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

Exploration of sexual dimorphism and inter-individual variability in multivariate parameter spaces for a pharmacokinetic compartment model

Pharmacokinetic models are particularly useful to study the underlying and complex physiological mechanisms contributing to clinical differences across patient subgroups or special populations. Unfortunately, the inherent variability of biological systems and knowledge gaps in physiological data limit confidence in model predictions for special populations. Sourcing data to reflect the desired physiologies can be resource intensive, particularly for a larger model. Thus, a critical step in model development for special populations involves an in-depth analysis of model inputs, which can be guided by Monte Carlo simulations. Such an approach enables the generation of parameter values by stochastic sampling that are subsequently restricted to the combinations that describe biologically plausible or target model output. Our approach utilized a published pharmacokinetic compartmental model to demonstrate how sampling in conjunction with global sensitivity analysis can be used to explore sexual dimorphism and inter-individual variability in multivariate parameter spaces for differentiation of model input and behavior across phenotypes. Despite limiting the model output to relatively narrow ranges, male and female phenotypes were associated with wide variability in both individual parameter values and combinations of parameters. Through an integrated approach using a support vector machine, principal component analysis and global sensitivity analysis, our approach revealed that specific combinations of parameters gave rise to a certain phenotype, while individual parameters influenced the shape of plasma concentration profile. Augmenting analysis of the model input with global sensitivity analysis enabled an understanding of both sexual dimorphism and inter-individual variability in pharmacokinetics. While the current study revealed how model input could be separated by sex for a simple compartment model, the approach could be extended to other patient factors, such as age or disease, and to a more complex physiologically-based model that describes absorption, distribution, metabolism, and elimination with more detail.

Application of Physiologically Based Pharmacokinetic Modeling to Predict Pharmacokinetics in Healthy Japanese Subjects

Pharmacokinetics (PKs) in Japanese healthy subjects were simulated for nine compounds using physiologically based PK (PBPK) models parameterized with physicochemical properties, preclinical absorption, distribution, metabolism, and excretion (ADME) data, and clinical PK data from non‐Japanese subjects. For each dosing regimen, 100 virtual trials were simulated and predicted/observed ratios for peak plasma concentration (C_max) and area under the curve (AUC) were calculated. As qualification criteria, it was prespecified that >80% of simulated trials should demonstrate ratios to observed data ranging from 0.5–2.0. Across all compounds and dose regimens studied, 93% of simulated C_max values in Japanese subjects fulfilled the criteria. Similarly, for AUC, 77% of single‐dosing regimens and 100% of multiple‐dosing regimens fulfilled the criteria. In summary, mechanistically incorporating the appropriate ADME properties into PBPK models, followed by qualification using non‐Japanese clinical data, can predict PKs in the Japanese population and lead to efficient trial design and conduct of Japanese phase I studies.

Predicting the need for a reduced drug dose, at first prescription

Prescribing the right drug with the right dose is a central tenet of precision medicine. We examined the use of patients’ prior Electronic Health Records to predict a reduction in drug dosage. We focus on drugs that interact with the P450 enzyme family, because their dosage is known to be sensitive and variable. We extracted diagnostic codes, conditions reported in clinical notes, and laboratory orders from Stanford’s clinical data warehouse to construct cohorts of patients that either did or did not need a dose change. After feature selection, we trained models to predict the patients who will (or will not) require a dose change after being prescribed one of 34 drugs across 23 drug classes. Overall, we can predict (AUC ≥ 0.70–0.95) a dose reduction for 23 drugs and 22 drug classes. Several of these drugs are associated with clinical guidelines that recommend dose reduction exclusively in the case of adverse reaction. For these cases, a reduction in dosage may be considered as a surrogate for an adverse reaction, which our system could indirectly help predict and prevent. Our study illustrates the role machine learning may take in providing guidance in setting the starting dose for drugs associated with response variability.

Physiologically based pharmacokinetic modelling of acute digoxin toxicity and the effect of digoxin-specific antibody fragments

CONTEXT

Recommended doses of digoxin-specific antibody fragments (digoxin-Fab) for treatment of acute digoxin poisoning are pharmacokinetically unsubstantiated and theoretically excessive. Physiologically based pharmacokinetic (PBPK) modelling creates clinical simulations which are closely related to physiological and pharmacokinetic behaviour. This paper details the formulation of a PBPK model of digoxin and explores its use as a simulation tool for acute digoxin toxicity and its management.

MATERIALS AND METHODS

A PBPK model of digoxin was constructed and validated for acute digoxin poisoning management by comparing simulations with observed individual acute overdose patients. These simulations were compared with standard two-compartment PK model simulations.

RESULTS

PBPK model simulations showed good agreement with post-absorption plasma concentrations of digoxin measured in 6 acute overdose patients. PBPK predictions were accurate to 1.5-fold or less of observed clinical values, proving to be more accurate than two-compartment simulations of the same patients which produced up to a 4.9-fold change.

CONCLUSIONS

Compared to conventional two-compartment modelling, PBPK modelling is superior in generating realistic simulations of acute digoxin toxicity and the response to digoxin-Fab. Simulation capacity provides realistic, continuous data which has the potential to substantiate alternative, less expensive, and safer digoxin-Fab dosing strategies for the treatment of acute digoxin toxicity.

