Annals of Occupational Hygiene Advance Access originally published online on September 20, 2004
Annals of Occupational Hygiene 2004 48(7):653-654; doi:10.1093/annhyg/meh059
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© British Occupational Hygiene Society Published by Oxford University Press;
Letter to the Editor |
Peaks of Inhalation Exposure
Department of Environmental Health, Osaka Prefectural Institute of Public Health, 1-3-69 Nakamichi, Higashinari-ku, Osaka 537-0025, Japan
Received 21 October 2003; in final form 19 March 2004
Analysis of peak exposure to chemicals is very important for clarifying the health effects of high short-term exposure. Preller et al. (2004)
obtained exposure data from various industries where spraying was used, and found five measures characterizing peak exposure. In general, the profile of variation of exposure concentration is expressed using distribution and autocorrelation. Distribution of exposure concentration is described as log-normal, which is expressed by two parameters: geometric mean (µg) and geometric standard deviation (
g). µg and g represent exposure intensity and magnitude of exposure variability, respectively. Autocorrelation is expressed by the autocorrelation coefficient (
). is the correlation coefficient between two exposure concentrations at different times, and relates to the speed of exposure variability. It is helpful to consider the relationships between these three parameters and Preller et al.'s four measures of peak exposure. My interpretation is as follows.
It was demonstrated that the diurnal distribution of exposure concentration with an average time of 7.5–60 min is log-normal (Kumagai et al., 1995). Although it was not demonstrated that the within-task distribution of exposure concentration with an average time of 5 s to 1 min is log-normal, I assume log-normal distribution in the following discussion.
For a log-normal distribution, mean (arithmetic mean, µ) is related to µg and g by the following equation:
 | (1) |
 | (2) |
g was observed among various industries (Kumagai et al., 1999), the effects of variations of µg and g on µ and Cmax can be evaluated separately. According to equations (1) and (2), as µg increases, both µ and Cmax increase. Similarly, as g increases, both µ and Cmax increase. Consequently, µ and Cmax are positively correlated with each other.
The average peak concentration is as follows:
 | (3) |
The above consideration suggests that three measures—µ, Cmax and average peak concentration—are positively correlated. These give the first factor of Preller et al.
The proportion of cumulative duration of troughs to duration of a task [P(C < µ)] is expressed by the following equation:
 | (4) |
 | (5) |
The ratio between the maximum and the average concentration within a peak (R) is expressed by the following equation:
 | (6) |
As stated above, because no correlation between µg and g was observed among various industries, the effect of the variation of µg and the effect of the variation of g can be evaluated separately. According to equation (5), as g increases, DV increases if DT and NV are fixed. It is difficult to clarify how R changes as g increases. It is probable that when g is low, as g increases, R increases. DV and R do not vary with µg. Consequently, when g is low, DV and R are positively correlated with each other, which gives the second factor shown by Preller et al.
The proportion of cumulative duration of peaks to duration of a task [P(C > µ)] is expressed by the following equations:
 | (7) |
 | (8) |
 | (9) |
The above discussion shows the correlations among Preller et al.'s five measures using the two parameters, µg and g. However, not all profiles of exposure variation can be expressed by these two parameters. DV, DP and NP/h cannot be calculated only by the two parameters, because equations (5), (8) and (9) contain NV, NP and NP, respectively.
The other parameter, , can express DV, DP and NP/h. is calculated from the following equation:
 | (10) |
is the correlation coefficient between two exposure concentrations at different times, and relates to the speed of exposure variability. Consequently, relates to DV, DP and NP/h. According to equation (9), as increases, DV and DP increase, and NP/h decreases.
The above discussion suggests that the traditional three parameters (µg, g, ) can express Preller et al.'s five measures (µ, DV, DP, R, NP/h). Thus, the three parameters are good ways to express exposure variation, but may be no use for intuitively visualizing exposure variation and for examining the biological effects of exposure variation. Cmax may be better than R for intuitively visualizing exposure variation. NP/h and DP are not independent of each other. Finally, I think that µ, Cmax, DP and DV are useful parameters for epidemiological studies.
REFERENCES
Kumagai S, Matsunaga I. (1995) Changes in the distribution of short-term exposure concentration with different averaging times. Am Ind Hyg Assoc J; 56: 24–31.[Web of Science][Medline]
Kumagai S, Matsunaga I. (1999) Within-shift variability of short-term exposure to organic solvent in indoor workplaces. Am Ind Hyg Assoc J; 60: 16–21.[Web of Science][Medline]
Preller L, Burstyn I, de Pater N, Kromhout H. (2004) Characteristics of peaks of inhalation exposure to solvents. Ann Occup Hyg; this issue.
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