PBPK Modeling to Simulate the Fate of Compounds in Living Organisms

Pharmacokinetics study the fate of xenobiotics in a living organism. Physiologically based pharmacokinetic (PBPK) models provide realistic descriptions of xenobiotics' absorption, distribution, metabolism, and excretion processes. They model the body as a set of homogeneous compartments representing organs, and their parameters refer to anatomical, physiological, biochemical, and physicochemical entities. They offer a quantitative mechanistic framework to understand and simulate the time-course of the concentration of a substance in various organs and body fluids. These models are well suited for performing extrapolations inherent to toxicology and pharmacology (e.g., between species or doses) and for integrating data obtained from various sources (e.g., in vitro or in vivo experiments, structure-activity models). In this chapter, we describe the practical development and basic use of a PBPK model from model building to model simulations, through implementation with an easily accessible free software.

A generic PBTK model implemented in the MCRA platform: Predictive performance and uses in risk assessment of chemicals

Physiologically-based toxicokinetic (PBTK) models are important tools for in vitro to in vivo or inter-species extrapolations in health risk assessment of foodborne and non-foodborne chemicals. Here we present a generic PBTK model implemented in the EuroMix toolbox, MCRA 9 and predict internal kinetics of nine chemicals (three endocrine disrupters, three liver steatosis inducers, and three developmental toxicants), in data-rich and data-poor conditions, when increasingly complex levels of parametrization are applied. At the first stage, only QSAR models were used to determine substance-specific parameters, then some parameter values were refined by estimates from substance-specific or high-throughput in vitro experiments. At the last stage, elimination or absorption parameters were calibrated based on available in vivo kinetic data. The results illustrate that parametrization plays a capital role in the output of the PBTK model, as it can change how chemicals are prioritized based on internal concentration factors. In data-poor situations, estimates can be far from observed values. In many cases of chronic exposure, the PBTK model can be summarized by an external to internal dose factor, and interspecies concentration factors can be used to perform interspecies extrapolation. We finally discuss the implementation and use of the model in the MCRA risk assessment platform.

Advancing human health risk assessment

The current/traditional human health risk assessment paradigm is challenged by recent scientific and technical advances, and ethical demands. The current approach is considered too resource intensive, is not always reliable, can raise issues of reproducibility, is mostly animal based and does not necessarily provide an understanding of the underlying mechanisms of toxicity. From an ethical and scientific viewpoint, a paradigm shift is required to deliver testing strategies that enable reliable, animal-free hazard and risk assessments, which are based on a mechanistic understanding of chemical toxicity and make use of exposure science and epidemiological data. This shift will require a new philosophy, new data, multidisciplinary expertise and more flexible regulations. Re-engineering of available data is also deemed necessary as data should be accessible, readable, interpretable and usable. Dedicated training to build the capacity in terms of expertise is necessary, together with practical resources allocated to education. The dialogue between risk assessors, risk managers, academia and stakeholders should be promoted further to understand scientific and societal needs. Genuine interest in taking risk assessment forward should drive the change and should be supported by flexible funding. This publication builds upon presentations made and discussions held during the break-out session 'Advancing risk assessment science - Human health' at EFSA's third Scientific Conference 'Science, Food and Society' (Parma, Italy, 18-21 September 2018).

Prediction of maternal and foetal exposures to perfluoroalkyl compounds in a Spanish birth cohort using toxicokinetic modelling

Prenatal exposures to perfluorooctanesulfonic acid (PFOS) and perfluorooctanoic acid (PFOA) have been associated with child health outcomes, but many of these associations remain poorly characterized. The aim of this work was to provide new indicators of foetal exposure for the Spanish INMA birth cohort. First, a pregnancy and lactation physiologically based pharmacokinetic (PBPK) model was calibrated in a population framework to provide quantitative estimates for the PFOA and PFOS placental transfers in humans. The estimated distributions indicated that PFOA crosses the placental barrier at a rate three times higher than PFOS and shows a higher variability between mothers. The PBPK model was then used to back-calculate the time-varying daily intakes of the INMA mothers corrected for their individual history from a spot maternal concentration. We showed the importance of accounting for the mothers' history as different dietary intakes can result in similar measured concentrations at one time point. Finally, the foetal exposure was simulated in target organs over pregnancy using the PBPK model and the estimated maternal intakes. We showed that the pattern of PFOA and PFOS exposures varies greatly among the foetuses. About a third has levels of either one compound always higher than the levels of the other compound. The other two thirds showed different ranking of PFOA and PFOS in terms of concentrations in the target organs. Our simulated foetal exposures bring additional information to the measured maternal spot concentrations and can help to better characterize the prenatal exposure in target organs during windows of susceptibility.

Generic physiologically-based toxicokinetic modelling for fish: Integration of environmental factors and species variability

One of the goals of environmental risk assessment is to protect the whole ecosystem from adverse effects resulting from exposure to chemicals. Many research efforts have aimed to improve the quantification of dose-response relationships through the integration of toxicokinetics. For this purpose, physiologically-based toxicokinetic (PBTK) models have been developed to estimate internal doses from external doses in a time-dependent manner. In this study, a generic PBTK model was developed and adapted for rainbow trout (Onchorhynchus mykiss), zebrafish (Danio rerio), fathead minnow (Pimephales promelas), and three-spined stickleback (Gasterosteus aculeatus). New mechanistic approaches were proposed for including the effects of growth and temperature in the model. Physiological parameters and their inter-individual variability were estimated based on the results of extensive literature searches or specific experimental data. The PBTK model was implemented for nine environmental contaminants (with log k_ow from -0.9 to 6.8) to predict whole-body concentrations and concentrations in various fish's organs. Sensitivity analyses were performed for a lipophilic and a hydrophilic compound to identify which parameters have most impact on the model's outputs. Model predictions were compared with experimental data according to dataset-specific exposure scenarios and were accurate: 50% of predictions were within a 3-fold factor for six out of nine chemicals and 75% of predictions were within a 3-fold factor for three of the most lipophilic compounds studied. Our model can be used to assess the influence of physiological and environmental factors on the toxicokinetics of chemicals and provide guidance for assessing the effect of those critical factors in environmental risk assessment.