The use of PBPK modeling across the pediatric age range using propofol as a case

The project SAFEPEDRUG aims to provide guidelines for drug research in children, based on bottom-up and top-down approaches. Propofol, one of the studied model compounds, was selected because it is extensively metabolized in liver and kidney, with an important role for the glucuronidation pathway. Besides, being a lipophilic molecule, it is distributed into fat tissues, from where it redistributes into the systemic circulation. In the past, both bottom-up (Physiologically based pharmacokinetic, PBPK) and top-down approaches (population pharmacokinetic, popPK) were applied to describe its pharmacokinetics (PK). In this work, a combination of the two was used to check their performance to describe PK in children and neonates (both term and preterm) using propofol as a case compound. First, in vitro data was generated in human liver microsomes and recombinant enzymes and used to develop an adult PBPK model in Simcyp^®. Activity adjustment factors (AAFs) were calculated to account for differences between in vitro and in vivo enzyme activity. Clinical data were analyzed using a 3-compartment model in NONMEM. These data were used to construct a retrograde PBPK model and for qualification of the PBPK models. Once an accurate in vivo clearance was obtained accounting for the contribution of the different metabolic pathways, the resulting PBPK models were challenged with new data for qualification. After that, the constructed adult PPBK model for propofol was extrapolated to the pediatric population. Both the default built-in and in vivo derived ontogeny functions were used to do so. The models were qualified by comparing their predicted PK parameters to published values, and by comparison of predicted concentration-time profiles to available clinical data. Clearance values were predicted well, especially when compared with values obtained from trials where long-term sampling was applied, whereas volume of distribution was lower compared to the most common popPK model predictions. Concentration-time profiles were predicted well up until and including the preterm neonatal population. In this work, it was thus shown that PBPK can be used to predict the PK up to and including the preterm neonatal population without the use of pediatric in vivo data. This work adds weight to the need for further development of PBPK models, especially regarding distribution modeling and the use of in vivo derived ontogeny functions.

A Strategy to Refine the Phenotyping Approach and Its Implementation to Predict Drug Clearance: A Physiologically Based Pharmacokinetic Simulation Study

The phenotyping approach to predict drug metabolism activity is often hampered by a lack of correlation between the probe and the drug of interest. In this article, we present a strategy to refine the phenotyping approach based on a physiologically based pharmacokinetic simulation (implemented in Simcyp Simulator version 17) using previously published models. The apparent clearance (CL/F) of erlotinib was better predicted by the sum of caffeine and i.v. midazolam CL/F (r²  = 0.60) compared to that of either probe drug alone. The clearance of atorvastatin and repaglinide had a strong correlation (r²  = 0.70 and 0.63, respectively) with that of pitavastatin (a SLCO1B1 probe). Use of multiple probes for drugs that are predominantly metabolized by more than one cytochrome P450 (CYP) enzyme should be considered. In a case in which hepatic uptake transporters play a significant role in the disposition of a drug, the pharmacokinetic of a transporter probe will provide better predictions of the drug clearance.

Review: Using physiologically based models to predict population responses to phytochemicals by wild vertebrate herbivores

To understand how foraging decisions impact individual fitness of herbivores, nutritional ecologists must consider the complex in vivo dynamics of nutrient-nutrient interactions and nutrient-toxin interactions associated with foraging. Mathematical modeling has long been used to make foraging predictions (e.g. optimal foraging theory) but has largely been restricted to a single currency (e.g. energy) or using simple indices of nutrition (e.g. fecal nitrogen) without full consideration of physiologically based interactions among numerous co-ingested phytochemicals. Here, we describe a physiologically based model (PBM) that provides a mechanistic link between foraging decisions and demographic consequences. Including physiological mechanisms of absorption, digestion and metabolism of phytochemicals in PBMs allows us to estimate concentrations of ingested and interacting phytochemicals in the body. Estimated phytochemical concentrations more accurately link intake of phytochemicals to changes in individual fitness than measures of intake alone. Further, we illustrate how estimated physiological parameters can be integrated with the geometric framework of nutrition and into integral projection models and agent-based models to predict fitness and population responses of vertebrate herbivores to ingested phytochemicals. The PBMs will improve our ability to understand the foraging decisions of vertebrate herbivores and consequences of those decisions and may help identify key physiological mechanisms that underlie diet-based ecological adaptations.

Can Population Modelling Principles be Used to Identify Key PBPK Parameters for Paediatric Clearance Predictions? An Innovative Application of Optimal Design Theory

PURPOSE

Physiologically-based pharmacokinetic (PBPK) models are essential in drug development, but require parameters that are not always obtainable. We developed a methodology to investigate the feasibility and requirements for precise and accurate estimation of PBPK parameters using population modelling of clinical data and illustrate this for two key PBPK parameters for hepatic metabolic clearance, namely whole liver unbound intrinsic clearance (CLint_,u,WL) and hepatic blood flow (Qh) in children.

METHODS

First, structural identifiability was enabled through re-parametrization and the definition of essential trial design components. Subsequently, requirements for the trial components to yield precise estimation of the PBPK parameters and their inter-individual variability were established using a novel application of population optimal design theory. Finally, the performance of the proposed trial design was assessed using stochastic simulation and estimation.

RESULTS

Precise estimation of CLint_,u,WL and Qh and their inter-individual variability was found to require a trial with two drugs, of which one has an extraction ratio (ER) ≤ 0.27 and the other has an ER ≥ 0.93. The proposed clinical trial design was found to lead to precise and accurate parameter estimates and was robust to parameter uncertainty.

