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%.

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Linear processes in media with dissipation arising in conductivity, optics, viscoelasticity, etc. are considered. Time-periodic fields in such media are described by linear differential equations for complex-valued potentials. The properties of the media are characterized by complex valued tensors, for example, by complex conductivity or complex elasticity tensors. Variational formulations are suggested for such problems: The functionals whose Euler equations coincide with the original ones are constructed. Four equivalent variational principles are obtained: two minimax and two minimal ones. The functionals of the obtained minimal variational principles are proportional to the energy dissipation averaged over the period of oscillation. The last principles can be used in the homogenization theory to obtain the bounds on the effective properties of composite materials with complex valued properties tensors.

Models for drugs exhibiting target-mediated drug disposition (TMDD) describe biological processes in which drug-target binding significantly influences both pharmacodynamics (PD) and pharmacokinetics (PK). TMDD models are often over-parameterized and their parameters are difficult to estimate based on available data. Approximations of the general model have been suggested, but even these simpler forms can be over-parameterized when, for example, target and drug-target complex concentrations are not available. This work i) reviews TMDD equations, their approximations and methods to study identifiability of model parameters; ii) reviews the publications that used TMDD equations to describe PK and PD of biologics; and iii) discusses issues of identifiability of the TMDD model parameters related to study design and data analysis. Examples demonstrate that use of the TMDD equations for the population PK and PD modeling is most successful when the target and drug-target complex concentrations are available in addition to the drug concentration data. TMDD parameter estimates can be trusted only when they are identifiable, that is, can be estimated from the available data with sufficient precision. Parameter identifiability analysis should be an integral part of the TMDD system investigation. It also should be used prospectively for optimal study design.

Treatment regimens involving obinutuzumab (GA101) demonstrated increased efficacy to rituximab in clinical trials for non-Hodgkin's lymphoma (NHL) and chronic lymphocytic leukemia (CLL). However, the pharmacokinetic (PK) properties and the exposure–response relationships of obinutuzumab still need to be fully described. Data from four clinical trials of obinutuzumab were analyzed to describe the PK properties in patients with NHL or CLL and the pharmacodynamic (PD) properties in patients with CLL. A population PK model with linear time-dependent clearance described the obinutuzumab concentration–time course. Diagnosis, baseline tumor size (BSIZ), body weight, and gender were the main covariates affecting obinutuzumab exposure. In patients with CLL, exposure was not associated with safety but showed positive trends of correlation with efficacy. Although efficacy correlated positively with exposure, since both efficacy and exposure correlated negatively with BSIZ, it was not possible to determine with certainty whether it would be beneficial to adjust the dose according to BSIZ.