The application of global sensitivity analysis in the development of a physiologically based pharmacokinetic model for m-xylene and ethanol co-exposure in humans

Analyzing parametric influences driving age-associated changes in absorption using a PBPK-GSA approach

The advanced age population may be susceptible to an increased risk of adverse effects due to increased drug exposure after oral dosing. Factors such as high-interindividual variability and lack of data has led to poor characterization of absorption's role in pharmacokinetic changes in this population. Physiologically based pharmacokinetic (PBPK) models are increasingly being used during the drug development process, as their unique qualities are advantageous in atypical scenarios such as drug-drug interactions or special populations such as older people. Along with relying on various sources of data, auxiliary tools including parameter estimation and sensitivity analysis techniques are employed to support model development and other applications. However, sensitivity analyses have mostly been limited to localized techniques in the majority of reported PBPK models using them. This is disadvantageous, since local sensitivity analyses are unsuitable for risk analysis, which require assessment of parametric interactions and proper coverage of the input space to better estimate and subsequently mitigate the effects of the phenomenon of interest. For this reason, this study seeks to integrate a global sensitivity analysis screening method with PBPK models based in PK-Sim® to characterize the consequences of potential changes in absorption that are often associated with advanced age. The Elementary Effects (Morris) method and visualization of the results are implemented in R and three model drugs representing Biopharmaceutical Classification System classes I-III that are expected to exhibit some sensitivity to three age-associated hypotheses were successfully tested.

An Overview of Physiologically-Based Pharmacokinetic Models for Forensic Science

A physiologically-based pharmacokinetic (PBPK) model represents the structural components of the body with physiologically relevant compartments connected via blood flow rates described by mathematical equations to determine drug disposition. PBPK models are used in the pharmaceutical sector for drug development, precision medicine, and the chemical industry to predict safe levels of exposure during the registration of chemical substances. However, one area of application where PBPK models have been scarcely used is forensic science. In this review, we give an overview of PBPK models successfully developed for several illicit drugs and environmental chemicals that could be applied for forensic interpretation, highlighting the gaps, uncertainties, and limitations.

Development, testing, parameterisation, and calibration of a human PBK model for the plasticiser, di (2-ethylhexyl) adipate (DEHA) using in silico, in vitro and human biomonitoring data

Introduction: A physiologically based biokinetic model for di (2-ethylhexyl) adipate (DEHA) based on a refined model for di-(2-propylheptyl) phthalate (DPHP) was developed to interpret the metabolism and biokinetics of DEHA following a single oral dosage of 50 mg to two male and two female volunteers. Methods: The model was parameterized using in vitro and in silico methods such as, measured intrinsic hepatic clearance scaled from in vitro to in vivo and algorithmically predicted parameters such as plasma unbound fraction and tissue:blood partition coefficients (PCs). Calibration of the DEHA model was achieved using concentrations of specific downstream metabolites of DEHA excreted in urine. The total fractions of ingested DEHA eliminated as specific metabolites were estimated and were sufficient for interpreting the human biomonitoring data. Results: The specific metabolites of DEHA, mono-2-ethyl-5-hydroxyhexyl adipate (5OH-MEHA), mono-2-ethyl-5-oxohexyl adipate (5oxo-MEHA), mono-5-carboxy-2-ethylpentyl adipate (5cx-MEPA) only accounted for ∼0.45% of the ingested DEHA. Importantly, the measurements of adipic acid, a non-specific metabolite of DEHA, proved to be important in model calibration. Discussion: The very prominent trends in the urinary excretion of the metabolites, 5cx-MEPA and 5OH-MEHA allowed the important absorption mechanisms of DEHA to be modelled. The model should be useful for the study of exposure to DEHA of the general human population.

Development, testing, parameterisation, and calibration of a human PBPK model for the plasticiser, di-(2-ethylhexyl) terephthalate (DEHTP) using in silico, in vitro and human biomonitoring data

