Optimal design for a study of butadiene toxicokinetics in humans

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.

Multistate models of developmental toxicity: Application to valproic acid-induced malformations in the zebrafish embryo

For the determination of acute toxicity of chemicals in zebrafish (Danio rerio) embryos, the OECD test guideline 236, relative to the Fish Embryo Toxicity Test (FET), stipulates a dose-response analysis of four lethal core endpoints and a quantitative characterization of abnormalities including their time-dependency. Routinely, the data are analyzed at the different observation times separately. However, observations at a given time strongly depend on the previous effects and should be analyzed jointly with them. To solve this problem, we developed multistate models for occurrence of developmental malformations and live events in zebrafish embryos exposed to eight concentrations of valproic acid (VPA) the first five days of life. Observations were recorded daily per embryo. We statistically infer on model structure and parameters using a numerical Bayesian framework. Hatching probability rate changed with time and we compared five forms of its time-dependence; a constant rate, a piecewise constant rate with a fixed hatching time at 48 h post fertilization, a piecewise constant rate with a variable hatching time, as well as a Hill and Gaussian form. A piecewise constant function of time adequately described the hatching data. The other transition rates were conditioned on the embryo body concentration of VPA, obtained using a physiologically-based pharmacokinetic model. VPA impacted mostly the malformation probability rate in hatched and non-hatched embryos. Malformation reversion probability rates were lowered by VPA. Direct mortality was low at the concentrations tested, but increased linearly with internal concentration. The model makes full use of data and gives a finer grain analysis of the teratogenic effects of VPA in zebrafish than the OECD-prescribed approach. We discuss the use of the model for obtaining toxicological reference values suitable for inter-species extrapolation. A general result is that complex multistate models can be efficiently evaluated numerically.

Modeling Pharmacokinetics

Pharmacokinetics is the study of 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 preliminary regional PBPK model of lung metabolism for improving species dependent descriptions of 1,3-butadiene and its metabolites

1,3-Butadiene (BD), a volatile organic chemical (VOC), is used in synthetic rubber production and other industrial processes. It is detectable at low levels in ambient air as well as in tobacco smoke and gasoline vapors. Inhalation exposures to high concentrations of BD have been associated with lung cancer in both humans and experimental animals, although differences in species sensitivity have been observed. Metabolically active lung cells such as Pulmonary Type I and Type II epithelial cells and club cells (Clara cells)(1) are potential targets of BD metabolite-induced toxicity. Metabolic capacities of these cells, their regional densities, and distributions vary throughout the respiratory tract as well as between species and cell types. Here we present a physiologically based pharmacokinetic (PBPK) model for BD that includes a regional model of lung metabolism, based on a previous model for styrene, to provide species-dependent descriptions of BD metabolism in the mouse, rat, and human. Since there are no in vivo data on BD pharmacokinetics in the human, the rat and mouse models were parameterized to the extent possible on the basis of in vitro metabolic data. Where it was necessary to use in vivo data, extrapolation from rat to mouse was performed to evaluate the level of uncertainty in the human model. A kidney compartment and description of downstream metabolism were also included in the model to allow for eventual use of available urinary and blood biomarker data in animals and humans to calibrate the model for estimation of BD exposures and internal metabolite levels. Results from simulated inhalation exposures to BD indicate that incorporation of differential lung region metabolism is important in describing species differences in pulmonary response and that these differences may have implications for risk assessments of human exposures to BD.

Bayesian inference

This chapter provides an overview of the Bayesian approach to data analysis, modeling, and statistical decision making. The topics covered go from basic concepts and definitions (random variables, Bayes' rule, prior distributions) to various models of general use in biology (hierarchical models, in particular) and ways to calibrate and use them (MCMC methods, model checking, inference, and decision). The second half of this Bayesian primer develops an example of model setup, calibration, and inference for a physiologically based analysis of 1,3-butadiene toxicokinetics in humans.

Alternative (non-animal) methods for cosmetics testing: current status and future prospects-2010

