Selection between Michaelis-Menten and target-mediated drug disposition pharmacokinetic models

Target-mediated drug disposition (TMDD) models have been applied to describe the pharmacokinetics of drugs whose distribution and/or clearance are affected by its target due to high binding affinity and limited capacity. The Michaelis-Menten (M-M) model has also been frequently used to describe the pharmacokinetics of such drugs. The purpose of this study is to investigate conditions for equivalence between M-M and TMDD pharmacokinetic models and provide guidelines for selection between these two approaches. Theoretical derivations were used to determine conditions under which M-M and TMDD pharmacokinetic models are equivalent. Computer simulations and model fitting were conducted to demonstrate these conditions. Typical M-M and TMDD profiles were simulated based on literature data for an anti-CD4 monoclonal antibody (TRX1) and phenytoin administered intravenously. Both models were fitted to data and goodness of fit criteria were evaluated for model selection. A case study of recombinant human erythropoietin was conducted to qualify results. A rapid binding TMDD model is equivalent to the M-M model if total target density R-tot is constant, and RtotKD/(K-D + C)(2) << 1 where K-D represents the dissociation constant and C is the free drug concentration. Under these conditions, M-M parameters are defined as: V-max = k(int)R(tot)V(c) and K-m = K-D where k(int) represents an internalization rate constant, and V-c is the volume of the central compartment. R-tot is constant if and only if k(int) = k(deg), where k(deg) is a degradation rate constant. If the TMDD model predictions are not sensitive to k(int) or k(deg) parameters, the condition of RtotKD/(K-D + C)(2) << 1 alone can preserve the equivalence between rapid binding TMDD and M-M models. The model selection process for drugs that exhibit TMDD should involve a full mechanistic model as well as reduced models. The best model should adequately describe the data and have a minimal set of parameters estimated with acceptable precision.