Incorporating physiological and biochemical mechanisms into pharmacokinetic-pharmacodynamic models: a conceptual framework

Personalized Dosing of Medicines for Children: A Primer on Pediatric Pharmacometrics for Clinicians

The widespread use of drugs for unapproved purposes remains common in children, primarily attributable to practical, ethical, and financial constraints associated with pediatric drug research. Pharmacometrics, the scientific discipline that involves the application of mathematical models to understand and quantify drug effects, holds promise in advancing pediatric pharmacotherapy by expediting drug development, extending applications, and personalizing dosing. In this review, we delineate the principles of pharmacometrics, and explore its clinical applications and prospects. The fundamental aspect of any pharmacometric analysis lies in the selection of appropriate methods for quantifying pharmacokinetics and pharmacodynamics. Population pharmacokinetic modeling is a data-driven method ('top-down' approach) to approximate population-level pharmacokinetic parameters, while identifying factors contributing to inter-individual variability. Model-informed precision dosing is increasingly used to leverage population pharmacokinetic models and patient data, to formulate individualized dosing recommendations. Physiologically based pharmacokinetic models integrate physicochemical drug properties with biological parameters ('bottom-up approach'), and is particularly valuable in situations with limited clinical data, such as early drug development, assessing drug-drug interactions, or adapting dosing for patients with specific comorbidities. The effective implementation of these complex models hinges on strong collaboration between clinicians and pharmacometricians, given the pivotal role of data availability. Promising advancements aimed at improving data availability encompass innovative techniques such as opportunistic sampling, minimally invasive sampling approaches, microdialysis, and in vitro investigations. Additionally, ongoing research efforts to enhance measurement instruments for evaluating pharmacodynamics responses, including biomarkers and clinical scoring systems, are expected to significantly bolster our capacity to understand drug effects in children.

Drug Exposure to Establish Pharmacokinetic-Response Relationships in Oncology

In the oncology field, understanding the relationship between the dose administered and the exerted effect is particularly important because of the narrow therapeutic index associated with anti-cancer drugs and the high interpatient variability. Therefore, in this review, we provide a critical perspective of the different methods of characterising treatment exposure in the oncology setting. The increasing number of modelling applications in oncology reflects the applicability and the impact of pharmacometrics on all phases of the drug development process and patient management as well. Pharmacometric modelling is a worthy component within the current paradigm of model-based drug development, but pharmacometric modelling techniques are also accessible for the clinician in the optimisation of current oncology therapies. Consequently, the application of population models in a hospital setting by generating close collaborations between physicians and pharmacometricians is highly recommended, providing a systematic means of developing and assessing model-based metrics as 'drivers' for various responses to treatments, which can then be evaluated as predictors for treatment success. Characterising the key determinants of variability in exposure is of particular importance for anticancer agents, as efficacy and toxicity are associated with exposure. We present the different strategies to describe and predict drug exposure that can be applied depending on the data available, with the objective of obtaining the most useful information in the patients' favour throughout the full drug cycle. Therefore, the objective of the present article is to review the different approaches used to characterise a patient's exposure to oncology drugs, which will result in a better understanding of the time course of the response and the magnitude of interpatient variability.

Translational approach from preclinical to clinical: comparison of dose finding methods of a new Bcl2 inhibitor using PK-PD modeling and interspecies extrapolation

The attrition rate of anticancer drugs during the clinical development remains very high. Interspecies extrapolation of anticancer drug pharmacodynamics (PD) could help to bridge the gap between preclinical and clinical settings and to improve drug development. Indeed, when combined with a physiologically-based-pharmacokinetics (PBPK) approach, PD interspecies extrapolation could be a powerful tool for predicting drug behavior in clinical trials. The present study aimed to explore this field for anticipating the clinical efficacy of a new Bcl-2 inhibitor, S 55746, for which dose ranging studies in xenografted mice and clinical data from a phase 1 trial involving cancer patients were available. Different strategies based on empirical or more mechanistic assumptions (based on PBPK-PD modelling) were developped and compared: the Rocchetti approach (ROC); the Orthogonal Rocchetti approach (oROC), a variant of ROC based on an orthogonal regression; the Consistent across species approach, bringing out an efficacy parameter assumed to be consistent across species; and the Scaling species-specific parameters approach, assuming the concentration-efficacy link is the same in mice as in humans, after allometric scaling. Empirical approaches (ROC and oROC) gave similar predictive performances and seemed to overestimate the active S 55746 dose compared to mechanistic approaches, while strategies elaborated from semi-mechanistic concepts and PBPK-PD modelling did not seem to be invalidated by clinical efficacy data. Also, empirical methods only predict a single dose level for the subsequent clinical studies, whereas mechanism-based strategies are more informative about the dose response relationship, highlighting the potential interest of such approaches in drug development.

