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Pharm Res. 2012 Mar;29(3):866-82. doi: 10.1007/s11095-011-0615-2. Epub 2011 Dec 1.

Theoretical considerations of target-mediated drug disposition models: simplifications and approximations.

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Department of Pharmacokinetics and Drug Metabolism, Amgen Inc., Thousand Oaks, California 91320, USA.



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).


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.


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.


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.

[Indexed for MEDLINE]

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