CONCLUSION

The proposed framework can be applied to other PBPK parameters and facilitate the development of PBPK models.

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.

A Semi-Mechanistic Population Pharmacokinetic Model of Nusinersen: An Antisense Oligonucleotide for the Treatment of Spinal Muscular Atrophy

A pharmacokinetic (PK) model was developed for nusinersen, an antisense oligonucleotide (ASO) that is the first approved treatment for spinal muscular atrophy (SMA). The model was built with data from 92 nonhuman primates (NHPs) following intrathecal doses (0.3–7 mg) and characterized the PK in cerebrospinal fluid (CSF), plasma, total spinal cord, brain, and pons. The estimated volumes were 13.6, 937, 4.5, 53.8, and 2.11 mL, respectively. Global sensitivity analysis demonstrated that the CSF‐to‐plasma drug distribution rate (0.09 hour⁻¹) is a major determinant of the maximum nusinersen concentration in central nervous system (CNS) tissues. Physiological age‐based and body weight‐based allometric scaling was implemented with exponent values of −0.08 and 1 for the rate constants and the volume of distribution, respectively. Simulations of the scaled model were in agreement with clinical observations from 52 pediatric phase I PK profiles. The developed model can be used to guide the design of clinical trials with ASOs.

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.

Biopharmaceutical considerations in paediatrics with a view to the evaluation of orally administered drug products - a PEARRL review

OBJECTIVES

In this review, the current biopharmaceutical approaches for evaluation of oral formulation performance in paediatrics are discussed.

KEY FINDINGS

The paediatric gastrointestinal (GI) tract undergoes numerous morphological and physiological changes throughout its development and growth. Some physiological parameters are yet to be investigated, limiting the use of the existing in vitro biopharmaceutical tools to predict the in vivo performance of paediatric formulations. Meals and frequencies of their administration evolve during childhood and affect oral drug absorption. Furthermore, the establishment of a paediatric Biopharmaceutics Classification System (pBCS), based on the adult Biopharmaceutics Classification System (BCS), requires criteria adjustments. The usefulness of computational simulation and modeling for extrapolation of adult data to paediatrics has been confirmed as a tool for predicting drug formulation performance. Despite the great number of successful physiologically based pharmacokinetic models to simulate drug disposition, the simulation of drug absorption from the GI tract is a complicating issue in paediatric populations.

SUMMARY

The biopharmaceutics tools for investigation of oral drug absorption in paediatrics need further development, refinement and validation. A combination of in vitro and in silico methods could compensate for the uncertainties accompanying each method on its own.

The safety evaluation of food flavouring substances: the role of metabolic studies

The safety assessment of a flavour substance examines several factors, including metabolic and physiological disposition data. The present article provides an overview of the metabolism and disposition of flavour substances by identifying general applicable principles of metabolism to illustrate how information on metabolic fate is taken into account in their safety evaluation. The metabolism of the majority of flavour substances involves a series both of enzymatic and non-enzymatic biotransformation that often results in products that are more hydrophilic and more readily excretable than their precursors. Flavours can undergo metabolic reactions, such as oxidation, reduction, or hydrolysis that alter a functional group relative to the parent compound. The altered functional group may serve as a reaction site for a subsequent metabolic transformation. Metabolic intermediates undergo conjugation with an endogenous agent such as glucuronic acid, sulphate, glutathione, amino acids, or acetate. Such conjugates are typically readily excreted through the kidneys and liver. This paper summarizes the types of metabolic reactions that have been documented for flavour substances that are added to the human food chain, the methodologies available for metabolic studies, and the factors that affect the metabolic fate of a flavour substance.

A Whole-Body Physiologically Based Pharmacokinetic Model for Colistin and Colistin Methanesulfonate in Rat

Colistin is a polymyxin antibiotic used to treat patients infected with multidrug-resistant Gram-negative bacteria (MDR-GNB). The objective of this work was to develop a whole-body physiologically based pharmacokinetic (WB-PBPK) model to predict tissue distribution of colistin in rat. The distribution of a drug in a tissue is commonly characterized by its tissue-to-plasma partition coefficient, K_p . Colistin and its prodrug, colistin methanesulfonate (CMS) K_p priors, were measured experimentally from rat tissue homogenates or predicted in silico. The PK parameters of both compounds were estimated fitting in vivo their plasma concentration-time profiles from six rats receiving an i.v. bolus of CMS. The variability in the data was quantified by applying a nonlinear mixed effect (NLME) modelling approach. A WB-PBPK model was developed assuming a well-stirred and perfusion-limited distribution in tissue compartments. Prior information on tissue distribution of colistin and CMS was investigated following three scenarios: K_p was estimated using in silico K_p priors (I) or K_p was estimated using experimental K_p priors (II) or K_p was fixed to the experimental values (III). The WB-PBPK model best described colistin and CMS plasma concentration-time profiles in scenario II. Colistin-predicted concentrations in kidneys in scenario II were higher than in other tissues, which was consistent with its large experimental K_p prior. This might be explained by a high affinity of colistin for renal parenchyma and active reabsorption into the proximal tubular cells. In contrast, renal accumulation of colistin was not predicted in scenario I. Colistin and CMS clearance estimates were in agreement with published values. The developed model suggests using experimental priors over in silico K_p priors for kidneys to provide a better prediction of colistin renal distribution. Such models might serve in drug development for interspecies scaling and investigate the impact of disease state on colistin disposition.

