Simulation for population analysis of Michaelis-Menten elimination kinetics

A simulation study was conducted to compare the cost and performance of various models for population analysis of the steady state pharmacokinetic data arising from a one-compartment model with Michaelis-Menten elimination. The usual Michaelis-Menten model (MM) and its variants provide no estimate of the volume of distribution, and generally give poor estimates of the maximal elimination rate and the Michaelis-Menten constant. The exact solution to the Michaelis-Menten differential equation (TRUE) requires a precise analysis method designed for estimation of population pharmacokinetic parameters (the first-order conditional estimation method) and also considerable computational time to estimate population mean parameters accurately. The one-compartment model with dose-dependent clearance (DDCL), in conjunction with the first-order conditional estimation or Laplacian method, ran approximately 20-fold faster than TRUE and gave accurate population mean parameters for a drug having a long biological half-life relative to the dosing interval. These findings suggest that the well-known MM and its variants should be used carefully for the analysis of blood concentrations of a drug with Michaelis-Menten elimination kinetics, and that TRUE, in conjunction with a precise analysis method, should be considered for estimating population pharmacokinetic parameters. In addition, DDCL is a promising alternative to TRUE with respect to computation time, when the dosing interval is short relative to the biological half-life of a drug.