Modeling Receptor-Mediated Processes with Dioxin: Implications for Pharmacokinetics and Risk Assessment

Dioxin (2,3,7,8-tetrachlorodibenzo- p -dioxin; TCDD), a widespread polychlorinated aromatic hydrocarbon, caused tumors in the liver and other sites when administered chronically to rats at doses as low as 0.01 μg/kg/day. It functions in combination with a cellular protein, the Ah receptor, to alter gene regulation, and this resulting modulation of gene expression is believed to be obligatory for both dioxin toxicity and carcinogenicity. The U.S. EPA is reevaluating its dioxin risk assessment and, as part of this process, will be developing risk assessment approaches for chemicals, such as dioxin, whose toxicity is receptor-mediated. This paper describes a receptor-mediated physiologically based pharmacokinetic (PB-PK) model for the tissue distribution and enzyme-inducing properties of dioxin and discusses the potential role of these models in a biologically motivated risk assessment. In this model, ternary interactions among the Ah receptor, dioxin, and DNA binding sites lead to enhanced production of specific hepatic proteins. The model was used to examine the tissue disposition of dioxin and the induction of both a dioxin-binding protein (presumably, cytochrome P4501A2), and cytochrome P4501A1. Tumor promotion correlated more closely with predicted induction of P4501A1 than with induction of hepatic binding proteins. Although increased induction of these proteins is not expected to be causally related to tumor formation, these physiological dosimetry and gene-induction response models will be important for biologically motivated dioxin risk assessments in determining both target tissue dose of dioxin and gene products and in examining the relationship between these gene products and the cellular events more directly involved in tumor promotion.     

Effects of the Mechanism of Receptor-Mediated Gene Expression on the Shape of the Dose-Response Curve

A mathematical model of receptor-mediated gene expression that includes receptor binding of natural and xenobiotic ligands, protein synthesis and degradation, and metabolism of the xenobiotic ligand was created to identify the determinants of the shape of the dose-response profile. Values of the model's parameters were varied to reflect alternative mechanisms of expression of the protein. These assumptions had dramatic effects on the computed response to a bolus dose of the xenobiotic ligand. If all processes in the model exhibit hyperbolic kinetics, the dose-response curves can appear sigmoidal but actually be linear with a positive slope at low doses. The slope of the curve only approached zero at low dose, indicative of a threshold for response, if binding of the xenobiotic ligand to the receptor exhibited positive cooperativity (ligand binding at one site increases the affinity for ligand at another binding site on the receptor). Positive cooperativity in the rate-limiting step of protein synthesis produced dose-response curves which were "U-shaped" at low doses, also indicative of a threshold. Positive cooperativity in the metabolism of the xenobiotic ligand produced dose-response curves that increased more rapidly than linearly with increasing dose. The model illustrates the fact that response cannot be predicted from qualitative mechanistic arguments alone; any assessment of risk to health from xenobiotic chemicals must be based on a detailed quantitative examination of the kinetic behavior of each chemical species individually.     

Exposure Reconstruction for the TCDD-Exposed NIOSH Cohort Using a Concentration- and Age-Dependent Model of Elimination