A physiologically based pharmacokinetic model for di-(2-ethylhexyl) terephthalate (DEHTP) based on a refined model for di-(2-propylheptyl) phthalate (DPHP) was developed to interpret the metabolism and biokinetics of DEHTP following a single oral dose of 50 mg to three male volunteers. In vitro and in silico methods were used to generate parameters for the model. For example, measured intrinsic hepatic clearance scaled from in vitro to in vivo and plasma unbound fraction and tissue:blood partition coefficients (PCs) were predicted algorithmically. Whereas the development and calibration of the DPHP model was based upon two data streams, blood concentrations of parent chemical and first metabolite and the urinary excretion of metabolites, the model for DEHTP was calibrated against a single data stream, the urinary excretion of metabolites. Despite the model form and structure being identical significant quantitative differences in lymphatic uptake between the models were observed. In contrast to DPHP the fraction of ingested DEHTP entering lymphatic circulation was much greater and of a similar magnitude to that entering the liver with evidence for the dual uptake mechanisms discernible in the urinary excretion data. Further, the absolute amounts absorbed by the study participants, were much higher for DEHTP relative to DPHP. The in silico algorithm for predicting protein binding performed poorly with an error of more than two orders of magnitude. The extent of plasma protein binding has important implications for the persistence of parent chemical in venous blood-inferences on the behaviour of this class of highly lipophilic chemicals, based on calculations of chemical properties, should be made with extreme caution. Attempting read across for this class of highly lipophilic chemicals should be undertaken with caution since basic adjustments to PCs and metabolism parameters would be insufficient, even when the structure of the model itself is appropriate. Therefore, validation of a model parameterized entirely with in vitro and in silico derived parameters would need to be calibrated against several human biomonitoring data streams to constitute a data rich source chemical to afford confidence for future evaluations of other similar chemicals using the read-across approach.

Development, Testing, Parameterisation and Calibration of a Human PBPK Model for the Plasticiser, Di-(2-propylheptyl) Phthalate (DPHP) Using in Silico, in vitro and Human Biomonitoring Data

A physiologically based pharmacokinetic model for Di-(2-propylheptyl) phthalate (DPHP) was developed to interpret the biokinetics in humans after single oral doses. The model was parameterized with in vitro and in silico derived parameters and uncertainty and sensitivity analysis was used during the model development process to assess structure, biological plausibility and behaviour prior to simulation and analysis of human biological monitoring data. To provide possible explanations for some of the counter-intuitive behaviour of the biological monitoring data the model included a simple lymphatic uptake process for DPHP and enterohepatic recirculation (EHR) for DPHP and the mono ester metabolite mono-(2-propylheptyl) phthalate (MPHP). The model was used to simultaneously simulate the concentration-time profiles of blood DPHP, MPHP and the urinary excretion of two metabolites, mono-(2-propyl-6-hydroxyheptyl) phthalate (OH-MPHP) and mono-(2-propyl-6-carboxyhexyl) phthalate (cx-MPHP). The availability of blood and urine measurements permitted a more robust qualitative and quantitative investigation of the importance of EHR and lymphatic uptake. Satisfactory prediction of blood DPHP and urinary metabolites was obtained whereas blood MPHP was less satisfactory. However, the delayed peak of DPHP concentration relative to MPHP in blood and second order metabolites in urine could be explained as a result of three processes: 1) DPHP entering the systemic circulation from the lymph, 2) rapid and very high protein binding and 3) the efficiency of the liver in removing DPHP absorbed via the hepatic route. The use of sensitivity analysis is considered important in the evaluation of uncertainty around in vitro and in silico derived parameters. By quantifying their impact on model output sufficient confidence in the use of a model should be afforded. This approach could expand the use of PBPK models since parameterization with in silico techniques allows for rapid model development. This in turn could assist in reducing the use of animals in toxicological evaluations by enhancing the utility of “read across” techniques.

pksensi: An R package to apply global sensitivity analysis in physiologically based kinetic modeling

Sensitivity analysis (SA) is an essential tool for modelers to understand the influence of model parameters on model outputs. It is also increasingly used in developing and assessing physiologically based kinetic (PBK) models. For instance, several studies have applied global SA to reduce the computational burden in the Bayesian Markov chain Monte Carlo-based calibration process PBK models. Although several SA algorithms and software packages are available, no comprehensive software package exists that allows users to seamlessly solve differential equations in a PBK model, conduct and visualize SA results, and discriminate between the non-influential model parameters that can be fixed and those that need calibration. Therefore, we developed an R package, named pksensi, to make global SA more accessible in PBK modeling. This package can investigate both uncertainty and sensitivity in PBK models, including those with multivariate model outputs. It also includes functions to check the convergence of the global SA results. Overall, pksensi improves the user experience of performing global SA and can create robust and reproducible results for decision making in PBK model calibration.

