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  Figure 4. The group mean total number of outer hair cells missing as a function of kurtosis in four separate studies using a noise exposure level of 100 dB(A). Adapted from Davis et al., 2009.
The second question emerged because an infinite combination of amplitudes, peak durations, and interpeak intervals can yield the same kurtosis value. To answer it, Qiu et al. (2013) exposed chinchillas to noises with a variety of temporal distributions, including different peak levels, interpeak intervals, and peak durations. The results showed that the hearing losses were reasonably independent of temporal distributions as long as noise levels and kurtosis values were the same.
What Have We Learned About
the Kurtosis Metric from Animal Experiments?
There are four key findings from this animal research (Hamernik et al., 2003; Qiu et al., 2013):
(1) Non-Gaussian noise is more hazardous than Gaussian noise equivalent energy, and kurtosis explains much of the increase.
(2) Hearing loss is proportional to kurtosis in that threshold shift and hearing loss increase as kurtosis increases for a fixed energy level.
(3) Both energy and kurtosis are necessary to assess the risk of hearing loss caused by a complex noise exposure. (4) For fixed values of kurtosis and energy, the detailed
temporal structure of an exposure does not have an
appreciable effect on hearing loss.
This body of animal data needed to be correlated with
comparable human noise exposure and audiometric data. Specifically, real industrial noise environments needed to be analyzed to measure their statistical and temporal properties and to quantify them in a form (e.g., kurtosis) that could be correlatedwithhearingthresholdsofnoise-exposedworkers.
Examining the Effects of Kurtosis in Industrial Settings
A preliminary study of the use of kurtosis with a cohort of Chinese industrial workers (Zhao et al., 2010) showed that the kurtosis metric could increase the accuracy of assessing the risk of high-frequency hearing loss in workers exposed to high levels of both Gaussian and non-Gaussian noise. This study utilized a new approach to characterize the hazardous effects of complex noise in which an energy- based metric, cumulative noise exposure, was combined with a kurtosis-related correction term.
To incorporate the kurtosis metric into the evaluation of non-Gaussian noise environments and to unify the data from the two noise classes (i.e., Gaussian and non- Gaussian), Zhao and colleagues developed a kurtosis adjustment formula using Earshen’s (1986) concept of cumulative noise exposure (CNE): CNE = LAeq,8h + K [log T/log 2], where LAeq,8h is the 8-hour A-weighted average exposure level, T is noise exposure duration in years, and K= ln(β) + 1.9. By introducing the kurtosis variable (K) intothetemporalcomponentoftheCNEcalculation,the two dose-response curves were made to overlap, essentially yielding an equivalent noise-induced effect for the two study groups (see Figure 5). Thus, the kurtosis statistic was used to quantify the difference in effect between the Gaussian and non-Gaussian noise environments.
Xie et al. (2016) conducted a larger study of 178 subjects exposed to complex non-Gaussian noise from two steel plants and 163 subjects exposed to Gaussian noise from a textile plant. The results showed that for similar cumulative noise exposures, the complex noise caused significantly more hearing loss than the Gaussian noise. By using the same kurtosis-adjusted cumulative noise exposure measure as before, the hearing loss curves from the complex noise and Gaussian noise overlapped once again. These results supported the results from Zhao et al. (2010).
The above studies lead to two important conclusions. First, the diversity of complex noise environments over many industries make it difficult to characterize the expected hearing loss with a single dose-response curve. Nevertheless, the relative stability of the relationship between hearing loss and continuous Gaussian noise may serve as a reference to compare with the results from a complex noise exposure. Second, the kurtosis statistic appears to be a reasonable candidate for modifying
42 Acoustics Today • Winter 2020

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