The 7th amendment to the EU Cosmetics Directive prohibits to put animal-tested cosmetics on the market in Europe after 2013. In that context, the European Commission invited stakeholder bodies (industry, non-governmental organisations, EU Member States, and the Commission's Scientific Committee on Consumer Safety) to identify scientific experts in five toxicological areas, i.e. toxicokinetics, repeated dose toxicity, carcinogenicity, skin sensitisation, and reproductive toxicity for which the Directive foresees that the 2013 deadline could be further extended in case alternative and validated methods would not be available in time. The selected experts were asked to analyse the status and prospects of alternative methods and to provide a scientifically sound estimate of the time necessary to achieve full replacement of animal testing. In summary, the experts confirmed that it will take at least another 7-9 years for the replacement of the current in vivo animal tests used for the safety assessment of cosmetic ingredients for skin sensitisation. However, the experts were also of the opinion that alternative methods may be able to give hazard information, i.e. to differentiate between sensitisers and non-sensitisers, ahead of 2017. This would, however, not provide the complete picture of what is a safe exposure because the relative potency of a sensitiser would not be known. For toxicokinetics, the timeframe was 5-7 years to develop the models still lacking to predict lung absorption and renal/biliary excretion, and even longer to integrate the methods to fully replace the animal toxicokinetic models. For the systemic toxicological endpoints of repeated dose toxicity, carcinogenicity and reproductive toxicity, the time horizon for full replacement could not be estimated.

A Bayesian population PBPK model for multiroute chloroform exposure

A Bayesian hierarchical model was developed to estimate the parameters in a physiologically based pharmacokinetic (PBPK) model for chloroform using prior information and biomarker data from different exposure pathways. In particular, the model provides a quantitative description of the changes in physiological parameters associated with hot-water bath and showering scenarios. Through Bayesian inference, uncertainties in the PBPK parameters were reduced from the prior distributions. Prediction of biomarker data with the calibrated PBPK model was improved by the calibration. The posterior results indicate that blood flow rates varied under two different exposure scenarios, with a two-fold increase of the skin's blood flow rate predicted in the hot-bath scenario. This result highlights the importance of considering scenario-specific parameters in PBPK modeling. To demonstrate the application of a probability approach in toxicological assessment, results from the posterior distributions from this calibrated model were used to predict target tissue dose based on the rate of chloroform metabolized in liver. This study demonstrates the use of the Bayesian approach to optimize PBPK model parameters for typical household exposure scenarios.

Modeling kinetics of a large-scale fed-batch CHO cell culture by Markov chain Monte Carlo method

Markov chain Monte Carlo (MCMC) method was applied to model kinetics of a fed-batch Chinese hamster ovary cell culture process in 5,000-L bioreactors. The kinetic model consists of six differential equations, which describe dynamics of viable cell density and concentrations of glucose, glutamine, ammonia, lactate, and the antibody fusion protein B1 (B1). The kinetic model has 18 parameters, six of which were calculated from the cell culture data, whereas the other 12 were estimated from a training data set that comprised of seven cell culture runs using a MCMC method. The model was confirmed in two validation data sets that represented a perturbation of the cell culture condition. The agreement between the predicted and measured values of both validation data sets may indicate high reliability of the model estimates. The kinetic model uniquely incorporated the ammonia removal and the exponential function of B1 protein concentration. The model indicated that ammonia and lactate play critical roles in cell growth and that low concentrations of glucose (0.17 mM) and glutamine (0.09 mM) in the cell culture medium may help reduce ammonia and lactate production. The model demonstrated that 83% of the glucose consumed was used for cell maintenance during the late phase of the cell cultures, whereas the maintenance coefficient for glutamine was negligible. Finally, the kinetic model suggests that it is critical for B1 production to sustain a high number of viable cells. The MCMC methodology may be a useful tool for modeling kinetics of a fed-batch mammalian cell culture process.

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).

On the volume of distribution at steady state and its relationship with two-compartmental models

The volume of distribution at steady state is considered to be one of the primary pharmacokinetic measurements obtained from in vivo experiments. This quantity is quite commonly calculated using moments of the observed concentration curve, the process being referred to as noncompartmental analysis. In this paper the underlying assumptions of noncompartmental analysis are analysed with regard to the observed behaviour of models with two compartments: one of which has elimination from the central compartment, the other from the peripheral tissue compartment. This is in order to clarify the relationship between volume of distribution and clearance. It is shown that these two models are indistinguishable from measurements in blood. Furthermore relationships between the parameter values for the two models are given so that they produce the same observed profile. Expressions are derived in a novel way that relates the volume of distribution to these model rate constants. The definitions of clearance and volume of distribution at steady state are investigated using several different mathematical techniques, demonstrating the consistency of the derived expressions. It is shown, in a manner that the authors believe is a new approach, that when the assumption of central elimination does not apply, noncompartmental analysis will under estimate the volume of distribution, whereas clearance remains unchanged. This is compared quantitatively with respect to the volume predicted where central elimination holds, and is a result of an extended mean residence time.

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.