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.

Human hepatocytes and cytochrome P450-selective inhibitors predict variability in human drug exposure more accurately than human recombinant P450s

BACKGROUND AND PURPOSE

Drugs metabolically eliminated by several enzymes are less vulnerable to variable compound exposure in patients due to drug-drug interactions (DDI) or if a polymorphic enzyme is involved in their elimination. Therefore, it is vital in drug discovery to accurately and efficiently estimate and optimize the metabolic elimination profile.

EXPERIMENTAL APPROACH

CYP3A and/or CYP2D6 substrates with well described variability in vivo in humans due to CYP3A DDI and CYP2D6 polymorphism were selected for assessment of fraction metabolized by each enzyme (fmCYP ) in two in vitro systems: (i) human recombinant P450s (hrP450s) and (ii) human hepatocytes combined with selective P450 inhibitors. Increases in compound exposure in poor versus extensive CYP2D6 metabolizers and by the strong CYP3A inhibitor ketoconazole were mathematically modelled and predicted changes in exposure were compared with in vivo data.

KEY RESULTS

Predicted changes in exposure were within twofold of reported in vivo values using fmCYP estimated in human hepatocytes and there was a strong linear correlation between predicted and observed changes in exposure (r2  = 0.83 for CYP3A, r2  = 0.82 for CYP2D6). Predictions using fmCYP in hrP450s were not as accurate (r2  = 0.55 for CYP3A, r2  = 0.20 for CYP2D6).

CONCLUSIONS AND IMPLICATIONS

The results suggest that variability in human drug exposure due to DDI and enzyme polymorphism can be accurately predicted using fmCYP from human hepatocytes and CYP-selective inhibitors. This approach can be efficiently applied in drug discovery to aid optimization of candidate drugs with a favourable metabolic elimination profile and limited variability in patients.

Population variability in animal health: Influence on dose-exposure-response relationships: Part II: Modelling and simulation

During the 2017 Biennial meeting, the American Academy of Veterinary Pharmacology and Therapeutics hosted a 1-day session on the influence of population variability on dose-exposure-response relationships. In Part I, we highlighted some of the sources of population variability. Part II provides a summary of discussions on modelling and simulation tools that utilize existing pharmacokinetic data, can integrate drug physicochemical characteristics with species physiological characteristics and dosing information or that combine observed with predicted and in vitro information to explore and describe sources of variability that may influence the safe and effective use of veterinary pharmaceuticals.

A Combined In Vitro/In Silico Approach to Identifying Off-Target Receptor Toxicity

Many xenobiotics can bind to off-target receptors and cause toxicity via the dysregulation of downstream transcription factors. Identification of subsequent off-target toxicity in these chemicals has often required extensive chemical testing in animal models. An alternative, integrated in vitro/in silico approach for predicting toxic off-target functional responses is presented to refine in vitro receptor identification and reduce the burden on in vivo testing. As part of the methodology, mathematical modeling is used to mechanistically describe processes that regulate transcriptional activity following receptor-ligand binding informed by transcription factor signaling assays. Critical reactions in the signaling cascade are identified to highlight potential perturbation points in the biochemical network that can guide and optimize additional in vitro testing. A physiologically based pharmacokinetic model provides information on the timing and localization of different levels of receptor activation informing whole-body toxic potential resulting from off-target binding.

First-Pass CYP3A-Mediated Metabolism of Midazolam in the Gut Wall and Liver in Preterm Neonates

To predict first‐pass and systemic cytochrome P450 (CYP) 3A‐mediated metabolism of midazolam in preterm neonates, a physiological population pharmacokinetic model was developed describing intestinal and hepatic midazolam clearance in preterm infants. On the basis of midazolam and 1‐OH‐midazolam concentrations from 37 preterm neonates (gestational age 26–34 weeks) receiving midazolam orally and/or via a 30‐minute intravenous infusion, intrinsic clearance in the gut wall and liver were found to be very low, with lower values in the gut wall (0.0196 and 6.7 L/h, respectively). This results in a highly variable and high total oral bioavailability of 92.1% (range, 67–95%) in preterm neonates, whereas this is around 30% in adults. This approach in which intestinal and hepatic clearance were separately estimated shows that the high bioavailability in preterm neonates is explained by, likely age‐related, low CYP3A activity in the liver and even lower CYP3A activity in the gut wall.

Model reduction in mathematical pharmacology : Integration, reduction and linking of PBPK and systems biology models

In this paper we present a framework for the reduction and linking of physiologically based pharmacokinetic (PBPK) models with models of systems biology to describe the effects of drug administration across multiple scales. To address the issue of model complexity, we propose the reduction of each type of model separately prior to being linked. We highlight the use of balanced truncation in reducing the linear components of PBPK models, whilst proper lumping is shown to be efficient in reducing typically nonlinear systems biology type models. The overall methodology is demonstrated via two example systems; a model of bacterial chemotactic signalling in Escherichia coli and a model of extracellular regulatory kinase activation mediated via the extracellular growth factor and nerve growth factor receptor pathways. Each system is tested under the simulated administration of three hypothetical compounds; a strong base, a weak base, and an acid, mirroring the parameterisation of pindolol, midazolam, and thiopental, respectively. Our method can produce up to an 80% decrease in simulation time, allowing substantial speed-up for computationally intensive applications including parameter fitting or agent based modelling. The approach provides a straightforward means to construct simplified Quantitative Systems Pharmacology models that still provide significant insight into the mechanisms of drug action. Such a framework can potentially bridge pre-clinical and clinical modelling - providing an intermediate level of model granularity between classical, empirical approaches and mechanistic systems describing the molecular scale.