Toxicokinetic models and related tools in environmental risk assessment of chemicals

Environmental risk assessment of chemicals for the protection of ecosystems integrity is a key regulatory and scientific research field which is undergoing constant development in modelling approaches and harmonisation with human risk assessment. This review focuses on state-of-the-art toxicokinetic tools and models that have been applied to terrestrial and aquatic species relevant to environmental risk assessment of chemicals. Both empirical and mechanistic toxicokinetic models are discussed using the results of extensive literature searches together with tools and software for their calibration and an overview of applications in environmental risk assessment. These include simple tools such as one-compartment models, multi-compartment models to physiologically-based toxicokinetic (PBTK) models, mostly available for aquatic species such as fish species and a number of chemical classes including plant protection products, metals, persistent organic pollutants, nanoparticles. Data gaps and further research needs are highlighted.

Identifiability of sorption parameters in stirred flow-through reactor experiments and their identification with a Bayesian approach

This paper addresses the methodological conditions -particularly experimental design and statistical inference- ensuring the identifiability of sorption parameters from breakthrough curves measured during stirred flow-through reactor experiments also known as continuous flow stirred-tank reactor (CSTR) experiments. The equilibrium-kinetic (EK) sorption model was selected as nonequilibrium parameterization embedding the K_d approach. Parameter identifiability was studied formally on the equations governing outlet concentrations. It was also studied numerically on 6 simulated CSTR experiments on a soil with known equilibrium-kinetic sorption parameters. EK sorption parameters can not be identified from a single breakthrough curve of a CSTR experiment, because K_d,1 and k^- were diagnosed collinear. For pairs of CSTR experiments, Bayesian inference allowed to select the correct models of sorption and error among sorption alternatives. Bayesian inference was conducted with SAMCAT software (Sensitivity Analysis and Markov Chain simulations Applied to Transfer models) which launched the simulations through the embedded simulation engine GNU-MCSim, and automated their configuration and post-processing. Experimental designs consisting in varying flow rates between experiments reaching equilibrium at contamination stage were found optimal, because they simultaneously gave accurate sorption parameters and predictions. Bayesian results were comparable to maximum likehood method but they avoided convergence problems, the marginal likelihood allowed to compare all models, and credible interval gave directly the uncertainty of sorption parameters θ. Although these findings are limited to the specific conditions studied here, in particular the considered sorption model, the chosen parameter values and error structure, they help in the conception and analysis of future CSTR experiments with radionuclides whose kinetic behaviour is suspected.

Assessment of Pentachlorophenol Exposure in Humans using the Clearance Concept

1 Pentachlorophenol (PeCP), a widely-used wood preservative, is a ubiquitous compound which has been found to be carcinogenic in mice. The objective of this study is to assess the average net daily intake of PeCP in cohorts of individuals who are: (1) not specifically exposed to PeCP, (2) residents of homes made of PeCP-treated logs and (3) occupationally exposed to PeCP.

2 The average net daily intake was calculated using a basic pharmacokinetic principle, the clearance (CL) concept: net daily intake equals CL (in 1 d-1) times the average steady-state concentration of PeCP in plasma ( Css). Css values reported in the literature were used for the calculations.

3 Because the two definitive studies on PeCP toxicokinetics in humans have given conflicting results, kinetic information from human exposure to PeCP was reviewed. Plasma clearance was estimated from retrospective analysis of urine and plasma concentrations measured in people after long-term exposure to PeCP. An overall clearance of 0.425 1 d-1 was obtained.

4 In groups of individuals who are not specifically exposed to PeCP, net daily intake estimated in eight countries varied from 5 μg (Nigeria) to 37 μg (The Netherlands). Net intake was between 51 μg d-1 and 157 μg d-1 in residents of homes made of PeCP-treated logs. In individuals occupationally exposed to PeCP, net daily intake varied widely (from 35 μg to about 24 000 μg) depending on the type of work.

Multiscale modelling approaches for assessing cosmetic ingredients safety

The European Union's ban on animal testing for cosmetic ingredients and products has generated a strong momentum for the development of in silico and in vitro alternative methods. One of the focus of the COSMOS project was ab initio prediction of kinetics and toxic effects through multiscale pharmacokinetic modeling and in vitro data integration. In our experience, mathematical or computer modeling and in vitro experiments are complementary. We present here a summary of the main models and results obtained within the framework of the project on these topics. A first section presents our work at the organelle and cellular level. We then go toward modeling cell levels effects (monitored continuously), multiscale physiologically based pharmacokinetic and effect models, and route to route extrapolation. We follow with a short presentation of the automated KNIME workflows developed for dissemination and easy use of the models. We end with a discussion of two challenges to the field: our limited ability to deal with massive data and complex computations.

Quantitative in vitro to in vivo extrapolation of tissues toxicity

Predicting repeated-dosing in vivo drug toxicity from in vitro testing and omics data gathering requires significant support in bioinformatics, mathematical modeling and statistics. We present here the major aspects of the work devoted within the framework of the European integrated Predict-IV to pharmacokinetic modeling of in vitro experiments, physiologically based pharmacokinetic (PBPK) modeling, mechanistic models of toxicity for the kidney and brain, large scale dose-response analyses methods and biomarker discovery tools. All of those methods have been applied to various extent to the drug datasets developed by the project's partners. Our approach is rather generic and could be adapted to other drugs or drug candidates. It marks a successful integration of the work of the different teams toward a common goal of predictive quantitative in vitro to in vivo extrapolation.

Integrated Testing Strategies (ITS) for safety assessment

Integrated testing strategies (ITS), as opposed to single definitive tests or fixed batteries of tests, are expected to efficiently combine different information sources in a quantifiable fashion to satisfy an information need, in this case for regulatory safety assessments. With increasing awareness of the limitations of each individual tool and the development of highly targeted tests and predictions, the need for combining pieces of evidence increases. The discussions that took place during this workshop, which brought together a group of experts coming from different related areas, illustrate the current state of the art of ITS, as well as promising developments and identifiable challenges. The case of skin sensitization was taken as an example to understand how possible ITS can be constructed, optimized and validated. This will require embracing and developing new concepts such as adverse outcome pathways (AOP), advanced statistical learning algorithms and machine learning, mechanistic validation and "Good ITS Practices".

