Reduction of a Whole-Body Physiologically Based Pharmacokinetic Model to Stabilise the Bayesian Analysis of Clinical Data

Parameter grouping and co-estimation in physiologically based kinetic models using genetic algorithms

Physiologically based kinetic (PBK) models are widely used in pharmacology and toxicology for predicting the internal disposition of substances upon exposure, voluntarily or not. Due to their complexity, a large number of model parameters need to be estimated, either through in silico tools, in vitro experiments, or by fitting the model to in vivo data. In the latter case, fitting complex structural models on in vivo data can result in overparameterization and produce unrealistic parameter estimates. To address these issues, we propose a novel parameter grouping approach, which reduces the parametric space by co-estimating groups of parameters across compartments. Grouping of parameters is performed using genetic algorithms and is fully automated, based on a novel goodness-of-fit metric. To illustrate the practical application of the proposed methodology, two case studies were conducted. The first case study demonstrates the development of a new PBK model, while the second focuses on model refinement. In the first case study, a PBK model was developed to elucidate the biodistribution of titanium dioxide (TiO2) nanoparticles in rats following intravenous injection. A variety of parameter estimation schemes were employed. Comparative analysis based on goodness-of-fit metrics demonstrated that the proposed methodology yields models that outperform standard estimation approaches, while utilizing a reduced number of parameters. In the second case study, an existing PBK model for perfluorooctanoic acid (PFOA) in rats was extended to incorporate additional tissues, providing a more comprehensive portrayal of PFOA biodistribution. Both models were validated through independent in vivo studies to ensure their reliability.

Predicting pharmacodynamic effects through early drug discovery with artificial intelligence-physiologically based pharmacokinetic (AI-PBPK) modelling

A mechanism-based pharmacokinetic/pharmacodynamic (PK/PD) model links the concentration-time profile of a drug with its therapeutic effects based on the underlying biological or physiological processes. Clinical endpoints play a pivotal role in drug development. Despite the substantial time and effort invested in screening drugs for favourable pharmacokinetic (PK) properties, they may not consistently yield optimal clinical outcomes. Furthermore, in the virtual compound screening phase, researchers cannot observe clinical outcomes in humans directly. These uncertainties prolong the process of drug development. As incorporation of Artificial Intelligence (AI) into the physiologically based pharmacokinetic/pharmacodynamic (PBPK) model can assist in forecasting pharmacodynamic (PD) effects within the human body, we introduce a methodology for utilizing the AI-PBPK platform to predict the PK and PD outcomes of target compounds in the early drug discovery stage. In this integrated platform, machine learning is used to predict the parameters for the model, and the mechanism-based PD model is used to predict the PD outcome through the PK results. This platform enables researchers to align the PK profile of a drug with desired PD effects at the early drug discovery stage. Case studies are presented to assess and compare five potassium-competitive acid blocker (P-CAB) compounds, after calibration and verification using vonoprazan and revaprazan.

A "middle-out approach" for the prediction of human drug disposition from preclinical data using simplified physiologically based pharmacokinetic (PBPK) models

Simplified physiologically based pharmacokinetic (PBPK) models using estimated tissue-to-unbound plasma partition coefficients (Kpus) were previously investigated by fitting them to in vivo pharmacokinetic (PK) data. After optimization with preclinical data, the performance of these models for extrapolation of distribution kinetics to human were evaluated to determine the best approach for the prediction of human drug disposition and volume of distribution (Vss) using PBPK modeling. Three lipophilic bases were tested (diazepam, midazolam, and basmisanil) for which intravenous PK data were available in rat, monkey, and human. The models with Kpu scalars using k-means clustering were generally the best for fitting data in the preclinical species and gave plausible Kpu values. Extrapolations of plasma concentrations for diazepam and midazolam using these models and parameters obtained were consistent with the observed clinical data. For diazepam and midazolam, the human predictions of Vss after optimization in rats and monkeys were better compared with the Vss estimated from the traditional PBPK modeling approach (varying from 1.1 to 3.1 vs. 3.7-fold error). For basmisanil, the sparse preclinical data available could have affected the model performance for fitting and the subsequent extrapolation to human. Overall, this work provides a rational strategy to predict human drug distribution using preclinical PK data within the PBPK modeling strategy.

Reduced physiologically-based pharmacokinetic model of dabigatran etexilate-dabigatran and its application for prediction of intestinal P-gp-mediated drug-drug interactions

BACKGROUND

Dabigatran etexilate (DABE) has been suggested as a clinical probe for intestinal P-glycoprotein (P-gp)-mediated drug-drug interaction (DDI) studies and, as an alternative to digoxin. Clinical DDI data with various P-gp inhibitors demonstrated a dose-dependent inhibition of P-gp with DABE. The aims of this study were to develop a joint DABE (prodrug)-dabigatran reduced physiologically-based-pharmacokinetic (PBPK) model and to evaluate its ability to predict differences in P-gp DDI magnitude between a microdose and a therapeutic dose of DABE.

