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.

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.

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.

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.

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.

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.

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.

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.

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.

Interspecies extrapolation of physiological pharmacokinetic parameter distributions.

Three methods (multiplicative, additive, and allometric) were developed to extrapolate physiological model parameter distributions across species, specifically from rats to humans. In the multiplicative approach, the rat model parameters are multiplied by the ratio of the mean values between humans and rats. Additive scaling of the distributions is defined by adding the difference between the average human value and the average rat value to each rat value. Finally, allometric scaling relies on established extrapolation relationships using power functions of body weight. A physiologically-based pharmacokinetic model was fitted independently to rat and human benzene disposition data. Human model parameters obtained by extrapolation and by fitting were used to predict the total bone marrow exposure to benzene and the quantity of metabolites produced in bone marrow. We found that extrapolations poorly predict the human data relative to the human model. In addition, the prediction performance depends largely on the quantity of interest. The extrapolated models underpredict bone marrow exposure to benzene relative to the human model. Yet, predictions of the quantity of metabolite produced in bone marrow are closer to the human model predictions. These results indicate that the multiplicative and allometric techniques were able to extrapolate the model parameter distributions, but also that rats do not provide a good kinetic model of benzene disposition in humans.

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.

Absorption rate vs. exposure: which is more useful for bioequivalence testing?

PURPOSE: The goals were to evaluate the usefulness of Cmax/AUClqc, ratio of the maximum plasma drug concentration to the area under the plasma concentration-time curve to the time of the last quantifiable concentration, in bioequivalence testing and to explore the use of exposure as a replacement for the concepts of rate and extent of drug absorption. METHODS: The bioequivalence of products differing in both rate (ka) and extent (F) of absorption was assessed under conditions similar to those encountered in a typical trial. A one-compartment model drug with first-order absorption (rate constant = ka) and eliminations was used. Variability was introduced in all model parameters using Monte Carlo techniques. The results were expressed in terms of the probability of declaring bioequivalence in a cross-over trial with 24 subjects using Cmax/AUClqc, AUClqc, and Cmax as bioequivalence measures. RESULTS: The outcome of a bioequivalence trial was shown to depend on the measure. Cmax/AUClqc reflected changes in ka, but not in F. AUClqc showed dependence on F, but virtually no dependence on ka. For Cmax, a 3- to 4-fold increase in ka and a concomittant 20% decrease in F, as well as corresponding changes in the opposite directions, resulted in bioequivalent outcomes. CONCLUSIONS: It was concluded that use of Cmax/AUClqc should be discouraged and that defining bioequivalence in terms of rate and extent of absorption has major problems. The goal of bioequivalence trials should be to assure that the shape of the concentration-time curve of the test product is sufficiently similar to that of the reference product. To this end, the use of "exposure" rather than "rate and extent of absorption" concepts is encouraged.

Population toxicokinetics of tetrachloroethylene.

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 tetrachloroethylene (PERC) in humans. We derive statistical distributions for the parameters of a physiological model of PERC, on the basis of data from Monster et al. (1979). The model adequately fits both prior physiological information and experimental data. An estimate of the relationship between PERC exposure and fraction metabolized is obtained. Our median population estimate for the fraction of inhaled tetrachloroethylene that is metabolized, at exposure levels exceeding current occupational standards, is 1.5% [95% confidence interval (0.52%, 4.1%)]. At levels approaching ambient inhalation exposure (0.001 ppm), the median estimate of the fraction metabolized is much higher, at 36% [95% confidence interval (15%, 58%)]. This disproportionality should be taken into account when deriving safe exposure limits for tetrachloroethylene and deserves to be verified by further experiments.