Rappaport et al. analysis, 243 had repeated measurements of air and urine, making a total of 391 matched air/urine samples. Subjects with repeated mea- surements had a median of three paired air and urine samples (range, 2–4). Benzene was measured in air using passive personal monitors (Organic Vapor Monitors, model 3500; 3M, St. Paul, MN, USA) fol- lowed by solvent desorption and gas chroma- tography (GC) with flame ionization detection (Vermeulen et al. 2004). A total of 161 air measurements were either missing or below the limit of detection (normally 0.2 ppm). We predicted air concentrations for these censored and missing air samples from the correspond- ing levels of urinary benzene, as described previously (Kim et al. 2006a). The estimated median exposure to benzene among the non- smoking female subjects was 0.644 ppm, with 10th and 90th percentile values of 0.002 ppm and 8.97 ppm, respectively (Table 1). We determined urinary benzene by GC-mass spectrometry (MS) using head-space solid-phase microextraction according to the method of Waidyanatha et al. (2001). Urinary phenol, hydroquinone, catechol, muconic acid, and SPMA were measured as trimethyl- silyl derivatives by GC-MS, after acid hydro- lysis of urine to release conjugates, according to Waidyanatha et al. (2004). Quantification of all urinary analytes was based on peak areas relative to the corresponding isotopically labeled internal standards. The Shanghai workers were exposed to essentially pure benzene, whereas all Tianjin workers were coexposed to toluene, and some were exposed to low levels (< 5 ppm) of other volatile organic compounds (Vermeulen et al. 2004). We previously found no significant effects of toluene coexposure on levels of ben- zene metabolites in the Tianjin workers (Kim et al. 2006b). Michaelis-Menten-like models. We examined relationships between levels of total metabolites and the corresponding air concentrations of benzene using nonlinear regression models (implemented with the SAS procedure NLIN; SAS Institute Inc., Cary, NC, USA). To consider saturable metabolism, we invoked Michaelis-Menten- like models, where the enzymatic velocity (v) was replaced with the level of total metab- olites (Y) (micromolar), and the substrate concentration with the air concentration of benzene (X) (parts per million). The asymp- totically maximum level of Y (designated Ymax) is analogous to vmax, and the benzene concentration X at which Y = Ymax/2 (des- ignated X50, in parts per million) is analo- gous to Km. We also assumed a background level of total metabolites Y0 (micromolar) due to endogenous and dietary sources of the individual compounds, particularly phe- nol, hydroquinone, and catechol (Kim et al. 2006a; McDonald et al. 2001). Given our hypothesis that two saturable pathways gov- erned benzene metabolism rather than one, we fit two Michaelis-Menten-like models to the data, one having a single metabolic path- way and the other having two pathways that 10,000 ) 1,000 M µ ( s e t i l o b a t e m l a t o T 100 10 0.001 competed for access to benzene (X). The fol- lowing expressions define the two models: ln(Y ) = ln (Y0 + Y X max 50+ × X X ) , [1] ln(Y ) = ln (Y0 + Y max,1× X X 50,1+ X + Y X max,2 50,2+ × X X ), [2] where the subscripts 1 and 2 in Equation 2 refer to the first and second metabolic pathways, respectively. We will refer to Equation 1 as the “one-pathway model” and to Equation 2 as the “two-pathway model.” Also, because the affinity of a given enzyme pathway is indicated by X50 (the benzene air concentration at which Y is half-maximal, analogous to Km), we define path- way 1 as the low-affinity pathway and pathway 2 as the high-affinity pathway, which is to say that X50,2 < X50,1. Each data pair (Y, X) represents the post- shift total metabolite concentration and the corresponding full-shift benzene air concen- tration for a given subject. For subjects with repeated measurements (n = 243), we used estimated geometric means of air and total metabolite levels. Given the highly skewed and heteroskedastic levels of benzene in air and total metabolites, natural log transforms of Y and the independent variables were used for regression analyses. Initial values for Y0, Ymax, X50, Ymax,1, and X50,1 were estimated from scatter plots of benzene metabolite levels versus benzene exposure. Because we defined meta- bolic pathway 2 as having higher affinity and lower capacity than metabolic pathway 1, we assigned initial values to Ymax,2 << Ymax,1 and to X50,2 << X50,1. However, the final model was not sensitive to initial values of these parameters. The estimated kinetic parameters were used to construct overall profiles and partial profiles for the one-pathway and two- pathway models. Uncertainties in the parame- ters estimated under Equation 1 and Equation 2 were evaluated via bootstrap resampling with replacement (n = 1,000, implemented with the SAS macro %boot). We used bootstrap results to estimate median, 2.5th, and 97.5th percentile values for each kinetic parameter in Equations 1 and 2 as well as the ratios Ymax,1:X50,1 and Ymax,2:X50,2, which represent maximum rates of metabolism (micromole per parts per million) for the two pathways (analo- gous to vmax/Km), respectively. Weights of evidence for models. In judg- ing the weight of evidence favoring either the one-pathway model or two-pathway model as a depiction of the true metabolism for benzene (i.e., “truth”), we employed criteria derived from information theory that offer advantages over hypothesis testing in selecting among candidate models derived from scien- tific considerations (Burnham and Anderson 0.01 0.1 1 10 100 Benzene (ppm) Figure 2. Scatterplot of levels of total metabolites versus the level of benzene in air for 263 nonsmoking female subjects. Open data points represent subjects from Tianjin, and solid points represent subjects from Shanghai. The dashed curve represents the benzene metabolite level predicted under the one- pathway model (Equation 1), and the solid curve represents the benzene metabolite level predicted under the two-pathway model (Equation 2). 948 ovlume 117 | number 6 | June 2009 • Environmental Health Perspectives