Implications of intercorrelation between hepatic CYP3A4-CYP2C8 enzymes for the evaluation of drug-drug interactions: a case study with repaglinide

AIMS

Statistically significant positive correlations are reported for the abundance of hepatic drug-metabolizing enzymes. We investigate, as an example, the impact of CYP3A4-CYP2C8 intercorrelation on the predicted interindividual variabilities of clearance and drug-drug interactions (DDIs) for repaglinide using physiologically based pharmacokinetic (PBPK) modelling.

METHODS

PBPK modelling and simulation were employed using Simcyp Simulator (v15.1). Virtual populations were generated assuming intercorrelations between hepatic CYP3A4-CYP2C8 abundances derived from observed values in 24 human livers. A repaglinide PBPK model was used to predict PK parameters in the presence and absence of gemfibrozil in virtual populations, and the results were compared with a clinical DDI study.

RESULTS

Coefficient of variation (CV) of oral clearance was 52.5% in the absence of intercorrelation between CYP3A4-CYP2C8 abundances, which increased to 54.2% when incorporating intercorrelation. In contrast, CV for predicted DDI (as measured by AUC ratio before and after inhibition) was reduced from 46.0% in the absence of intercorrelation between enzymes to 43.8% when incorporating intercorrelation: these CVs were associated with 5th/95th percentiles (2.48-11.29 vs. 2.49-9.69). The range of predicted DDI was larger in the absence of intercorrelation (1.55-77.06) than when incorporating intercorrelation (1.79-25.15), which was closer to clinical observations (2.6-12).

CONCLUSIONS

The present study demonstrates via a systematic investigation that population-based PBPK modelling incorporating intercorrelation led to more consistent estimation of extreme values than those observed in interindividual variabilities of clearance and DDI. As the intercorrelations more realistically reflect enzyme abundances, virtual population studies involving PBPK and DDI should avoid using Monte Carlo assignment of enzyme abundance.

New Perspectives in Clinical Pharmacokinetics-1: the Importance of Updating the Teaching in Pharmacokinetics that both Clearance and Elimination Rate Constant Approaches Are Mathematically Proven Equally Valid

The healing professions have only about four main therapeutic tools at their disposal-surgery, drugs, physical therapy, and psychotherapy. For the general profession of internal medicine, drug therapy is its primary tool. Providing an understanding of the state-of-the-art in therapeutic methods, grounded in solid scientific and mathematical rigor, is therefore of the utmost clinical importance for both physicians and clinical pharmacists. This is particularly true where rapidly evolving scientific changes require an up-to-date education upon which students can rely. Unfortunately, relatively little attention has been paid to training clinical pharmacokineticists and physicians to manage drug therapy optimally for patients under their care in their everyday practice. In this paper, we discuss one of these basic deficiencies from the perspective of the longstanding controversy in pharmacokinetic modeling: whether the volume and clearance approach or the volume and rate constant approach is somehow "better". We examine this controversy using the mathematical principle of invariance, which to our knowledge has not been done before. The conclusion of this analysis is that both approaches are rigorously proven mathematically to be equally valid. We also discuss some implications of these equally valid approaches from the framework of mechanistic and non-compartmental models. Ultimately, the conclusion is that the choice of one parameterization over the other is based on preference or usefulness for research or clinical practice, but no longer, because of this analysis, on science.

Physiologically Based Pharmacokinetic Model Qualification and Reporting Procedures for Regulatory Submissions: A Consortium Perspective

This work provides a perspective on the qualification and verification of physiologically based pharmacokinetic (PBPK) platforms/models intended for regulatory submission based on the collective experience of the Simcyp Consortium members. Examples of regulatory submission of PBPK analyses across various intended applications are presented and discussed. European Medicines Agency (EMA) and US Food and Drug Administration (FDA) recent draft guidelines regarding PBPK analyses and reporting are encouraging, and to advance the use and acceptability of PBPK analyses, more clarity and flexibility are warranted.

Challenges and Opportunities for Increasing the Knowledge Base Related to Drug Biotransformation and Pharmacokinetics during Growth and Development

It is generally acknowledged that there is a need and role for informative pharmacokinetic models to improve predictions and simulation as well as individualization of drug therapy in pediatric populations of different ages and developmental stages. This special issue contains more than 20 papers responding to the challenge of providing new information on scaling factors, ontogeny functions for drug metabolizing enzymes and transporters, the mechanisms underlying the observed developmental trajectories for these gene products, age-dependent changes in physiologic processes affecting drug disposition in children, as well as in vitro and in vivo studies describing the relative contribution of ontogeny and genetic factors as sources of variability in drug disposition in children. Considered together, these contributions serve to illustrate some of the current limitations regarding sample availability, number, and quality, but also provide a framework that allows for the potential value of the results of a given study to be interpreted within the context of these limitations. Among the challenges for the future are improving our understanding of the mechanisms regulating age-dependent changes in factors influencing drug disposition and response, thereby facilitating generalization to systems lacking detailed data, better integrating age-dependent changes in pharmacokinetics with age-dependent changes in pharmacodynamics, and allowing better predictability and individualization of drug disposition and response across the pediatric age spectrum.

