A Model Template Approach for Rapid Evaluation and Application of Physiologically Based Pharmacokinetic Models: Extension to Volatile Organic Compounds

Chemical risk assessors use physiologically based pharmacokinetic (PBPK) models to perform dosimetric calculations, including extrapolations between exposure scenarios, species, and populations of interest. Assessors should complete a thorough quality assurance (QA) review to ensure biological accuracy and correct implementation prior to using these models. This process can be time-consuming, and we developed a PBPK model template that allows for faster, more efficient QA review. The model template consists of a single model "superstructure" with equations and logic commonly found in PBPK models, allowing users to implement a wide variety of chemical-specific PBPK models. QA review can be completed more quickly than for conventional PBPK model implementations because the general model equations have already been reviewed and only parameters describing chemical-specific model and exposure scenarios need review for any given model implementation. We have expanded a previous version of the PBPK model template by adding features commonly included in PBPK models for volatile organic compounds (VOCs). We included multiple options for representing concentrations in blood, describing metabolism, and modeling gas exchange processes to allow for inhalation exposures. We created PBPK model template implementations of published models for seven VOCs: dichloromethane, methanol, chloroform, styrene, vinyl chloride, trichloroethylene, and carbon tetrachloride. Simulations performed using our template implementations matched published simulation results to a high degree of accuracy (maximum observed percent error: 1%). Thus, the model template approach can now be applied to a broader class of chemical-specific PBPK models while continuing to bolster efficiency of QA processes that should be conducted prior to using models for risk assessment applications.

A Generic Pharmacokinetic Model for Quantifying Mother-to-Offspring Transfer of Lipophilic Persistent Environmental Chemicals

Lipophilic persistent environmental chemicals (LPECs) can accumulate in a woman's body and transfer to her developing child across the placenta and via breast milk. To assess health risks associated with developmental exposures to LPECs, we developed a pharmacokinetic (PK) model that quantifies mother-to-offspring transfer of LPECs during pregnancy and lactation and facilitates internal dosimetry calculations for offspring. We parameterized the model for mice, rats, and humans using time-varying functions for body mass and milk consumption rates. The only required substance-specific parameter is the elimination half-life of the LPEC in the animal species of interest. We used the model to estimate whole-body concentrations in mothers and offspring following maternal exposures to hexachlorobenzene (HCB) and 2,2',4,4',5,5'-hexachlorobiphenyl (PCB 153) and compared these with measured concentrations from animal studies. We also compared estimated concentrations for humans to those generated using a previously published human LPEC PK model. Finally, we compared human equivalent doses (HEDs) calculated using our model and an allometric scaling method. Estimated and observed whole-body concentrations of HCB and PCB 153 in offspring followed similar trends and differed by less than 60%. Simulations of human exposure yielded concentration estimates comparable to those generated using the previously published model, with concentrations in offspring differing by less than 12%. HEDs calculated using our PK model were about 2 orders of magnitude lower than those generated using allometric scaling. Our PK model can be used to calculate internal dose metrics for offspring and corresponding HEDs and thus informs assessment of developmental toxicity risks associated with LPECs.

A Model Template Approach for Rapid Evaluation and Application of Physiologically Based Pharmacokinetic Models for Use in Human Health Risk Assessments: A Case Study on Per- and Polyfluoroalkyl Substances

Physiologically based pharmacokinetic (PBPK) models are commonly used in risk assessments to perform inter- and intraspecies extrapolations as well as to extrapolate between different dosing scenarios; however, they must first undergo quality assurance review, which can be a time-consuming process, especially when model code is not readily available. We developed and implemented (using R and MCSim) a PBPK model template capable of replicating published model results for several chemical-specific PBPK models. This model template allows for faster quality assurance review because the general model equations only need to be reviewed once, and application to a specific chemical then only requires reviewing input parameters. The model template can implement PBPK models with oral and intravenous exposure routes, varying numbers of tissue compartments, renal reabsorption, and multiple elimination pathways, including fecal, urinary, and biliary. Using the model template, we reproduced published model simulation results for perfluorohexanesulfonic acid, perfluorononanoic acid, perfluorodecanoic acid, perfluorooctanoate, and perflouorooctane sulfonate. We also show that the template can be a useful tool for identifying potential model errors. Thus, the model template allows for faster evaluation and review of published PBPK models and provides a proof of concept for using this approach with broader classes of chemical-specific PBPK models.

A Physiologically Based Pharmacokinetic Model for Naphthalene With Inhalation and Skin Routes of Exposure

Naphthalene, a volatile organic compound present in moth repellants and petroleum-based fuels, has been shown to induce toxicity in mice and rats during chronic inhalation exposures. Although simpler default methods exist for extrapolating toxicity points of departure from animals to humans, using a physiologically based pharmacokinetic (PBPK) model to perform such extrapolations is generally preferred. Confidence in PBPK models increases when they have been validated using both animal and human in vivo pharmacokinetic (PK) data. A published inhalation PBPK model for naphthalene was previously shown to predict rodent PK data well, so we sought to evaluate this model using human PK data. The most reliable human data available come from a controlled skin exposure study, but the inhalation PBPK model does not include a skin exposure route; therefore, we extended the model by incorporating compartments representing the stratum corneum and the viable epidermis and parameters that determine absorption and rate of transport through the skin. The human data revealed measurable blood concentrations of naphthalene present in the subjects prior to skin exposure, so we also introduced a continuous dose-rate parameter to account for these baseline blood concentration levels. We calibrated the three new parameters in the modified PBPK model using data from the controlled skin exposure study but did not modify values for any other parameters. Model predictions then fell within a factor of 2 of most (96%) of the human PK observations, demonstrating that this model can accurately predict internal doses of naphthalene and is thus a viable tool for use in human health risk assessment.

GRADE Guidelines 30: the GRADE approach to assessing the certainty of modeled evidence-An overview in the context of health decision-making

OBJECTIVES

The objective of the study is to present the Grading of Recommendations Assessment, Development, and Evaluation (GRADE) conceptual approach to the assessment of certainty of evidence from modeling studies (i.e., certainty associated with model outputs).

STUDY DESIGN AND SETTING

Expert consultations and an international multidisciplinary workshop informed development of a conceptual approach to assessing the certainty of evidence from models within the context of systematic reviews, health technology assessments, and health care decisions. The discussions also clarified selected concepts and terminology used in the GRADE approach and by the modeling community. Feedback from experts in a broad range of modeling and health care disciplines addressed the content validity of the approach.

RESULTS

Workshop participants agreed that the domains determining the certainty of evidence previously identified in the GRADE approach (risk of bias, indirectness, inconsistency, imprecision, reporting bias, magnitude of an effect, dose-response relation, and the direction of residual confounding) also apply when assessing the certainty of evidence from models. The assessment depends on the nature of model inputs and the model itself and on whether one is evaluating evidence from a single model or multiple models. We propose a framework for selecting the best available evidence from models: 1) developing de novo, a model specific to the situation of interest, 2) identifying an existing model, the outputs of which provide the highest certainty evidence for the situation of interest, either "off-the-shelf" or after adaptation, and 3) using outputs from multiple models. We also present a summary of preferred terminology to facilitate communication among modeling and health care disciplines.

CONCLUSION

This conceptual GRADE approach provides a framework for using evidence from models in health decision-making and the assessment of certainty of evidence from a model or models. The GRADE Working Group and the modeling community are currently developing the detailed methods and related guidance for assessing specific domains determining the certainty of evidence from models across health care-related disciplines (e.g., therapeutic decision-making, toxicology, environmental health, and health economics).

Issues in assessing the health risks of n-butanol

A literature review and health effects evaluation were conducted for n-butanol, a chemical that occurs naturally in some foods, which is an intermediate in the production of butyl esters and can be used as a gasoline additive or blend. Studies evaluating n-butyl acetate were included in the review as n-butyl acetate is rapidly converted to n-butanol following multiple routes of exposure. The primary n-butanol health effects identified were developmental and nervous system endpoints. In conducting the literature review and evaluating study findings, the following observations were made: (1) developmental findings were consistently identified; (2) neurodevelopmental findings were inconsistent; (3) evidence for nervous system effects was weak; (4) comparing internal doses from oral and inhalation exposures using physiologically based pharmacokinetic models introduces uncertainties; and (5) a lack of mechanistic information for n-butanol resulted in the reliance on mechanistic data for ethanol, which may or may not be applicable to n-butanol. This paper presents findings from a literature review on the health effects of n-butanol and proposes research to help reduce uncertainty that exists due to database limitations.

