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 Kd 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 Kd,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.

Kinetics and dynamics of cyclosporine A in three hepatic cell culture systems.

In vitro experiments have a high potential to improve current chemical safety assessment and reduce the number of animals used. However, most studies conduct hazard assessment alone, largely ignoring exposure and kinetic parameters. Therefore, in this study the kinetics of cyclosporine A (CsA) and the dynamics of CsA-induced cyclophilin B (Cyp-B) secretion were investigated in three widely used hepatic in vitro models: primary rat hepatocytes (PRH), primary human hepatocytes (PHH) and HepaRG cells. Cells were exposed daily to CsA for up to 14 days. CsA in cells and culture media was quantified by LC-MS/MS and used for pharmacokinetic modeling. Cyp-B was quantified by western blot analysis in cells and media. All cell systems took up CsA rapidly from the medium after initial exposure and all showed a time- and concentration-dependent Cyp-B cellular depletion and extracellular secretion. Only in PRH an accumulation of CsA over 14 days repeated exposure was observed. Donor-specific effects in CsA clearance were observed in the PHH model and both PHH and HepaRG cells significantly metabolized CsA, with no bioaccumulation being observed after repeated exposure. The developed kinetic models are described in detail and show that all models under-predict the in vivo hepatic clearance of CsA, but to different extents with 27-, 24- and 2-fold for PRH, PHH and HepaRG cells, respectively. This study highlights the need for more attention to kinetics in in vitro studies.

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.

Parameter variability and the interpretation of physiologically based pharmacokinetic modeling results.

For the past several years we have been working with models of benzene distribution and metabolism, principally in the rat, but more recently in humans. Our biologically related objectives have been primarily to assist our laboratory-based colleagues in their quest for understanding of the mechanisms by which benzene exerts its toxic action. A secondary goal has been to develop or adapt models useful in risk assessment applications. We have also had methodological goals that relate to applications of sensitivity analysis on the one hand, but more fundamentally to the connection between experimental data and model structure and parameterization. This paper presents an overview of our work in these areas.

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.

Possible risk of endometriosis for Seveso, Italy, residents: an assessment of exposure to dioxin.

A recent study by Rier et al. showed that rhesus monkeys exposed daily for 4 years to 5 or 25 ppt of dioxin in food develop endometriosis, with incidence and severity related to dose. We aimed to determine whether the total time-integrated dioxin exposure of a human population could be comparable to that of Rier's monkeys. We selected a sample of residents of Seveso, Italy, who were acutely exposed to high levels of dioxin following an accident in 1976. We conducted a toxicokinetic analysis which takes into account species and exposure differences in dose and timing between humans and monkeys. The area under the time-concentration curve for dioxin in fat, which corresponds to cumulative exposure over time, ranges for some of the most heavily exposed Seveso residents from approximately 1.7 x 10(6) ppt-days to 1.1 x 10(8) ppt-days. These values exceed in all cases the values for the monkeys exposed to 25 ppt or 5 ppt. Given their exposure, the Seveso population should be an ideal epidemiologic cohort to rule out or confirm whether exposure to dioxin leads to an increased risk of endometriosis in humans.

Evaluating health risks from occupational exposure to pesticides and the regulatory response.

In this study, we used measurements of occupational exposures to pesticides in agriculture to evaluate health risks and analyzed how the federal regulatory program is addressing these risks. Dose estimates developed by the State of California from measured occupational exposures to 41 pesticides were compared to standard indices of acute toxicity (LD50) and chronic effects (reference dose). Lifetime cancer risks were estimated using cancer potencies. Estimated absorbed daily doses for mixers, loaders, and applicators of pesticides ranged from less than 0.0001% to 48% of the estimated human LD50 values, and doses for 10 of 40 pesticides exceeded 1% of the estimated human LD50 values. Estimated lifetime absorbed daily doses ranged from 0.1% to 114,000% of the reference doses developed by the U.S. Environmental Protection Agency, and doses for 13 of 25 pesticides were above them. Lifetime cancer risks ranged from 1 per million to 1700 per million, and estimates for 12 of 13 pesticides were above 1 per million. Similar results were obtained for field workers and flaggers. For the pesticides examined, exposures pose greater risks of chronic effects than acute effects. Exposure reduction measures, including use of closed mixing systems and personal protective equipment, significantly reduced exposures. Proposed regulations rely primarily on requirements for personal protective equipment and use restrictions to protect workers. Chronic health risks are not considered in setting these requirements. Reviews of pesticides by the federal pesticide regulatory program have had little effect on occupational risks. Policy strategies that offer immediate protection for workers and that are not dependent on extensive review of individual pesticides should be pursued.

Population toxicokinetics of benzene.

In assessing the distribution and metabolism of toxic compounds in the body, measurements are not always feasible for ethical or technical reasons. Computer modeling offers a reasonable alternative, but the variability and complexity of biological systems pose unique challenges in model building and adjustment. Recent tools from population pharmacokinetics, Bayesian statistical inference, and physiological modeling can be brought together to solve these problems. As an example, we modeled the distribution and metabolism of benzene in humans. We derive statistical distributions for the parameters of a physiological model of benzene, on the basis of existing data. The model adequately fits both prior physiological information and experimental data. An estimate of the relationship between benzene exposure (up to 10 ppm) and fraction metabolized in the bone marrow is obtained and is shown to be linear for the subjects studied. Our median population estimate for the fraction of benzene metabolized, independent of exposure levels, is 52% (90% confidence interval, 47-67%). At levels approaching occupational inhalation exposure (continuous 1 ppm exposure), the estimated quantity metabolized in the bone marrow ranges from 2 to 40 mg/day.