Physiological fidelity or model parsimony? The relative performance of reverse-toxicokinetic modeling approaches

Background

Physiologically-based toxicokinetic (PBTK) models are often developed to facilitate in vitro to in vivo extrapolation (IVIVE) using a top-down, compartmental approach, favoring architectural simplicity over physiological fidelity despite the lack of general guidelines relating model design to dynamical predictions. Here we explore the impact of design choice (high vs. low fidelity) on chemical distribution throughout an animal’s organ system.

Results

We contrast transient dynamics and steady states of three previously proposed PBTK models of varying complexity in response to chemical exposure. The steady states for each model were determined analytically to predict exposure conditions from tissue measurements. Steady state whole-body concentrations differ between models, despite identical environmental conditions, which originates from varying levels of physiological fidelity captured by the models. These differences affect the relative predictive accuracy of the inverted models used in exposure reconstruction to link effects-based exposure data with whole-organism response thresholds obtained from in vitro assay measurements.

Conclusions

Our results demonstrate how disregarding physiological fideltiy in favor of simpler models affects the internal dynamics and steady state estimates for chemical accumulation within tissues, which, in turn, poses significant challenges for the exposure reconstruction efforts that underlie many IVIVE methods. Developing standardized systems-level models for ecological organisms would not only ensure predictive consistency among future modeling studies, but also ensure pragmatic extrapolation of in vivo effects from in vitro data or modeling exposure-response relationships.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-017-0407-3) contains supplementary material, which is available to authorized users.

Combining the 'bottom up' and 'top down' approaches in pharmacokinetic modelling: fitting PBPK models to observed clinical data

Pharmacokinetic models range from being entirely exploratory and empirical, to semi-mechanistic and ultimately complex physiologically based pharmacokinetic (PBPK) models. This choice is conditional on the modelling purpose as well as the amount and quality of the available data. The main advantage of PBPK models is that they can be used to extrapolate outside the studied population and experimental conditions. The trade-off for this advantage is a complex system of differential equations with a considerable number of model parameters. When these parameters cannot be informed from in vitro or in silico experiments they are usually optimized with respect to observed clinical data. Parameter estimation in complex models is a challenging task associated with many methodological issues which are discussed here with specific recommendations. Concepts such as structural and practical identifiability are described with regards to PBPK modelling and the value of experimental design and sensitivity analyses is sketched out. Parameter estimation approaches are discussed, while we also highlight the importance of not neglecting the covariance structure between model parameters and the uncertainty and population variability that is associated with them. Finally the possibility of using model order reduction techniques and minimal semi-mechanistic models that retain the physiological-mechanistic nature only in the parts of the model which are relevant to the desired modelling purpose is emphasized. Careful attention to all the above issues allows us to integrate successfully information from in vitro or in silico experiments together with information deriving from observed clinical data and develop mechanistically sound models with clinical relevance.

Pharmacokinetic Modeling of Intra-arterial Nimodipine Therapy for Subarachnoid Hemorrhage-Related Cerebral Vasospasm

PURPOSE

Intra-arterial (IA) administration of nimodipine has been shown to be an effective treatment for subarachnoid hemorrhage-related cerebral vasospasm. The concentrations achieved in cerebral arteries during this procedure, though, are unknown. Therefore, there are no clinical studies investigating dose-dependent effects of nimodipine. We aimed at providing a pharmacokinetic model for IA nimodipine therapy for this purpose.

METHODS

A two-compartment pharmacokinetic model for intravenous nimodipine therapy was modified and used to assess cerebral arterial nimodipine concentration during IA nimodipine infusion into the internal carotid artery (ICA).

RESULTS

According to our simulations, continuous IA nimodipine infusion at 2 mg/h and 1 mg/h resulted in steady-state cerebral arterial concentrations of about 200 ng/ml and 100 ng/ml assuming an ICA blood flow of 200 ml/min and a clearance of 70 l/h. About 85 % of the maximal concentration is achieved within the first minute of IA infusion independent on the infusion dose. Within the range of physiological and pharmacokinetic data available in the literature, ICA blood flow has more impact on cerebral arterial concentration than nimodipine clearance.

CONCLUSION

The presented pharmacokinetic model is suitable for estimations of cerebral arterial nimodipine concentration during IA infusion. It may, for instance, assist in dose-dependent analyses of angiographic results.