Gaining Mechanistic Insight Into Coproporphyrin I as Endogenous Biomarker for OATP1B-Mediated Drug-Drug Interactions Using Population Pharmacokinetic Modeling and Simulation

This study evaluated coproporphyrin I (CPI) as a selective endogenous biomarker of OATP1B‐mediated drug–drug interactions (DDIs) relative to clinical probe rosuvastatin using nonlinear mixed‐effect modeling. Plasma and urine CPI data in the presence/absence of rifampicin were modeled to describe CPI synthesis, elimination clearances, and obtain rifampicin in vivo OATP Ki. The biomarker showed stable interoccasion baseline concentrations and low interindividual variability (<25%) in subjects with wildtype SLCO1B1. Biliary excretion was the dominant CPI elimination route (maximal >85%). Estimated rifampicin in vivo unbound OATP Ki (0.13 μM) using CPI data was 2‐fold lower relative to rosuvastatin. Model‐based simulations and power calculations confirmed sensitivity of CPI to identify moderate and weak OATP1B inhibitors in an adequately powered clinical study. Current analysis provides the most detailed evaluation of CPI as an endogenous OATP1B biomarker to support optimal DDI study design; further pharmacogenomic and DDI data with a panel of inhibitors are required.

Evaluation and calibration of high-throughput predictions of chemical distribution to tissues

Toxicokinetics (TK) provides critical information for integrating chemical toxicity and exposure assessments in order to determine potential chemical risk (i.e., the margin between toxic doses and plausible exposures). For thousands of chemicals that are present in our environment, in vivo TK data are lacking. The publicly available R package "httk" (version 1.8, named for "high throughput TK") draws from a database of in vitro data and physico-chemical properties in order to run physiologically-based TK (PBTK) models for 553 compounds. The PBTK model parameters include tissue:plasma partition coefficients (K_p) which the httk software predicts using the model of Schmitt (Toxicol In Vitro 22 (2):457-467, 2008). In this paper we evaluated and modified httk predictions, and quantified confidence using in vivo literature data. We used 964 rat K_p measured by in vivo experiments for 143 compounds. Initially, predicted K_p were significantly larger than measured K_p for many lipophilic compounds (log₁₀ octanol:water partition coefficient > 3). Hence the approach for predicting K_p was revised to account for possible deficiencies in the in vitro protein binding assay, and the method for predicting membrane affinity was revised. These changes yielded improvements ranging from a factor of 10 to nearly a factor of 10,000 for 83 K_p across 23 compounds with only 3 K_p worsening by more than a factor of 10. The vast majority (92%) of K_p were predicted within a factor of 10 of the measured value (overall root mean squared error of 0.59 on log₁₀-transformed scale). After applying the adjustments, regressions were performed to calibrate and evaluate the predictions for 12 tissues. Predictions for some tissues (e.g., spleen, bone, gut, lung) were observed to be better than predictions for other tissues (e.g., skin, brain, fat), indicating that confidence in the application of in silico tools to predict chemical partitioning varies depending upon the tissues involved. Our calibrated model was then evaluated using a second data set of human in vivo measurements of volume of distribution (V_ss) for 498 compounds reviewed by Obach et al. (Drug Metab Dispos 36(7):1385-1405, 2008). We found that calibration of the model improved performance: a regression of the measured values as a function of the predictions has a slope of 1.03, intercept of - 0.04, and R² of 0.43. Through careful evaluation of predictive methods for chemical partitioning into tissues, we have improved and calibrated these methods and quantified confidence for TK predictions in humans and rats.

Evaluation and calibration of high-throughput predictions of chemical distribution to tissues

Toxicokinetics (TK) provides critical information for integrating chemical toxicity and exposure assessments in order to determine potential chemical risk (i.e., the margin between toxic doses and plausible exposures). For thousands of chemicals that are present in our environment, in vivo TK data are lacking. The publicly available R package "httk" (version 1.8, named for "high throughput TK") draws from a database of in vitro data and physico-chemical properties in order to run physiologically-based TK (PBTK) models for 553 compounds. The PBTK model parameters include tissue:plasma partition coefficients (Kp) which the httk software predicts using the model of Schmitt (Toxicol In Vitro 22 (2):457-467, 2008). In this paper we evaluated and modified httk predictions, and quantified confidence using in vivo literature data. We used 964 rat Kp measured by in vivo experiments for 143 compounds. Initially, predicted Kp were significantly larger than measured Kp for many lipophilic compounds (log10 octanol:water partition coefficient > 3). Hence the approach for predicting Kp was revised to account for possible deficiencies in the in vitro protein binding assay, and the method for predicting membrane affinity was revised. These changes yielded improvements ranging from a factor of 10 to nearly a factor of 10,000 for 83 Kp across 23 compounds with only 3 Kp worsening by more than a factor of 10. The vast majority (92%) of Kp were predicted within a factor of 10 of the measured value (overall root mean squared error of 0.59 on log10-transformed scale). After applying the adjustments, regressions were performed to calibrate and evaluate the predictions for 12 tissues. Predictions for some tissues (e.g., spleen, bone, gut, lung) were observed to be better than predictions for other tissues (e.g., skin, brain, fat), indicating that confidence in the application of in silico tools to predict chemical partitioning varies depending upon the tissues involved. Our calibrated model was then evaluated using a second data set of human in vivo measurements of volume of distribution (Vss) for 498 compounds reviewed by Obach et al. (Drug Metab Dispos 36(7):1385-1405, 2008). We found that calibration of the model improved performance: a regression of the measured values as a function of the predictions has a slope of 1.03, intercept of - 0.04, and R2 of 0.43. Through careful evaluation of predictive methods for chemical partitioning into tissues, we have improved and calibrated these methods and quantified confidence for TK predictions in humans and rats.