METHODS

A joint DABE-dabigatran PBPK model was developed with a mechanistic intestinal model accounting for the regional P-gp distribution in the gastrointestinal tract. Model input parameters were estimated using DABE and dabigatran pharmacokinetic (PK) clinical data obtained after administration of DABE alone or with a strong P-gp inhibitor, itraconazole, and over a wide range of DABE doses (from 375 µg to 400 mg). Subsequently, the model was used to predict extent of DDI with additional P-gp inhibitors and with different DABE doses.

RESULTS

The reduced DABE-dabigatran PBPK model successfully described plasma concentrations of both prodrug and metabolite following administration of DABE at different dose levels and when co-administered with itraconazole. The model was able to capture the dose dependency in P-gp mediated DDI. Predicted magnitude of itraconazole P-gp DDI was higher at the microdose (predicted vs. observed median fold-increase in AUC_+inh/AUC_control (min-max) = 5.88 (4.29-7.93) vs. 6.92 (4.96-9.66) ) compared to the therapeutic dose (predicted median fold-increase in AUC_+inh/AUC_control = 3.48 (2.37-4.84) ). In addition, the reduced DABE-dabigatran PBPK model predicted successfully the extent of DDI with verapamil and clarithromycin as P-gp inhibitors. Model-based simulations of dose staggering predicted the maximum inhibition of P-gp when DABE microdose was concomitantly administered with itraconazole solution; simulations also highlighted dosing intervals required to minimise the DDI risk depending on the DABE dose administered (microdose vs. therapeutic).

CONCLUSIONS

This study provides a modelling framework for the evaluation of P-gp inhibitory potential of new molecular entities using DABE as a clinical probe. Simulations of dose staggering and regional differences in the extent of intestinal P-gp inhibition for DABE microdose and therapeutic dose provide model-based guidance for design of prospective clinical P-gp DDI studies.

In Silico Modeling and Simulation to Guide Bioequivalence Testing for Oral Drugs in a Virtual Population

Model-informed drug discovery and development (MID3) shows great advantages in facilitating drug development. A physiologically based pharmacokinetic model is one of the powerful computational approaches of MID3, and the emerging field of virtual bioequivalence is well recognized to be the future of the physiologically based pharmacokinetic model. Based on the translational link between in vitro, in silico, and in vivo, virtual bioequivalence study can evaluate the similarity and potential difference of pharmacokinetic and clinical performance between test and reference formulations. With the aid of virtual bioequivalence study, the pivotal information of clinical trials can be provided to streamline the development for both new and generic drugs. However, a regulatory framework of virtual bioequivalence study has not reached its full maturity. Therefore, this article aims to present an overview of the current status of bioequivalence study, identify the framework of virtual bioequivalence studies for oral drugs, and also discuss the future opportunities of virtual bioequivalence in supporting the waiver and optimization of in vivo clinical trials.

Physiologically Based Pharmacokinetic/Pharmacodynamic Modeling to Support Waivers of In Vivo Clinical Studies: Current Status, Challenges, and Opportunities

Physiologically based pharmacokinetic/pharmacodynamic (PBPK/PD) modeling has been extensively applied to quantitatively translate in vitro data, predict the in vivo performance, and ultimately support waivers of in vivo clinical studies. In the area of biopharmaceutics and within the context of model-informed drug discovery and development (MID3), there is a rapidly growing interest in applying verified and validated mechanistic PBPK models to waive in vivo clinical studies. However, the regulatory acceptance of PBPK analyses for biopharmaceutics and oral drug absorption applications, which is also referred to variously as "PBPK absorption modeling" [Zhang et al. CPT: Pharmacometrics Syst. Pharmacol. 2017, 6, 492], "physiologically based absorption modeling", or "physiologically based biopharmaceutics modeling" (PBBM), remains rather low [Kesisoglou et al. J. Pharm. Sci. 2016, 105, 2723] [Heimbach et al. AAPS J. 2019, 21, 29]. Despite considerable progress in the understanding of gastrointestinal (GI) physiology, in vitro biopharmaceutic and in silico tools, PBPK models for oral absorption often suffer from an incomplete understanding of the physiology, overparameterization, and insufficient model validation and/or platform verification, all of which can represent limitations to their translatability and predictive performance. The complex interactions of drug substances and (bioenabling) formulations with the highly dynamic and heterogeneous environment of the GI tract in different age, ethnic, and genetic groups as well as disease states have not been yet fully elucidated, and they deserve further research. Along with advancements in the understanding of GI physiology and refinement of current or development of fully mechanistic in silico tools, we strongly believe that harmonization, interdisciplinary interaction, and enhancement of the translational link between in vitro, in silico, and in vivo will determine the future of PBBM. This Perspective provides an overview of the current status of PBBM, reflects on challenges and knowledge gaps, and discusses future opportunities around PBPK/PD models for oral absorption of small and large molecules to waive in vivo clinical studies.

