusion.J. Pharmacokin. Biopharm. 6:135–152 (1978).

    CAS  Article  Google Scholar 

  5. 5.

    K. C. Yeh and K. C. Kwan. A comparison of numerical integrating logarithms by trapezoidal, Lagrange, and spline approximation.J. Pharmacokin. Biopharm. 6:79–98 (1978).

    CAS  Article  Google Scholar 

  6. 6.

    P. G. Welling, L. L. Lyons, W. A. Craig, and G. A. Trochta. Influence of diet and fluid on bioavailability of theophylline.Clin. Pharmacol. Ther. 17:475–480 (1975).

    CAS  PubMed  Google Scholar 

  7. 7.

    P. G. Welling, P. A. Koch, C. C. Lau, and W. A. Craig. Bioavailability of tetracycline and doscycline in fasted and nonfasted subjects.Antimicrob. Agents Chemother. 11:462–469 (1977).

    CAS  PubMed Central  PubMed  Article  Google Scholar 

  8. 8.

    S. A. Kaplan, R. E. Weinfeld, C. W. Abruzzo, and M. Lewis. Pharmacokinetic profile of sulfisoxazole following intravenous, intramuscular, and oral administration to man.J. Pharm. Sci. 61:773–778 (1972).

    CAS  PubMed  Article  Google Scholar 

  9. 9.

    C. T. Ueda and B. S. Dzindzio. Quinidine kinetics in congestive heart failure.Clin. Pharmacol. Ther. 23:158–164 (1978).

    CAS  PubMed  Google Scholar 

  10. 10.

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

    CAS  PubMed  Article  Google Scholar 

  11. 11.

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

    CAS  Article  Google Scholar 

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Chiou, W.L. Critical evaluation of the potential error in pharmacokinetic studies of using the linear trapezoidal rule method for the calculation of the area under the plasma level-time curve. Journal of Pharmacokinetics and Biopharmaceutics 6, 539–546 (1978).

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Key words

  • trapezoidal rule
  • area under the curve
  • pharmacokinetics
  • clearance
  • bioavailability
  • integration method
  • sulfisoxazole