Permethrin is a broad-spectrum pyrethroid insecticide and among the most widely used insecticides in homes and crops. Managing the risks for pesticides such as permethrin depends on the ability to consider diverse exposure scenarios and their relative risks. Physiologically based pharmacokinetic models of delta methrin disposition were modified to describe permethrin kinetics in the rat and human. Unlike formulated deltamethrin which consists of a single stereoisomer, permethrin is formulated as a blend of cis- and trans-diastereomers. We assessed time courses for cis-permethrin and trans-permethrin in several tissues (brain, blood, liver, and fat) in the rat following oral administration of 1 and 10mg/kg permethrin (cis/trans: 40/60). Accurate simulation of permethrin in the rat suggests that a generic model structure is promising for modeling pyrethroids. Human in vitro data and appropriate anatomical information were used to develop a provisional model of permethrin disposition with structures for managing oral, dermal, and inhalation routes of exposure. The human permethrin model was used to evaluate dietary and residential exposures in the U.S. population as estimated by EPA's Stochastic Human Exposure and Dose Simulation model. Simulated cis- and trans-DCCA, metabolites of permethrin, were consistent with measured values in the National Health and Nutrition Examination Survey, indicating that the model holds promise for assessing population exposures and quantifying dose metrics.

We compare two approaches for inclusion of uncertainty/variability in modelling growth in size-structured population models. One entails imposing a probabilistic structure on growth rates in the population while the other involves formulating growth as a stochastic Markov diffusion process. We present a theoretical analysis that allows one to include comparable levels of uncertainty in the two distinct formulations in making comparisons of the two approaches.

In this paper, we compare two computationally efficient approximation methods for the estimation of growth rate distributions in size-structured population models. After summarizing the underlying theoretical framework, we present several numerical examples as validation of the theory. Furthermore, we compare the results from a spline based approximation method and a delta function based approximation method for the inverse problem involving the estimation of the distributions of growth rates in size-structured mosquitofish populations. Convergence as well as sensitivity of the estimates with respect to noise in the data are discussed for both approximation methods. 1 Report Documentation PageForm Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.

We discuss inverse problem results for problems involving the estimation of probability distributions using aggregate data for growth in populations. We begin with a mathematical model describing variability in the early growth process of size-structured shrimp populations and discuss a computational methodology for the design of experiments to validate the model and estimate growth rate distributions in shrimp populations. Parameter estimation findings using experimental data from experiments so designed for shrimp populations cultivated at Advanced BioNutrition Corporation are presented illustrating the usefulness of mathematical and statistical modeling in understanding the uncertainty in the growth dynamics of such populations.

Toxicokinetics (TK) provides critical information for integrating chemical toxicity and exposure assessments in order to determine potential chemical risk (i.e., the margin between toxic doses and plausible exposures). For thousands of chemicals that are present in our environment, in vivo TK data are lacking. The publicly available R package "httk" (version 1.8, named for "high throughput TK") draws from a database of in vitro data and physico-chemical properties in order to run physiologically-based TK (PBTK) models for 553 compounds. The PBTK model parameters include tissue:plasma partition coefficients (K) which the httk software predicts using the model of Schmitt (Toxicol In Vitro 22 (2):457-467, 2008). In this paper we evaluated and modified httk predictions, and quantified confidence using in vivo literature data. We used 964 rat K measured by in vivo experiments for 143 compounds. Initially, predicted K were significantly larger than measured K for many lipophilic compounds (log octanol:water partition coefficient > 3). Hence the approach for predicting K was revised to account for possible deficiencies in the in vitro protein binding assay, and the method for predicting membrane affinity was revised. These changes yielded improvements ranging from a factor of 10 to nearly a factor of 10,000 for 83 K across 23 compounds with only 3 K worsening by more than a factor of 10. The vast majority (92%) of K were predicted within a factor of 10 of the measured value (overall root mean squared error of 0.59 on log-transformed scale). After applying the adjustments, regressions were performed to calibrate and evaluate the predictions for 12 tissues. Predictions for some tissues (e.g., spleen, bone, gut, lung) were observed to be better than predictions for other tissues (e.g., skin, brain, fat), indicating that confidence in the application of in silico tools to predict chemical partitioning varies depending upon the tissues involved. Our calibrated model was then evaluated using a second data set of human in vivo measurements of volume of distribution (V) for 498 compounds reviewed by Obach et al. (Drug Metab Dispos 36(7):1385-1405, 2008). We found that calibration of the model improved performance: a regression of the measured values as a function of the predictions has a slope of 1.03, intercept of - 0.04, and R of 0.43. Through careful evaluation of predictive methods for chemical partitioning into tissues, we have improved and calibrated these methods and quantified confidence for TK predictions in humans and rats.