Area under the curve as a dose metric for promotional responses following 2,3,7,8-tetrachlorodibenzo-p-dioxin exposure.

An underlying basis of risk assessment is that an equivalent risk for a specified dose metric exists that allows for extrapolation of dose-response relationships between species. To better understand the use of area under the curve (AUC) as a dose metric for complex biological responses following 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) exposure, a study was designed using a physiologically based pharmacokinetic model in the female Sprague-Dawley rat that would result in equivalent AUCs of total liver TCDD with differing patterns of exposure. In the first group, rats received a high peak dose of 3500 ng TCDD/kg twice per week in the first week followed by a lower TCDD dose of 81 ng/kg twice per week for the remainder of the study. In the second group, rats received a gavage dose of 350 ng TCDD/kg in corn oil twice per week for the study duration of 15 weeks. Age-matched control rats received corn oil as a vehicle control. Placental glutathione S-transferase (PGST)-positive foci were measured in representative liver lobes by immunohistochemistry, as a representative complex biological response resulting from TCDD exposure. The median volume fraction was 0.045% in control rats and was significantly elevated in TCDD treatment groups. However, the volume fraction of PGST-positive foci was significantly higher in the TCDD group given the high peak dose during the first week of TCDD treatment compared with the group receiving the same average daily dose over the study duration: 0.74 versus 0.20%, respectively. These findings suggest that the peak magnitude of TCDD in liver rather than AUC may play a significant role in the induction of complex biological responses by TCDD.

Impact of physiologically based pharmacokinetic modeling on benchmark dose calculations for TCDD-induced biochemical responses.

In risk assessment, noncancer risk is currently estimated using a no observed adverse effect level (NOAEL) from an experimental dose-response study, divided by uncertainty factors, to estimate a presumably safe level of human exposure. A benchmark dose approach, in which an effective dose (ED) resulting in a specified percentage increase over background for effects is estimated by empirical modeling, has been proposed as a replacement for the NOAEL methodology. The aim of this analysis is to compare methods for estimation of body burden resulting in a 1 or 10% maximum increase over background (BB(01) or BB(10)) for biochemical responses following exposure to 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) in female Sprague-Dawley rats. In one method, an ED resulting in a prespecified increase in response over background was estimated using average daily doses and an empirical Hill model. The ED was then converted to an equivalent body burden by a simple kinetic model assuming steady-state conditions, half-life of TCDD in the rat, and 100% absorption of TCDD. Alternatively, a mechanistic physiologically based pharmacokinetic (PBPK) model of TCDD in the rat was used to predict body burdens for administered doses. These PBPK-modeled body burdens were then used directly by the Hill model to calculate a BB(01) or BB(10). In general, the body burden values derived from EDs were within five-fold of BB(01) or BB(10) calculated from the PBPK model. BB(01) and BB(10) values from both methods were within two orders of magnitude of current human general population exposure to all dioxin-like compounds.

Use of sensitivity analysis to assess reliability of metabolic and physiological models.

Because ethical considerations often preclude directly determining the human health effects of treatments or interventions by experimentation, such effects are estimated by extrapolating reactions predicted from animal experiments. Under such conditions, it must be demonstrated that the reliability of the extrapolated predictions is not excessively affected by inherent data limitations and other components of model specification. This is especially true of high-level models composed of ad hoc algebraic equations whose parameters do not correspond to specific physical properties or processes. Models based on independent experimental data restricting the numerical space of parameters that do represent actual physical properties can be represented at a more detailed level. Sensitivities of the computed trajectories to parameter variations permit more detailed attribution of uncertainties in the predictions to these low-level properties. S-systems, in which parameters are estimated empirically, and physiological models, whose parameters can be estimated accurately from independent data, are used to illustrate the applicability of trajectory sensitivity analysis to lower-level models.

Pharmacokinetics of sodium nitrite-induced methemoglobinemia in the rat.