Development, Testing, Parameterization, and Calibration of a Human Physiologically Based Pharmacokinetic Model for the Plasticizer, Hexamoll® Diisononyl-Cyclohexane-1, 2-Dicarboxylate Using In Silico, In Vitro, and Human Biomonitoring Data

A physiologically based pharmacokinetic model for Hexamoll^® diisononyl-cyclohexane-1, 2-dicarboxylate was developed to interpret the biokinetics in humans after single oral doses. The model was parameterized with in vitro and in silico derived parameters and uncertainty and sensitivity analysis was used during the model development process to assess structure, biological plausibility and behavior prior to simulation and analysis of human biological monitoring data. The model provided good simulations of the urinary excretion (Curine) of two metabolites; cyclohexane-1,2-dicarboxylic acid mono hydroxyisononyl ester (OH-MINCH) and cyclohexane-1, 2-dicarboxylic acid mono carboxyisononyl ester (cx-MINCH) from the biotransformation of mono-isononyl-cyclohexane-1, 2-dicarboxylate (MINCH), the monoester metabolite of di-isononyl-cyclohexane-1,2-dicarboxylate. However, good simulations could be obtained, with and without, a lymphatic compartment. Selection of an appropriate model structure was informed by sensitivity analysis which could identify and quantify the contribution to variability in Curine by parameters, such as, the fraction of oral dose that directly entered the lymphatic compartment and therefore by-passed the liver and the fraction of MINCH bio-transformed to cx-MINCH and OH-MINCH. By constraining these parameters within biologically plausible limits the presence of a lymphatic compartment was deemed an important component of model structure. Furthermore, the use of sensitivity analysis is important in the evaluation of uncertainty around in silico derived parameters. By quantifying their impact on model output sufficient confidence in the use of a model should be afforded. This type of approach could expand the use of physiologically based pharmacokinetic models since parameterization with in silico techniques allows for rapid model development. This in turn could assist in reducing the use of animals in toxicological evaluations by enhancing the utility of “read across” techniques.

Applying a Global Sensitivity Analysis Workflow to Improve the Computational Efficiencies in Physiologically-Based Pharmacokinetic Modeling

Traditionally, the solution to reduce parameter dimensionality in a physiologically-based pharmacokinetic (PBPK) model is through expert judgment. However, this approach may lead to bias in parameter estimates and model predictions if important parameters are fixed at uncertain or inappropriate values. The purpose of this study was to explore the application of global sensitivity analysis (GSA) to ascertain which parameters in the PBPK model are non-influential, and therefore can be assigned fixed values in Bayesian parameter estimation with minimal bias. We compared the elementary effect-based Morris method and three variance-based Sobol indices in their ability to distinguish “influential” parameters to be estimated and “non-influential” parameters to be fixed. We illustrated this approach using a published human PBPK model for acetaminophen (APAP) and its two primary metabolites APAP-glucuronide and APAP-sulfate. We first applied GSA to the original published model, comparing Bayesian model calibration results using all the 21 originally calibrated model parameters (OMP, determined by “expert judgment”-based approach) vs. the subset of original influential parameters (OIP, determined by GSA from the OMP). We then applied GSA to all the PBPK parameters, including those fixed in the published model, comparing the model calibration results using this full set of 58 model parameters (FMP) vs. the full set influential parameters (FIP, determined by GSA from FMP). We also examined the impact of different cut-off points to distinguish the influential and non-influential parameters. We found that Sobol indices calculated by eFAST provided the best combination of reliability (consistency with other variance-based methods) and efficiency (lowest computational cost to achieve convergence) in identifying influential parameters. We identified several originally calibrated parameters that were not influential, and could be fixed to improve computational efficiency without discernable changes in prediction accuracy or precision. We further found six previously fixed parameters that were actually influential to the model predictions. Adding these additional influential parameters improved the model performance beyond that of the original publication while maintaining similar computational efficiency. We conclude that GSA provides an objective, transparent, and reproducible approach to improve the performance and computational efficiency of PBPK models.

Recent Advances in Development and Application of Physiologically-Based Pharmacokinetic (PBPK) Models: a Transition from Academic Curiosity to Regulatory Acceptance

There is a renewed surge of interest in applications of physiologically-based pharmacokinetic (PBPK) models by the pharmaceutical industry and regulatory agencies. Developing PBPK models within a systems pharmacology context allows separation of the parameters pertaining to the animal or human body (the system) from that of the drug and the study design which is essential to develop generic drug-independent models used to extrapolate PK/PD properties in various healthy and patient populations. This has expanded the classical paradigm to a ‘predict-learn-confirm-apply’ concept. Recently, a number of drug labels are informed by simulation results generated using PBPK models. These cases show that either the simulations are used in lieu of conducting clinical studies or have informed the drug label that otherwise would have been silent in some specific situations. It will not be surprising to see applications of these models in implementing precision dosing at the point of care in the near future.