Application of a Bayesian approach to physiological modelling of mavoglurant population pharmacokinetics

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.

Bayesian PBPK modeling using R/Stan/Torsten and Julia/SciML/Turing.Jl

Physiologically-based pharmacokinetic (PBPK) models are mechanistic models that are built based on an investigator's prior knowledge of the in vivo system of interest. Bayesian inference incorporates an investigator's prior knowledge of parameters while using the data to update this knowledge. As such, Bayesian tools are well-suited to infer PBPK model parameters using the strong prior knowledge available while quantifying the uncertainty on these parameters. This tutorial demonstrates a full population Bayesian PBPK analysis framework using R/Stan/Torsten and Julia/SciML/Turing.jl.

Population PBPK modeling using parametric and nonparametric methods of the Simcyp Simulator, and Bayesian samplers

Physiologically‐based pharmacokinetic (PBPK) models usually include a large number of parameters whose values are obtained using in vitro to in vivo extrapolation. However, such extrapolations can be uncertain and may benefit from inclusion of evidence from clinical observations via parametric inference. When clinical interindividual variability is high, or the data sparse, it is essential to use a population pharmacokinetics inferential framework to estimate unknown or uncertain parameters. Several approaches are available for that purpose, but their relative advantages for PBPK modeling are unclear. We compare the results obtained using a minimal PBPK model of a canonical theophylline dataset with quasi‐random parametric expectation maximization (QRPEM), nonparametric adaptive grid estimation (NPAG), Bayesian Metropolis‐Hastings (MH), and Hamiltonian Markov Chain Monte Carlo sampling. QRPEM and NPAG gave consistent population and individual parameter estimates, mostly agreeing with Bayesian estimates. MH simulations ran faster than the others methods, which together had similar performance.

Bayesian population physiologically-based pharmacokinetic model for robustness evaluation of withdrawal time in tilapia aquaculture administrated to florfenicol

The antimicrobial residues of aquacultural production is a growing public concern, leading to reexamine the method for establishing robust withdrawal time and ensuring food safety. Our study aims to develop the optimizing population physiologically-based pharmacokinetic (PBPK) model for assessing florfenicol residues in the tilapia tissues, and for evaluating the robustness of the withdrawal time (WT). Fitting with published pharmacokinetic profiles that experimented under temperatures of 22 and 28 °C, a PBPK model was constructed by applying with the Bayesian Markov chain Monte Carol (MCMC) algorithm to estimate WTs under different physiological, environmental and dosing scenarios. Results show that the MCMC algorithm improves the estimates of uncertainty and variability of PBPK-related parameters, and optimizes the simulation of the PBPK model. It is noteworthy that posterior sets generated from temperature-associated datasets to be respectively used for simulating residues under corresponding temperature conditions. Simulating the residues under regulated regimen and overdosing scenarios for Taiwan, the estimated WTs were 12-16 days at 22 °C and 9-12 days at 28 °C, while for the USA, the estimated WTs were 14-18 and 11-14 days, respectively. Comparison with the regulated WT of 15 days, results indicate that the current WT has well robustness and resilience in the environment of higher temperatures. The optimal Bayesian population PBPK model provides effective analysis for determining WTs under scenario-specific conditions. It is a new insight into the increasing body of literature on developing the Bayesian-PBPK model and has practical implications for improving the regulation of food safety.

Population pharmacokinetic reanalysis of a Diazepam PBPK model: a comparison of Stan and GNU MCSim

The aim of this study is to benchmark two Bayesian software tools, namely Stan and GNU MCSim, that use different Markov chain Monte Carlo (MCMC) methods for the estimation of physiologically based pharmacokinetic (PBPK) model parameters. The software tools were applied and compared on the problem of updating the parameters of a Diazepam PBPK model, using time-concentration human data. Both tools produced very good fits at the individual and population levels, despite the fact that GNU MCSim is not able to consider multivariate distributions. Stan outperformed GNU MCSim in sampling efficiency, due to its almost uncorrelated sampling. However, GNU MCSim exhibited much faster convergence and performed better in terms of effective samples produced per unit of time.

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.

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.

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.

Modelling of atorvastatin pharmacokinetics and the identification of the effect of a BCRP polymorphism in the Japanese population

AIM

Ethnicity plays a modulating role in atorvastatin pharmacokinetics (PK), with Asian patients reported to have higher exposure compared with Caucasians. Therefore, it is difficult to safely extrapolate atorvastatin PK data and models across ethnic groups. This work aims to develop a population PK model for atorvastatin and its pharmacologically active metabolites specifically for the Japanese population. Subsequently, it aimed to identify genetic polymorphisms affecting atorvastatin PK in this population.

METHODS

Atorvastatin acid (ATA) and ortho-hydroxy-atorvastatin acid (o-OH-ATA) plasma concentrations, clinical/demographic characteristics and genotypes for 18 (3, 3, 1, 1, 7, 2 and 1 in the ABCB1, ABCG2, CYP3A4, CYP3A5, SLCO1B1, SLCO2B1 and PPARA genes, respectively) genetic polymorphisms were collected from 27 Japanese individuals (taking 10 mg atorvastatin once daily) and analysed using a population PK modelling approach.

RESULTS

The population PK model developed (one-compartment for ATA linked through metabolite formation to an additional compartment describing the disposition of o-OH-ATA) accurately described the observed data and the associated population variability. Our analysis suggested that patients carrying one variant allele for the rs2622604 polymorphism (ABCG2) show a 55% (95% confidence interval: 16-131%) increase in atorvastatin oral bioavailability relative to the value in individuals without the variant allele.

CONCLUSION

The current work reports the identification in the Japanese population of a BCRP polymorphism, not previously associated with the PK of any statin, that markedly increases ATA and o-OH-ATA exposure. The model developed may be of clinical importance to guide dosing recommendations tailored specifically for the Japanese.

Physiologically Based Pharmacokinetic Modeling of Drug Transporters to Facilitate Individualized Dose Prediction

Physiologically based pharmacokinetic modeling is a commonly used strategy in the drug development and regulatory submissions. This commentary provides a critical overview of the current status of physiologically based pharmacokinetic methodologies to predict transporter-mediated pharmacokinetics, in addition to the impact of disease and genetics with respect to local and systemic concentration.

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.

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

Whole-body physiologically based pharmacokinetic (PBPK) models are increasingly used in drug development for their ability to predict drug concentrations in clinically relevant tissues and to extrapolate across species, experimental conditions and sub-populations. A whole-body PBPK model can be fitted to clinical data using a Bayesian population approach. However, the analysis might be time consuming and numerically unstable if prior information on the model parameters is too vague given the complexity of the system. We suggest an approach where (i) a whole-body PBPK model is formally reduced using a Bayesian proper lumping method to retain the mechanistic interpretation of the system and account for parameter uncertainty, (ii) the simplified model is fitted to clinical data using Markov Chain Monte Carlo techniques and (iii) the optimised reduced PBPK model is used for extrapolation. A previously developed 16-compartment whole-body PBPK model for mavoglurant was reduced to 7 compartments while preserving plasma concentration-time profiles (median and variance) and giving emphasis to the brain (target site) and the liver (elimination site). The reduced model was numerically more stable than the whole-body model for the Bayesian analysis of mavoglurant pharmacokinetic data in healthy adult volunteers. Finally, the reduced yet mechanistic model could easily be scaled from adults to children and predict mavoglurant pharmacokinetics in children aged from 3 to 11 years with similar performance compared with the whole-body model. This study is a first example of the practicality of formal reduction of complex mechanistic models for Bayesian inference in drug development.