Physiologically based modelling of the pharmacokinetics of three beta-lactam antibiotics after intra-mammary administration in dairy cows

Understanding the pharmacokinetics of intra-mammary antibiotics is important for the prediction of drug residues in milk and for the design of optimal dosage regimens. Unfortunately, compartmental pharmacokinetic models are not valid for this unique system. A minimal physiologically based pharmacokinetic model is presented incorporating the physiology of milk secretion, drug administration at the quarter level, drug absorption and dispersion, drug retention during the inter-milking interval and episodic drug elimination at milking. The primary objective of the study was the development and exploration of a model for major factors controlling drug concentration in milk, rather than generation of rigorously predictive pharmaco-statistical models for any particular drug. This model was implemented in a two-stage approach, using published concentration data for penicillin, cefuroxime, cephapirin and desacetyl-cephapirin in milk of healthy cows. Model simulations evaluated sensitivity and developed predictions of drug residues. The model successfully predicted both drug concentrations and drug residues in milk. The postmilking residual milk volume did not adequately explain antibiotic pharmacokinetics, requiring additional considerations for drug retention. Local sensitivity analysis indicated that increasing the number of quarters treated, the dosage, or the duration of the inter-milking interval prolonged both the persistence of drug residues and the duration that antibiotic concentration exceeded typical minimum inhibitory concentrations. The model was flexible across different beta-lactam drugs as a general description of intra-mammary pharmacokinetics. This model is suitable for the design and analysis of dosage regimens, and could be applied for the prediction of withholding periods when these antibiotic preparations are used off-label. The final model indicates that explicit consideration of the milking regimen is fundamental to the design and interpretation of pharmacokinetic studies of antibiotics in bovine milk.

Automated proper lumping for simplification of linear physiologically based pharmacokinetic systems

Physiologically based pharmacokinetic (PBPK) models are an important type of systems model used commonly in drug development before commencement of first-in-human studies. Due to structural complexity, these models are not easily utilised for future data-driven population pharmacokinetic (PK) analyses that require simpler models. In the current study we aimed to explore and automate methods of simplifying PBPK models using a proper lumping technique. A linear 17-state PBPK model for fentanyl was identified from the literature. Four methods were developed to search the optimal lumped model, including full enumeration (the reference method), non-adaptive random search (NARS), scree plot plus NARS, and simulated annealing (SA). For exploratory purposes, it was required that the total area under the fentanyl arterial concentration–time curve (AUC) between the lumped and original models differ by 0.002% at maximum. In full enumeration, a 4-state lumped model satisfying the exploratory criterion was found. In NARS, a lumped model with the same number of lumped states was found, requiring a large number of random samples. The scree plot provided a starting lumped model to NARS and the search completed within a short time. In SA, a 4-state lumped model was consistently delivered. In simplify an existing linear fentanyl PBPK model, SA was found to be robust and the most efficient and may be suitable for general application to other larger-scale linear systems. Ultimately, simplified PBPK systems with fundamental mechanisms may be readily used for data-driven PK analyses.

Development of a nonlinear hierarchical model to describe the disposition of deuterium in mother-infant pairs to assess exclusive breastfeeding practice

The World Health Organization recommends exclusive breastfeeding (EBF) for the first 6 months after birth. The deuterium oxide dose-to-the-mother (DTM) technique is used to distinguish EBF based on a cut-off (< 25 g/day) of water intake from sources other than breastmilk. This value is based on a theoretical threshold and has not been verified in field studies. The aim of this study was to estimate the water intake cut-off value that can be used to define EBF practice. One hundred and twenty-one healthy infants, aged 2.5-5.5 months who were deemed to be EBF were recruited. After administration of deuterium to the mothers, saliva was sampled from mother and infant pairs over a 14-day period. Validation of infant feeding practices was conducted via home observation over six non-consecutive days with caregiver recall. A fully Bayesian framework using a gradient-based Markov chain Monte Carlo approach implemented in Stan was used to estimate the cut-off of non-milk water intake of EBF infants. From the original data set, 113 infants were determined to be EBF and provided 1500 paired mother-infant observations. The deuterium saliva concentrations were best described by two linked 1-compartment models (mother and infant), with body weight as a covariate on the mother's volume of distribution and infant's body weight on infant's water clearance rate. The cut-off value was based on the 90th percentile of the posterior distribution of non-milk water intake and was 86.6 g/day. This cut-off value can be used in future field studies in other geographic regions to determine exclusivity of breast feeding practices in order to determine their potential public health needs.

