Health Assessment Document for Diesel Emissions - NSCEP | US ...

1 d: Dose of organics, mg/cm 2 of lung epithelial surface
2
3 fll: Dose-related initiation rate (per cell per day) that depends on flo (background rate), d, and
4 D by f.! I =·f.!o(l +ad+ bD); a and bare paramaters to be estimated.
5
6 flz: Probability of producing a malignant cell at the end of an initiated cell (1-cell) lifetime
7
8 a: The probability that anI-cell divides into two daughter cells at the end of its lifetime
9
1 0 q: Probability that a single malignant cell will develop into a maligl}ant tumor
11
12 y: 1/y is the mean I-celllifetime in days; a cell lifetime ends if it either goes into mitosis, or
13 cell death. Note that if one assumes that the probability for a cell to get into mitosis is
1 4 about the same as cell death then the mean cell lifetime can be conveniently interpreted as
1 5 time to mitosis (i.e., cell turnover time); thus, shorter cell lifetime implies more frequent
16 cell division. Note that the time to mitosis is a random variable here, not a fixed constant
1 7 as in the assumption made in the Greenfield et al. (1984) model that has been used
18 extensively by Cohen and Ellwein (1988) to analyze experimental bladder cancer.
19
20 · N: Number of(normal) target cells
21
22 B.3.2. Practical Considerations
23 By statistical theory alone the E-M algorithm developed in this report provides an elegant.
24 procedure which can be used to test hypotheses whether a particular parameter is influenced by
25 organics and carbon core individually or both together. For instance, one could postulate that the
26 parameter y (reciprocal of which represents mean cell lifetime) is given by y(d,Di) = y 0 + Ynd +
27 y 12 Di, and then proceed to test a null hypothesis that y 11 = 0, no effect of organics on cell
28 lifetime. This temptation, however, must be resisted because there would be too many
2 9 parameters that must be estimated if such statistical tests are to be performed. Therefore, rather
30 than performing such a statistical exercise, we proceed with a biologically plausible assumption
31 that parameters q and y depend only on lung burden of carbon core, C.
32 The duration ofthe Mauderly et al. study was about 940 days. To construct a dose-
33 response model with time-dependent lung burden, the time interval (0,940] is divided into
34 five subintervals; each subinterval spans 6 mo except for the last subinterval, which spans from
35 730 (2 years) to 940 days. Corresponding to an ambient air concentration of diesel emissions in
3 6 mg/m 3 , the deposition-retention model developed by Yu et al. is useq to calculate dosimetric ( d,
37 Di), I= 1, 2, ... , 5, where organics dose, d, is not changing with time because it reaches steady
38 state quickly after exposure begins and Di is the lung burden of carbon core during the ith
3 9 subinterval.
40 The assumptions about dose-parameters relationship are given below.
2/1198 B-5 DRAFT--DO NOT CITE OR QUOTE