Revision of the affinity constant for perchlorate binding to the sodium-iodide symporter based on in vitro and human in vivo data

A series of previously published physiologically based pharmacokinetic (PBPK) models describe the effect of perchlorate on iodide uptake by the thyroid, with the mechanism being competitive inhibition of iodide transport by the sodium-iodide symporter (NIS). Hence a key parameter of these models is the affinity of perchlorate for the NIS, characterized as the Michaelis-Menten kinetic constant, K_m . However, when model predictions were compared to published results of a human study measuring radio-iodide uptake (RAIU) inhibition after controlled perchlorate exposures, it was found to only fit the lowest exposure level and underpredicted RAIU inhibition at higher levels. Published in vitro data, in which perchlorate-induced inhibition of iodide uptake via the NIS was measured, were re-analyzed. K_m for binding of perchlorate to the NIS originally derived from these data, 1.5 μm, had been obtained using Lineweaver-Burk plots, which allow for linear regression but invert the signal-noise of the data. Re-fitting these data by non-linear regression of the non-inverted data yielded a 60% lower value for the K_m , 0.59 μm. Substituting this value into the PBPK model for an average adult human significantly improved model agreement with the human RAIU data for exposures <100 μg kg^-1  day^-1 . Thus, this lower K_m value both fits the in vitro NIS kinetics and provides better predictions of human in vivo RAIU data. This change in K_m increases the predicted sensitivity of humans to perchlorate over twofold for low-level exposures. Published 2016. This article is a U.S. Government work and is in the public domain in the USA. Published 2016. This article is a U.S. Government work and is in the public domain in the USA.

Human health effects of dichloromethane: key findings and scientific issues

BACKGROUND

The U.S. EPA's Integrated Risk Information System (IRIS) completed an updated toxicological review of dichloromethane in November 2011.

OBJECTIVES

In this commentary we summarize key results and issues of this review, including exposure sources, identification of potential health effects, and updated physiologically based pharmacokinetic (PBPK) modeling.

METHODS

We performed a comprehensive review of primary research studies and evaluation of PBPK models.

DISCUSSION

Hepatotoxicity was observed in oral and inhalation exposure studies in several studies in animals; neurological effects were also identified as a potential area of concern. Dichloromethane was classified as likely to be carcinogenic in humans based primarily on evidence of carcinogenicity at two sites (liver and lung) in male and female B6C3F1 mice (inhalation exposure) and at one site (liver) in male B6C3F1 mice (drinking-water exposure). Recent epidemiologic studies of dichloromethane (seven studies of hematopoietic cancers published since 2000) provide additional data raising concerns about associations with non-Hodgkin lymphoma and multiple myeloma. Although there are gaps in the database for dichloromethane genotoxicity (i.e., DNA adduct formation and gene mutations in target tissues in vivo), the positive DNA damage assays correlated with tissue and/or species availability of functional glutathione S-transferase (GST) metabolic activity, the key activation pathway for dichloromethane-induced cancer. Innovations in the IRIS assessment include estimation of cancer risk specifically for a presumed sensitive genotype (GST-theta-1+/+), and PBPK modeling accounting for human physiological distributions based on the expected distribution for all individuals 6 months to 80 years of age.

CONCLUSION

The 2011 IRIS assessment of dichloromethane provides insights into the toxicity of a commonly used solvent.

Active and peripheral anionic sites of acetylcholinesterase have differential modulation effects on cell proliferation, adhesion and neuritogenesis in the NG108-15 cell line

The classical enzymatic role of acetylcholinesterase (AChE) is to terminate impulse transmission at cholinergic synapses through rapid hydrolysis of acetylcholine (ACh). Inactivation of this enzyme's catalytic site is the primary mechanism of acute toxicity of OP insecticides (e.g. parathion, chlorpyrifos). There is now sufficient evidence to suggest that AChE has a neurotrophic function that may be altered by organophosphate (OP) exposure, resulting in defects of neuronal growth and development, though the clarification of the mechanisms involved require further in vitro investigation. In the present study, the mouse neuroblastoma×rat glioma hybrid NG108-15 cell line was used to investigate the differential effects between inhibition of the catalytic site and peripheral anionic site (PAS) of acetylcholinesterase (AChE) on cell adhesion, proliferation and neuritogenesis, in the presence and absence of human red blood cell (hRBC) AChE (ED3.1.1.7). AChE active-site inhibitor paraoxon (PO; 0.1-1.0μM), when added to NG108-15 cells grown on AChE-coated plates, had no effect on cell proliferation, but exerted a significant reduction in strongly adherent viable cells accompanied by mostly short process formations, with 18% of cells considered to be neuritogenic, similar to that observed on uncoated plates. In contrast, PO had no significant effect on cell adhesion and proliferation of NG108-15 cells on uncoated plates. The PAS-ligand thioflavin-T (Th-T; 0.5-25μM), however, decreased cell adhesion and proliferation, on both uncoated and ACh-E coated plates, with less magnitude on AChE-coated plates. Taken together, these results suggest that strong cell adherence and neuritogenesis are sensitive to PO in this cell culture model, with no impact on proliferation, in the presence of membrane bound AChE-coating, while there is no sensitivity to PO on uncoated plates. On the other hand, binding of Th-T directly to the PAS affects both cell adherence and proliferation, with less magnitude in the presence of membrane-bound AChE. The current study indicates that PO is deleterious in neural development during critical periods of strong cell adhesion and differentiation, interfering with AChE trophic function.

The use of PBPK models to inform human health risk assessment: case study on perchlorate and radioiodide human lifestage models

Physiologically-based pharmacokinetic (PBPK) models are often submitted to or selected by agencies, such as the U.S. Environmental Protection Agency (U.S. EPA) and Agency for Toxic Substances and Disease Registry, for consideration for application in human health risk assessment (HHRA). Recently, U.S. EPA evaluated the human PBPK models for perchlorate and radioiodide for their ability to estimate the relative sensitivity of perchlorate inhibition on thyroidal radioiodide uptake for various population groups and lifestages. The most well-defined mode of action of the environmental contaminant, perchlorate, is competitive inhibition of thyroidal iodide uptake by the sodium-iodide symporter (NIS). In this analysis, a six-step framework for PBPK model evaluation was followed, and with a few modifications, the models were determined to be suitable for use in HHRA to evaluate relative sensitivity among human lifestages. Relative sensitivity to perchlorate was determined by comparing the PBPK model predicted percent inhibition of thyroidal radioactive iodide uptake (RAIU) by perchlorate for different lifestages. A limited sensitivity analysis indicated that model parameters describing urinary excretion of perchlorate and iodide were particularly important in prediction of RAIU inhibition; therefore, a range of biologically plausible values available in the peer-reviewed literature was evaluated. Using the updated PBPK models, the greatest sensitivity to RAIU inhibition was predicted to be the near-term fetus (gestation week 40) compared to the average adult and other lifestages; however, when exposure factors were taken into account, newborns were found to be populations that need further evaluation and consideration in a risk assessment for perchlorate.

Application of an updated physiologically based pharmacokinetic model for chloroform to evaluate CYP2E1-mediated renal toxicity in rats and mice

Physiologically based pharmacokinetic (PBPK) models are tools for interpreting toxicological data and extrapolating observations across species and route of exposure. Chloroform (CHCl(3)) is a chemical for which there are PBPK models available in different species and multiple sites of toxicity. Because chloroform induces toxic effects in the liver and kidneys via production of reactive metabolites, proper characterization of metabolism in these tissues is essential for risk assessment. Although hepatic metabolism of chloroform is adequately described by these models, there is higher uncertainty for renal metabolism due to a lack of species-specific data and direct measurements of renal metabolism. Furthermore, models typically fail to account for regional differences in metabolic capacity within the kidney. Mischaracterization of renal metabolism may have a negligible effect on systemic chloroform levels, but it is anticipated to have a significant impact on the estimated site-specific production of reactive metabolites. In this article, rate parameters for chloroform metabolism in the kidney are revised for rats, mice, and humans. New in vitro data were collected in mice and humans for this purpose and are presented here. The revised PBPK model is used to interpret data of chloroform-induced kidney toxicity in rats and mice exposed via inhalation and drinking water. Benchmark dose (BMD) modeling is used to characterize the dose-response relationship of kidney toxicity markers as a function of PBPK-derived internal kidney dose. Applying the PBPK model, it was also possible to characterize the dose response for a recent data set of rats exposed via multiple routes simultaneously. Consistent BMD modeling results were observed regardless of species or route of exposure.

