Risk of Hearing Loss Caused by Multiple Acoustic Impulses in the Framework of Biovariability

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Wang, Hongyun
Burgei, Wesley A.
Zhou, Hong
Risk of Significant Hearing Loss Injury
Dose-Response Relation for Multiple Acoustic Impulses
A Crowd With Heterogeneous Individual Injury Probabilities
Date of Issue
Scientific Research Publishing Inc.
We consider the hearing loss injury among subjects in a crowd with a wide spectrum of individual intrinsic injury probabilities due to biovariability. For multiple acoustic impulses, the observed injury risk of a crowd vs the effective combined dose follows the logistic dose-response relation. The injury risk of a crowd is the average fraction of injured. The injury risk was measured in experiments as follows: each subject is individually exposed to a sequence of acoustic impulses of a given intensity and the injury is recorded; results of multiple individual subjects were assembled into data sets to mimic the response of a crowd. The effective combined dose was adjusted by varying the number of impulses in the sequence. The most prominent feature observed in experiments is that the injury risk of the crowd caused by multiple impulses is significantly less than the value predicted based on assumption that all impulses act independently in causing injury and all subjects in the crowd are statistically identical. Previously, in the case where all subjects are statistically identical (i.e., no biovariability), we interpreted the observed injury risk caused by multiple impulses in terms of the immunity effects of preceding impulses on subsequent impulses. In this study, we focus on the case where all sound exposure events act independently in causing injury regardless of whether one is preceded by another (i.e., no immunity effect). Instead, we explore the possibility of interpreting the observed logistic dose-response relation in the framework of biovariability of the crowd. Here biovariability means that subjects in the crowd have their own individual injury probabilities. That is, some subjects are biologically less or more susceptible to hearing loss injury than others. We derive analytically the distribution of individual injury probability that produces the observed logistic dose-response relation. For several parameter values, we prove that the derived distribution is mathematically a proper density function. We further study the asymptotic approximations for the density function and discuss their significance in practical numerical computation with finite precision arithmetic. Our mathematical analysis implies that the observed logistic dose-response relation can be theoretically explained in the framework of biovariability in the absence of immunity effect.
The article of record as published may be found at
Series/Report No
Applied Mathematics
Other Units
Naval Postgraduate School (U.S.)
NPS Report Number
Joint Non-Lethal Weapons Directorate of US Department of Defense
25 p.
Wang, H., Burgei, W.A. and Zhou, H. (2018) Risk of Hearing Loss Caused by Multiple Acoustic Impulses in the Framework of Biovariability. Health, 10, 604-628.
Distribution Statement
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.