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.

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.

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.

Optimization issues in physiological toxicokinetic modeling: a case study with benzene.

This paper compares two methods for global optimization of physiologically based toxicokinetic models: Monte Carlo optimization, which searches randomly for the optimum; and the simplex method, which updates systematically an array of parameter values. Two measures of goodness-of-fit are also contrasted: criterion function and likelihood. A 14-parameter model of benzene distribution in rats is used to illustrate these techniques. Simplex optimization yields better fits overall. However, the measurement of uncertainty offered by Monte Carlo simulations is a major argument in favor of their use.

Mechanisms of benzene carcinogenesis: application of a physiological model of benzene pharmacokinetics and metabolism.

A physiological pharmacokinetic model for benzene, incorporating metabolic transformations, is used to explore why benzene, but not phenol--its primary metabolite--is carcinogenic at many sites in rats. The model has been parametrized using in vitro or in vivo experimental data. Ranges, rather than fixed values, were assigned to the parameters. The model-predicted levels of phenol and hydroquinone in the tissues are consistently higher when phenol, rather than benzene, is administered. This result demonstrates that the differential carcinogenicity of the two compounds is not explainable in the context of this pharmacokinetic analysis. It also indicates that the phenol-hydroquinone pathway alone is unlikely to account for the carcinogenic effects of benzene. Other metabolites must therefore also be involved.

Pharmacokinetic concepts in assessing intake of pentachlorophenol by rats after exposure through drinking water.

The objective of this study was to predict concentrations of a toxicant in plasma after exposure to the toxicant through drinking water using basic pharmacokinetic principles. As an example, we studied pentachlorophenol (PCP), a widely used wood preservative of public health concern as an environmental pollutant. We added PCP to the drinking water (30 micrograms/mL) of five rats for 3 days. Blood was sampled, and water consumption was monitored every 12 h on the days 1 and 2 and every 3 h on day 3. After a 4-day washout, a PCP dose of 2.5 mg/kg was given intravenously, and blood was withdrawn at selected times for 2 days. PCP concentrations in plasma were measured by capillary gas chromatography. A one-compartment model with zero-order input and kinetic parameters (clearance, volume of distribution, and bioavailability) estimated after intravenous administration adequately predicted PCP concentrations in plasma during exposure to PCP. The average steady-state concentration (Css), which reflects the overall exposure, was predicted using the clearance (CL) concept [i.e., Css = (bioavailability.rate of intake)/CL] and compared with the observed value. The data for PCP demonstrate the potential utility of CL and other kinetic concepts in assessing exposure to a toxicant in drinking water, food, or air.

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.

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 l 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 micrograms (Nigeria) to 37 micrograms (The Netherlands). Net intake was between 51 micrograms d-1 and 157 micrograms d-1 in residents of homes made of PeCP-treated logs. In individuals occupationally exposed to PeCP, net daily intake varied widely (from 35 micrograms to about 24,000 micrograms) depending on the type of work.

Pentachlorophenol carcinogenicity: extrapolation of risk from mice to humans.

1. Pentachlorophenol (PCP) has been found to be carcinogenic in mice. The objective of this study was to extrapolate to humans the risk of cancer from data obtained in mice using information on disposition, serum protein binding and metabolism of PCP across species. 2. A review of the literature indicates that neither PCP nor a mutagenic metabolite, tetrachlorohydroquinone (TCHQ), has been specifically identified as responsible for the carcinogenicity. In addition, the occurrence of TCHQ as a metabolite of PCP in humans is still questionable. Therefore, cancer risk assessment is performed on the assumption that PCP itself is responsible for the carcinogenicity. 3. For interspecies extrapolation, a new method in which interspecies differences in clearance and serum protein binding are taken into account is used. The method gives estimates of equivalent human doses of PCP which are up to 4 times smaller than those obtained using body surface area. For both interspecies extrapolation methods, the estimated virtually-safe doses of PCP are smaller than the average daily intakes reported in groups of subjects nonspecifically exposed to PCP. Corresponding extra risks of cancer for lifetime exposure are from 20 to 140 times greater than the acceptable extra risk (10(-6)). The results obtained with this approach indicate that PCP is a possible public health hazard.

An analysis of exposure rate effects for benzene using a physiologically based pharmacokinetic model.

A new physiological pharmacokinetic model was used to explore the effect of exposure rate on the rate of formation of several crucial metabolites of benzene. Metabolite formation was compared following exposure to benzene over the course of an 8-hr workday and following a single exposure for 15 min. These exposures were based on the permissible exposure limit and short-term exposure limit of the benzene standard set by the Occupational Safety and Health Administration. The model was parametrized using in vitro and in vivo experimental data on benzene toxicokinetics and metabolism. Ranges, rather than fixed values, were assigned to the parameters. Model predictions show that the amounts of hydroquinone, catechol, and muconaldehyde formed in the body following a peak exposure to 32 ppm of benzene over 15 min are on average 20% higher than those formed following an equivalent dose of 1 ppm over an 8-hr period. The health consequences of these findings and the implications for policy concerning short-term exposure limits are discussed.