Recent studies demonstrating a concentration dependence of elimination of 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) suggest that previous estimates of exposure for occupationally exposed cohorts may have underestimated actual exposure, resulting in a potential overestimate of the carcinogenic potency of TCDD in humans based on the mortality data for these cohorts. Using a database on U.S. chemical manufacturing workers potentially exposed to TCDD compiled by the National Institute for Occupational Safety and Health (NIOSH), we evaluated the impact of using a concentration- and age-dependent elimination model (CADM) (Aylward et al., 2005) on estimates of serum lipid area under the curve (AUC) for the NIOSH cohort. These data were used previously by Steenland et al. (2001) in combination with a first-order elimination model with an 8.7-year half-life to estimate cumulative serum lipid concentration (equivalent to AUC) for these workers for use in cancer dose-response assessment. Serum lipid TCDD measurements taken in 1988 for a subset of the cohort were combined with the NIOSH job exposure matrix and work histories to estimate dose rates per unit of exposure score. We evaluated the effect of choices in regression model (regression on untransformed vs. ln-transformed data and inclusion of a nonzero regression intercept) as well as the impact of choices of elimination models and parameters on estimated AUCs for the cohort. Central estimates for dose rate parameters derived from the serum-sampled subcohort were applied with the elimination models to time-specific exposure scores for the entire cohort to generate AUC estimates for all cohort members. Use of the CADM resulted in improved model fits to the serum sampling data compared to the first-order models. Dose rates varied by a factor of 50 among different combinations of elimination model, parameter sets, and regression models. Use of a CADM results in increases of up to five-fold in AUC estimates for the more highly exposed members of the cohort compared to estimates obtained using the first-order model with 8.7-year half-life. This degree of variation in the AUC estimates for this cohort would affect substantially the cancer potency estimates derived from the mortality data from this cohort. Such variability and uncertainty in the reconstructed serum lipid AUC estimates for this cohort, depending on elimination model, parameter set, and regression model, have not been described previously and are critical components in evaluating the dose-response data from the occupationally exposed populations.     

A Study of the Shape of Dose-Response Curves for Acute Lethality at Low Response: A "Megadaphnia Study"

Dose-response curves were developed for the immobilization response in Daphnia magna to four toxicants. The purpose of this work was to study the effect of the form of the model and the number of concentration levels used on the estimates of typical low-dose effective concentrations (1%, 5%, 10%). The generalized four-parameter logistic model was used as the reference. When using 12 concentration levels, one of the logistic family two- or three-parameter models was shown reliably to represent each of these various sets of dose-response data, and to provide adequate estimates of EC01 and EC05, as well as EC10 and EC50. For two of the toxicants, an asymmetric model was required. When reducing the number of concentrations to five, the EC10 and EC50 were well estimated by the probit model, with acceptable results at the EC05 level.     

Reproducibility of the Dose-Response Curve of Steroid-Induced Cleft Palate in Mice

Pregnant CD-1 mice were exposed to cortisone acetate at doses ranging from 20 to 100 mg/kg/ day on days 10-13 by oral and intramuscular routes. Multiple replicate assays were conducted under identical conditions to assess the reproducibility of the dose–response curve for cleft palate. The data were fitted to the probit, logistic, multistage or Armitage-Doll, and Weibull dose-response model separately for each route of exposure. The curves were then tested for parallel slopes (probit and logistic models) or coincidence of model parameters (multistage and Weibull models). The 19 replicate experiments had a wide range of slope estimates, wider for the oral than for the intramuscular experiments. For all models and both routes of exposure the null hypothesis of equality of slopes was rejected at a significant level of p < 0.001. For the intramuscular group of replicates, rejection of slope equality could in part be explained by not maintaining a standard dosing regime. The rejection of equivalence of dose-response curves from replicate studies showed that it is difficult to reproduce dose-response data of a single study within the limits defined by the dose-response model. This has important consequences for quantitative risk assessment, public health measures, or development of mechanistic theories which are typically based on a single animal bioassay.     

Dose-Response Model for 13 Strains of Salmonella

Data from a human feeding trial with healthy men were used to develop a dose-response model for 13 strains of Salmonella and to determine the effects of strain variation on the shape of the dose-response curve. Dose-response data for individual strains were fit to a three-phase linear model to determine minimum, median, and maximum illness doses, which were used to define Pert distributions in a computer simulation model. Pert distributions for illness dose of individual strains were combined in an Excel spreadsheet using a discrete distribution to model strain prevalence. In addition, a discrete distribution was used to model dose groups and thus create a model that simulated human feeding trials. During simulation of the model with @Risk, an illness dose and a dose consumed were randomly assigned to each consumption event in the simulated feeding trial and if the illness dose was greater than the dose consumed then the model predicted no illness, otherwise the model predicted that an illness would occur. To verify the dose-response model predictions, the original feeding trial was simulated. The dose-response model predicted a median of 69 (range of 43-101) illnesses compared to 74 in the original trial. Thus, its predictions were in agreement with the data used to develop it. However, predictions of the model are only valid for eggnog, healthy men, and the strains and doses of Salmonella used to develop it. When multiple strains of Salmonella were simulated together, the predicted dose-response curves were irregular in shape. Thus, the sigmoid shape of dose-response curves in feeding trials with one strain of Salmonella may not accurately reflect dose response in naturally contaminated food where multiple strains may be present.     