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.

Reverse Translation in PBPK and QSP: Going Backwards in Order to Go Forward With Confidence

Significant events have taken place shaping the recent industrialization of physiologically based pharmacokinetic in vitro-in vivo extrapolation (PBPK-IVIVE) use in drug development. Due to our knowledge gaps about drug-independent systems parameters, there are limitations in the use of purely IVIVE-based (bottom-up) approaches. This has encouraged combining the classical data analysis (top-down) with PBPK-IVIVE-linked models in order to optimize model parameters by taking advantage of observed clinical data. This concept, when initiated after clinical observations, can be viewed as "reverse translation," since it refers back to available systems information preclinical data before trying to describe the observations. This review demonstrates the advantages of such strategies in filling knowledge gaps and discusses the perceived hurdles in widening applications. It is paramount that no clinical data are assessed on their own, but in conjunction with other studies for that drug in different populations and/or other similar drugs in the same population.

Combining "Bottom-up" and "Top-down" Approaches to Assess the Impact of Food and Gastric pH on Pictilisib (GDC-0941) Pharmacokinetics

Pictilisib, a weakly basic compound, is an orally administered, potent, and selective pan-inhibitor of phosphatidylinositol 3-kinases for oncology indications. To investigate the significance of high-fat food and gastric pH on pictilisib pharmacokinetics (PK) and enable label recommendations, a dedicated clinical study was conducted in healthy volunteers, whereby both top-down (population PK, PopPK) and bottom-up (physiologically based PK, PBPK) approaches were applied to enhance confidence of recommendation and facilitate the clinical development through scenario simulations. The PopPK model identified food (for absorption rate constant (Ka )) and proton pump inhibitors (PPI, for relative bioavailability (Frel ) and Ka ) as significant covariates. Food and PPI also impacted the variability of Frel . The PBPK model accounted for the supersaturation tendency of pictilisib, and gastric emptying physiology successfully predicted the food and PPI effect on pictilisib absorption. Our research highlights the importance of applying both quantitative approaches to address critical drug development questions.

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.

Humans Vary, So Cardiac Models Should Account for That Too!

The utilization of mathematical modeling and simulation in drug development encompasses multiple mathematical techniques and the location of a drug candidate in the development pipeline. Historically speaking they have been used to analyze experimental data (i.e., Hill equation) and clarify the involved physical and chemical processes (i.e., Fick laws and drug molecule diffusion). In recent years the advanced utilization of mathematical modeling has been an important part of the regulatory review process. Physiologically based pharmacokinetic (PBPK) models identify the need to conduct specific clinical studies, suggest specific study designs and propose appropriate labeling language. Their application allows the evaluation of the influence of intrinsic (e.g., age, gender, genetics, disease) and extrinsic [e.g., dosing schedule, drug-drug interactions (DDIs)] factors, alone or in combinations, on drug exposure and therefore provides accurate population assessment. A similar pathway has been taken for the assessment of drug safety with cardiac safety being one the most advanced examples. Mechanistic mathematical model-informed safety evaluation, with a focus on drug potential for causing arrhythmias, is now discussed as an element of the Comprehensive in vitro Proarrhythmia Assay. One of the pillars of this paradigm is the use of an in silico model of the adult human ventricular cardiomyocyte to integrate in vitro measured data. Existing examples (in vitro—in vivo extrapolation with the use of PBPK models) suggest that deterministic, epidemiological and clinical data based variability models can be merged with the mechanistic models describing human physiology. There are other methods available, based on the stochastic approach and on population of models generated by randomly assigning specific parameter values (ionic current conductance and kinetic) and further pruning. Both approaches are briefly characterized in this manuscript, in parallel with the drug-specific variability.

Mechanistic Physiologically Based Pharmacokinetic Modeling of the Dissolution and Food Effect of a Biopharmaceutics Classification System IV Compound-The Venetoclax Story

Venetoclax, a selective B-cell lymphoma-2 inhibitor, is a biopharmaceutics classification system class IV compound. The aim of this study was to develop a physiologically based pharmacokinetic (PBPK) model to mechanistically describe absorption and disposition of an amorphous solid dispersion formulation of venetoclax in humans. A mechanistic PBPK model was developed incorporating measured amorphous solubility, dissolution, metabolism, and plasma protein binding. A middle-out approach was used to define permeability. Model predictions of oral venetoclax pharmacokinetics were verified against clinical studies of fed and fasted healthy volunteers, and clinical drug interaction studies with strong CYP3A inhibitor (ketoconazole) and inducer (rifampicin). Model verification demonstrated accurate prediction of the observed food effect following a low-fat diet. Ratios of predicted versus observed C_max and area under the curve of venetoclax were within 0.8- to 1.25-fold of observed ratios for strong CYP3A inhibitor and inducer interactions, indicating that the venetoclax elimination pathway was correctly specified. The verified venetoclax PBPK model is one of the first examples mechanistically capturing absorption, food effect, and exposure of an amorphous solid dispersion formulated compound. This model allows evaluation of untested drug-drug interactions, especially those primarily occurring in the intestine, and paves the way for future modeling of biopharmaceutics classification system IV compounds.