Computational pharmacokinetics at a crossroads

This first special issue of In Silico Pharmacology focuses on computational pharmacokinetics since they are an important part of integrated applications in computational pharmacology. The important topics of model structure, model parameterization, improved organ description, and modeling of drug-drug interactions are covered. They are actually at the crossroads between several emerging disciplines which will shape the future of therapeutic treatments and public health.

A computational model to predict rat ovarian steroid secretion from in vitro experiments with endocrine disruptors

A finely tuned balance between estrogens and androgens controls reproductive functions, and the last step of steroidogenesis plays a key role in maintaining that balance. Environmental toxicants are a serious health concern, and numerous studies have been devoted to studying the effects of endocrine disrupting chemicals (EDCs). The effects of EDCs on steroidogenic enzymes may influence steroid secretion and thus lead to reproductive toxicity. To predict hormonal balance disruption on the basis of data on aromatase activity and mRNA level modulation obtained in vitro on granulosa cells, we developed a mathematical model for the last gonadal steps of the sex steroid synthesis pathway. The model can simulate the ovarian synthesis and secretion of estrone, estradiol, androstenedione, and testosterone, and their response to endocrine disruption. The model is able to predict ovarian sex steroid concentrations under normal estrous cycle in female rat, and ovarian estradiol concentrations in adult female rats exposed to atrazine, bisphenol A, metabolites of methoxychlor or vinclozolin, and letrozole.

Zonation related function and ubiquitination regulation in human hepatocellular carcinoma cells in dynamic vs. static culture conditions

Background

Understanding hepatic zonation is important both for liver physiology and pathology. There is currently no effective systemic chemotherapy for human hepatocellular carcinoma (HCC) and its pathogenesis is of special interest. Genomic and proteomic data of HCC cells in different culture models, coupled to pathway-based analysis, can help identify HCC-related gene and pathway dysfunctions.

Results

We identified zonation-related expression profiles contributing to selective phenotypes of HCC, by integrating relevant experimental observations through gene set enrichment analysis (GSEA). Analysis was based on gene and protein expression data measured on a human HCC cell line (HepG2/C3A) in two culture conditions: dynamic microfluidic biochips and static Petri dishes. Metabolic activity (HCC-related cytochromes P450) and genetic information processing were dominant in the dynamic cultures, in contrast to kinase signaling and cancer-specific profiles in static cultures. That, together with analysis of the published literature, leads us to propose that biochips culture conditions induce a periportal-like hepatocyte phenotype while standard plates cultures are more representative of a perivenous-like phenotype. Both proteomic data and GSEA results further reveal distinct ubiquitin-mediated protein regulation in the two culture conditions.

Conclusions

Pathways analysis, using gene and protein expression data from two cell culture models, confirmed specific human HCC phenotypes with regard to CYPs and kinases, and revealed a zonation-related pattern of expression. Ubiquitin-mediated regulation mechanism gives plausible explanations of our findings. Altogether, our results suggest that strategies aimed at inhibiting activated kinases and signaling pathways may lead to enhanced metabolism-mediated drug resistance of treated tumors. If that were the case, mitigating inhibition or targeting inactive forms of kinases would be an alternative.

Development of a physiologically based kinetic model for 99m-technetium-labelled carbon nanoparticles inhaled by humans

Particulate air pollution is associated with respiratory and cardiovascular morbidity and mortality. Recent studies investigated whether and to which extent inhaled ultrafine particles are able to translocate into the bloodstream in humans. However, their conclusions were conflicting. We developed a physiologically based kinetic model for (99m)technetium-labelled carbon nanoparticles (Technegas). The model was designed to analyse imaging data. It includes different translocation rates and kinetics for free technetium, and small and large technetium-labelled particles. It was calibrated with data from an experiment designed to assess the fate of nanoparticles in humans after inhalation of Technegas. The data provided time courses of radioactivity in the liver, stomach, urine, and blood. Parameter estimation was performed in a Bayesian context with Markov chain Monte Carlo (MCMC) techniques. Our analysis points to a likely translocation of particle-bound technetium from lung to blood, at a rate about twofold lower than the transfer rate of free technetium. Notably, restricting the model so that only free technetium would have been able to reach blood circulation resulted in much poorer fits to the experimental data. The percentage of small particles able to translocate was estimated at 12.7% of total particles. The percentage of unbound technetium was estimated at 6.7% of total technetium. To our knowledge, our model is the first PBPK model able to use imaging data to describe the absorption and distribution of nanoparticles. We believe that our modeling approach using Bayesian and MCMC techniques provides a reasonable description on which to base further model refinement.

Physiologically based modelling and prediction of drug interactions

A major challenge for drug development and environmental or occupational health is the prediction of pharmacokinetic and pharmacodynamic interactions between drugs, natural chemicals or environmental contaminants. This article reviews briefly past developments in the area of physiologically based pharmacokinetic (PBPK) modelling of interactions. It also demonstrates a systems biology approach to the question, and the capabilities of new software tools to facilitate that development. Individual Systems Biology Markup Language models of metabolic pathways can now be automatically merged and coupled to a template PBPK pharmacokinetic model, using for example the GNU MCSim software. The global model generated is very efficient and able to simulate the interactions between a theoretically unlimited number of substances. Development time and the number of model parameter increase only linearly with the number of substances considered, even though the number of possible interactions increases exponentially.

GNU MCSim: Bayesian statistical inference for SBML-coded systems biology models

SUMMARY

Statistical inference about the parameter values of complex models, such as the ones routinely developed in systems biology, is efficiently performed through Bayesian numerical techniques. In that framework, prior information and multiple levels of uncertainty can be seamlessly integrated. GNU MCSim was precisely developed to achieve those aims, in a general non-linear differential context. Starting with version 5.3.0, GNU MCSim reads in and simulates Systems Biology Markup Language models. Markov chain Monte Carlo simulations can be used to generate samples from the joint posterior distribution of the model parameters, given a dataset and prior distributions. Hierarchical statistical models can be used. Optimal design of experiments can also be investigated.

AVAILABILITY AND IMPLEMENTATION

The GNU GPL source is available at (http://savannah.gnu.org/projects/mcsim). A distribution package is at (http://www.gnu.org/software/mcsim). GNU MCSim is written in standard C and runs on any platform supporting a C compiler. Supplementary Material is available online at (http://www.gnu.org/software/mcsim).