Application of a Biologically-Based RFD Estimation Method to Tetrachlorodibenzo-P-Dioxin (TCDD) Mediated Immune Suppression and Enzyme Induction

The current methods for a reference dose (RfD) determination can be enhanced through the use of biologically-based dose-response analysis. Methods developed here utilizes information from tetrachlorodibenzo- p -dioxin (TCDD) to focus on noncancer endpoints, specifically TCDD mediated immune system alterations and enzyme induction. Dose-response analysis, using the Sigmoid-Emax (EMAX) function, is applied to multiple studies to determine consistency of response. Through the use of multiple studies and statistical comparison of parameter estimates, it was demonstrated that the slope estimates across studies were very consistent. This adds confidence to the subsequent effect dose estimates. This study also compares traditional methods of risk assessment such as the NOAEL/safety factor to a modified benchmark dose approach which is introduced here. Confidence in the estimation of an effect dose (ED₁₀) was improved through the use of multiple datasets. This is key to adding confidence to the benchmark dose estimates. In addition, the Sigmoid-Emax function when applied to dose-response data using nonlinear regression analysis provides a significantly improved fit to data increasing confidence in parameter estimates which subsequently improve effect dose estimates.     

Characterizing Dose-Response Relationships in Multiple Cancer Bioassays

In the evaluation of chemical compounds for carcinogenic risk, regulatory agencies such as the U.S. Environmental Protection Agency and National Toxicology Program (NTP) have traditionally fit a dose-response model to data from rodent bioassays, and then used the fitted model to estimate a Virtually Safe Dose or the dose corresponding to a very small increase (usually 10(-6)) in risk over background. Much recent interest has been directed at incorporating additional scientific information regarding the properties of the specific chemical under investigation into the risk assessment process, including biological mechanisms of cancer induction, metabolic pathways, and chemical structure and activity. Despite the fact that regulatory agencies are currently poised to allow use of nonlinear dose-response models based on the concept of an underlying threshold for nongenotoxic chemicals, there have been few attempts to investigate the overall relationship between the shape of dose-response curves and mutagenicity. Using data from an historical database of NTP cancer bioassays, the authors conducted a repeated-measures Analysis of the estimated shape from fitting extended Weibull dose-response curves. It was concluded that genotoxic chemicals have dose-response curves that are closer to linear than those for nongenotoxic chemicals, though on average, both types of compounds have dose-response curves that are convex and the effect of genotoxicity is small.     

Dose-Response Models for Inhalation of Bacillus anthracis Spores: Interspecies Comparisons

Because experiments with Bacillus anthracis are costly and dangerous, the scientific, public health, and engineering communities are served by thorough collation and analysis of experiments reported in the open literature. This study identifies available dose-response data from the open literature for inhalation exposure to B. anthracis and, via dose-response modeling, characterizes the response of nonhuman animal models to challenges. Two studies involving four data sets amenable to dose-response modeling were found in the literature: two data sets of response of guinea pigs to intranasal dosing with the Vollum and ATCC-6605 strains, one set of responses of rhesus monkeys to aerosol exposure to the Vollum strain, and one data set of guinea pig response to aerosol exposure to the Vollum strain. None of the data sets exhibited overdispersion and all but one were best fit by an exponential dose-response model. The beta-Poisson dose-response model provided the best fit to the remaining data set. As indicated in prior studies, the response to aerosol challenges is a strong function of aerosol diameter. For guinea pigs, the LD₅₀ increases with aerosol size for aerosols at and above 4.5 μm. For both rhesus monkeys and guinea pigs there is about a 15-fold increase in LD₅₀ when aerosol size is increased from 1 μm to 12 μm. Future experimental research and dose-response modeling should be performed to quantify differences in responses of subpopulations to B. anthracis and to generate data allowing development of interspecies correction factors.     