Physiologically based pharmacokinetic model use in risk assessment--Why being published is not enough

A panel of experts in physiologically based pharmacokinetic (PBPK) modeling and relevant quantitative methods was convened to describe and discuss model evaluation criteria, issues, and choices that arise in model application and computational tools for improving model quality for use in human health risk assessments (HHRAs). Although publication of a PBPK model in a peer-reviewed journal is a mark of good science, subsequent evaluation of published models and the supporting computer code is necessary for their consideration for use in HHRAs. Standardized model evaluation criteria and a thorough and efficient review process can reduce the number of review and revision iterations and hence the time needed to prepare a model for application. Efficient and consistent review also allows for rapid identification of needed model modifications to address HHRA-specific issues. This manuscript reports on the workshop where a process and criteria that were created for PBPK model review were discussed along with other issues related to model review and application in HHRA. Other issues include (1) model code availability, portability, and validity; (2) probabilistic (e.g., population-based) PBPK models and critical choices in parameter values to fully characterize population variability; and (3) approaches to integrating PBPK model outputs with other HHRA tools, including benchmark dose modeling. Two specific case study examples are provided to illustrate challenges that were encountered during the review and application process. By considering the frequent challenges encountered in the review and application of PBPK models during the model development phase, scientists may be better able to prepare their models for use in HHRAs.

Uncertainties in biologically-based modeling of formaldehyde-induced respiratory cancer risk: identification of key issues

In a series of articles and a health-risk assessment report, scientists at the CIIT Hamner Institutes developed a model (CIIT model) for estimating respiratory cancer risk due to inhaled formaldehyde within a conceptual framework incorporating extensive mechanistic information and advanced computational methods at the toxicokinetic and toxicodynamic levels. Several regulatory bodies have utilized predictions from this model; on the other hand, upon detailed evaluation the California EPA has decided against doing so. In this article, we study the CIIT model to identify key biological and statistical uncertainties that need careful evaluation if such two-stage clonal expansion models are to be used for extrapolation of cancer risk from animal bioassays to human exposure. Broadly, these issues pertain to the use and interpretation of experimental labeling index and tumor data, the evaluation and biological interpretation of estimated parameters, and uncertainties in model specification, in particular that of initiated cells. We also identify key uncertainties in the scale-up of the CIIT model to humans, focusing on assumptions underlying model parameters for cell replication rates and formaldehyde-induced mutation. We discuss uncertainties in identifying parameter values in the model used to estimate and extrapolate DNA protein cross-link levels. The authors of the CIIT modeling endeavor characterized their human risk estimates as "conservative in the face of modeling uncertainties." The uncertainties discussed in this article indicate that such a claim is premature.

Sensory irritation response in rats: modeling, analysis and validation

Inhaled gases can cause respiratory depression by irritating (stimulating) nerves in the nasal cavity. Respiratory depression, in turn, decreases the rate of delivery of those gases to the stimulated nerves, potentially leading to a complex feedback response. In order to better understand how the nervous system responds to such chemicals, a mathematical model is created to describe how the presence of irritants affects respiration in the rat. The ordinary differential equation model describes the dosimetry of these reactive gases in the respiratory tract, with particular focus on the physiology of the upper respiratory tract, and on the neurological control of respiration rate due to signaling from the irritant-responsive nerves in the nasal cavity. The ventilation equation is altered to account for an apparent change in dynamics between the initial ventilation decrease and the recovery to steady state as seen in formaldehyde exposure data. Further, the model is evaluated and improved through optimization of particular parameters to describe formaldehyde-induced respiratory response data and through sensitivity analysis. The model predicts the formaldehyde data well, and hence the model is thought to be a reasonable description of the physiological system of sensory irritation. The model is also expected to translate well to other irritants.

Uncertainties in the CIIT model for formaldehyde-induced carcinogenicity in the rat: a limited sensitivity analysis-I

Scientists at the CIIT Centers for Health Research (Conolly et al., 2000, 2003; Kimbell et al., 2001a, 2001b) developed a two-stage clonal expansion model of formaldehyde-induced nasal cancers in the F344 rat that made extensive use of mechanistic information. An inference of their modeling approach was that formaldehyde-induced tumorigenicity could be optimally explained without the role of formaldehyde's mutagenic action. In this article, we examine the strength of this result and modify select features to examine the sensitivity of the predicted dose response to select assumptions. We implement solutions to the two-stage cancer model that are valid for nonhomogeneous models (i.e., models with time-dependent parameters), thus accounting for time dependence in variables. In this reimplementation, we examine the sensitivity of model predictions to pooling historical and concurrent control data, and to lumping sacrificed animals in which tumors were discovered incidentally with those in which death was caused by the tumors. We found the CIIT model results were not significantly altered with the nonhomogeneous solutions. Dose-response predictions below the range of exposures where tumors occurred in the bioassays were highly sensitive to the choice of control data. In the range of exposures where tumors were observed, the model attributed up to 74% of the added tumor probability to formaldehyde's mutagenic action when our reanalysis restricted the use of the National Toxicology Program (NTP) historical control data to only those obtained from inhalation exposures. Model results were insensitive to hourly or daily temporal variations in DNA protein cross-link (DPX) concentration, a surrogate for the dose-metric linked to formaldehyde-induced mutations, prompting us to utilize weekly averages for this quantity. Various other biological and mathematical uncertainties in the model have been retained unmodified in this analysis. These include model specification of initiated cell division and death rates, and uncertainty and variability in the dose response for cell replication rates, issues that will be considered in a future paper.

A delayed nonlinear PBPK model for genistein dosimetry in rats

Genistein is an endocrine-active compound (EAC) found in soy products. It has been linked to beneficial effects such as mammary tumor growth suppression and adverse endocrine-related effects such as reduced birth weight in rats and humans. In its conjugated form, genistein is excreted in the bile, which is a significant factor in its pharmacokinetics. Experimental data suggest that genistein induces a concentration-dependent suppression of biliary excretion. In this article, we describe a physiologically based pharmacokinetic (PBPK) model that focuses on biliary excretion with the goal of accurately simulating the observed suppression. The mathematical model is a system of nonlinear differential equations with state-dependent delay to describe biliary excretion. The model was analyzed to examine local existence and uniqueness of a solution to the equations. Furthermore, unknown parameters were estimated, and the mathematical model was compared against published experimental data.

Physiologically-based pharmacokinetic modeling of benzene in humans: a Bayesian approach

Benzene is myelotoxic and leukemogenic in humans exposed at high doses (>1 ppm, more definitely above 10 ppm) for extended periods. However, leukemia risks at lower exposures are uncertain. Benzene occurs widely in the work environment and also indoor air, but mostly below 1 ppm, so assessing the leukemia risks at these low concentrations is important. Here, we describe a human physiologically-based pharmacokinetic (PBPK) model that quantifies tissue doses of benzene and its key metabolites, benzene oxide, phenol, and hydroquinone after inhalation and oral exposures. The model was integrated into a statistical framework that acknowledges sources of variation due to inherent intra- and interindividual variation, measurement error, and other data collection issues. A primary contribution of this work is the estimation of population distributions of key PBPK model parameters. We hypothesized that observed interindividual variability in the dosimetry of benzene and its metabolites resulted primarily from known or estimated variability in key metabolic parameters and that a statistical PBPK model that explicitly included variability in only those metabolic parameters would sufficiently describe the observed variability. We then identified parameter distributions for the PBPK model to characterize observed variability through the use of Markov chain Monte Carlo analysis applied to two data sets. The identified parameter distributions described most of the observed variability, but variability in physiological parameters such as organ weights may also be helpful to faithfully predict the observed human-population variability in benzene dosimetry.

