title: Explicit solution of integrated 1 - exp equation for predicting accumulation and decline of concentrations for drugs obeying nonlinear saturation kinetics.
abstract: To describe nonlinear, saturable pharmacokinetics, the Michaelis-Menten equation is frequently used. However, the Michaelis-Menten equation has no integrated solution for concentrations but only for the time factor. Application of the Lambert W function was proposed recently to obtain an integrated solution of the Michaelis-Menten equation. As an alternative to the Michaelis-Menten equation, a 1 - exp equation has been used to describe saturable kinetics, with the advantage that the integrated 1 - exp equation has an explicit solution for concentrations. We used the integrated 1 - exp equation to predict the accumulation kinetics and the nonlinear concentration decline for a proposed fictive drug. In agreement with the recently proposed method, we found that for the integrated 1 - exp equation no steady state is obtained if the maximum rate of change in concentrations (Vmax) within interval (Tau) is less than the difference between peak and trough concentrations (Vmax x Tau < C peak - C trough).
authors.affiliation: Nephrology, Medical Faculty, University of Ulm, Ulm, Germany. frieder.keller@uni-ulm.de
authors.forename: Frieder
authors.initials: F
authors.lastname: Keller
authors.forename: Bertram
authors.initials: B
authors.lastname: Hartmann
authors.forename: David
authors.initials: D
authors.lastname: Czock
mesh_terms: D016903:Drug Monitoring / Q000379:methods; D006801:Humans; D017711:Nonlinear Dynamics; D010599:Pharmacokinetics