Assessment of Pharmacokinetic Drug-Drug Interactions in Humans: In Vivo Probe Substrates for Drug Metabolism and Drug Transport Revisited

Pharmacokinetic parameters of selective probe substrates are used to quantify the activity of an individual pharmacokinetic process (PKP) and the effect of perpetrator drugs thereon in clinical drug-drug interaction (DDI) studies. For instance, oral caffeine is used to quantify hepatic CYP1A2 activity, and oral dagibatran etexilate for intestinal P-glycoprotein (P-gp) activity. However, no probe substrate depends exclusively on the PKP it is meant to quantify. Lack of selectivity for a given enzyme/transporter and expression of the respective enzyme/transporter at several sites in the human body are the main challenges. Thus, a detailed understanding of the role of individual PKPs for the pharmacokinetics of any probe substrate is essential to allocate the effect of a perpetrator drug to a specific PKP; this is a prerequisite for reliably informed pharmacokinetic models that will allow for the quantitative prediction of perpetrator effects on therapeutic drugs, also in respective patient populations not included in DDI studies.

Automated Scale Reduction of Nonlinear QSP Models With an Illustrative Application to a Bone Biology System

Integrating quantitative systems pharmacology (QSP) into pharmacokinetics/pharmacodynamics (PKPD) has resulted in models that are highly complex and often not amenable to further exploration via estimation or design. Because QSP models are usually depicted using nonlinear differential equations it is not straightforward to apply some model reduction techniques, such as proper lumping. In this study, we explore the combined use of linearization and proper lumping as a general method to simplification of a nonlinear QSP model. We illustrate this with a bone biology model and the reduced model was then applied to describe bone mineral density (BMD) changes due to denosumab dosing. The methodologies used in this study can be applied to other multiscale models for developing a mechanism-based structural model for future analyses.

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.

Selection and Qualification of Simplified QSP Models When Using Model Order Reduction Techniques

Quantitative systems pharmacology (QSP) models are increasingly used in drug development to provide a deep understanding of the mechanism of action of drugs and to identify appropriate disease targets. Such models are, however, not suitable for estimation purposes due to their high dimensionality. Based on any desired and specific input-output relationship, the system may be reduced to a model with fewer states and parameters. However, any simplification process will be a trade-off between model performance and complexity. In this study, we develop a weighted composite criterion which brings together the opposing indices of performance and dimensionality. The weighting factor can be determined by qualification of the simplified model based on a visual predictive check (VPC) using the precision of each parameter. The weighted criterion and model qualification techniques were illustrated with three examples: a simple compartmental pharmacokinetic model, a physiologically based pharmacokinetic (PBPK) example, and a semimechanistic model for bone mineral density. When considering the PBPK example, this automated search identified the same reduced model which had been detected in a previous report, as well as a simpler model which had not been previously identified. The simpler bone mineral density model provided an adequate description of the response even after 1 year from the initiation of treatment. The proposed criterion together with a VPC provides a natural way for model order reduction that can be fully automated and applied to multiscale models.

An introduction to physiologically-based pharmacokinetic models

Physiologically-based pharmacokinetic (PBPK) models represent drug kinetics in one or more 'real' organs (and hence require submodels of organs/tissues) and they describe 'whole-body' kinetics by joining together submodels with drug transport by blood flow as dictated by anatomy. They attempt to reproduce 'measureable' physiological and/or pharmacokinetic processes rather than more abstract rate constants and volumes. PBPK models may be built using a 'bottom-up' approach, where parameters are chosen from first principles, literature, or in vitro data as opposed to a 'top-down' approach, where all parameters are estimated from data. The basic principles of PBPK models are described, focusing on the equations for three individual organs: a single flow-limited compartment describing distribution only, a membrane-limited compartment describing distribution, and a single flow-limited compartment with elimination. These organ models are linked to make a basic three-compartment physiological model of the whole body. PBPK models are particularly suited to scaling kinetics across body size (e.g., adult to neonate) and species (e.g., animal to first-in-man) as physiology and pharmacology can be represented by independent parameters. Maturation models can be incorporated as for compartmental models. PBPK models are now available in commercial software packages, and are perhaps now more accessible than ever. Alternatively, even complex PBPK models can be represented in generic differential equation-solving software using the simple principles described here. The relative ease of constructing the code for PBPK models belies the most difficult aspect of their implementation-collecting, collating, and justifying the data used to parameterize the model.