Time to reach steady state and prediction of steady-state concentrations for drugs obeying Michaelis-Menten elimination kinetics

  • John G. Wagner


Using a numerical integration method, concentration-time data were simulated using the one-compartment open model both with bolus intravenous administration and oral administration (first-order absorption) after multiple doses administered at constant time intervals and for each model for five different doses. Constants used produced data very similar to those which have been reported for phenytoin in the literature. In the simulation of oral data, sufficient concentrations were recorded to allow estimation of the maximum (C n max ), average (¯) Cn, and minimum (C n min ) concentrations during each dosage interval, but for the intravenous data only C n max and C n min values were recorded. The approach to steady state was monoexponential for low doses and biexponential for higher doses. The half-life of the final first-order approach to the steady-state concentration was approximately linearly related to the final steady-state concentration. For the intravenous data the number of doses required to reach 95% of C ss min was a linear function of 0.95 C ss min . A simple difference plot allows any given steady-state concentration of the three to be estimated from non-steady-state concentrations. When C n min values are measured, as in therapeutic drug monitoring, the fitting of C ss min vs. dose rate (D/τ) data leads to operationally useful parameters, V m app and K m app , which are not the true kinetic parameters, Vm and Km, whereas fitting of ¯Css vs d/τ data does lead to estimation of Vm and Km.

Key words

time to reach steady state prediction of steady-state concentrations Michaelis-Menten elimination kinetics 


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Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

  • John G. Wagner
    • 1
  1. 1.College of Pharmacy and Upjohn Center for Clinical PharmacologyThe University of MichiganAnn Arbor

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