Geometrical dose distribution

Assessments of risks associated with the use of chlorpyrifos insecticide products for workers have been made. The assessments are based on the results of field studies conducted in citrus groves, a Christmas tree farm, cauliflower and tomato fields, and greenhouses that utilized both passive dosimetry and biomonitoring techniques to determine exposure. The biomonitoring results likely provide the best estimate of absorbed dose of chlorpyrifos, and these have been compared to the acute and chronic no observed effect levels (NOELs) for chlorpyrifos. Standard margin-of-exposure (MOE) calculations using the geometric mean of the data are performed however, probability (Student s f-test) and distributional (Monte Carlo simulation) analyses are deemed to provide more realistic evaluations of exposure and risk to the exposed population. 

Boecker, 1973) exposed to other radioactive aerosols was also reviewed. An analysis of the data from both studies suggested that for beagles exposed by inhalation to radioactive 144Ce aerosols, individuals in the population would receive radiation doses to a given organ within a fog-normal distribution characterized by a geometric standard deviation of 2. 

By the Method of Frequency the stimulus range is selected in discrete intervals so that the frequency of positive answers is distributed over the range between 1% and 99%. In general, the frequency of positive responses either for an individual or for a group, is cumulatively normally distributed over a geometric intensity continuum. The absolute odor threshold can then be defined as the effective dose corresponding to an arbitrarily selected frequency of positive responses, ordinarily 50% ED50 Effective dose at the 50% level. 

The quantal dose-response curve is actually a cumulative plot of the normal frequency distribution curve. The frequency distribution curve, in this case relating the minimum protective dose to the frequency with which it occurs in the population, generally is bell shaped. If one graphs the cumulative frequency versus dose, one obtains the sigmoid-shaped curve of Figure 22A. The sigmoid shape is a characteristic of most dose-response curves when the dose is plotted on a geometric, or log, scale. 

TABLE 3.7 Predicted Potency Distributions Using the Ideal Mixing Model, a Geometric Standard Deviation of 2, and Experimental Doses and Corresponding Particle Diameters Reported by Rohrs et al.4... 

Emphasis has also been placed on the particle size distribution and the uniform size distribution of the API rather than on the mean particle size alone by other authors.1416 Rohrs et al.16 give a nomograph for identifying the maximum median particle diameter to pass USP 28 stage I content uniformity criteria with 99% confidence as a function of dose as well as width of particle size distribution (geometrical standard deviation). 

Fig. 1. Geometrical a- and j8-dose rate distribution for spent nuclear fuel 100 years after discharge.

Figure 7.16 Histogram of posterior predictive check based on the observed data in Table 7.4. Concentration data were simulated for 26 subjects under the original experimental design and sampling times at each dose using population values and variance components randomly drawn from the bootstrap distribution of the final model parameter estimates (FOCE-I Table 7.5). The geometric mean concentration at 6-h postdose (top) and AUC to 12-h postdose (bottom) was calculated. This process was repeated 250 times.

---