Physiologically-based pharmacokinetic modeling of genistein in rats, Part I: Model development

Genistein is a phytoestrogen-a plant-derived compound that binds to and activates the estrogen receptor-occurring at high levels in soy beans and food products, leading to widespread human exposure. The numerous scientific publications available describing genistein's dosimetry, mechanisms of action, and identified or putative health effects in both experimental animals and humans make it ideal for examination as an example of endocrine-active compound (EAC). We developed a physiologically-based pharmacokinetic (PBPK) model to quantify the internal, target-tissue dosimetry of genistein in adult rats. Complexities of the model include enterohepatic circulation, binding of both genistein and its conjugates to plasma proteins, and the multiple compartments used to describe transport through the bile duct and gastrointestinal tract. Other aspects of the model are simple perfusion-limited transport to the tissue groups and first-order rates of metabolism, uptake, and excretion. We describe here the model structure and initial calibration of the model by fitting to a large data set for Wistar rats. The model structure can be readily extrapolated to describe genistein dosimetry in humans or modified to describe the dosimetry of other phytoestrogens and phenolic EACs. The model does a fair job of capturing the pharmacokinetics. Although it does not describe the interindividual variability and we have not identified a single set of parameters that provide a good fit to the data for both oral and intravenous exposures, we believe it provides a good initial attempt at PBPK modeling for genistein, which can serve as a template for other phytoestrogens and in the design of future experiments and research that can be used to fill data gaps and better estimate model parameters.

Human Respiratory Tract Cancer Risks of Inhaled Formaldehyde: Dose-Response Predictions Derived From Biologically-Motivated Computational Modeling of a Combined Rodent and Human Dataset

Formaldehyde inhalation at 6 ppm and above causes nasal squamous cell carcinoma (SCC) in F344 rats. The quantitative implications of the rat tumors for human cancer risk are of interest, since epidemiological studies have provided only equivocal evidence that formaldehyde is a human carcinogen. Conolly et al. (Toxicol. Sci. 75, 432-447, 2003) analyzed the rat tumor dose-response assuming that both DNA-reactive and cytotoxic effects of formaldehyde contribute to SCC development. The key elements of their approach were: (1) use of a three-dimensional computer reconstruction of the rat nasal passages and computational fluid dynamics (CFD) modeling to predict regional dosimetry of formaldehyde; (2) association of the flux of formaldehyde into the nasal mucosa, as predicted by the CFD model, with formation of DNA-protein cross-links (DPX) and with cytolethality/regenerative cellular proliferation (CRCP); and (3) use of a two-stage clonal growth model to link DPX and CRCP with tumor formation. With this structure, the prediction of the tumor dose response was extremely sensitive to cell kinetics. The raw dose-response data for CRCP are J-shaped, and use of these data led to a predicted J-shaped dose response for tumors, notwithstanding a concurrent low-dose-linear, directly mutagenic effect of formaldehyde mediated by DPX. In the present work the modeling approach used by Conolly et al. (ibid.) was extended to humans. Regional dosimetry predictions for the entire respiratory tract were obtained by merging a three-dimensional CFD model for the human nose with a one-dimensional typical path model for the lower respiratory tract. In other respects, the human model was structurally identical to the rat model. The predicted human dose response for DPX was obtained by scale-up of a computational model for DPX calibrated against rat and rhesus monkey data. The rat dose response for CRCP was used "as is" for the human model, since no preferable alternative was identified. Three sets of baseline parameter values for the human clonal growth model were obtained through separate calibrations against respiratory tract cancer incidence data for nonsmokers, smokers, and a mixed population of nonsmokers and smokers, respectively. Additional risks of respiratory tract cancer were predicted to be negative up to about one ppm for all three cases when the raw CRCP data from the rat were used. When a hockey-stick-shaped model was fit to the rat CRCP data and used in place of the raw data, positive maximum likelihood estimates (MLE) of additional risk were obtained. These MLE estimates were lower, for some comparisons by as much as 1,000-fold, than MLE estimates from previous cancer dose-response assessments for formaldehyde. Breathing rate variations associated with different physical activity levels did not make large changes in predicted additional risks. In summary, this analysis of the human implications of the rat SCC data indicates that (1) cancer risks associated with inhaled formaldehyde are de minimis (10(-6) or less) at relevant human exposure levels, and (2) protection from the noncancer effects of formaldehyde should be sufficient to protect from its potential carcinogenic effects.

Modeling and optimal regulation of erythropoiesis subject to benzene intoxication

Benzene (C(6)H(6)) is a highly flammable, colorless liquid. Ubiquitous exposures result from its presence in gasoline vapors, cigarette smoke, and industrial processes. Benzene increases the incidence of leukemia in humans when they are exposed to high doses for extended periods; however, leukemia risks in humans subjected to low exposures are uncertain. The exposure-dose- response relationship of benzene in humans is expected to be nonlinear because benzene undergoes a series of metabolic transformations, detoxifying and activating, resulting in various metabolites that exert toxic effects on the bone marrow. Since benzene is a known human leukemogen, the toxicity of benzene in the bone marrow is of most importance. And because blood cells are produced in the bone marrow, we investigated the effects of benzene on hematopoiesis (blood cell production and development). An age-structured model was used to examine the process of erythropoiesis, the development of red blood cells. This investigation proved the existence and uniqueness of the solution of the system of coupled partial and ordinary differential equations. In addition, we formulated an optimal control problem for the control of erythropoiesis and performed numerical simulations to compare the performance of the optimal feedback law and another feedback function based on the Hill function.

A distributed-parameter model for formaldehyde uptake and disposition in the rat nasal lining

DNA-protein cross-links (DPX) serve as a dosimeter for inhaled formaldehyde and are associated with tumor induction in rat nasal passages after chronic exposure to 6 ppm and above. To determine the role of epithelium-specific morphometry in formaldehyde-induced patterns of injury, we developed a mathematical model that links airflow-driven formaldehyde uptake with DPX formation in regions of the rat nose with high and low tumor incidence. A three-dimensional, anatomically accurate computational fluid dynamics model of rat nasal airflow and inhaled gas uptake was integrated with a physiologically based mathematical model incorporating tissue thickness, formaldehyde diffusion, its removal by enzymatic and nonenzymatic processes, and DNA distribution in the nasal mucosa to predict DPX formation. The model implicitly incorporates the reversible conversion of formaldehyde to methylene glycol. Where possible, parameter values were taken from the literature or estimated using published correlations. The Michaelis-Menten kinetic constants Vmax and Km, as well as a first-order constant for formaldehyde removal, were left as fitted parameters. The resultant model fit to the experimentally measured DPX in the high- and low-tumor-incidence regions of the rat nasal passages was very good. Sensitivity analysis indicates that among the fitted parameters, model fits are most sensitive to Vmax and that predictions were sensitive to changes in tissue thickness when all other parameters are held constant. The model structure facilitates extrapolation to primates and humans and application to other soluble, reactive gases.

Biologically motivated computational modeling of formaldehyde carcinogenicity in the F344 rat

Formaldehyde inhalation at 6 ppm and above causes nasal squamous cell carcinoma (SCC) in F344 rats. The human health implications of this effect are of significant interest since human exposure to environmental formaldehyde is widespread, though at lower concentrations than those that cause cancer in rats. In this article, which is part of a larger effort to predict the human cancer risks of inhaled formaldehyde, we describe biologically motivated quantitative modeling of the exposure-tumor response continuum in the rat. An anatomically realistic, three-dimensional fluid dynamics model of the F344 rat nasal airways was used to predict site-specific flux of formaldehyde from inhaled air into tissue, since both SCC and preneoplastic lesions develop in a characteristic site-specific pattern. Flux into tissue was used as a dose metric for two modes of action, direct mutagenicity and cytolethality-regenerative cellular proliferation (CRCP), which in turn were linked to key parameters of a two-stage clonal growth model. The direct mutagenicity mode of action was represented by a low dose linear dose-response model of DNA-protein cross-link (DPX) formation. An empirical J-shaped dose-response model and a threshold model fit to the empirical data were used for CRCP. In the clonal growth model, the probability of mutation per cell generation was a function of the tissue concentration of DPX while the rate of cell division was calculated from the CRCP data. Maximum likelihood methods were used to estimate parameter values. Survivor (a nontumor outcome) and tumor data for controls from the National Toxicology Program database and from two formaldehyde inhalation bioassays were used for likelihood calculations. The J-shaped dose-response for CRCP provided a better description of the SCC data than did the threshold model. Sensitivity analyses indicated that the rodent tumor response is due to the CRCP mode of action, with the directly mutagenic pathway having little, if any, influence. When evaluated in light of modeling and database uncertainties, particularly the specification of the clonal growth model and the dose-response data for CRCP, this work provides suggestive though not definitive evidence for a J-shaped dose-response for formaldehyde-mediated nasal SCC in the F344 rat.

