Occupational Exposure to Carbon Nanotubes and Nanofibers

The other BMDS models failed to converge or, infurther statistical evaluation, showed non-uniqueparameter solutions. The continuous dose-responsedata were fit with a polynomial model of degree 2for all data with three or more dose groups, and degree1 (linear) for data with two groups (see TableA–1 for dose groups).P values for goodness of fit were computed for theindividual BMDS models (based on likelihoodmethods) [US EPA 2007]. Model fit was consideredadequate at P > 0.05 (i.e., testing for lack offit), although the P values based on likelihood ratiotests may not be a reliable indicator of modelfit in the studies with few animals per group. Thenumber of animals per dose group in each studyis given in Table A–1. EPA typically uses a P > 0.1criteria for BMD model fit [US EPA 2012]. Eithercriteria is considered reasonable and representsa trade-off in the type I or type II error. That is,P > 0.1 provides more power to reject an incorrectmodel, while P > 0.05 provides less chance ofrejecting a correct model. The BMD model fits toeach data set are shown in Figure A–1 (subchronicstudies), Figure A–2 (short-term studies, dichotomousresponse), and Figure A–3 (short-term studies,continuous response).A.2.3.4 Human-equivalent Dose andWorking Lifetime ExposureThe rodent BMD(L)s were extrapolated to humansbased on species-specific differences in the alveolarepithelial surface area of the lungs (i.e., by normalizingthe dose per unit of cell surface area). It is assumedthat humans and animals would have equalresponse to an equivalent dose (i.e., mass of CNTper unit surface area of lungs). The human-equivalentBMD and BMDL estimates were the target lungdoses used to estimate, respectively, the maximumlikelihood estimate (MLE) and 95% lower confidencelimit (95% LCL) estimate of the MLE, asan 8-hr TWA exposure concentration during a 45-year working lifetime.The human-equivalent BMD and BMDL estimateswere calculated as follows:Equation A–4:Human-equivalent BMD(L) =Rodent BMD(L) × [AlvSA human / AlvSA rodent]where the values used for alveolar lung surface area(AlvSA) were 102 m2 (human) [Stone et al. 1992];0.4 m2 (rat) and 0.055 m2 (mouse) [Mercer et al.2008]. In Tables A–3 through A–5, the humanequivalentBMD(L)s were multiplied by 0.001 mg/µg to obtain the units of mg per lung.The human-equivalent BMD(L)s are expressed asthe mass (mg) of CNT in the lungs. The workinglifetime airborne mass concentration that wouldresult in the BMD(L) human-equivalent lung massdose was calculated based on either depositiononly (no lung clearance) or retention (lung depositionand clearance), as described below.(a) Deposited lung doseEquation A–5:Estimated 8-hr TWA (µg/m3) =Human-equivalent BMD(L) (µg) /[8-hr worker air inhaled (m3/day) × Alveolar DepositionFraction × Work Days]The values assumed include 9.6 m3 8-hr air intake(reference worker [ICRP 1994]); alveolar depositionfraction based on aerodynamic particle size(Table A–2); and working lifetime days (250 days/yr × 45 yr).(b) Retained lung doseThe MPPD 2.0 human model [CIIT and RIVM2006] for inhaled poorly soluble spherical particleswas used to estimate the working lifetime exposureconcentration that would result in the humanequivalentBMD(L) lung burden estimates. This wasdone by a systematic search to identify the 8-hr timeweighted average (TWA) airborne concentrationover a 45-year working lifetime that predicted thetarget lung burden. The input parameters used inthe MPPD human model (Yeh and Schum humandeposition model option) include CNT aerodynamicparticle size (MMAD, GSD) (Table A–2); inhalabilityadjustment; oronasal-normal augmenter;NIOSH CIB 65 • Carbon Nanotubes and Nanofibers105