Level A in vitro-in vivo Correlation (IVIVC) Model with Bayesian Approach to Formulation Series

In vitro-in vivo correlation (IVIVC) models for formulation series are useful in drug development, but the current models are limited by their inability to include data variability in the predictions. Our goal was to develop a level A IVIVC model that provides predictions with probabilities. The Bayesian approach was used to describe uncertainty related to the model and the data. Three bioavailability studies of levosimendan were used to develop IVIVC model. Dissolution was tested at pH 5.8 with basket. The IVIVC model with Bayesian approach consisted of prior and observed data. All observed data were fitted to the one-compartment model together with prior data. Probability distributions of pharmacokinetic parameters and concentration time profiles were obtained. To test the external predictability of IVIVC model, only dissolution data of formulations E and F were used. The external predictability was good. The possibility to utilize all observed data when constructing IVIVC model, can be considered as a major strength of Bayesian approach. For levosimendan capsule data traditional IVIVC model was not predictable. The usefulness of IVIVC model with Bayesian approach was shown with our data, but the same approach can be used more widely for formulation optimization and for dissolution based biowaivers.

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.

Impact of pharmacokinetic-pharmacodynamic model linearization on the accuracy of population information matrix and optimal design

Influence of experimental design on hyperparameter estimates precision when performing a population pharmacokinetic-pharmacodynamic (PK-PD) analysis has been shown by several studies and various approaches have been proposed for optimizing or evaluating such designs. Some of these methods rely on the optimization of a suitable scalar function of the population information matrix. Unfortunately for the nonlinear models encountered in pharmacokinetics or pharmacodynamics the latter is particularly difficult to evaluate. Under some assumptions and after a linearization of the PK-PD model a closed form of this matrix can be obtained which considerably simplifies its calculation but leads to an approximation. The aim of this paper is to evaluate the quality of the latter and its potential impact, when comparing or optimizing population designs and to relate it to Bates and Watts curvature measures. Two models commonly used in PK-PD were considered and nominal hyperparameter values when chosen for each one. Several population designs were studied and the associated population information matrix was computed for each using the approximate procedure and also using a reference method. Design optimizations were calculated under constraints for each model from the reference and approximate population information matrix. Nonlinearity curvatures were also computed for every model and design. The impact of model linearization when calculating the population information matrix was then examined in terms of lower bound accuracies on the hyperparameter estimates, design criterion variation, as well as D-optimal population designs, these results being related to nonlinearity curvature measures. Our results emphasize the influence of the parameter effects curvature when deriving the lower bounds of the hyperparameter estimates precision for a given design from the approximate population information matrix especially for hyperparameters quantifying the PK-PD interindividual variability. No discrepancies were detected between the population D-optimal designs obtained from the approximate and reference matrix despite some minor differences in criterion variation with respect to the design. More pronounced differences were, however, observed when comparing the amplitudes of criterion variation which can lead to errors when calculating design efficiencies. From a practical point of view, a strategy easily applicable by the pharmacokineticist for avoiding such problems in the context of population design optimization or comparison is then proposed.

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.

Development of a preliminary physiologically based toxicokinetic (PBTK) model for 1,3-butadiene risk assessment

Potential health effects of human exposure to 1,3-butadiene (BD) are of concern due to the use of BD in industry and its low-level presence throughout the environment. Physiologically based toxicokinetic (PBTK) models of BD in rodents have been developed by multiple research groups in an effort to explain species differences in toxicity (especially carcinogenic potency) through toxicokinetics. PBTK modeling of dose metrics related to a non-cancer endpoint, ovotoxicity in experimental animals, was conducted. The cumulative area under the blood concentration vs. time curve (AUC) for the metabolite diepoxybutane (butadiene diepoxide, DEB) was found to be consistent with ovotoxicity in mice and rats exposed to BD by inhalation or epoxybutene (butadiene monoepoxide, EB) or DEB by intraperitoneal injection. This suggests that cumulative DEB AUC may also be an appropriate metric for possible human risk. A preliminary human PBTK model was assembled for the eventual assessment of reproductive risk to humans and for prioritizing the determination of model parameters. The preliminary model accurately predicted published data on exhaled breath BD concentrations in a human volunteer exposed to BD by inhalation. The fit was relatively insensitive to the rate constant for BD epoxidation. Sensitivity analyses were conducted on this human PBTK model. Using a range of published rate constants, human blood DEB was found to be sensitive to rates of epoxidation of EB to DEB and hydrolysis of EB and DEB, but not BD epoxidation. Because of the large ranges of rates measured in vitro for these reactions, different combinations of in-vitro rates produce varying predictions of blood DEB concentration. Thus, validation of a human PBTK model with human biomonitoring data will be essential to produce a PBTK model that can be applied to risk assessment.

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.