title: Theoretical considerations of target-mediated drug disposition models: simplifications and approximations.
abstract: OBJECTIVE
  To clarify relationships among various types of target-mediated disposition (TMD) models including the Michaelis-Menten, quasi-steady-state (Qss), and rapid binding models and propose measures for the closeness of some models as approximations to the general TMD model (Mager and Jusko, J Pharmacokinet Pharmacodyn 28(6):507-532, 2001).
  
  
  METHODS
  Based on the classic singular perturbation theory by selecting appropriate scales of time, we derive requirements with which the Michaelis-Menten and Qss models are suitable approximations. Under the Qss assumption we show that other simplifications of the general TMD model can be similarly obtained as the Michaelis-Menten and Qss models. We compare these models by simulations using known application examples.
  
  
  RESULTS
  The Michaelis-Menten and Qss models are direct simplifications of the general TMD model and, moreover, suitable approximations if certain specific requirements on the parameters are met.
  
  
  CONCLUSIONS
  As a first attempt to quantify the closeness of some simplifications to the general TMD model, our work should provide a more rigorous basis for the theoretical and practical research of TMD models, which are important for investigating the pharmacokinetic-pharmacodynamic relationships of many biological compounds.
authors: Department of Pharmacokinetics and Drug Metabolism, Amgen Inc., Thousand Oaks, California 91320, USA. peimingm@amgen.com
authors: Peiming
authors: P
authors: Ma
mesh_terms: D000818:Animals; D003198:Computer Simulation; D016503:Drug Delivery Systems; D006801:Humans; D008954:Models, Biological; D004364:Pharmaceutical Preparations / Q000008:administration & dosage*; D010599:Pharmacokinetics; D010600:Pharmacology
chemical_list: D004364:Pharmaceutical Preparations