Age, Weight, and CYP2D6 Genotype Are Major Determinants of Primaquine Pharmacokinetics in African Children

Low-dose primaquine is recommended to prevent Plasmodium falciparum malaria transmission in areas threatened by artemisinin resistance and areas aiming for malaria elimination. Community treatment campaigns with artemisinin-based combination therapy in combination with the gametocytocidal primaquine dose target all age groups, but no studies thus far have assessed the pharmacokinetics of this gametocytocidal drug in African children. We recruited 40 children participating in a primaquine efficacy trial in Burkina Faso to study primaquine pharmacokinetics. These children received artemether-lumefantrine and either a 0.25- or a 0.40-mg/kg primaquine dose. Seven blood samples were collected from each participant for primaquine and carboxy-primaquine plasma levels determinations: one sample was collected before primaquine administration and six after primaquine administration according to partially overlapping sampling schedules. Physiological population pharmacokinetic modeling was used to assess the impact of weight, age, and CYP2D6 genotype on primaquine and carboxy-primaquine pharmacokinetics. Despite linear weight normalized dosing, the areas under the plasma concentration-time curves and the peak concentrations for both primaquine and carboxy-primaquine increased with age and body weight. Children who were CYP2D6 poor metabolizers had higher levels of the parent compound, indicating a lower primaquine CYP2D6-mediated metabolism. Our data indicate that primaquine and carboxy-primaquine pharmacokinetics are influenced by age, weight, and CYP2D6 genotype and suggest that dosing strategies may have to be reconsidered to maximize the transmission-blocking properties of primaquine. (This study has been registered at ClinicalTrials.gov under registration no. NCT01935882.)

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.

Computational modeling of the cell-autonomous mammalian circadian oscillator

This review summarizes various mathematical models of cell-autonomous mammalian circadian clock. We present the basics necessary for understanding of the cell-autonomous mammalian circadian oscillator, modern experimental data essential for its reconstruction and some special problems related to the validation of mathematical circadian oscillator models. This work compares existing mathematical models of circadian oscillator and the results of the computational studies of the oscillating systems. Finally, we discuss applications of the mathematical models of mammalian circadian oscillator for solving specific problems in circadian rhythm biology.

Evaluation of Drug-Drug Interaction Potential Between Sacubitril/Valsartan (LCZ696) and Statins Using a Physiologically Based Pharmacokinetic Model

Sacubitril/valsartan (LCZ696) has been approved for the treatment of heart failure. Sacubitril is an in vitro inhibitor of organic anion-transporting polypeptides (OATPs). In clinical studies, LCZ696 increased atorvastatin C_max by 1.7-fold and area under the plasma concentration-time curve by 1.3-fold, but had little or no effect on simvastatin or simvastatin acid exposure. A physiologically based pharmacokinetics modeling approach was applied to explore the underlying mechanisms behind the statin-specific LCZ696 drug interaction observations. The model incorporated OATP-mediated clearance (CL_int,T) for simvastatin and simvastatin acid to successfully describe the pharmacokinetic profiles of either analyte in the absence or presence of LCZ696. Moreover, the model successfully described the clinically observed drug effect with atorvastatin. The simulations clarified the critical parameters responsible for the observation of a low, yet clinically relevant, drug-drug interaction DDI between sacubitril and atorvastatin and the lack of effect with simvastatin acid. Atorvastatin is administered in its active form and rapidly achieves C_max that coincide with the low C_max of sacubitril. In contrast, simvastatin requires a hydrolysis step to the acid form and therefore is not present at the site of interactions at sacubitril concentrations that are inhibitory. Similar models were used to evaluate the drug-drug interaction risk for additional OATP-transported statins which predicted to maximally result in a 1.5-fold exposure increase.

Physiologically-Based Pharmacokinetic Modeling of Macitentan: Prediction of Drug-Drug Interactions

INTRODUCTION

Macitentan is a novel dual endothelin receptor antagonist for the treatment of pulmonary arterial hypertension (PAH). It is metabolized by cytochrome P450 (CYP) enzymes, mainly CYP3A4, to its active metabolite ACT-132577.

METHODS

A physiological-based pharmacokinetic (PBPK) model was developed by combining observations from clinical studies and physicochemical parameters as well as absorption, distribution, metabolism and excretion parameters determined in vitro.

RESULTS

The model predicted the observed pharmacokinetics of macitentan and its active metabolite ACT-132577 after single and multiple dosing. It performed well in recovering the observed effect of the CYP3A4 inhibitors ketoconazole and cyclosporine, and the CYP3A4 inducer rifampicin, as well as in predicting interactions with S-warfarin and sildenafil. The model was robust enough to allow prospective predictions of macitentan-drug combinations not studied, including an alternative dosing regimen of ketoconazole and nine other CYP3A4-interacting drugs. Among these were the HIV drugs ritonavir and saquinavir, which were included because HIV infection is a known risk factor for the development of PAH.

CONCLUSION

This example of the application of PBPK modeling to predict drug-drug interactions was used to support the labeling of macitentan (Opsumit).