Benchmark dose risk assessment for formaldehyde using airflow modeling and a single-compartment, DNA-protein cross-link dosimetry model to estimate human equivalent doses

Formaldehyde induced squamous-cell carcinomas in the nasal passages of F344 rats in two inhalation bioassays at exposure levels of 6 ppm and above. Increases in rates of cell proliferation were measured by T. M. Monticello and colleagues at exposure levels of 0.7 ppm and above in the same tissues from which tumors arose. A risk assessment for formaldehyde was conducted at the CIIT Centers for Health Research, in collaboration with investigators from Toxicological Excellence in Risk Assessment (TERA) and the U.S. Environmental Protection Agency (U.S. EPA) in 1999. Two methods for dose-response assessment were used: a full biologically based modeling approach and a statistically oriented analysis by benchmark dose (BMD) method. This article presents the later approach, the purpose of which is to combine BMD and pharmacokinetic modeling to estimate human cancer risks from formaldehyde exposure. BMD analysis was used to identify points of departure (exposure levels) for low-dose extrapolation in rats for both tumor and the cell proliferation endpoints. The benchmark concentrations for induced cell proliferation were lower than for tumors. These concentrations were extrapolated to humans using two mechanistic models. One model used computational fluid dynamics (CFD) alone to determine rates of delivery of inhaled formaldehyde to the nasal lining. The second model combined the CFD method with a pharmacokinetic model to predict tissue dose with formaldehyde-induced DNA-protein cross-links (DPX) as a dose metric. Both extrapolation methods gave similar results, and the predicted cancer risk in humans at low exposure levels was found to be similar to that from a risk assessment conducted by the U.S. EPA in 1991. Use of the mechanistically based extrapolation models lends greater certainty to these risk estimates than previous approaches and also identifies the uncertainty in the measured dose-response relationship for cell proliferation at low exposure levels, the dose-response relationship for DPX in monkeys, and the choice between linear and nonlinear methods of extrapolation as key remaining sources of uncertainty.

Multiple stable periodic solutions in a model for hormonal control of the menstrual cycle

This study presents a nonlinear system of delay differential equations to model the concentrations of five hormones important for regulation and maintenance of the menstrual cycle. Linear model components for the ovaries and pituitary were previously analyzed and reported separately. Results for the integrated model are now presented here. This model predicts serum levels of ovarian and pituitary hormones which agree with data in the literature for normally cycling women. In addition, the model indicates the existence and stability of an abnormal cycle. Hence, the model may be used to simulate the effects of external hormone therapies on abnormally cycling women as well as the effects of exogenous compounds on normally cycling women. Such simulations may be helpful in understanding the role of xenobiotics in fertility problems, in predicting successful hormone therapies, and for testing hormonal methods of birth control.

Dosimetry modeling of inhaled formaldehyde: comparisons of local flux predictions in the rat, monkey, and human nasal passages

Formaldehyde-induced nasal squamous cell carcinomas in rats and squamous metaplasia in rats and rhesus monkeys occur in specific regions of the nose with species-specific distribution patterns. Experimental approaches addressing local differences in formaldehyde uptake patterns and dose are limited by the resolution of dissection techniques used to obtain tissue samples and the rapid metabolism of absorbed formaldehyde in the nasal mucosa. Anatomically accurate, 3-dimensional computational fluid dynamics models of F344 rat, rhesus monkey, and human nasal passages were used to estimate and compare regional inhaled formaldehyde uptake patterns predicted among these species. Maximum flux values, averaged over a breath, in nonsquamous epithelium were estimated to be 2620, 4492, and 2082 pmol/(mm(2)-h-ppm) in the rat, monkey, and human respectively. Flux values predicted in sites where cell proliferation rates were measured as similar in rats and monkeys were also similar, as were fluxes predicted in a region of high tumor incidence in the rat nose and the anterior portion of the human nose. Regional formaldehyde flux estimates are directly applicable to clonal growth modeling of formaldehyde carcinogenesis to help reduce uncertainty in human cancer risk estimates.

Dosimetry modeling of inhaled formaldehyde: binning nasal flux predictions for quantitative risk assessment

Interspecies extrapolations of tissue dose and tumor response have been a significant source of uncertainty in formaldehyde cancer risk assessment. The ability to account for species-specific variation of dose within the nasal passages would reduce this uncertainty. Three-dimensional, anatomically realistic, computational fluid dynamics (CFD) models of nasal airflow and formaldehyde gas transport in the F344 rat, rhesus monkey, and human were used to predict local patterns of wall mass flux (pmol/[mm(2)-h-ppm]). The nasal surface of each species was partitioned by flux into smaller regions (flux bins), each characterized by surface area and an average flux value. Rat and monkey flux bins were predicted for steady-state inspiratory airflow rates corresponding to the estimated minute volume for each species. Human flux bins were predicted for steady-state inspiratory airflow at 7.4, 15, 18, 25.8, 31.8, and 37 l/min and were extrapolated to 46 and 50 l/min. Flux values higher than half the maximum flux value (flux median) were predicted for nearly 20% of human nasal surfaces at 15 l/min, whereas only 5% of rat and less than 1% of monkey nasal surfaces were associated with fluxes higher than flux medians at 0.576 l/min and 4.8 l/min, respectively. Human nasal flux patterns shifted distally and uptake percentage decreased as inspiratory flow rate increased. Flux binning captures anatomical effects on flux and is thereby a basis for describing the effects of anatomy and airflow on local tissue disposition and distributions of tissue response. Formaldehyde risk models that incorporate flux binning derived from anatomically realistic CFD models will have significantly reduced uncertainty compared with risk estimates based on default methods.

A review of quantitative studies of benzene metabolism

Benzene is a ubiquitous, highly flammable, colorless liquid that is a known hematotoxin, myelotoxin, and human leukemogen. Benzene-induced toxicity in animals is clearly mediated by its metabolism. The mechanisms of acute hemato- and myelotoxicity in humans are almost certainly the same as in animals, and there is compelling evidence that metabolism is requisite for the induction of leukemia in humans. A very large number of experimental investigations of benzene metabolism have been conducted with animals, both in vivo and in vitro. There have also been many investigations of benzene metabolism in humans and with human tissues, Although the blood or tissue concentrations of benzene metabolites in humans resulting from benzene exposure have never been measured. Further, a number of mathematical models of benzene metabolism and dosimetry have been developed. In this article, we consider results from both experimental and mathematical modeling research, with particular emphasis on the last decade, and discuss the factors that are likely to be most influential in the metabolism of benzene.

Physiologically based pharmacokinetic modeling of benzene metabolism in mice through extrapolation from in vitro to in vivo

Benzene (C6H6) is a highly flammable, colorless liquid. Ubiquitous exposures result from its presence in gasoline vapors, cigarette smoke, and industrial processes. Benzene increases the incidence of leukemia in humans when they are exposed to high doses for extended periods; however, leukemia risks in humans at low exposures are uncertain. The exposure-dose-response relationship of benzene in humans is expected to be nonlinear because benzene undergoes a series of metabolic transformations, detoxifying and activating, in the liver, resulting in multiple metabolites that exert toxic effects on the bone marrow. We developed a physiologically based pharmacokinetic model for the uptake and elimination of benzene in mice to relate the concentration of inhaled and orally administered benzene to the tissue doses of benzene and its key metabolites, benzene oxide, phe nol, and hydroquinone. As many parameter values as possible were taken from the literature; in particular, metabolic parameters obtained from in vitro studies with mouse liver were used since comparable parameters are also available for humans. Parameters estimated by fitting the model to published data were first-order rate constants for pathways lacking in vitro data and the concentrations of microsomal and cytosolic protein, which effectively alter overall enzyme activity. The model was constrained by using the in vitro metabolic parameters (maximum velocities, first-order rate constants, and saturation parameters), and data from multiple laboratories and experiments were used. Despite these constraints and sources of variability, the model simulations matched the data reasonably well in most cases, showing that in vitro metabolic constants can be successfully extrapolated to predict in vivo data for benzene metabolism and dosimetry. Therefore in vitro metabolic constants for humans can subsequently be extrapolated to predict the dosimetry of benzene and its metabolites in humans. This will allow us to better estimate the risks of adverse effects from low-level benzene exposures.

