Peiming Ma

Approximations of the target-mediated drug disposition model and identifiability of model parameters

Models for drugs exhibiting target-mediated drug disposition (TMDD) play an important role in the investigation of biological products (Mager and Jusko 2001). These models are often overparameterized and difficult to converge. A simpler quasi-equilibrium (QE) approximation of the general model has been suggested (Mager and Krzyzanski 2005), but even this simpler form can be overparameterized when, for example, drug target level is not available. This work (a) introduces quasi-steady-state (QSS) and Michaelis-Menten (MM) approximations of the TMDD model, (b) derives the relationships between the parameters of the TMDD, QE, QSS and MM models, (c) investigates the parameter ranges where the simplified approximations are equivalent to the TMDD model, (d) proposes an algorithm for establishing identifiability of these models, and (e) tests this algorithm on simulated datasets. The proposed QSS approximation is more general than the QE approximation: it degenerates into the QE approximation when the internalization rate of the drug-target complex is much smaller than its dissociation rate. The proposed identifiability analysis algorithm may be applied to provide justification for use of simplified approximations, avoiding use of incorrect parameter estimates of over-parameterized TMDD models while simultaneously saving time and resources required for the pharmacokinetics analysis of drugs with TMDD. The utility of the derived approximations and of the identifiability algorithm was demonstrated on the examples of the simulated data sets. The simulation examples indicated that the QSS model may be preferable to the QE model when the internalization rate of the drug-target complex significantly exceeds its dissociation rate. The MM approximation may be adequate when the drug concentration significantly exceeds the target concentrations or when the target occupancy is close to 100%.

Theoretical Considerations of Target-Mediated Drug Disposition Models: Simplifications and Approximations

ABSTRACTPurposeTo 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).MethodsBased 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.ResultsThe 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.ConclusionsAs 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.

The Utility of Modeling and Simulation Approaches to Evaluate Immunogenicity Effect on the Therapeutic Protein Pharmacokinetics

While therapeutic proteins (TP), particularly recombinant human proteins and fully human monoclonal antibodies, are designed to have a low immunogenic potential in humans, a clinical immune response does sometimes occur and cannot be predicted from preclinical studies. Changes in TP pharmacokinetics may be perceived as an early indication of antibody formation and serve as a surrogate for later changes in efficacy and safety in individual subjects. Given the substantial increase in number of biological products, including biosimilars, there is an urgent need to quantitatively predict and quantify the immune response and any consequential changes in TP pharmacokinetics. The purpose of this communication is to review the utility of population-based modeling and simulation approaches developed to date for investigating the development of an immune response and assessing its impact on TP pharmacokinetics. Two examples of empirical modeling approaches for pharmacokinetic assessment are presented. The first example presents methods to analyze pharmacokinetic data in the presence of anti-drug antibody (ADA) and confirm the effect of immunogenicity on TP pharmacokinetics in early phases of drug development. The second example provides a framework to analyze pharmacokinetic data in the absence or with very low incidence of ADA and confirm with enough power the lack of an immunogenicity effect on TP pharmacokinetics in late phases of drug development. Finally, a theoretical mechanism-based modeling framework is presented to mathematically relate the complex interaction among TP, their targets, and ADA.

Population pharmacokinetic-pharmacodynamic modeling of omecamtiv mecarbil, a cardiac myosin activator, in healthy volunteers and patients with stable heart failure.

Data from 3 clinical trials of omecamtiv mecarbil in healthy volunteers and patients with stable heart failure (HF) were analyzed using a nonlinear mixed‐effects model to investigate omecamtiv mecarbils pharmacokinetics and relationship between plasma concentration and systolic ejection time (SET) and Doppler‐derived left ventricular outflow tract stroke volume (LVOTSV). Omecamtiv mecarbil pharmacokinetics were described by a linear 2‐compartment model with a zero‐order input rate for intravenous administration and first‐order absorption for oral administration. Oral absorption half‐life was 0.62 hours, and absolute bioavailability was estimated as 90%; elimination half‐life was approximately 18.5 hours. Variability in pharmacokinetic parameters was not explained by patient baseline characteristics. Omecamtiv mecarbil plasma concentration was directly correlated with increases in SET and LVOTSV between healthy volunteers and patients with HF. The maximum increase from baseline in SET (delta SET) estimated by an Emax model was 137 milliseconds. LVOTSV increased linearly from baseline by 1.6 mL per 100 ng/mL of omecamtiv mecarbil. Model‐based simulations for several immediate‐release oral dose regimens (37.5, 50, and 62.5 mg dosed every 8, 12, and 24 hours) showed that a pharmacodynamic effect (delta SET ≥20 milliseconds) could be maintained in the absence of excessive omecamtiv mecarbil plasma concentrations.