TCDD Exposure-Response Analysis and Risk Assessment

We examined the relation between cancer mortality and time-dependent cumulative exposure to 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) estimated from a concentration- and age-dependent kinetic model of elimination, and we estimated incremental cancer risks at age 75. Data from the National Institute for Occupational Safety and Health study of 3,538 workers with occupational exposure to TCDD were analyzed using standardized mortality ratios and Cox regression procedures. Analyses adjusted for potential confounding by age, year of birth, and race and considered exposure lag periods of 0, 10, or 15 years. Other potential confounders including smoking and other occupational exposures were evaluated indirectly. To explore the influence of extreme values of cumulative TCDD ppt-years, we restricted the analysis to observations with exposure below the 95th percentile or used logarithmic (ln) transformed exposure values. We applied penalized smoothing splines to examine variation in the exposure-response relation across the exposure range. TCDD was not statistically significantly associated with cancer mortality using the full data set, regardless of the lag period. When we restricted the analysis to observations with exposure below the 95th percentile, TCDD was associated positively with cancer mortality, particularly when a 15-year lag was applied (untransformed exposure data: regression coefficient , standard error (s.e.) = 1.4 x 10(-6), p < 0.05; ln-transformed exposure data: , s.e. = 2.9 x 10(-2), p < 0.05). The estimated incremental lifetime risk of mortality at age 75 from all cancers was about 6 to more than 10 times lower than previous estimates derived from this cohort using exposure models that did not consider the age and concentration dependence of TCDD elimination.     

Properties of Model-Averaged BMDLs: A Study of Model Averaging in Dichotomous Response Risk Estimation

Model averaging (MA) has been proposed as a method of accounting for model uncertainty in benchmark dose (BMD) estimation. The technique has been used to average BMD dose estimates derived from dichotomous dose-response experiments, microbial dose-response experiments, as well as observational epidemiological studies. While MA is a promising tool for the risk assessor, a previous study suggested that the simple strategy of averaging individual models' BMD lower limits did not yield interval estimators that met nominal coverage levels in certain situations, and this performance was very sensitive to the underlying model space chosen. We present a different, more computationally intensive, approach in which the BMD is estimated using the average dose-response model and the corresponding benchmark dose lower bound (BMDL) is computed by bootstrapping. This method is illustrated with TiO(2) dose-response rat lung cancer data, and then systematically studied through an extensive Monte Carlo simulation. The results of this study suggest that the MA-BMD, estimated using this technique, performs better, in terms of bias and coverage, than the previous MA methodology. Further, the MA-BMDL achieves nominal coverage in most cases, and is superior to picking the "best fitting model" when estimating the benchmark dose. Although these results show utility of MA for benchmark dose risk estimation, they continue to highlight the importance of choosing an adequate model space as well as proper model fit diagnostics.     

Models of Neurotoxicity: Extrapolation of Benchmark Doses in Vitro

In risk assessment, no observed exposure level (NOAEL) and benchmark dose (BMD) are usually derived either from epidemiological studies in humans or from animal experiments. In many in vitro studies, concentration-effect/response curves have been analyzed using different mathematical models finalized to the identification of EC50. In the present article, we propose a model to fit dose-response curves in vitro. The BMD approach has been used to compare the cell viability (MIT assay) of different rat (C6 and PC12, glial and neuronal, respectively) and human cell lines (D384 and SK-N-MC, glial and neuronal, respectively) after 24-hour exposure to the following neurotoxic substances: manganese chloride (MnCl2), methyl-mercury (Me-Hg), and the enantiomers of styrene oxide (SO). For all rat and human cell lines, the potency of the examined compounds was: MnCl2 < S-SO < R-SO < Me-Hg. A preliminary comparison with in vivo toxicity data for these substances gave rise to consistent results. Whereas a reasonable agreement between in vitro and in vivo data has been found for Mn and styrene oxide, a wide scatter of LOAEL has been reported for Me-Hg and these appear to be either much higher or lower than the BMD for the MIT assay we observed in vitro.     