A model of gonadotropin regulation during the menstrual cycle in women: qualitative features

Increasing concerns that environmental contaminants may disrupt the endocrine system require development of mathematical tools to predict the potential for such compounds to significantly alter human endocrine function. The endocrine system is largely self-regulating, compensating for moderate changes in dietary phytoestrogens (e.g., in soy products) and normal variations in physiology. However, severe changes in dietary or oral exposures or in health status (e.g., anorexia), can completely disrupt the menstrual cycle in women. Thus, risk assessment tools should account for normal regulation and its limits. We present a mathematical model for the synthesis and release of luteinizing hormone (LH) and follicle-stimulating hormone (FSH) in women as a function of estrogen, progesterone, and inhibin blood levels. The model reproduces the time courses of LH and FSH during the menstrual cycle and correctly predicts observed effects of administered estrogen and progesterone on LH and FSH during clinical studies. The model should be useful for predicting effects of hormonally active substances, both in the pharmaceutical sciences and in toxicology and risk assessment.

Haber's rule: a special case in a family of curves relating concentration and duration of exposure to a fixed level of response for a given endpoint

The concept that the product of the concentration (C) of a substance and the length of time (t) it is administered produces a fixed level of effect for a given endpoint has been ascribed to Fritz Haber, who was a German scientist in the early 1900s. He contended that the acute lethality of war gases could be assessed by the amount of the gas in a cubic meter of air (i.e. the concentration) multiplied by the time in min that the animal had to breathe the air before death ensued (i.e. C x t=k). While Haber recognized that C x t=k was applicable only under certain conditions, many toxicologists have used his rule to analyze experimental data whether or not their chemicals, biological endpoints, and exposure scenarios were suitable candidates for the rule. The fact that the relationship between C and t is linear on a log-log scale and could easily be solved by hand, led to early acceptance among toxicologists, particularly in the field of entomology. In 1940, a statistician named Bliss provided an elegant treatment on the relationships among exposure time, concentration, and the toxicity of insecticides. He proposed solutions for when the log-log plot of C and t was composed of two or more rectilinear segments, for when the log-log plot was curvilinear, and for when the slope of the dosage-mortality curve was a function of C. Despite the fact that Haber's rule can underestimate or overestimate effects (and consequently risks), it has been used in various settings by regulatory bodies. Examples are presented from the literature of data sets that follow Haber's rule as well as those that do not. Haber's rule is put into perspective by showing that it is simply a special case in a family of power law curves relating concentration and duration of exposure to a fixed level of response for a given endpoint. Also shown is how this power law family can be used to examine the three-dimensional surface relating C, t, and varying levels of response. The time has come to move beyond the limited view of C and t relationships inferred by Haber's rule to the use of the broader family of curves of which this rule is a special case.

Inhibition of cytochrome P450 2E1 decreases, but does not eliminate, genotoxicity mediated by 1,3-butadiene

1,3-Butadiene (BD), a rodent carcinogen, is metabolized to mutagenic and DNA-reactive epoxides. In vitro data suggest that this oxidation is mediated by cytochrome P450 2E1 (CYP2E1). In this study, we tested the hypothesis that oxidation of BD by CYP2E1 is required for genotoxicity to occur. Inhalation exposures were conducted with B6C3F1 mice using a closed-chamber technique, and the maximum rate of butadiene oxidation was estimated. The total amount of butadiene metabolized was then correlated with the frequency of micronuclei (MN). Three treatment groups were used: (1) mice with no pretreatment; (2) mice pretreated with 1,2-trans-dichloroethylene (DCE), a specific CYP2E1 inhibitor; and (3) mice pretreated with 1-aminobenzotriazole (ABT), an irreversible inhibitor of cytochromes P450. Mice in all 3 groups were exposed to an initial BD concentration of 1100 ppm, and the decline in concentration of BD in the inhalation chamber with time, due to uptake and metabolism of BD, was monitored using gas chromatography. A physiologically based pharmacokinetic model was used to analyze the gas uptake data, estimate V(max) for BD oxidation, and compute the total amount of BD metabolized. Model simulations of the gas uptake data predicted the maximum rate of BD oxidation would be reduced by 60% and 100% for the DCE- and ABT-pretreated groups, respectively. Bone marrow was harvested 24 h after the onset of the inhalation exposure and analyzed for frequency of micronuclei in polychromatic erythrocytes (MN-PCE). The frequency of MN-PCE per 1000 PCE in mice exposed to BD was 28.2 +/- 3.1, 19.8 +/- 2.5, and 12.3 +/- 1.9, for the mice with no pretreatment, DCE-pretreated mice and ABT-pretreated mice, respectively. Although inhibition of CYP2E1 decreased BD-mediated genotoxicity, it did not completely eliminate genotoxic effects. These data suggest that other P450 isoforms may contribute significantly to the metabolic activation of BD and resultant genotoxicity.

Relative roles of convection and chemical reaction for the disposition of formaldehyde and ozone in nasal mucus

The mucociliary apparatus is an important respiratory-tract defense system that may provide significant protection of the underlying epithelium from gases and vapors. Limiting-case calculations were performed to determine the significance of convective mucus transport and chemical reaction for formaldehyde (HCHO) and ozone (O(3)) in rat nasal respiratory epithelial mucus. Less than 4.6% of absorbed HCHO can be bound to amino groups (serum albumin) after 20 min of exposure. Thus, at the slowest measured mucus flow rates in rats, approximately 1 mm/min, a fluid element of mucus could travel more than 2 cm before binding 5% of absorbed HCHO, by which time the element would probably leave the nose (the site of toxic responses). In other calculations, HCHO removed by chemical reaction from a volume of mucus exposed for longer times was determined to be less than 0.54% of that removed by mucus flow (convection). Given the solubility of HCHO in mucus (water) and estimates of total mucus flow, however, as much as 22-42% of inhaled HCHO may be removed by total mucus flow. Alternately, O(3) dissolved in mucus would react completely with unsaturated fatty acids in 8.3 x 10(-4) s, in which time the mucus could flow no more than approximately 0.42 microm at the maximum reported flow rate of 30 mm/min. Even if a volume of mucus is flushed by net flow in 1 s, the amount of O(3) removed by flow would only be 0.12% of that removed by chemical reaction. Finally, based on the solubility of ozone, less than 8.0 x 10(-5)% of inhaled material could be removed from the nose by mucus flow. These results indicate which mucociliary processes are significant in site-specific dosimetry modeling.

Use of a mathematical model of rodent in vitro benzene metabolism to predict human in vitro metabolism data

Benzene, a ubiquitous environmental pollutant, is known to cause leukemia and aplastic anemia in humans and hematotoxicity and myelotoxicity in rodents. Toxicity is thought to be exerted through oxidative metabolites formed in the liver, primarily via pathways mediated by cytochrome P450 2E1 (CYP2E1). Phenol, hydroquinone and trans-trans-muconaldehyde have all been hypothesized to be involved in benzene-induced toxicity. Recent reports indicate that benzene oxide is produced in vitro and in vivo and may be sufficiently stable to reach the bone marrow. Our goal was to improve existing mathematical models of microsomal benzene metabolism by including time course data for benzene oxide, by obtaining better parameter estimates and by determining if enzymes other than CYP2E1 are involved. Microsomes from male B6C3F1 mice and F344 rats were incubated with [(14)C]benzene (14 microM), [(14)C]phenol (303 microM) and [(14)C]hydroquinone (8 microM). Benzene and phenol were also incubated with mouse microsomes in the presence of trans-dichloroethylene, a CYP2E1 inhibitor, and benzene was incubated with trichloropropene oxide, an epoxide hydrolase inhibitor. These experiments did not indicate significant contributions of enzymes other than CYP2E1. Mathematical model parameters were fitted to rodent data and the model was validated by predicting human data. Model simulations predicted the qualitative behavior of three human time course data sets and explained up to 81% of the total variation in data from incubations of benzene for 16 min with microsomes from nine human individuals. While model predictions did deviate systematically from the data for benzene oxide and trihydroxybenzene, overall model performance in predicting the human data was good. The model should be useful in quantifying human risk due to benzene exposure and explicitly accounts for interindividual variation in CYP2E1 activity.