Dose selection using a semi-mechanistic integrated glucose-insulin-glucagon model: designing phase 2 trials for a novel oral glucokinase activator

Selecting dosing regimens for phase 2 studies for a novel glucokinase activator LY2599506 is challenging due to the difficulty in modeling and assessing hypoglycemia risk. A semi-mechanistic integrated glucose-insulin-glucagon (GIG) model was developed in NONMEM based on pharmacokinetic, glucose, insulin, glucagon, and meal data obtained from a multiple ascending dose study in patients with Type 2 diabetes mellitus treated with LY2599506 for up to 26 days. The series of differential equations from the NONMEM model was translated into an R script to prospectively predict 24-h glucose profiles following LY2599506 treatment for 3 months for a variety of doses and dosing regimens. The reduction in hemoglobin A1c (HbA1c) at the end of the 3-month treatment was estimated using a transit compartment model based on the simulated fasting glucose values. Two randomized phase 2 studies, one with fixed dosing and the other employing conditional dose titration were conducted. The simulation suggested that (1) Comparable HbA1c lowering with lower hypoglycemia risk occurs with titration compared to fixed-dosing; and (2) A dose range of 50-400 mg BID provides either greater efficacy or lower hypoglycemia incidence or both than glyburide. The predictions were in reasonable agreement with the observed clinical data. The model predicted HbA1c reduction and hypoglycemia risk provided the basis for the decision to focus on the dose-titration trial and for the selection of doses for the demonstration of superiority of LY2599506 to glyburide. The integrated GIG model represented a valuable tool for the evaluation of hypoglycemia incidence.

Assessment of glycemic response to an oral glucokinase activator in a proof of concept study: application of a semi-mechanistic, integrated glucose-insulin-glucagon model

A proof of concept study was conducted to investigate the safety and tolerability of a novel oral glucokinase activator, LY2599506, during multiple dose administration to healthy volunteers and subjects with Type 2 diabetes mellitus (T2DM). To analyze the study data, a previously established semi-mechanistic integrated glucose-insulin model was extended to include characterization of glucagon dynamics. The model captured endogenous glucose and insulin dynamics, including the amplifying effects of glucose on insulin production and of insulin on glucose elimination, as well as the inhibitory influence of glucose and insulin on hepatic glucose production. The hepatic glucose production in the model was increased by glucagon and glucagon production was inhibited by elevated glucose concentrations. The contribution of exogenous factors to glycemic response, such as ingestion of carbohydrates in meals, was also included in the model. The effect of LY2599506 on glucose homeostasis in subjects with T2DM was investigated by linking a one-compartment, pharmacokinetic model to the semi-mechanistic, integrated glucose-insulin-glucagon system. Drug effects were included on pancreatic insulin secretion and hepatic glucose production. The relationships between LY2599506, glucose, insulin, and glucagon concentrations were described quantitatively and consequently, the improved understanding of the drug-response system could be used to support further clinical study planning during drug development, such as dose selection.

Physiologically based toxicokinetic modelling as a tool to support risk assessment: three case studies

In this contribution we present three case studies of physiologically based toxicokinetic (PBTK) modelling in regulatory risk assessment. (1) Age-dependent lower enzyme expression in the newborn leads to bisphenol A (BPA) blood levels which are near the levels of the tolerated daily intake (TDI) at the oral exposure as calculated by EFSA. (2) Dermal exposure of BPA by receipts, car park tickets, and so forth, contribute to the exposure towards BPA. However, at the present levels of dermal exposure there is no risk for the adult. (3) Dermal exposure towards coumarin via cosmetic products leads to external exposures of two-fold the TDI. PBTK modeling helped to identify liver peak concentration as the metric for liver toxicity. After dermal exposure of twice the TDI, the liver peak concentration was lower than that present after oral exposure with the TDI dose. In the presented cases, PBTK modeling was useful to reach scientifically sound regulatory decisions.

In vitro pharmacokinetic/pharmacodynamic models in anti-infective drug development: focus on TB

For rapid anti-tuberculosis (TB) drug development in vitro pharmacokinetic/pharmacodynamic (PK/PD) models are useful in evaluating the direct interaction between the drug and the bacteria, thereby guiding the selection of candidate compounds and the optimization of their dosing regimens. Utilizing in vivo drug-clearance profiles from animal and/or human studies and simulating them in an in vitro PK/PD model allows the in-depth characterization of antibiotic activity of new and existing antibacterials by generating time–kill data. These data capture the dynamic interplay between mycobacterial growth and changing drug concentration as encountered during prolonged drug therapy. This review focuses on important PK/PD parameters relevant to anti-TB drug development, provides an overview of in vitro PK/PD models used to evaluate the efficacy of agents against mycobacteria and discusses the related mathematical modeling approaches of time–kill data. Overall, it provides an introduction to in vitro PK/PD models and their application as critical tools in evaluating anti-TB drugs.