Dose Response for Infectivity of Several Strains of Campylobacter jejuni in Chickens

Although some major risk studies have been done for Campylobacter jejuni, its dose response is not well characterized. Only a single human study is available, providing dose-response information for only a single isolate. As substantial heterogeneity in infectivity has been acknowledged for other pathogens, it remains unknown how well this single study represents the dose-response relation for this pathogen. As future human challenge studies with Campylobacter are unlikely, we have to find other means of studying its infectivity. Several dose-response studies have been done using chickens as host organisms. These studies may be used to obtain quantitative information on the variation in infectivity among different isolates of this pathogen. A hierarchical Bayesian model is well suited to describe heterogeneity, and we demonstrate how the beta-Poisson model of microbial infection may be adapted to allow for within- and between-isolate variation. Isolates tested in chickens can be categorized into two distinct groups: lab-adapted and fresh isolates, and we show how the hierarchical dose-response model can be used to quantitatively describe their differences. Fresh isolates show higher colonization potential and less within-isolate variation than lab isolates. The results indicate that Campylobacter jejuni is highly infectious in chickens. Different isolates show great variation in infectivity, especially between lab and fresh isolates, indicating that human clinical (volunteer) studies on infectivity must be interpreted cautiously.     

Issues in Qualitative and Quantitative Risk Analysis for Developmental Toxicology1

The qualitative and quantitative evaluation of risk in developmental toxicology has been discussed in several recent publications.(^1–3) A number of issues still are to be resolved in this area. The qualitative evaluation and interpretation of end points in developmental toxicology depends on an understanding of the biological events leading to the end points observed, the relationships among end points, and their relationship to dose and to maternal toxicity. The interpretation of these end points is also affected by the statistical power of the experiments used for detecting the various end points observed. The quantitative risk assessment attempts to estimate human risk for developmental toxicity as a function of dose. The current approach is to apply safety (uncertainty) factors to die no observed effect level (NOEL). An alternative presented and discussed here is to model the experimental data and apply a safety factor to an estimated risk level to achieve an “acceptable” level of risk. In cases where the dose-response curves upward, this approach provides a conservative estimate of risk. This procedure does not preclude the existence of a threshold dose. More research is needed to develop appropriate dose-response models that can provide better estimates for low-dose extrapolation of developmental effects.     

Calculation of Benchmark Doses from Continuous Data

A benchmark dose (BMD) is the dose of a substance that corresponds to a prescribed increase in the response (called the benchmark response or BMR) of a health effect. A statistical lower bound on the benchmark dose (BMDL) has been proposed as a replacement for the no-observed-adverse-effect-level (NOAEL) in setting acceptable human exposure levels. A method is developed in this paper for calculating BMDs and BMDLs from continuous data in a manner that is consistent with those calculated from quantal data. The method involves defining an abnormal response, either directly by specifying a cutoff x₀ that separates continuous responses into normal and abnormal categories, or indirectly by specifying the proportion P₀ of abnormal responses expected among unexposed subjects. The method does not involve actually dichotomizing individual continuous responses into quantal responses, and in certain cases can be applied to continuous data in summarized form (e.g., means and standard deviations of continuous responses among subjects in discrete dose groups). In addition to specifying the BMR and either x₀ or P₀ , the method requires specification of the distribution of continuous responses, including specification of the dose-response θ(d) for a measure of central tendency. A method is illustrated for selecting θ(d) to make the probability of an abnormal response any desired dose-response function. This enables the same dose-response model (Weibull, log-logistic, etc.) to be used for the probability of an abnormal response, regardless of whether the underlying data are continuous or quantal. Whenever the continuous responses are normally distributed with standard deviation σ (independent of dose), the method is equivalent to defining the BMD as the dose corresponding to a prescribed change in the mean response relative to σ.     