Characterizing Uncertainty and Variability in Physiologically Based Pharmacokinetic Models: State of the Science and Needs for Research and Implementation

Physiologically based pharmacokinetic (PBPK) models are used in mode-of-action based risk and safety assessments to estimate internal dosimetry in animals and humans. When used in risk assessment, these models can provide a basis for extrapolating between species, doses, and exposure routes or for justifying nondefault values for uncertainty factors. Characterization of uncertainty and variability is increasingly recognized as important for risk assessment; this represents a continuing challenge for both PBPK modelers and users. Current practices show significant progress in specifying deterministic biological models and nondeterministic (often statistical) models, estimating parameters using diverse data sets from multiple sources, using them to make predictions, and characterizing uncertainty and variability of model parameters and predictions. The International Workshop on Uncertainty and Variability in PBPK Models, held 31 Oct-2 Nov 2006, identified the state-of-the-science, needed changes in practice and implementation, and research priorities. For the short term, these include (1) multidisciplinary teams to integrate deterministic and nondeterministic/statistical models; (2) broader use of sensitivity analyses, including for structural and global (rather than local) parameter changes; and (3) enhanced transparency and reproducibility through improved documentation of model structure(s), parameter values, sensitivity and other analyses, and supporting, discrepant, or excluded data. Longer-term needs include (1) theoretical and practical methodological improvements for nondeterministic/statistical modeling; (2) better methods for evaluating alternative model structures; (3) peer-reviewed databases of parameters and covariates, and their distributions; (4) expanded coverage of PBPK models across chemicals with different properties; and (5) training and reference materials, such as cases studies, bibliographies/glossaries, model repositories, and enhanced software. The multidisciplinary dialogue initiated by this Workshop will foster the collaboration, research, data collection, and training necessary to make characterizing uncertainty and variability a standard practice in PBPK modeling and risk assessment.

Development of a physiologically based toxicokinetic model for butadiene and four major metabolites in humans: Global sensitivity analysis for experimental design issues

1,3-Butadiene (BD) is metabolized in humans and rodents to mutagenic and carcinogenic species. Our previous work has focused on developing a physiologically based toxicokinetic (PBTK) model for BD to estimate its metabolic rate to 1,2-epoxy-3-butene (EB), using exhaled breath BD concentrations in human volunteers exposed by inhalation. In this paper, we extend our BD model to describe the kinetics of its four major metabolites EB, 1,2:3,4-diepoxybutane (DEB), 3-butene-1,2-diol (BDD), and 3,4-epoxy-1,2-butanediol (EBD), and to test whether the extended model and experimental data (to be collected for BD and metabolites in humans) are together adequate to estimate the metabolic rate constants of each of the above chemicals. Global sensitivity analyses (GSA) were conducted to evaluate the relative importance of the model parameters on model outputs during the 20min of exposure and the 40min after exposure ended. All model parameters were studied together with various potentially measurable model outputs: concentrations of BD and EB in exhaled air, concentrations of BD and all metabolites in venous blood, and cumulated amounts of urinary metabolites excreted within 24h. Our results show that pulmonary absorption of BD and subsequent distribution and metabolism in the well-perfused tissues compartment are the critical processes in the toxicokinetics of BD and metabolites. In particular, three parameters influence numerous outputs: the blood:air partition coefficient for BD, the metabolic rate of BD to EB, and the volume of the well-perfused tissues. Other influential parameters include other metabolic rates, some partition coefficients, and parameters driving the gas exchanges (in particular, for BD outputs). GSA shows that the impact of the metabolic rate of BD to EB on the BD concentrations in exhaled air is greatly increased if a few of the model's important parameters (such as the blood:air partition coefficient for BD) are measured experimentally. GSA also shows that all the transformation pathways described in the PBTK model may not be estimable if only data on the studied outputs are collected, and that data on a specific output for a chemical may not inform all the transformations involving that chemical.

Sequential updating of a new dynamic pharmacokinetic model for caffeine in premature neonates

BACKGROUND AND OBJECTIVE

Caffeine treatment is widely used in nursing care to reduce the risk of apnoea in premature neonates. To check the therapeutic efficacy of the treatment against apnoea, caffeine concentration in blood is an important indicator. The present study was aimed at building a pharmacokinetic model as a basis for a medical decision support tool.

METHODS

In the proposed model, time dependence of physiological parameters is introduced to describe rapid growth of neonates. To take into account the large variability in the population, the pharmacokinetic model is embedded in a population structure. The whole model is inferred within a Bayesian framework. To update caffeine concentration predictions as data of an incoming patient are collected, we propose a fast method that can be used in a medical context. This involves the sequential updating of model parameters (at individual and population levels) via a stochastic particle algorithm.

RESULTS

Our model provides better predictions than the ones obtained with models previously published. We show, through an example, that sequential updating improves predictions of caffeine concentration in blood (reduce bias and length of credibility intervals). The update of the pharmacokinetic model using body mass and caffeine concentration data is studied. It shows how informative caffeine concentration data are in contrast to body mass data.

CONCLUSION

This study provides the methodological basis to predict caffeine concentration in blood, after a given treatment if data are collected on the treated neonate.

The application of a Bayesian approach to the analysis of a complex, mechanistically based model

The Bayesian approach has been suggested as a suitable method in the context of mechanistic pharmacokinetic-pharmacodynamic (PK-PD) modeling, as it allows for efficient use of both data and prior knowledge regarding the drug or disease state. However, to this day, published examples of its application to real PK-PD problems have been scarce. We present an example of a fully Bayesian re-analysis of a previously published mechanistic model describing the time course of circulating neutrophils in stroke patients and healthy individuals. While priors could be established for all population parameters in the model, not all variability terms were known with any degree of precision. A sensitivity analysis around the assigned priors used was performed by testing three different sets of prior values for the population variance terms for which no data were available in the literature: "informative", "semi-informative", and "noninformative", respectively. For all variability terms, inverse gamma distributions were used. It was possible to fit the model to the data using the "informative" priors. However, when the "semi-informative" and "noninformative" priors were used, it was impossible to accomplish convergence due to severe correlations between parameters. In addition, due to the complexity of the model, the process of defining priors and running the Markov chains was very time-consuming. We conclude that the present analysis represents a first example of the fully transparent application of Bayesian methods to a complex, mechanistic PK-PD problem with real data. The approach is time-consuming, but enables us to make use of all available information from data and scientific evidence. Thereby, it shows potential both for detection of data gaps and for more reliable predictions of various outcomes and "what if" scenarios.