Identification of benzene oxide as a product of benzene metabolism by mouse, rat, and human liver microsomes

Benzene is a ubiquitous environmental pollutant that is known to cause hematotoxicity and leukemia in humans. The initial oxidative metabolite of benzene has long been suspected to be benzene oxide (3,5-cyclohexadiene-1,2-oxide). During in vitro experiments designed to characterize the oxidative metabolism of [14C]benzene, a metabolite was detected by HPLC-radioactivity analysis that did not elute with other known oxidative metabolites. The purpose of our investigation was to prove the hypothesis that this metabolite was benzene oxide. Benzene (1 mM) was incubated with liver microsomes from human donors, male B6C3F1 mice, or male Fischer-344 rats, NADH (1 mM), and NADPH (1 mM) in 0.1 M sodium phosphate buffer (pH 7.4) and then extracted with methylene chloride. Gas chromatography-mass spectrometry analysis of incubation extracts for mice, rats, and humans detected a metabolite whose elution time and mass spectrum matched that of synthetic benzene oxide. The elution time of the benzene oxide peak was approximately 4.1 min, while phenol eluted at approximately 8 min. Benzene oxide also coeluted with the HPLC peak of the previously unidentified metabolite. Based on the 14C activity of this peak, the concentration of benzene oxide was determined to be approximately 18 microM, or 7% of total benzene metabolites, after 18 min of incubation of mouse microsomes with 1 mM benzene. The metabolite was not observed in incubations using heat-inactivated microsomes. This is the first demonstration that benzene oxide is a product of hepatic benzene metabolism in vitro. The level of benzene oxide detected suggests that benzene oxide is sufficiently stable to reach significant levels in the blood of mice, rats, and humans and may be translocated to the bone marrow. Therefore benzene oxide should not be excluded as a possible metabolite involved in benzene-induced leukemogenesis.

Physiologically based pharmacokinetic modeling of 1,3-butadiene, 1,2-epoxy-3-butene, and 1,2:3,4-diepoxybutane toxicokinetics in mice and rats

1,3-Butadiene (BD) is a more potent tumor inducer in mice than in rats. BD also shows striking differences in metabolic activation, with substantially higher blood concentrations of 1,2:3,4-diepoxybutane (butadiene diepoxide; BDE) in BD-exposed mice than in similarly exposed rats. The objective of this study was to develop a single mechanistic model structure capable of describing BD disposition in both species. To achieve this objective, known pathways of 1,2-epoxy-3-butene (butadiene monoepoxide; BMO) and BDE metabolism were incorporated into a physiologically based pharmacokinetic model by scaling rates determined in vitro. With this model structure, epoxide clearance was underestimated for both rats and mice. Improved simulation of blood epoxide concentrations was achieved by addition of first-order metabolism in the slowly perfused tissues, verified by simulation of data on the time course for BMO elimination after i.v. injection of BMO. Blood concentrations of BD were accurately predicted for mice and rats exposed by inhalation to constant concentrations of BD. However, if all BD was assumed to be metabolized to BMO, blood concentrations of BMO were overpredicted. By assuming that only a fraction of BD metabolism produces BMO, blood concentrations of BMO could be predicted over a range of BD exposure concentrations for both species. In vitro and in vivo studies suggest an alternative cytochrome P-450-mediated pathway for BD metabolism that does not yield BMO. Including an alternative pathway for BD metabolism in the model also gave accurate predictions of blood BDE concentrations after inhalation of BD. Blood concentrations of BMO and BDE observed in both mice and rats are best explained by the existence of an alternative pathway for BD metabolism which does not produce BMO.

Comparison of inhaled formaldehyde dosimetry predictions with DNA-protein cross-link measurements in the rat nasal passages

Kimbell and coworkers (Toxicol, Appl. Pharmacol, 121, 253-263, 1993) developed a computational fluid dynamics (CFD) model of a F344 rat nasal passage to quantify local wall mass flux (uptake rate) of inhaled chemical. To simulate formaldehyde uptake, Kimbell et al. assumed that mass transfer of formaldehyde from the air into the nasal lining was fast and complete. This was approximated in the CFD model by setting the formaldehyde concentration at the airway walls to zero. Experimental confirmation of formaldehyde mass-flux predictions is desirable if the CFD model is to be used for predicting formaldehyde dosimetry. The purpose of this study was to see if the CFD model predictions of formaldehyde mass flux are consistent with laboratory data on formaldehyde dosimetry. In this study, a mathematical model of the nasal lining was modified to link CFD dosimetry predictions for inhaled formaldehyde with measured tissue disposition of inhaled gas. This model treats the nasal lining as a single, well-stirred compartment, accounts for formaldehyde reaction via saturable and first-order pathways, and allows comparison of model-predicted DNA-protein cross-links (DPX) with regional DPX measured in formaldehyde-exposed rats. Effective Michaelis-Menten kinetic parameters (Vmax = 3040 microM/min and Km = 59 microM) and a pseudo-first-order rate constant for elimination of formaldehyde by nonsaturable pathways (kf = 6 min-1) were estimated (fit) using an average mass flux derived from experimentally measured uptake of formaldehyde. DPX predictions obtained using the estimated kinetic parameters and linking the CFD model to the nasal-lining model compared well with experimentally measured DPX. The close correlation between predicted and measured DPX in the rat nasal passage supports the CFD model predictions of formaldehyde mass flux at the level of resolution provided by the experimental data.

Mechanistic considerations in benzene physiological model development

Benzene, an important industrial solvent, is also present in unleaded gasoline and cigarette smoke. The hematotoxic effects of benzene in humans are well documented and include aplastic anemia, pancytopenia, and acute myelogenous leukemia. However, the risks of leukemia at low exposure concentrations have not been established. A combination of metabolites (hydroquinone and phenol, for example) may be necessary to duplicate the hematotoxic effect of benzene, perhaps due in part to the synergistic effect of phenol on myeloperoxidase-mediated oxidation of hydroquinone to the reactive metabolite benzoquinone. Because benzene and its hydroxylated metabolites (phenol, hydroquinone, and catechol) are substrates for the same cytochrome P450 enzymes, competitive interactions among the metabolites are possible. In vivo data on metabolite formation by mice exposed to various benzene concentrations are consistent with competitive inhibition of phenol oxidation by benzene. In vitro studies of the metabolic oxidation of benzene, phenol, and hydroquinone are consistent with the mechanism of competitive interaction among the metabolites. The dosimetry of benzene and its metabolites in the target tissue, bone marrow, depends on the balance of activation processes such as enzymatic oxidation and deactivation processes such as conjugation and excretion. Phenol, the primary benzene metabolite, can undergo both oxidation and conjugation. Thus the potential exists for competition among various enzymes for phenol. Zonal localization of phase I and phase II enzymes in various regions of the liver acinus also impacts this competition. Biologically based dosimetry models that incorporate the important determinants of benzene flux, including interactions with other chemicals, will enable prediction of target tissue doses of benzene and metabolites at low exposure concentrations relevant for humans.

Physiologically based pharmacokinetic modeling of blood and tissue epoxide measurements for butadiene

In vitro and in vivo butadiene (BD) metabolism data from laboratory animals were integrated into a rodent physiologically based pharmacokinetic (PBPK) model with flow- and diffusion-limited compartments. The resulting model describes experimental data from multiple sources under scenarios such as closed chamber inhalation and nose-only flow-through inhalation exposures. Incorporation of diurnal glutathione (GSH) variation allows accurate simulation of GSH changes observed in air control nose-only exposures and BD exposures. An isolated tissue model based on rate parameters determined in vitro predicts the decrease in epoxide concentrations in intact animals during the time lag between exsanguination and tissue removal for tissues capable of epoxide biotransformation, providing a better indication of in vivo dosimetry. Further refinements of the model are required relative to model predictions of an important BD metabolite, diepoxybutane.

Benzene: a case study in parent chemical and metabolite interactions

Benzene, an important industrial solvent, is also present in unleaded gasoline and cigarette smoke. The hematotoxic effects of benzene in humans are well documented and include aplastic anemia and pancytopenia, and acute myelogenous leukemia. A combination of metabolites (hydroquinone and phenol for example) is apparently necessary to duplicate the hematotoxic effect of benzene, perhaps due in part to the synergistic effect of phenol on myeloperoxidase-mediated oxidation of hydroquinone to the reactive metabolite benzoquinone. Since benzene and its hydroxylated metabolites (phenol, hydroquinone and catechol) are substrates for the same cytochrome P450 enzymes, competitive interactions among the metabolites are possible. In vivo data on metabolite formation by mice exposed to various benzene concentrations are consistent with competitive inhibition of phenol oxidation by benzene. In vitro studies of the metabolic oxidation of benzene, phenol and hydroquinone are consistent with the mechanism of competitive interaction among the metabolites. The dosimetry of benzene and its metabolites in the target tissue, bone marrow, depends on the balance of activation processes such as enzymatic oxidation and deactivation processes such as conjugation and excretion. Phenol, the primary benzene metabolite, can undergo both oxidation and conjugation. Thus, the potential exists for competition among various enzymes for phenol. However, zonal localization of Phase I and Phase II enzymes in various regions of the liver acinus regulates this competition. Biologically-based dosimetry models that incorporate the important determinants of benzene flux, including interactions with other chemicals, will enable prediction of target tissue doses of benzene and metabolites at low exposure concentrations relevant for humans.

