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A method to efficiently simulate diffusion and reaction in a single-file system is presented. By considering all possible configurations of M species in a length N one-dimensional pore, a deterministic model consisting of (M+1)N variables can be constructed for the system. The order of the system can then be significantly reduced by considering only pairs of adjacent cells, or (M+1)2(N−1) doublets. This lumped model is able to capture the most important correlations between cells when the dominant mode of transport is through single-site hops. Extensions of this method for higher dimensional pores and more complex molecular interactions are discussed. The results of the approximation are compared to results of the full deterministic model, and new situations are investigated. The implications of single-file behavior are discussed for reversible reactions and molecules of different mobilities.

Biomonitoring Equivalents (BEs) are defined as the concentration of a chemical (or metabolite) in a biological medium (blood, urine, human milk, etc.) consistent with defined exposure guidance values or toxicity criteria including reference doses and reference concentrations (RfD and RfCs), minimal risk levels (MRLs), or tolerable daily intakes (TDIs) [Hays, S.M., Becker, R.A., Leung, H.W., Aylward, L.L., Pyatt, D.W., 2007. Biomonitoring equivalents: a screening approach for interpreting biomonitoring results from a public health risk perspective. Regul. Toxicol. Pharmacol. 47(1), 96-109]. The utility of the BE is to provide a screening tool for placing biomonitoring data into a health risk context. A Panel of experts took part in the Biomonitoring Equivalents Expert Workshop to discuss the various technical issues associated with calculating BEs and developed a set of guidelines for use in the derivation of BEs. Issues addressed included the role of the point of departure (POD) in BE derivation, the appropriate application of human and animal kinetic data and models, consideration of default uncertainty factor components in the context of internal dose-based extrapolations, and relevance of mode of action to technical choices in kinetic modeling and identification of screening values. The findings from this Expert Panel Workshop on BE derivation are presented and provide a set of guidelines and considerations for use in BE derivation.

A conceptual/computational framework for exposure reconstruction from biomarker data combined with auxiliary exposure-related data is presented, evaluated with example applications, and examined in the context of future needs and opportunities. This framework employs physiologically based toxicokinetic (PBTK) modeling in conjunction with numerical "inversion" techniques. To quantify the value of different types of exposure data "accompanying" biomarker data, a study was conducted focusing on reconstructing exposures to chlorpyrifos, from measurements of its metabolite levels in urine. The study employed biomarker data as well as supporting exposure-related information from the National Human Exposure Assessment Survey (NHEXAS), Maryland, while the MENTOR-3P system (Modeling ENvironment for TOtal Risk with Physiologically based Pharmacokinetic modeling for Populations) was used for PBTK modeling. Recently proposed, simple numerical reconstruction methods were applied in this study, in conjunction with PBTK models. Two types of reconstructions were studied using (a) just the available biomarker and supporting exposure data and (b) synthetic data developed via augmenting available observations. Reconstruction using only available data resulted in a wide range of variation in estimated exposures. Reconstruction using synthetic data facilitated evaluation of numerical inversion methods and characterization of the value of additional information, such as study-specific data that can be collected in conjunction with the biomarker data. Although the NHEXAS data set provides a significant amount of supporting exposurerelated information, especially when compared to national studies such as the National Health and Nutrition Examination Survey (NHANES), this information is still not adequate for detailed reconstruction of exposures under several conditions, as demonstrated here. The analysis presented here provides a starting point for introducing improved designs for future biomonitoring studies, from the perspective of exposure reconstruction; identifies specific limitations in existing exposure reconstruction methods that can be applied to population biomarker data; and suggests potential approaches for addressing exposure reconstruction from such data.

Carbofuran (2,3-dihydro-2,2-dimethyl-7-benzofuranyl-N-methylcarbamate), a broad spectrum N-methyl carbamate insecticide, and its metabolite, 3-hydroxycarbofuran, exert their toxicity by reversibly inhibiting acetylcholinesterase (AChE). To characterize AChE inhibition from carbofuran exposure, a physiologically based pharmacokinetic/pharmacodynamic (PBPK/PD) model was developed in the Exposure-Related Dose Estimating Model (ERDEM) platform for the Sprague-Dawley (SD) rat. Experimental estimates of physiological, biochemical, and physicochemical model parameters were obtained or based on data from the open literature. The PBPK/PD model structure included carbofuran metabolism in the liver to 16 known metabolites, enterohepatic circulation of glucuronic acid conjugates, and excretion in urine and feces. Bolus doses by ingestion of 50 microg/kg and 0.5 mg/kg carbofuran were simulated for the blood and brain AChE activity. The carbofuran ERDEM simulated a half-life of 5.2 h for urinary clearance, and the experimental AChE activity data were reproduced for the blood and brain. Thirty model parameters were found influential to the model outputs and were chosen for perturbation in Monte Carlo simulations to evaluate the impact of their variability on the model predictions. Results of the simulation runs indicated that the minimum AChE activity in the blood ranged from 29.3 to 79.0% (as 5th and 95th percentiles) of the control level with a mean of 55.9% (standard deviation = 15.1%) compared to an experimental value of 63%. The constructed PBPK/PD model for carbofuran in the SD rat provides a foundation for extrapolating to a human model that can be used for future risk assessment.

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