A biologically based mathematical model was created to characterize time and dose-dependent relationships between exposure to nitrite and induction of methemoglobinemia. The model includes mass action equations for processes known to occur: oral absorption of nitrite, elimination from the plasma, partitioning between plasma and erythrocytes, binding of nitrite to hemoglobin and methemoglobin, and the free radical chain reaction for hemoglobin oxidation. The model also includes Michaelis-Menten kinetics for methemoglobin reductase-catalyzed regeneration of hemoglobin. Body weight-scaled rate constants for absorption (k(a)) and elimination (k(e)), the effective erythrocyte/plasma partition coefficient (P), and the apparent K(m) for methemoglobin reductase were the only parameters estimated by formal optimization to reproduce the observed time course data. Time courses of plasma nitrite concentrations and blood levels of hemoglobin and methemoglobin in male and female rats that had received single intravenous or oral doses of sodium nitrite were measured. Peak plasma levels of nitrite were achieved in both sexes approximately 30 min after oral exposure, and peak methemoglobin levels were achieved after 100 min. The model predicts that 10% of the hemoglobin is oxidized to the ferric form after oral doses of 15.9 mg/kg in male rats and 11.0 mg/kg in female rats and after intravenous doses of 8.9 and 7.1 mg/kg in male and female rats, respectively. The t(1/2) for recovery from methemoglobinemia was 60 to 120 min depending on dose and route of administration. A sensitivity analysis of the model was performed to identify to which parameters the predictions of the model were most sensitive and guide attempts to simplify the model. Replacement of the V(max) of methemoglobin reductase with a value representative of humans predicted a 10% methemoglobinemia following an intravenous dose of 5.8 mg/kg, in close agreement with an observed value of 5.7 mg/kg for humans.

The association between biomarker-based exposure estimates for phthalates and demographic factors in a human reference population.

Population-based estimates of environmental exposures using biomarkers can be difficult to obtain for a variety of reasons, including problems with limits of detection, undersampling of key strata, time between exposure and sampling, variation across individuals, variation within individuals, and the ability to find and interpret a given biomarker. In this article, we apply statistical likelihoods, weighted sampling, and regression methods for censored data to the analysis of biomarker data. Urinary metabolites for seven phthalates, reported by Blount et al., are analyzed using these methods. In the case of the phthalates data, we assumed the underlying model to be a log-normal distribution with the mean of the distribution defined as a function of a number of demographic variables that might affect phthalate levels in individuals. Included as demographic variables were age, sex, ethnicity, residency, family income, and education level. We conducted two analyses: an unweighted analysis where phthalate distributions were estimated with changes in the means of these distributions as a function of demographic variables, and a weighted prediction for the general population in which weights were assigned for a subset of the population depending on the frequency of their demographic variables in the general U.S. population. We used statistical tests to determine whether any of the demographic variables affected mean phthalate levels. Individuals with only a high school education had higher levels of di-n-butyl phthalate than individuals with education beyond high school. Subjects who had family income less than $1,500 in the month before sampling and/or only high school education had higher levels of n-butyl benzyl phthalate levels than other groupings. Di(2-ethylhexyl) phthalate was higher in males and/or in urban populations and/or in people who had family income less than $1,500 per month. Our findings suggest that there may be significant demographic variations in exposure and/or metabolism of phthalates and that health-risk assessments for phthalate exposure in humans should consider different potential risk groups.

Robustness of MetaNet graph models: predicting control of urea production in humans.

Urea production in human liver was described by a MetaNet graph, a flowchart-like representation of metabolic pathways that includes parameters for the kinetic constants of the constituent enzymes. Formal operations on the graph facilitate the identification of ligand-binding equilibria that participate in feedback regulation in the network of biochemical reactions. The state of the biochemical network is specified by the concentrations of the intermediates. At any particular time, the influence of an identified locus of regulation is proportional to the respective fractional saturation of the corresponding binding site. Enzymes that make or consume the feedback chemicals share in the control of the strength of the feedback signal in proportion to their fractional saturation. This model predicts control of urea production by the processes that deliver amino groups to the urea cycle enzymes more than by the cycle enzymes themselves. Mitochondrial membrane transport processes are important for transmission of information through the network, but irreversible enzymes and processes far from equilibrium control the strength of the feedback signal. Systematic variation of the parameter values by amounts comparable to the expected variability of their measured values indicated a high probability of invariance in the identities of the predicted control points. The properties of the model are consistent with those of error-tolerant scale-free networks. These results demonstrate the robustness of a MetaNet model's predictions with respect to uncertainties in the values of its parameters.