Experimental design for parameter estimation through sensitivity analysis

Parameter estimates can be obtained by fitting a numerical simulation model to experimental data, but these estimates may be biased and/or imprecise because of noise in the experimental data. Appropriate choice of experimental conditions, such as exposure or substrate concentrations and sampling times, can minimize the effect of experimental noise on parameter estimates, thus reducing bias and improving precision. This article describes a technique for selecting experimental (initial) conditions and measurement times for optimal parameter estimation. The technique makes use of a user-supplied mathematical simulation model for the process under study with a set of "current" parameter values specified. These "current" parameter values are the best that can be obtained using all available experimental data and/or literature information at the time when design calculations are performed. Early in a modeling study, the "current" parameter values will be tentative--based on a relatively small amount of information. Later in a study, the "current" parameter values may be known to reasonable accuracy, but final confirmation is desired. The technique uses the simulation model to calculate a numerical index for each possible experimental design. The numerical index, or Information Index, is a measure of the response of a simulation model to changes in parameter values, described by Kalogerakis and Luus (1983, 1984). The experimental design with the greatest value of Information Index is the one under which parameters can be most precisely estimated. Computation of the Information Index, described in detail, can be somewhat complicated, depending on the software available. The results, however, are simple to interpret and provide valuable information on the quality of alternate proposed experiments. The technique is applicable to a broad range of dynamical systems. Its use is demonstrated by application to a simulation model being developed to describe the in vitro metabolism of benzene by mouse liver microsomes.

Critical issues in benzene toxicity and metabolism: the effect of interactions with other organic chemicals on risk assessment

Benzene, an important industrial solvent, is also present in unleaded gasoline and cigarette smoke. The hematotoxic effects of benzene are well documented and include aplastic anemia and pancytopenia. Some individuals exposed repeatedly to cytotoxic concentrations of benzene develop acute myeloblastic anemia. It has been hypothesized that metabolism of benzene is required for its toxicity, although administration of no single benzene metabolite duplicates the toxicity of benzene. Several investigators have demonstrated that a combination of metabolites (hydroquinone and phenol, for example) is necessary to duplicate the hematotoxic effect of benzene. Enzymes implicated in the metabolic activation of benzene and its metabolites include the cytochrome P450 monooxygenases and myeloperoxidase. Since benzene and its hydroxylated metabolites (phenol, hydroquinone, and catechol) are substrates for the same cytochrome P450 enzymes, competitive interactions among the metabolites are possible. In vivo data on metabolite formation by mice exposed to various benzene concentrations are consistent with competitive inhibition of phenol oxidation by benzene. Other organic molecules that are substrates for cytochrome P450 can inhibit the metabolism of benzene. For example, toluene has been shown to inhibit the oxidation of benzene in a noncompetitive manner. Enzyme inducers, such as ethanol, can alter the target tissue dosimetry of benzene metabolites by inducing enzymes responsible for oxidation reactions involved in benzene metabolism. The dosimetry of benzene and its metabolites in the target tissue, bone marrow, depends on the balance of activation processes, such as enzymatic oxidation, and deactivation processes, like conjugation and excretion.(ABSTRACT TRUNCATED AT 250 WORDS)

Benzene metabolism by human liver microsomes in relation to cytochrome P450 2E1 activity

Low levels of benzene from sources including cigarette smoke and automobile emissions are ubiquitous in the environment. Since the toxicity of benzene probably results from oxidative metabolites, an understanding of the profile of biotransformation of low levels of benzene is critical in making a valid risk assessment. To that end, we have investigated metabolism of a low concentration of [14C]benzene (3.4 microM) by microsomes from human, mouse and rat liver. The extent of phase I benzene metabolism by microsomal preparations from 10 human liver samples and single microsomal preparations from both mice and rats was then related to measured activities of cytochrome P450 (CYP) 2E1. Measured CYP 2E1 activities, as determined by hydroxylation of p-nitrophenol, varied 13-fold (0.253-3.266 nmol/min/mg) for human samples. The fraction of benzene metabolized in 16 min ranged from 10% to 59%. Also at 16 min, significant amounts of oxidative metabolites were formed. Phenol was the main metabolite formed by all but two human microsomal preparations. In those samples, both of which had high CYP 2E1 activity, hydroquinone was the major metabolite formed. Both hydroquinone and catechol formation showed a direct correlation with CYP 2E1 activity over the range of activities present. A simulation model was developed based on a mechanism of competitive inhibition between benzene and its oxidized metabolites, and was fit to time-course data for three human liver preparations. Model calculations for initial rates of benzene metabolism ranging from 0.344 to 4.442 nmol/mg/min are directly proportional to measured CYP 2E1 activities. The model predicted the dependence of benzene metabolism on the measured CYP 2E1 activity in human liver samples, as well as in mouse and rat liver samples. These results suggest that differences in measured hepatic CYP 2E1 activity may be a major factor contributing to both interindividual and interspecies variations in hepatic metabolism of benzene. Validation of this system in vivo should lead to more accurate assessment of the risk of benzene's toxicity following low-level exposure.

Benzene and phenol metabolism by mouse and rat liver microsomes

Benzene, an important industrial solvent and constituent of unleaded gasoline, causes leukemia and aplastic anemia in humans. Mice are more sensitive than rats to benzene toxicity, though neither species has been shown to respond consistently with benzene-induced leukemia. Benzene biotransformation in liver to phenol, hydroquinone, catechol and/or muconaldehyde is thought to be necessary for its hematotoxicity and/or genotoxicity. Our goal is to develop a mathematical simulation model capable of describing the pathways and kinetics of benzene metabolism by rat and mouse liver microsomes and to assess the role of species metabolic differences in species sensitivity. Microsomes were incubated with 4 microM [U-14C]-benzene or 4 microM [U-14C]phenol. Metabolite production was quantified by extraction into ethyl acetate, HPLC separation and liquid scintillation spectroscopy. After 45 min, mouse liver microsomes converted 20% of the benzene to phenol, 31% to hydroquinone and 2% to catechol. Rat liver microsomes converted 23% of benzene to phenol, 8% to hydroquinone and 0.5% to catechol. Production of hydroquinone and catechol continued for 90 min for mouse liver microsomes, while production by rat liver microsomes had virtually ceased by 90 min. Muconic acid production by mouse liver microsomes was < 0.2% and < 0.04% from benzene and phenol respectively after 90 min. A quantitative simulation model was constructed to describe the in vitro metabolism of benzene, incorporating the reaction sequences: benzene-->phenol-->catechol-->trihydroxybenzene and phenol-->hydroquinone-->trihydroxybenzene. In the model, all of the reaction steps are assumed to be catalyzed by the same enzyme(s), cytochrome(s) P450, and benzene, phenol, hydroquinone and catechol in solution are all assumed to compete, through reversible binding, for the same reaction site(s) on cytochrome(s) P450. The simulation model accurately described both the benzene and phenol kinetic data, supporting this proposed mechanism. In particular, this model suggests that the observed inhibition of benzene on phenol metabolism, and of phenol on benzene metabolism, occurs through competition for a common reaction site, which can also bind catechol and hydroquinone.

An integrated modeling-experimental strategy for the analysis of metabolic pathways

An inherent problem in studying the behavior of a metabolic pathway is the impossibility of developing a complete, detailed model that includes all the cellular processes that have an impact on the set of fluxes in such a pathway. Lacking this, one requires some means of modeling the interactions between a metabolic pathway and other cellular processes for the purpose of analyzing pathway characteristics within the cell (e.g., determining sensitivity coefficients for various steps in the pathway) with a minimal amount of time and effort. A general framework is developed for studying these issues in a rigorous manner. Using this framework, detailed knowledge about a metabolic pathway (i.e., a set of rate expressions for steps in the pathway) can be combined with the results from a relatively simple set of experiments in order to obtain estimates for the sensitivity of the pathway to enzyme activities, inhibition constants, and other parameters that determine the pathway's behavior, while accounting for the pathway's interaction with the rest of the cellular metabolism. A model system representing amino acid production is used to illustrate the problem and to provide results based on computational experiments. The modeling strategy described here should be useful in genetic design to improve pathway fluxes and metabolic network selectivity.