Toxicokinetics of Inhaled Trichloroethylene and Tetrachloroethylene in Humans at 1 ppm: Empirical Results and Comparisons with Previous Studies

Trichloroethylene (TRI) and tetrachloroethylene (TETRA) are solvents that have been widely used in a variety of industries, and both are widespread environmental contaminants. In order to provide a better basis for understanding their toxicokinetics at environmental exposures, seven human volunteers were exposed by inhalation to 1 ppm of TRI or TETRA for 6 h, with biological samples collected for analysis during exposure and up to 6-days postexposure. Concentrations of TRI, TETRA, free trichloroethanol (TCOH), total TCOH (free TCOH plus glucuronidated TCOH), and trichloroacetic acid (TCA) were determined in blood and urine; TRI and TETRA concentrations were measured in alveolar breath. Toxicokinetic time courses and empirical analyses of classical toxicokinetic parameters were compared with those reported in previous human volunteer studies, most of which involved exposures that were at least 10-fold higher. Qualitatively, TRI and TETRA toxicokinetics were consistent with previous human studies. Quantitatively, alveolar retention and clearance by exhalation were similar to those found previously but blood and urine data suggest a number of possible toxicokinetic differences. For TRI, data from the current study support lower apparent blood-air partition coefficients, greater apparent metabolic clearance, less TCA production, and greater glucuronidation of TCOH as compared to previous studies. For TETRA, the current data suggest TCA formation that is similar or slightly lower than that of previous studies. Variability and uncertainty in empirical estimates of total TETRA metabolism are substantial, with confidence intervals among different studies substantially overlapping. Relative contributions to observed differences from concentration-dependent toxicokinetics and interindividual and interoccasion variability remain to be determined.

Evaluation of antiangiogenic treatment effects on tumors' microcirculation by Bayesian physiological pharmacokinetic modeling and magnetic resonance imaging

A physiological pharmacokinetic (PBPK) model was used to estimate tumor microcirculation in nude mice with a grafted tumor. The kinetics of a rapid clearance blood pool agent, Vistarem, were investigated by dynamic MRI after bolus administration. Signal enhancements were recorded in arterial blood and in tumor tissue. To analyze these data, we developed a whole-body mathematical model of the agent's biodistribution using physiological parameters. The model included six compartments: arterial and venous plasma, tumor (split into capillaries and interstitium), and the rest of the body (also split into capillaries and interstitium). As an application, changes in tumor microcirculation parameters were evaluated in mice receiving either an antiangiogenic treatment (ZD4190) or a placebo. The analysis was performed in a Bayesian framework, and the model was fitted to experimental data using Markov Chain Monte Carlo techniques. Results showed a significant difference in tumor microcirculation between the two groups of mice when the microcirculation parameters are considered together. This whole-body physiological model enables to analyze jointly data in tumor tissue and in arterial blood. This leads to accurate estimates of microcirculation parameters and the evaluation of their uncertainty.

Use of a chemical probe to increase safety for human volunteers in toxicokinetic studies

To avoid interspecies extrapolation in toxicokinetics and drug development, it is convenient to directly develop human data. In that case, exposure dose should pose null or negligible risk to the exposed individual, but still be sufficiently high to allow quantification. We propose to reduce the dose received by human volunteers during exposure, and to compensate for loss of information by exposing the same volunteers to a nontoxic agent. This method was applied to develop 1,3-butadiene (BD) exposure protocols for humans. To study the potential of such a procedure, we worked with simulated data. Three exposure times (20, 10, and 5 minutes) and four exposure concentrations (2, 1, 0.8, and 0.5 ppm) were used to define 12 inhalation exposure scenarios for BD. Isoflurane was used as a probe, with simulated exposure of 20 subjects to 20 ppm isoflurane during 15 minutes. Isoflurane or BD-exhaled air concentrations were supposed to be measured 10 times. A three-compartment physiological toxicokinetic model was used to jointly describe BD and isoflurane data. For each subject, BD data were analyzed, in a Bayesian framework, either alone or together with the isoflurane data. The precision of BD metabolic rate constant or fraction metabolized was increased, and bias reduced, when BD and probe data were considered jointly. An exposure to 10 ppm x min BD and 300 ppm x min isoflurane gave equivalent precision and bias as a unique exposure to 40 ppm x min BD. The BD dose received by volunteers could therefore be at least quartered if BD exposure was supplemented with that of a probe.

Lumping in Pharmacokinetics

Pharmacokinetic (PK) models simplify biological complexity by dividing the body into interconnected compartments. The time course of the chemical's amount (or concentration) in each compartment is then expressed as a system of ordinary differential equations. The complexity of the resulting system of equations can rapidly increase if a precise description of the organism is needed. However, difficulties arise when the PK model contains more variables and parameters than comfortable for mathematical and computational treatment. To overcome such difficulties, mathematical lumping methods are new and powerful tools. Such methods aim at reducing a differential system by aggregating several variables into one. Typically, the lumped model is still a differential equation system, whose variables are interpretable in terms of variables of the original system. In practice, the reduced model is usually required to satisfy some constraints. For example, it may be necessary to keep state variables of interest for prediction unlumped. To accommodate such constraints, constrained lumping methods have are also available. After presenting the theory, we study, here, through practical examples, the potential of such methods in toxico/pharmacokinetics. As a tutorial, we first simplify a 2-compartment pharmacokinetic model by symbolic lumping. We then explore the reduction of a 6-compartment physiologically based pharmacokinetic model for 1,3-butadiene with numerical constrained lumping. The lumping methods presented here can be easily automated, and are applicable to first-order ordinary differential equation systems.