Stochasticity in Physiologically Based Kinetics Models: Implications for Cancer Risk Assessment

In case of low-dose exposure to a substance, its concentration in cells is likely to be stochastic. Assessing the consequences of this stochasticity in toxicological risk assessment requires the coupling of macroscopic dynamics models describing whole-body kinetics with microscopic tools designed to simulate stochasticity. In this article, we propose an approach to approximate stochastic cell concentration of butadiene in the cells of diverse organs. We adapted the dynamics equations of a physiologically based pharmacokinetic (PBPK) model and used a stochastic simulator for the system of equations that we derived. We then coupled kinetics simulations with a deterministic hockey stick model of carcinogenicity. Stochasticity induced substantial modifications relative to dose-response curve, compared with the deterministic situation. In particular, there was nonlinearity in the response and the stochastic apparent threshold was lower than the deterministic one. The approach that we developed could easily be extended to other biological studies to assess the influence of stochasticity at macroscopic scale for compound dynamics at the cell level.     

Predictive Bayesian Microbial Dose-Response Assessment Based on Suggested Self-Organization in Primary Illness Response: Cryptosporidium parvum

The probability of illness caused by very low doses of pathogens cannot generally be tested due to the numbers of subjects that would be needed, though such assessments of illness dose response are needed to evaluate drinking water standards. A predictive Bayesian dose-response assessment method was proposed previously to assess the unconditional probability of illness from available information and avoid the inconsistencies of confidence-based approaches. However, the method uses knowledge of the conditional dose-response form, and this form is not well established for the illness endpoint. A conditional parametric dose-response function for gastroenteric illness is proposed here based on simple numerical models of self-organized host-pathogen systems and probabilistic arguments. In the models, illnesses terminate when the host evolves by processes of natural selection to a self-organized critical value of wellness. A generalized beta-Poisson illness dose-response form emerges for the population as a whole. Use of this form is demonstrated in a predictive Bayesian dose-response assessment for cryptosporidiosis. Results suggest that a maximum allowable dose of 5.0 x 10(-7) oocysts/exposure (e.g., 2.5 x 10(-7) oocysts/L water) would correspond with the original goals of the U.S. Environmental Protection Agency Surface Water Treatment Rule, considering only primary illnesses resulting from Poisson-distributed pathogen counts. This estimate should be revised to account for non-Poisson distributions of Cryptosporidium parvum in drinking water and total response, considering secondary illness propagation in the population.     

Dioxin–An Analysis of the Major Human Studies: Comparison with Animal-Based Cancer Risks

Several major epidemiological studies have reported significant mortality rates (SMRs) for both rare cancers (soft tissue sarcoma, non-Hodgkin's, lymphoma, liver) and the more common cancers (lung, colon, etc), all allegedly caused by TCDD. In this paper, we use the potency of TCDD in animals to establish a plausible worst case cancer risk and ask whether its likely that TCDD is responsible for the epidemiological findings assuming the animal carcinogenic potency is applicable to the conditions of human exposure. Two new features of the technique are the use of measured TCDD blood levels in both animals and humans for dose scale-up and the calculation of an integrated life-time exposure for the exposed workers using measured blood levels. On the basis of the stated assumptions it appears unlikely that any of the major epidemiological studies, with the possible exception of the NIOSH study⁽¹⁾have adequate power to detect the common cancers potentially caused by TCDD.     

The Beta Poisson Dose-Response Model Is Not a Single-Hit Model

The choice of a dose-response model is decisive for the outcome of quantitative risk assessment. Single-hit models have played a prominent role in dose-response assessment for pathogenic microorganisms, since their introduction. Hit theory models are based on a few simple concepts that are attractive for their clarity and plausibility. These models, in particular the Beta Poisson model, are used for extrapolation of experimental dose-response data to low doses, as are often present in drinking water or food products. Unfortunately, the Beta Poisson model, as it is used throughout the microbial risk literature, is an approximation whose validity is not widely known. The exact functional relation is numerically complex, especially for use in optimization or uncertainty analysis. Here it is shown that although the discrepancy between the Beta Poisson formula and the exact function is not very large for many data sets, the differences are greatest at low doses--the region of interest for many risk applications. Errors may become very large, however, in the results of uncertainty analysis, or when the data contain little low-dose information. One striking property of the exact single-hit model is that it has a maximum risk curve, limiting the upper confidence level of the dose-response relation. This is due to the fact that the risk cannot exceed the probability of exposure, a property that is not retained in the Beta Poisson approximation. This maximum possible response curve is important for uncertainty analysis, and for risk assessment of pathogens with unknown properties.