Estimation Aspects of the Michaelis–Menten Model

Abstract

This paper studies the Michaelis–Menten model (MM), which plays an important role in pharmacokinetics, from a theoretical as well as a computational point of view. An analytical method for the nonlinear least squares estimation of the MM is introduced. It is proved that the MM model has not a unique parameter estimation (through the nonlinear least squares), and there is not a unique optimal experimental design and might not have a unique D-optimal design. An iterative process, based on the Sequential approach, is also introduced and tested on various data sets for the MM model. A different approach is also discussed which provides an initial estimate that increases the convergence rate of the Fully Sequential approach. Several examples demonstrate the provided methods.