Propylene glycol monomethyl ether. A three-generation study of isomer beta effects on reproductive and developmental parameters in rats

Propylene glycol monomethyl ether (PGME) is widely used as a solvent in numerous commercial products. Its chemical synthesis leads to the formation of two isomers: alpha and beta, the latter being usually present in the range of 0.5-1.5%. Isomer alpha has been shown to be of low toxicity. Isomer beta raises concerns as to its reproductive and developmental effects. We evaluated the reproductive and developmental toxicity of two different commercial mixes of PGME (Mix A: 99% isomer alpha and 0.5% isomer beta, Mix B: 98.5% isomer alpha and 1.5% isomer beta) on Sprague-Dawley rats. The use of two mixes allowed us to differentiate between isomer alpha and isomer beta effects. Male and female rats were exposed through drinking water to mixes A or B during a gametogenesis cycle (64 days for males and 15 days for females) to 0, 2, 5, 10 and 15% (v/v) of each mix. These animals (F0) and the three following generations (F1, F2 and F3) were followed. We observed a statistically significant decrease in the number of pups in isomer alpha-treated animals of generation F1 and a nondose-related variation of the sex ratio in F1 and F2 generations after PGME mix B treatment. The most important effect observed was a decrease in testicular and epididymal sperm counts in relation to PGME isomer beta in acute daily exposure, on the first parental generation. The effect evidenced on sex ratio needs further work in order to assay the potential persistent effects of PGME exposure.

Pharmacokinetic–pharmacodynamic models for categorical toxicity data

We propose a pharmacokinetic-pharmacodynamic (PK/PD) model (with possibly different choices for the PD link) for categorical toxicity data analysis. This is extension of the one-comportment model that applies to toxic endpoints categorised by grades (e.g., benign, mild, severe, and very severe). The model assumes that the area under the curve (AUC) of the internal quantity of the chemical substance is the critical dose-metric that drives the acute toxic phenomenon. That model handles time-varying concentrations and takes into account follow-up time, i.e., time at which effects are observed. Moreover the model bridges mechanistically based dose-response models and standard dose-response models, retaining the advantages of both. We use Markov chain-Monte Carlo (MCMC) simulations to fit the model to mortality data for mice exposed to chlorine, rats exposed to ammonia, and categorical data (different severity levels) from acute exposures of rats and humans to hydrogen sulfide.

Extension of the isobolographic approach to interactions studies between more than two drugs: illustration with the convulsant interaction between pefloxacin, norfloxacin, and theophylline in rats

This work proposes a model to characterize the additivity or the nonadditivity of combinations of more than two agents. Using a Bayesian framework, we modeled the variability between experimental subjects, the errors that occurred during data collection, and the relationship between effects and concentrations of agents at the effect site. The model was used to characterize the additivity (or non-additivity) of norfloxacin, pefloxacin, and theophylline in causing maximal seizures in male Sprague Dawley rats. Animals received the drugs separately or in various combinations. Drug infusion was stopped at the onset of maximal seizures, and cerebrospinal fluid samples were collected for determination of drug concentration by high-performance liquid chromatography. The model was fitted to concentration data using Markov Chain Monte Carlo techniques. Results showed that induction of seizures by mixtures of theophylline and pefloxacin were additive. Seizure induction by mixtures of norfloxacin and pefloxacin or norfloxacin and theophylline were not additive and, given the model, these drugs interacted negatively. There was no triple interaction effect between the drugs. This study demonstrates the ease with which mixtures of more than two drugs can be analyzed with the proposed model.

Intratracheal instillation of cytoplasmic granules from Phleum pratense pollen induces IgE- and cell-mediated responses in the Brown Norway rat

BACKGROUND

Release of cytoplasmic granules from grass pollen upon contact with water is thought to be an important source of airborne allergens.

OBJECTIVES

To investigate the humoral and cellular responses to intratracheal instillation of Phleum pratense (timothy grass) pollen cytoplasmic granules (PCG) in the Brown Norway rat.

METHODS

PCG were purified from timothy grass pollen by filtration through 5-microm-mesh filters. Rats were sensitized (day 0) and challenged (day 21) intratracheally with purified PCG suspended in saline (6 x 10(6) PCG/rat). Rats were then challenged 4 weeks later (1.5 x 10(6) PCG/rat). Blood samples, bronchial lymph nodes and lungs were collected from the rats 4 days after the second challenge. PCG-specific IgE and IgG1 levels and specificity were determined by ELISA and Western blotting. Pollen, pollen extract and PCG-induced proliferation of lymph node cells were monitored by [(3)H]-thymidine incorporation in a lymph node assay. Histopathological examination was carried out on the lungs.

RESULTS

Specific IgE and IgG1 were present in the sera. Cultured lymph node cells proliferated in the presence of pollen, pollen extract and PCG. Western blots showed that all major pollen allergens are recognized by IgE and IgG1 from PCG-treated rats. Histopathological examination revealed features of a mild allergic reaction.

CONCLUSIONS

In our rat model of allergy, purified timothy grass PCG instillation induced specific antibodies and lymph node cell responses, comparable to those obtained with intact pollen.

Environmental benzene exposure assessment for parent-child pairs in Rouen, France

There is a lack of data on environmental benzene exposure in children. In this study, we compared personal benzene exposure and inhalation uptake in a group of children to those of their parents. We also compared levels of urinary benzene metabolites, trans,trans-muconic acid (MA) and hydroquinone (HQ), for those two groups, and assessed the correlation between personal benzene exposure and urinary MA and HQ concentrations. The study was performed on 21, 2-3-year-old children and their parents recruited on a voluntary basis among non-smokers from the three largest day-care centers of the town of Rouen in France. Average benzene concentrations were measured over 5 consecutive days with diffusive samplers. The following simultaneous measurements were carried out: personal exposure of the parents, concentrations inside and outside the day care centers, and inside the volunteer's bedrooms. Morning and evening urine samples were collected during the same period. Benzene personal exposure levels were 14.4+/-7.7 microg/m(3) and 11.09+/-6.15 microg/m(3) in parents and children, respectively. Benzene inhalation uptake estimates were 2.51+/-1.23 microg/kg/day in the group of parents and 5.68+/-3.17 microg/kg/day in the group of children. Detectable levels of MA and HQ were found in 85% and 100% of the samples, respectively. Intra-individual variation of urinary MA and HQ concentrations expressed as a coefficient of variation (CV) ranged from 63 to 232% and from 13 to 144%, respectively. Mean values of MA and HQ (in mg/g creatinine) were 1.6- and 1.8-fold higher in the group of children than in the group of parents (P=0.008 and P<0.0001, respectively). Significant correlations between metabolites levels and benzene were not found.

