These three parameters were optimized to minimize the value of the objective function (OF) representing the difference between empirical and modeled data: equation(3) OF=(⁢ln⁡Cmea−ln⁡Cmodel)2OF=⁢ln⁡Cmea−ln⁡Cmodel2where Cmea and Cmodel are empirical and modeled concentrations,

respectively. The model was implemented in Microsoft Excel 2013 and optimized using the Solver add-in. Historical intake trends and intrinsic elimination rates are modeled. The reduction half-life for intake is calculated using adult reference intakes in the peak intake year and 2000 under the assumption of first-order decrease of intakes. The intrinsic elimination half-life for each chemical is calculated as ln(2) / kE. Three indicators, i.e. coefficients of determination (R2), residues weighted by number of empirical data points (OF/n), and 95% confidence factor around the Selleck Luminespib fit (CF), were used to evaluate the goodness of fit of the model to the empirical

data and to verify that there was no bias introduced by our model fitting procedure. Values of the three indicators that we used to evaluate the performance of the model and the reliability of our estimates are reported in Table 1. These results are also demonstrated graphically in SI-3 (see Supplementary material). For most PCBs and OCPs, the empirical cross-sectional data can Apoptosis inhibitor be explained by our model with R2 higher than 0.7, and OF/n < 0.13.

In these cases, the modeled concentrations fall within a 95% CF of less than 2.16. However, there are three exceptional cases where the model fits to the biomonitoring data are not as good: β-HCH, HCB, and p,p′-DDT (bold entries in Table 1). High OF/n values for β-HCH and HCB indicated a relatively large discrepancy between the modeled and empirical cross-sectional data. The measured values of β-HCH are highly variable in pooled samples of people of the same age (see Supplementary material, Fig. S1-l). The model cannot explain the variability adequately, leading to a poor correlation and large CF. This high variability might represent a high degree of inter-individual variability in body burdens in the underlying Fenbendazole population. As a result, very long half-lives of over 5000 years were modeled for β-HCH, which are not plausible. In contrast, the low R2 and relatively high OF/n values for the model fit to empirical data for HCB are due to an apparent outlying group of older people who had higher body burdens than expected from the model fit (see Supplementary material, Fig. S1-k). The intrinsic elimination half-life (6.4 years) and intake trend for HCB calculated by the optimized model are not sensitive to the inclusion of this outlying datum. For p,p′-DDT, despite the relatively low R2 (= 0.377), the modeled data fall within a narrow confidence interval (CF = 2.