Decrease in ovalbumin-induced pulmonary allergic response by benzaldehyde but not acetaldehyde exposure in a Guinea pig model

The pulmonary effects of two environmentally relevant aldehydes were investigated in nonsensitized or ovalbumin (OA)-sensitized guineapigs (GPs). Four-week-old male Hartley GPs, weighing about 400 g, were intraperitoneally injected with 1 ml of an NaCl solution containing 100 microg OA and 100 mg Al(OH)(3). They were then exposed to either acetaldehyde (200 ppb) or benzaldehyde (500 ppb) for 4 wk (6 h/d, 5 d/wk). At the end of exposure, GPs were challenged with an OA aerosol (0.1% in NaCl) and pulmonary functions were measured. The day after, guinea pigs were anesthetized and several endpoints related to inflammatory and allergic responses were assessed in blood, whole-lung histology, and bronchoalveolar lavage (BAL). Sensitized nonexposed GPs showed bronchial hyperresponsiveness to OA and an increased number of eosinophils in blood and BAL, together with a rise in total protein and leukotrienes (LTB(4) and LTC(4)/D(4)/E(4)) in BAL. In nonsensitized GPs, exposure to acetaldehyde or benzaldehyde did not induce any change in the tested parameters, with the exception of irritation of the respiratory tract as detected by histology and an increased number of alveolar macrophages in animals exposed to acetaldehyde. In sensitized GPs, exposure to acetaldehyde induced a moderate irritation of the respiratory tract but no change in biological parameters linked to the inflammatory and allergic responses. In contrast, exposure to benzaldehyde induced a decrease both in OA-induced bronchoconstriction and in eosinophil and neutrophil numbers in BAL, an increase in the bronchodilatator mediator prostaglandin E(2) (PGE(2)), and a decrease in the bronchoconstrictor mediators LTC(4)/D(4)/E(4). Further investigations are needed to determine if the attenuated response observed in sensitized GPs exposed to benzaldehyde is due to an alteration of the mechanism of sensitization or to a more direct effect on various mechanisms of the allergic response.

Genetic and dietary factors affecting human metabolism of 1,3-butadiene

The objective of this project was to determine the factors associated with differences in butadiene (BD) inhalation uptake and the rate of metabolism for BD to epoxy butene by monitoring exhaled breath during and after a brief exposure to BD in human volunteers. A total of 133 subjects (equal males and females; four racial groups) provided final data. Volunteers gave informed consent and completed a questionnaire including diet and alcohol use. A venous blood sample was collected for genotyping CYP2E1. Subjects received a 20 min exposure to 2.0 ppm of BD, followed by a 40 min washout period. The total administered dose was 0.6 ppm*h, which is in the range of everyday exposures. Ten, 1 or 2 min exhaled breath samples (five during and five after exposure) were collected using an optimized strategy. BD was determined by GC-FID analysis. Breathing activity (minute ventilation, breath frequency and tidal volume) was measured to estimate alveolar ventilation. After the washout period, 250 mg of chlorzoxazone were administered and urine samples collected for 6 h to measure 2E1 phenotype. The total BD uptake during exposure (inhaled BD minus exhaled) was estimated. A three-compartment PBPK model was fitted to each subject's breath measurements to estimate personal and population model parameters, including in-vivo BD metabolic rate. A hierarchical Bayesian PBPK model was fit by Monte Carlo simulations to estimate model parameters. Regression and ANOVA analyses were performed. Earlier data analysis showed wide ranges for both total uptake BD and metabolic rate. Both varied significantly by sex and age, and showed suggestive differences by race, with Asians having the highest rates. The analyses reported here found no correlation between total BD uptake and metabolic rate. No significant differences were found for oxidation rates by 2E1 genotype or phenotype, but the rates showed trends consistent with reported differences by genotype and phenotype for chlorzoxazone metabolism. No effects on metabolic rate were observed for long-term alcohol consumption, or consumption in the past 24 h. Overall, neither dietary factors nor genetic differences explained much of the wide variability in metabolic rates. Population characteristics, age, sex, and race, were the most important explanatory variables, but a large fraction of the total variability in metabolism remains to be explained.

Assessing the reliability of PBPK models using data from methyl chloride-exposed, non-conjugating human subjects

Physiologically based pharmacokinetic (PBPK) models are often optimized by adjusting metabolic parameters so as to fit experimental toxicokinetic data. The estimates of the metabolic parameters are then conditional on the assumed values for all other parameters. Meanwhile, the reliability of other parameters, or the structural model, is usually not questioned. Inhalation exposures with human volunteers in our laboratory show that non-conjugators lack metabolic capacity for methyl chloride entirely, and that elimination in these subjects takes place via exhalation only. Therefore, data from these methyl chloride exposures provide an excellent opportunity to assess the general reliability of standard inhalation PBPK models for humans. A hierarchical population PBPK model for methyl chloride was developed. The model was fit to the experimental data in a Bayesian framework using Markov chain Monte Carlo (MCMC) simulation. In a Bayesian analysis, it is possible to merge a priori knowledge of the physiological, anatomical and physicochemical parameters with the information embedded in the experimental toxicokinetic data obtained in vivo. The resulting estimates are both statistically and physiologically plausible. Model deviations suggest that a pulmonary sub-compartment may be needed in order to describe the inhalation and exhalation of volatile adequately. The results also indicate that there may be significant intra-individual variability in the model parameters. To our knowledge, this is the first time that the toxicokinetics of a non-metabolized chemical is used to assess population PBPK parameters. This approach holds promise for more elaborate experiments in order to assess the reliability of PBPK models in general.

Applications of population approaches in toxicology

Many experimental or observational studies in toxicology are best analysed in a population framework. Recent examples include investigations of the extent and origin of intra-individual variability in toxicity studies, incorporation of genotypic information to address intra-individual variability, optimal design of experiments, and extension of toxicokinetic modelling to the analysis of biomarker studies. Bayesian statistics provide powerful numerical methods for fitting population models, particularly when complex mechanistic models are involved. Challenges and limitations to the use of population models, in terms of basic structure, computational burden, ease of implementation and data accessibility, are identified and discussed.

Statistical issues in toxicokinetic modeling: a bayesian perspective

Determining the relationship between an exposure and the resulting target tissue dose is a critical issue encountered in quantitative risk assessment (QRA). Classical or physiologically based toxicokinetic (PBTK) models can be useful in performing that task. Interest in using these models to improve extrapolations between species, routes, and exposure levels in QRA has therefore grown considerably in recent years. In parallel, PBTK models have become increasingly sophisticated. However, development of a strong statistical foundation to support PBTK model calibration and use has received little attention. There is a critical need for methods that address the uncertainties inherent in toxicokinetic data and the variability in the human populations for which risk predictions are made and to take advantage of a priori information on parameters during the calibration process. Natural solutions to these problems can be found in a Bayesian statistical framework with the help of computational techniques such as Markov chain Monte Carlo methods. Within such a framework, we have developed an approach to toxicokinetic modeling that can be applied to heterogeneous human or animal populations. This approach also expands the possibilities for uncertainty analysis. We present a review of these efforts and other developments in these areas. Appropriate statistical treatment of uncertainty and variability within the modeling process will increase confidence in model results and ultimately contribute to an improved scientific basis for the estimation of occupational and environmental health risks.

Statistical analysis of Fisher et al. PBPK model of trichloroethylene kinetics

Two physiologically based pharmacokinetic models for trichloroethylene (TCE) in mice and humans were calibrated with new toxicokinetic data sets. Calibration is an important step in model development, essential to a legitimate use of models for research or regulatory purposes. A Bayesian statistical framework was used to combine prior information about the model parameters with the data likelihood to yield posterior parameter distributions. For mice, these distributions represent uncertainty. For humans, the use of a population statistical model yielded estimates of both variability and uncertainty in human toxicokinetics of TCE. After adjustment of the models by Markov chain Monte Carlo sampling, the mouse model agreed with a large part of the data. Yet, some data on secondary metabolites were not fit well. The posterior parameter distributions obtained for mice were quite narrow (coefficient of variation [CV] of about 10 or 20%), but these CVs might be underestimated because of the incomplete fit of the model. The data fit, for humans, was better than for mice. Yet, some improvement of the model is needed to correctly describe trichloroethanol concentrations over long time periods. Posterior uncertainties about the population means corresponded to 10-20% CV. In terms of human population variability, volumes and flows varied across subject by approximately 20% CV. The variability was somewhat higher for partition coefficients (between 30 and 40%) and much higher for the metabolic parameters (standard deviations representing about a factor of 2). Finally, the analysis points to differences between human males and females in the toxicokinetics of TCE. The significance of these differences in terms of risk remains to be investigated.

Statistical analysis of Clewell et al. PBPK model of trichloroethylene kinetics

A physiologically based pharmacokinetic model for trichloroethylene (TCE) in rodents and humans was calibrated with published toxicokinetic data sets. A Bayesian statistical framework was used to combine previous information about the model parameters with the data likelihood, to yield posterior parameter distributions. The use of the hierarchical statistical model yielded estimates of both variability between experimental groups and uncertainty in TCE toxicokinetics. After adjustment of the model by Markov chain Monte Carlo sampling, estimates of variability for the animal or human metabolic parameters ranged from a factor of 1.5-2 (geometric standard deviation [GSD]). Uncertainty was of the same order as variability for animals and higher than variability for humans. The model was used to make posterior predictions for several measures of cancer risk. These predictions were affected by both uncertainties and variability and exhibited GSDs ranging from 2 to 6 in mice and rats and from 2 to 10 for humans.

Analysis of PBPK models for risk characterization

Adoption of a Bayesian framework for risk characterization permits the seamless integration of different kinds of information available in order to choose and parameterize risk models. It also becomes easy to disentangle uncertainty from variability, through hierarchical statistical modeling. Appropriate numerical techniques can be found, for example, in the recently developed arsenal of Markov chain, Monte Carlo simulations. The developments in this area can actually be viewed as extensions of the traditional or standard Monte Carlo methods for uncertainty analysis. Following a brief review of the techniques, examples of Bayesian analyses of physiologically-based pharmacokinetic models are presented for tetrachloroethylene and dichloromethane. The discussion touches on some open problems and perspectives for the proposed methods.

Optimal design for a study of butadiene toxicokinetics in humans

The derivation of the optimal design for an upcoming toxicokinetic study of butadiene in humans is presented. The specific goal of the planned study is to obtain a precise estimate of butadiene metabolic clearance for each study subject, together with a good characterization of its population variance. We used a two-compartment toxicokinetic model, imbedded in a hierarchical population model of variability, in conjunction with a preliminary set of butadiene kinetic data in humans, as a basis for design optimization. Optimization was performed using Monte Carlo simulations. Candidate designs differed in the number and timing of exhaled air samples to be collected. Simulations indicated that only 10 air samples should be necessary to obtain a coefficient of variation of 15% for the estimated clearance rate, if the timing of those samples is properly chosen. Optimal sampling times were found to closely bracket the end of exposure. This efficient design will allow the recruitment of more subjects in the study, in particular to match prescribed levels of accuracy in the estimate of the population variance of the butadiene metabolic rate constant. The techniques presented here have general applicability to the design of human and animal toxicology studies.

A group sequential approach to crossover trials for average bioequivalence

Group sequential methods to allow the possibility of early termination of a trial due to sufficiently convincing results are a standard in therapeutic clinical trials but have been little considered in bioequivalence trials. We investigate the statistical properties of one group sequential approach to bioequivalence trials. In particular, we are interested in maintenance of level (5%), quantification of any loss of power, and the probability of early stopping. These properties are assessed via data simulated according to a pharmacokinetic model. We find that there are cases where a group sequential approach has a substantial probability of early stopping, with essentially no loss of power.

Choice of student's t- or Wilcoxon-based confidence intervals for assessment of average bioequivalence

An open question in the analysis of average bioequivalence is whether the nonparametric (Wilcoxon) or parametric (t) approaches to two one-sided tests is preferable. Previous work has made particular distributional assumptions as to the distribution of AUC and C(max). Instead, we simulate data according to a pharmacokinetic model for an immediate-release formulation. We find that both approaches have estimated level consistent with the nominal 5%. The only concern is a possible anticonservativeness of the parametric approach for C(max). Further, the nonparametric approach is consistently less powerful than the parametric for the cases studied.